Fama-MacBeth 1973: Replication and Extension
Serginio Sylvain �
Graduate School of EconomicsUniversity of Chicago
Chicago, IL 60615, USA
October 11, 2013
Abstract
I reproduce the results of Fama and MacBeth (1973) and extend this paper inseveral ways. First, I use twenty-five test portfolios constructed using a double-sort onbetas and standard deviations of the residuals of the underlying securities (while stillmaintaining the same timing assumptions and method of Fama and MacBeth; 1973).I find that the coefficient on the average standard deviation of the residuals becomessignificant in the cross-sectional regressions, even for the 1929-1968 time period. Thisgoes against some of the results in Fama and MacBeth (1973) and hints that theseresults may not have been robust. In particular, I alternate between using an equal-weighted and value-weighted NYSE portfolio as proxy for the market portfolio. I alsoalternate the construction of the test portfolio estimates between equal-weighting andvalue-weighting of the underlying securities estimates. I find that the Fama-MacBeth(1973) results are unaffected by these variations if the test portfolios are constructedusing a single sort on betas as done in Fama-MacBeth (1973). But with test portfoliosbuilt with a dual-sort much of the Fama-MacBeth (1973) results are undone.
�I am grateful to Aaron Foss for providing me with helpful comments, suggestions, and feedback.
1
1 Introduction
Fama and MacBeth (1973) proposed a method of testing some asset pricing implicationsthat arise from the assumption of normally distributed portfolio1 returns and risk-averseinvestors. In particular, these two assumption imply that investors would choose portfoliosby trading off between the expected returns and the standard deviations of returns of saidportfolios. More specifically, the investors choose portfolios that have minimum varianceper unit of expected return. Thus investors only hold portfolios that are mean-variance-efficient2 (MVE). Therefore, the expected return on any portfolio p held by investors is suchthat EpRpq � EpR0,eq � βp,erEpReq �EpR0,eqs. Here Re is the return on any MVE portfolioe, R0,e is the return on a portfolio with zero beta with respect to portfolio e, and βp,e is theregression coefficient from regressing Rp on Re.
If there exists a risk-free rate at which investors can borrow (as in the Sharpe-Lintner model)or if there is unlimited short-selling of securities (as in the Black model), with common be-liefs and efficient markets3 then the market portfolio (the value-weighted sum of all investorsportfolio holdings where the weights are given be the respective investor’s wealth) can beshown to be MVE. Thus we can replace portfolio e in the above equation with the marketportfolio M and obtain the CAPM.
Fama and MacBeth (1973) proposed the following specification to test three implicationsof this result.
Rp � γ0,t � γ1,tβp,t�1 � γ2,tβ2p,t�1 � γ3,tsp,t�1peiq � ηp,t @p (1)
The author use this specification to test
1. Linearity: EpRpq is linear in βp, the systematic risk of portfolio p. Linearity impliesthat γ2,t should not be statistically different from zero.
2. Only the systematic risk measured by βp is priced. Therefore, γ3,t should also bestatistically indistinguishable from zero.
3. There is positive expected risk-return trade-off. Thus the null hypothesis Epγ1,tq ¤ 0should be rejected.
The method used in Fama-MacBeth (1973) is very popular even today. It consists of firstusing time-series regressions of individual securities against (a proxy for) the market portfolioand then grouping the securities into twenty portfolios according to their beta coefficients.The next step is to run the cross-sectional regression using equation (1) for each month andthen calculate the average of the coefficients over the time period considered to obtain ¯γj. Iwill describe the method in detail later.
1Note that portfolios can contain one ore more securities.2For the derivation of this result, see Foundations of Finance Chap. 5, Fama (1976).3Market efficiency here means that when investors form expectations they use the “true” joint probability
density function for security prices implied by the information set that is relevant for determining securityprices (see Foundations of Finance Chap. 5, Famal; 1976)
2
Although the method is still widely used many of the results in the paper have not re-mained valid in subsequent testing periods and with further investigation. More specifically,Fama-MacBeth (1973) shows that for the time period 1929-1968 the model described abovehas performed fairly well. ¯γ2,t and ¯γ3,t were not significantly different from zero (in a statis-tical sense). Thus Fama-MacBeth (1973) fails to reject that conditional on markets beingefficient, the tests portfolios are mean-variance efficient in the set of securities spanned bythe proxy for the market portfolio and the test portfolios. However, later research wouldshow that the model performs poorly.
Indeed, in Fama and French (2006) the authors “conclude that the CAPM has fatal problemsthroughout the 1926 to 2004 period”. Furthermore, Fama and French (1996) also show thatthere may be additional state variables of interest to investors4. The authors find that athree factor model with excess returns of the market portfolio on the risk-free security, thedifference in returns between portfolios of small and large stocks and the difference in returnsbetween portfolios of high and low book-to-market value captures a lot of the anomalies inexpected returns produced by the CAPM5. With the benefit of hindsight, it is all the moresurprising that the model performed so well in the pre-1968 period. In particular, Fama andMacBeth (1973) use the equal-weighted NYSE portfolio as a proxy for the market portfo-lio. In theory, the market portfolio should be the value-weighted portfolio of total investorswealth which includes human capital and other assets not tradeable or readily measurable.Furthermore, any test of asset pricing model is a joint test of market efficiency and of theequilibrium implications of the model’s assumptions. Given the strong assumptions behindthe model, and with the benefit of hindsight it is not surprising that a fair amount of evi-dence was later found against the model.
The question I would like to address in my paper is what could have been done in Fama-MacBeth (1973) to reveal some of the flaws of the model. In particular, I replicate theauthors results and through a few robustness checks I show that the results are not consis-tent. Keeping the same method used in the paper, I alternate between using a value-weightedor equal-weighted NYSE portfolio as proxy for the market portfolio, using value-weightedor equal-weighted underlying securities estimates to build the test portfolios estimates andusing dual-sort rather than single-sort test portfolios. I find that with a double-sort on betaand standard deviation of the residuals of the underlying securities, many of the results inFama-MacBeth (1973) in favor of the model disappear.
4Or that at least additional excess returns are needed to span the true market portfolio of investor’swealth
5We should note that one cannot test the CAPM because the true market portfolio of investors’ wealth isnot observed. Furthermore, any test of the CAPM would be a joint test of the CAPM and market efficiency.Nonetheless, to be concise, to avoid confusion and to be consitent with the literature I will use CAPM todescribe the following model EpRpq � EpR0,M q � βp,M rEpRM q � EpR0,M qs; where M is a proxy for themarket porfolio (eg. NYSE value-weighted portfolio).
3
2 Method
I use the NYSE securities provided by CRSP and follow the Fama and MacBeth (1973)method. I start with a formation period of seven years during which I run the time seriesregression for each security’s monthly return, Ri,t, against the returns of the proxy for themarket portfolio (the value-weighted or equal weighted NYSE index), RM,t.
Ri,t � α � βiRM,t � ei,t
To produce the single-sort portfolios, I group the securities into twenty portfolios (one foreach beta quantile). To produce double-sort portfolios, first I sort the securities according totheir beta coefficient. Then I sort the securities in each beta-quantile according to the samplestandard deviation of the error term (spei,tq). Lastly, I group the securities into twenty-fiveportfolios (one for each of the 5 � 5 quantiles).
I follow each portfolio formation period with an estimation period where I regress the under-lying security returns of each portfolio against the returns of the market proxy. I collect thebeta coefficients and calculate the respective portfolio beta by taking an equal-weighted ora value-weighted sum of the underlying securities beta estimates. That is βp,t �
°Ni�1 xiβi,t;
where xi is the weight corresponding to security i in portfolio p. The testing period is fouryears long. In particular each month t of the testing period I run the regression specifiedby equation (1). In this cross-sectional regression βp,t is as defined above and the other
regressors6 are sp,tpei,tq �°Ni�1 xispei,tq and β2
p,t �°Ni�1 xiβ
2i,t.
The last step consists of taking the sample averages of γjt across the time periods of in-terest to obtain the desired statistics. Each estimation period is an increasing time windowwhich starts five year prior to the testing period. The estimation window increases by oneyear for every year of the testing period (excluding the first year). Thus the portfolio betasare updated annually and these betas are estimated one to twelve month prior to the dateof the portfolio returns in testing regressions. I restrict the analysis to securities that havedata for all five years of the preceding estimation period and at least four years of the for-mation period. To be consistent with Fama-Macbeth (1973) the length of the first formationperiod 1926-1929 will be four years rather than seven. Table 1 replicates and extends Table1 from Fama-Macbeth (1973) and provides information on the formation, estimation andtesting periods. Notice that the sample the authors use in Fama-Macbeth (1973) is from1926 through 6/1968. I extend their sample through 12/2010. The number of securities inthe formation, estimation and testing periods are slightly different from those in Fama andMacbeth (1973) mostly due to changes in the CRSP dataset over the last few decades.
6I use o to denote values estimated from a regression and distinguish estimates from true values. In thelimit as the sample gets infinitely large these estimates converge to the true values of the coefficients. Thusγ0 is an estimate of γ0, the true value of the coefficient. I use o to denote sample averages and o to denoterandom variables.
4
! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1926629 1927633 1931637 1935641 1939645Initial!estimation!period 1930634 1934638 1938642 1942646 1946650Testing!period 1935638 1939642 1943646 1947650 1951654No.!of!securities!available 711 779 807 921 1024No.!of!securities!meeting ! ! ! ! !!!data!requirement 415 581 608 717 760! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 !! ! ! ! ! !Portfolio!formation!period 1943649 1947653 1951657 1955661 !Initial!estimation!period 1950654 1954658 1958662 1962666 !Testing!period 1955658 1959662 1963666 1967668 !No.!of!securities!available 1062 1071 1189 1284 !No.!of!securities!meeting ! ! ! ! !!!data!requirement 823 869 882 863 !! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1959665 1963669 1967673 1971677 1975681Initial!estimation!period 1966670 1970674 1974678 1978682 1982686Testing!period 1971674 1975678 1979682 1983686 1987690No.!of!securities!available 1339 1518 1568 1488 1469No.!of!securities!meeting ! ! ! ! !!!data!requirement 827 928 1074 1105 978! ! ! ! ! !! ! ! ! ! !!! 1 2 3 4 5! ! ! ! ! !Portfolio!formation!period 1979685 1983689 1987693 1991697 1995601Initial!estimation!period 1986690 1990694 1994698 1998602 2002606Testing!period 1991694 1995698 1999602 2003606 2007610No.!of!securities!available 1565 2176 2429 2024 2005No.!of!securities!meeting ! ! ! ! !!!data!requirement 899 951 1011 1094 1239
TABLE!1PORTFOLIO!FORMATION,!ESTIMATION!AND!TESTING!PERIODS
PERIODS
PERIODS
PERIODS
PERIODS
Table 1
5
3 Results
3.1 Summary statistics
Most of the results will consist of producing different versions of the tables from Fama-Macbeth (1973). In describing the results I will limit the discussion to and show summaryresults for 1) the original Fama-Macbeth (1973) tables which I extend to include data for1968-2010; I will label the resulting tables, Table #a, 2) a version of the tables using boththe value-weighted NYSE market portfolio proxy and value-weighted averages of the under-lying securities βi and speitq to construct the corresponding portfolio-level estimates for thetwenty portfolios (labelled Table #d), 3) the original Fama and Macbeth (1973) tables butwith the twenty-five dual-sort portfolios (labelled Table #e), and 4) the results from usingboth the value-weighted NYSE market portfolio proxy and a value-weighted average of theunderlying securities βi and speitq to construct the twenty-five dual-sort portfolios estimates(labelled Table #h). I will include other variations of the tables in the Appendix.
First, I replicate and extend Table 2 from Fama and Macbeth (1973) below. The proxyfor the market portfolio is the equal-weighted NYSE index and the test portfolios are thetwenty beta-sorted portfolios. I obtain point estimates very similar to those in Fama andMacbeth (1973) for the 1926-1968 period. I display the result on Table 2a, below. In par-ticular, the portfolio betas range from 0.24 for the first quantile to 1.56 for the twentiethquantile. Also notice that for the first quantile the average beta increases from 0.24 to 0.66for the estimation periods 1934-38 through 1966-70. But then it monotonically decreasesfor the subsequent estimation periods 1974-78 to 2002-06 from 0.56 to 0.23. This may behinting that the nature of the betas have changed at lowest portfolio beta-quantile betweenthe time period 1926-1968 (used in the Fama and Macbeth; 1973) and the subsequent timeperiod 1968-2010. Although I cannot rule out small sample bias as the cause of these results,time-varying betas may also be part of the reason.
In order to determine how robust these estimates are I produce the following variationsof Table 2. First, in Table 2d (of the Appendix), I show the resulting table when I use boththe value-weighted NYSE market portfolio proxy and value-weighted averages of the under-lying securities βi and speitq to construct the corresponding portfolio estimates. I calculatethe percentage difference between Table 2d and Table 2a and display the results graphicallyon Figure (1a), shown below. Along the x-axis are the seven statistics of interest in thefollowing order: the portfolio beta βp,t�1, the estimated standard error of the portfolio beta
spβp,t�1q, the square of the correlation between the portfolio return and the market portfolioproxy return rpRp, Rmq
2, the estimated standard deviation of the portfolio return spRpq, thestandard deviation of the residuals from regressing portfolio returns against market port-folio proxy returns spepq, the weighted-average of the standard deviations of the residualsfrom regressing each underlying security returns again the market portfolio proxy returnssp,t�1peiq, and spepq{sp,t�1peiq. The y-axis lists the respective portfolio. And the z-axis showsthe percentage deviations from Table 2a.
6
Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11
0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.2035 0.2229 0.1966 0.0828 0.0669 0.0421 0.0298 0.0150 0.0155 0.02670.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.84210.0759 0.0944 0.0912 0.0931 0.1012 0.0949 0.1161 0.0998 0.0996 0.11590.0302 0.0283 0.0282 0.0267 0.0224 0.0256 0.0324 0.0231 0.0265 0.02680.0838 0.0838 0.0838 0.0838 0.0838 0.0838 0.0838 0.0733 0.0733 0.07330.3600 0.3372 0.3372 0.3191 0.2678 0.3056 0.3866 0.3149 0.3622 0.3652
1 1 1 1 1 1 1 1 1
0.2475 0.4370 0.6118 0.6406 0.7170 0.7622 0.9228 0.9761 0.9810 1.00400.0334 0.0035 0.0208 0.0045 0.0163 0.0105 0.0524 0.0437 0.0235 0.01650.7474 0.7927 0.8047 0.8439 0.8890 0.8508 0.9034 0.9077 0.9265 0.95100.03551 0.0396 0.0527 0.0429 0.0466 0.0488 0.0540 0.0547 0.0619 0.05800.01784 0.0180 0.0233 0.0169 0.0155 0.0189 0.0168 0.0166 0.0168 0.01280.0542 0.0542 0.0544 0.0542 0.0544 0.0544 0.0544 0.0544 0.0544 0.05440.3294 0.3326 0.4281 0.3128 0.2852 0.3465 0.3081 0.3050 0.3084 0.2358
1 1 1 1 1 1 1 1 1
0.4597 0.5366 0.6250 0.6502 0.7220 0.7432 0.8038 0.8287 0.8420 0.89770.0297 0.0080 0.0283 0.0398 0.0362 0.0393 0.0304 0.0399 0.0392 0.03040.6149 0.6981 0.7725 0.8659 0.9095 0.8965 0.9034 0.9403 0.9430 0.92470.02409 0.0219 0.0269 0.0286 0.0317 0.0312 0.0338 0.0388 0.0372 0.03630.01495 0.0120 0.0128 0.0105 0.0095 0.0100 0.0105 0.0095 0.0089 0.01000.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.0399 0.03990.3744 0.3007 0.3211 0.2624 0.2391 0.2512 0.2633 0.2376 0.2221 0.2496
1 1 1 1 1 1 1 1 1
0.4394 0.5873 0.7484 0.7549 0.7627 0.8164 0.9793 0.9823 0.9838 1.01600.0224 0.0222 0.0568 0.0489 0.0119 0.0049 0.0145 0.0067 0.0080 0.01000.7957 0.8430 0.8760 0.8900 0.9188 0.9152 0.9360 0.9467 0.9251 0.93220.0335 0.0350 0.0359 0.0338 0.0361 0.0373 0.0405 0.0418 0.0423 0.04200.01514 0.0139 0.0127 0.0112 0.0103 0.0109 0.0102 0.0097 0.0116 0.01100.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.04980.3040 0.2787 0.2539 0.2251 0.2064 0.2182 0.2056 0.1939 0.2321 0.2197
1 1 1 1 1 1 1 1 1
0.6101 0.6206 0.6965 0.7659 0.7854 0.8456 0.8679 0.9535 0.9550 0.95710.0391 0.0154 0.0220 0.0189 0.0200 0.0127 0.0136 0.0379 0.0284 0.02410.7802 0.7152 0.7641 0.8635 0.8874 0.9128 0.9263 0.9451 0.9560 0.94580.04056 0.0388 0.0415 0.0456 0.0468 0.0450 0.0539 0.0501 0.0553 0.04940.01901 0.0207 0.0201 0.0169 0.0157 0.0133 0.0146 0.0117 0.0116 0.01150.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.06940.2740 0.2981 0.2903 0.2429 0.2262 0.1917 0.2106 0.1690 0.1673 0.1659
0.5587 0.5745 0.6114 0.6488 0.7423 0.7487 0.7946 0.8527 0.8551 0.87230.0368 0.0270 0.0121 0.0200 0.0227 0.0295 0.0202 0.0196 0.0110 0.01550.7538 0.7835 0.8032 0.9065 0.9078 0.9223 0.9111 0.9169 0.9446 0.93080.05202 0.0493 0.0488 0.0490 0.0501 0.0529 0.0561 0.0521 0.0619 0.05890.02581 0.0230 0.0217 0.0150 0.0152 0.0147 0.0167 0.0150 0.0146 0.01550.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.0595 0.05950.4338 0.3858 0.3641 0.2516 0.2558 0.2477 0.2809 0.2526 0.2448 0.2604
1 1 1 1 1 1 1 1 1
0.5491 0.6146 0.6556 0.6696 0.7329 0.7536 0.7905 0.8103 0.8618 0.91540.0286 0.0165 0.0143 0.0173 0.0149 0.0135 0.0075 0.0119 0.0106 0.02320.6371 0.5766 0.7363 0.8325 0.8207 0.8695 0.9027 0.9324 0.9043 0.93740.03336 0.0291 0.0347 0.0391 0.0364 0.0393 0.0425 0.0422 0.0441 0.04640.0201 0.0189 0.0178 0.0160 0.0154 0.0142 0.0132 0.0110 0.0136 0.01160.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0474 0.0596 0.04740.4245 0.4001 0.3758 0.3383 0.3257 0.3001 0.2796 0.2316 0.2290 0.2450
1 1 1 1 1 1 1 1 1
0.4535 0.5258 0.6075 0.6612 0.7792 0.7859 0.8080 0.9175 1.0300 1.04700.0522 0.0681 0.0565 0.0310 0.0334 0.0341 0.0564 0.0306 0.0280 0.03110.2653 0.3506 0.4916 0.6653 0.7747 0.7783 0.7853 0.8352 0.8238 0.85340.02637 0.0274 0.0322 0.0315 0.0363 0.0366 0.0403 0.0369 0.0429 0.04920.0226 0.0220 0.0229 0.0182 0.0172 0.0172 0.0187 0.0150 0.0180 0.01890.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0367 0.0457 0.03670.6165 0.6011 0.6255 0.4964 0.4700 0.4700 0.5096 0.4089 0.3942 0.5140
1 1 1 1 1 1 1 1 1
0.2567 0.3555 0.4157 0.5775 0.6683 0.7887 0.8396 0.8742 0.9014 0.93920.0248 0.0218 0.0228 0.0592 0.0481 0.0264 0.0552 0.0217 0.0156 0.02020.2612 0.1635 0.4095 0.4788 0.6937 0.7833 0.6700 0.9215 0.8208 0.84750.02507 0.0328 0.0333 0.0421 0.0392 0.0432 0.0460 0.0474 0.0456 0.05150.02155 0.0300 0.0256 0.0304 0.0217 0.0201 0.0264 0.0133 0.0193 0.02010.0572 0.0568 0.0572 0.0572 0.0549 0.0549 0.0549 0.0549 0.0554 0.05540.3768 0.5278 0.4475 0.5314 0.3948 0.3666 0.4816 0.2421 0.3486 0.3627
1 1 1 1 1 1 1 1 1
0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0205 0.0203 0.0218 0.0724 0.0207 0.0507 0.0503 0.0744 0.0050 0.01890.4433 0.3691 0.5467 0.6055 0.7747 0.7985 0.8758 0.9157 0.8708 0.90360.02464 0.0244 0.0287 0.0282 0.0329 0.0313 0.0305 0.0345 0.0341 0.03660.01839 0.0194 0.0193 0.0177 0.0156 0.0141 0.0107 0.0100 0.0122 0.01140.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0447 0.0447 0.0447 0.04470.4126 0.4351 0.4333 0.3976 0.3504 0.3154 0.2400 0.2239 0.2735 0.2540
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12a:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
7
1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 1 1 1 1
0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.0170 0.0147 0.0249 0.0586 0.0614 0.0677 0.0577 0.0703 0.0574 0.02180.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.8421 0.84210.1149 0.1065 0.1097 0.1177 0.1248 0.1148 0.1233 0.1237 0.1215 0.14030.0221 0.0251 0.0288 0.0311 0.0333 0.0298 0.0324 0.0314 0.0276 0.03670.0733 0.0733 0.0851 0.0851 0.0851 0.0851 0.0851 0.0851 0.0851 0.08510.3017 0.3419 0.3382 0.3655 0.3916 0.3494 0.3799 0.3687 0.3243 0.4309
1 1 1 1 1 1 1 1 1
1.0410 1.1320 1.2130 1.2240 1.2330 1.3220 1.3270 1.3660 1.3710 1.55200.0186 0.0139 0.0238 0.0244 0.0089 0.0077 0.0247 0.0154 0.0246 0.04780.9529 0.9328 0.9151 0.8908 0.9134 0.9488 0.9102 0.8157 0.9715 0.84590.0654 0.0693 0.0755 0.0814 0.0832 0.0730 0.0837 0.1049 0.0862 0.11980.0142 0.0180 0.0220 0.0269 0.0245 0.0165 0.0251 0.0450 0.0145 0.04700.0544 0.0527 0.0544 0.0527 0.0527 0.0527 0.0527 0.0527 0.0527 0.05270.2608 0.3408 0.4041 0.5107 0.4647 0.3136 0.4760 0.8545 0.2760 0.8927
1 1 1 1 1 1 1 1 1
0.9478 1.0360 1.0480 1.1070 1.1910 1.2940 1.3900 1.4030 1.5570 1.56000.0258 0.0069 0.0320 0.0069 0.0097 0.0243 0.0337 0.0219 0.0537 0.04140.9531 0.9411 0.9171 0.9382 0.9473 0.9327 0.9452 0.9048 0.8850 0.79960.0377 0.0411 0.0454 0.0420 0.0447 0.0460 0.0523 0.0509 0.0554 0.05950.0082 0.0100 0.0131 0.0105 0.0103 0.0119 0.0122 0.0157 0.0188 0.02660.0430 0.0430 0.0399 0.0399 0.0430 0.0430 0.0430 0.0430 0.0430 0.04300.1899 0.2322 0.3272 0.2617 0.2387 0.2775 0.2845 0.3656 0.4372 0.6200
1 1 1 1 1 1 1 1 1
1.0740 1.1140 1.1590 1.1650 1.2000 1.2180 1.2410 1.2460 1.4770 1.49900.0285 0.0196 0.0191 0.0149 0.0229 0.0158 0.0064 0.0613 0.0248 0.05410.9387 0.9486 0.9428 0.8992 0.9463 0.9338 0.9236 0.9052 0.9175 0.86580.0462 0.0450 0.0487 0.0458 0.0490 0.0495 0.0490 0.0564 0.0567 0.05760.0114 0.0102 0.0117 0.0145 0.0114 0.0127 0.0135 0.0174 0.0163 0.02110.0498 0.0517 0.0517 0.0517 0.0498 0.0501 0.0517 0.0501 0.0501 0.05010.2295 0.1974 0.2255 0.2816 0.2279 0.2545 0.2622 0.3467 0.3249 0.4215
1 1 1 1 1 1 1 1 1
1.0110 1.0250 1.0360 1.0390 1.0470 1.1130 1.1260 1.1500 1.3020 1.45000.0314 0.0269 0.0194 0.0202 0.0251 0.0363 0.0423 0.0571 0.0287 0.04990.9426 0.9579 0.9439 0.9645 0.9495 0.9299 0.9402 0.9294 0.9407 0.93690.0565 0.0519 0.0587 0.0617 0.0562 0.0631 0.0641 0.0660 0.0672 0.07160.0135 0.0107 0.0139 0.0116 0.0126 0.0167 0.0157 0.0175 0.0164 0.01800.0694 0.0694 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0590 0.05900.1949 0.1534 0.2323 0.1941 0.2110 0.2791 0.2619 0.2929 0.2773 0.3047
0.8786 0.9812 1.0080 1.0760 1.0900 1.0960 1.1040 1.1930 1.2510 1.43300.0190 0.0215 0.0161 0.0200 0.0275 0.0305 0.0280 0.0173 0.0172 0.02260.9353 0.9582 0.9569 0.9460 0.9469 0.9540 0.9671 0.9482 0.9084 0.92170.0636 0.0643 0.0692 0.0717 0.0712 0.0700 0.0803 0.0780 0.0900 0.09270.0162 0.0132 0.0144 0.0167 0.0164 0.0150 0.0146 0.0178 0.0272 0.02590.0595 0.0595 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.0564 0.05640.2720 0.2211 0.2543 0.2952 0.2905 0.2659 0.2581 0.3145 0.4827 0.4596
1 1 1 1 1 1 1 1 1
0.9296 0.9563 0.9936 1.0270 1.0430 1.1120 1.1530 1.2480 1.2560 1.51400.0187 0.0179 0.0091 0.0094 0.0189 0.0113 0.0209 0.0182 0.0536 0.02360.8934 0.9298 0.9114 0.9356 0.9238 0.9094 0.9343 0.8893 0.8347 0.90060.0492 0.0475 0.0462 0.0489 0.0471 0.0492 0.0553 0.0477 0.0592 0.06430.0161 0.0126 0.0138 0.0124 0.0130 0.0148 0.0142 0.0159 0.0241 0.02030.0474 0.0474 0.0596 0.0474 0.0596 0.0596 0.0596 0.0596 0.0594 0.05940.3396 0.2656 0.2310 0.2621 0.2182 0.2488 0.2379 0.2663 0.4046 0.3408
1 1 1 1 1 1 1 1 1
1.0610 1.0850 1.0920 1.0990 1.1190 1.1340 1.1790 1.1940 1.2340 1.32800.0142 0.0076 0.0097 0.0117 0.0128 0.0067 0.0183 0.0180 0.0296 0.03500.9021 0.7938 0.8482 0.7453 0.8128 0.8187 0.8754 0.7588 0.5742 0.80910.0440 0.0462 0.0518 0.0541 0.0441 0.0509 0.0500 0.0594 0.0634 0.07080.0138 0.0210 0.0202 0.0273 0.0191 0.0217 0.0177 0.0292 0.0414 0.03100.0367 0.0367 0.0457 0.0367 0.0457 0.0457 0.0457 0.0457 0.0457 0.04570.3754 0.5726 0.4413 0.7453 0.4176 0.4742 0.3862 0.6384 0.9051 0.6773
1 1 1 1 1 1 1 1 1
0.9516 0.9613 1.0310 1.0490 1.1770 1.2470 1.2640 1.2880 1.3370 1.55700.0066 0.0270 0.0297 0.0505 0.0402 0.0294 0.0347 0.0281 0.0248 0.05940.8129 0.8314 0.9045 0.8686 0.8904 0.8405 0.9068 0.9060 0.8271 0.81060.0539 0.0516 0.0582 0.0622 0.0640 0.0732 0.0692 0.0682 0.0766 0.08250.0233 0.0212 0.0180 0.0225 0.0212 0.0292 0.0211 0.0209 0.0318 0.03590.0461 0.0563 0.0461 0.0563 0.0461 0.0461 0.0461 0.0461 0.0461 0.04610.5059 0.3762 0.3902 0.4005 0.4593 0.6337 0.4579 0.4532 0.6903 0.7784
1 1 1 1 1 1 1 1 1
0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0237 0.0134 0.0082 0.0248 0.0128 0.0319 0.0322 0.0081 0.0054 0.00960.8741 0.8719 0.8852 0.8781 0.8971 0.8796 0.8819 0.8871 0.8786 0.84990.0398 0.0462 0.0437 0.0423 0.0477 0.0509 0.0504 0.0508 0.0488 0.05820.0141 0.0165 0.0148 0.0148 0.0153 0.0177 0.0173 0.0171 0.0170 0.02260.0434 0.0434 0.0351 0.0352 0.0352 0.0354 0.0354 0.0354 0.0354 0.03530.3255 0.3811 0.4226 0.4197 0.4356 0.4990 0.4897 0.4826 0.4804 0.6392
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12a:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
8
(a) This figure displays the percentage difference need spacebetween Table 2d and Table 2a. In Table 2d, I use theneedvalue-weighted NYSE as a market portfolio proxy and andI use a value-weighted of the underlying securities βi and
and speitq to construct βp,t�1 and sp,t�1peiq for the twentytwenty portfolios. Table 2a is the original table from FamaFama-Macbeth (1973).
(b) This figure displays the percentage difference betweenTable 2e and Table 2a. In Table 2e, I use the equal-weightedNYSE as a market portfolio proxy and I use the equal-weighted underlying securities βi and speitq to construct
βp,t�1 and sp,t�1peiq for the twenty-five double-sort port-folios. To calculate the percentage differences I use porfolios1, 5, 10, 16 and 20 from Fama-MacBeth (1973) and the cor-responding beta-quintile of the 5 � 5 test portfolios.
(c) This figure displays the percentage difference betweenTable 2h and Table 2a. In Table 2h, I use the value-weightedNYSE as a market portfolio proxy and I use value-weightedunderlying securities βi and speitq to construct βp,t�1 andsp,t�1peiq for the twenty-five double-sort portfolios. To cal-culate the percentage differences I use porfolios 1, 5, 10, 16and 20 from Fama-MacBeth (1973) and the correspondingbeta-quintile of the 5 � 5 test portfolios.
Figure 1: The x-axis show the following statistics: 1) the portfolio beta βp,t�1, 2) the estimated standard error
of the portfolio beta spβp,t�1q, 3) the square of the correlation between the portfolio return and the marketportfolio proxy return rpRp, Rmq2, 4) the estimated standard deviation of the portfolio return spRpq, 5) thestandard deviation of the residuals from regressing portfolio returns against market portfolio proxy returnsspepq, 6) the weighted-average of the standard deviations of the residuals from regressing each underlyingsecurity returns again the market portfolio proxy returns sp,t�1peiq, and 7) spepq{sp,t�1peiq. The y-axis liststhe respective portfolio. And the z-axis shows the percentage deviations from Table 2a.
One of the most striking features of Figure (1a) is that statistics 7, spepq{sp,t�1peiq seemsto be much larger when the market proxy is the value-weighted NYSE compared to whenan equal-weighted NYSE index is used. This holds for all portfolio quantiles. In particular,this statistics increases by 50-150%. This implies that the equal-weighted NYSE is betterat predicting the twenty beta-sorted portfolios of Fama and Macbeth (1973) than the value-weighted NYSE. Indeed, this is confirmed by statistics 3, rpRp, Rmq
2, which is a measureof the goodness of fit. We can observe that the difference between rpRp, Rmq
2 from Table2d and Table 2a is slightly negative for all twenty portfolios; thus the fit is slightly worsewhen I use the value-weighted NYSE as a proxy for the market portfolio. Notice that theportfolio betas (statistics 1) are slightly greater on Table 2d than Table 2a. Recall that
βx,y �covpx,yqσ2y
and corrpx, yq � covpx,yqσxσy
. Since the magnitude of the correlation between Rp
and Rm is smaller on Table 2d than on Table 2a and since βp,t�1 is larger on Table 2d thanon Table 2a, it may be that the volatility in the test portfolio returns is larger when we usethe value-weighted NYSE as proxy for the market portfolio, that the value-weighted NYSEis less volatile than the equal-weighted NYSE and that the covariance between the portfolioreturns and the market proxy returns increases. I do find that the estimated standard de-viation of the test portfolio returns (statistics 4) are a bit larger on Table 2d. Later, I willalso show that the equal-weighted NYSE has a greater standard deviation than the value-weighted NYSE. I find that on average the equal-weighted NYSE portfolio has a standarddeviation that is twenty-six percent greater than that of the value-weighted NYSE portfolio.Thus, using the value-weighted NYSE market portfolio proxy leads to larger standard errorsfor the portfolio betas (statistics 2 is increasingly larger as the beta-quantile increases), andlower covariance between the test portfolio returns and the proxy for the market returns.But since the value-weighted NYSE is less volatile than the equal-weighted NYSE the levelof the portfolio betas increases a bit but the goodness of fit for the regression of the testportfolio returns against the market proxy returns decreases slightly.
I then repeat the exercise with the twenty-five portfolios based on a dual-sort of betas andstandard deviation of the returns on the underlying securities (the results are in Tables 2e,2f, 2g and 2h). Table 2h is displayed below. I also include the percentage difference be-tween Table 2e and Table 2a on Figure (1b). On Figure (1b) we can see that the differencesbetween Tables 2e and 2a are less systematic. Nonetheless, the change in the statistics 7,spepq{sp,t�1peiq, is more than ten percent for most of the portfolios. Figure (1c) shows thedifference between Table 2h and Table 2a. Here the results are qualitatively similar to thoseof Figure (1a). However, the magnitude of statistics 5, spepq, and statistics 7, spepq{sp,t�1peiq,are much greater. This hints that model (1) will have difficulties pricing the portfolio returnswhen the test portfolios estimates are constructed using a value-weighted approach and/orwhen the test portfolios are constructed from a dual sort on betas and standard deviationof the residuals of the underlying securities.
10
Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11
0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.3208 0.2990 0.2972 0.2452 0.1587 0.1563 0.1640 0.1504 0.1740 0.1670 0.1778 0.1844 0.21740.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.44010.1490 0.0855 0.0868 0.1178 0.1268 0.1102 0.0955 0.1087 0.1162 0.1596 0.1121 0.1000 0.13250.1115 0.0508 0.0452 0.0737 0.0943 0.0571 0.0488 0.0590 0.0754 0.1208 0.0636 0.0503 0.06770.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0593 0.0593 0.05932.5550 1.1640 1.0360 1.6890 2.1610 1.3100 1.1190 1.3540 1.7280 2.7700 1.0710 0.8470 1.1420
1 1 1 1 1 1 1 1 1 1 1 1
0.5582 0.6192 0.8563 1.0730 1.1020 1.1220 1.1390 1.1730 1.2260 1.3720 1.4600 1.5730 1.63900.1171 0.0267 0.0755 0.1247 0.1106 0.0688 0.0533 0.0413 0.0208 0.0361 0.0531 0.0880 0.10470.4898 0.7589 0.1020 0.1930 0.6181 0.7678 0.6575 0.7801 0.6143 0.6204 0.8232 0.5185 0.65460.05024 0.0428 0.0805 0.1170 0.0678 0.0494 0.0632 0.0488 0.0644 0.0795 0.0506 0.0616 0.06290.03589 0.0210 0.0763 0.1051 0.0419 0.0238 0.0370 0.0229 0.0400 0.0490 0.0213 0.0427 0.03690.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0441 0.0540 0.05400.8135 0.4761 1.7300 2.3820 0.9498 0.5401 0.8385 0.5192 0.9067 1.1100 0.4822 0.7918 0.6842
1 1 1 1 1 1 1 1 1 1 1 1
0.4110 0.6066 0.7508 0.8363 0.8659 0.9766 1.0570 1.0650 1.1080 1.1430 1.1710 1.2300 1.25600.1141 0.0573 0.0258 0.0422 0.0492 0.0651 0.0449 0.0366 0.0317 0.0204 0.0223 0.0362 0.03940.5048 0.4156 0.4498 0.4648 0.3043 0.7522 0.6366 0.5915 0.4788 0.3736 0.7766 0.6463 0.63850.02798 0.0331 0.0309 0.0329 0.0353 0.0372 0.0459 0.0391 0.0455 0.0411 0.0397 0.0453 0.04440.01969 0.0253 0.0229 0.0241 0.0294 0.0185 0.0277 0.0250 0.0329 0.0325 0.0188 0.0270 0.02670.0440 0.0440 0.0440 0.0440 0.0440 0.0406 0.0440 0.0440 0.0400 0.0406 0.0440 0.0406 0.04060.4471 0.5754 0.5208 0.5467 0.6684 0.4565 0.6287 0.5671 0.8210 0.8005 0.4264 0.6639 0.6580
1 1 1 1 1 1 1 1 1 1 1 1
0.4092 0.4104 0.5256 0.5512 0.7272 0.7319 0.7516 0.7728 0.8975 0.9153 0.9633 0.9719 1.02000.0562 0.0713 0.0540 0.0514 0.0855 0.0803 0.0544 0.0462 0.0357 0.0375 0.0566 0.0477 0.05460.6912 0.6154 0.6353 0.5635 0.6025 0.6186 0.5762 0.5245 0.5787 0.5684 0.6314 0.5666 0.58410.03464 0.0385 0.0380 0.0471 0.0503 0.0431 0.0453 0.0548 0.0485 0.0581 0.0421 0.0541 0.06010.01925 0.0239 0.0229 0.0311 0.0317 0.0266 0.0295 0.0378 0.0315 0.0381 0.0256 0.0356 0.03870.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0407 0.0445 0.0445 0.0445 0.04450.4726 0.5857 0.5631 0.7644 0.7786 0.6540 0.7238 0.9283 0.7729 0.8578 0.5754 0.8017 0.8714
1 1 1 1 1 1 1 1 1 1 1 1
0.5930 0.6672 0.7041 0.7730 0.7769 0.7876 0.8807 0.9703 0.9964 1.0040 1.0060 1.0510 1.05200.0810 0.0349 0.0411 0.0325 0.0413 0.0528 0.0262 0.0197 0.0206 0.0196 0.0429 0.0360 0.04050.6384 0.5769 0.5021 0.5893 0.5538 0.6901 0.7126 0.6112 0.5143 0.5143 0.6547 0.7050 0.71500.0416 0.0472 0.0468 0.0624 0.0786 0.0466 0.0487 0.0578 0.0687 0.0879 0.0516 0.0521 0.05890.02502 0.0307 0.0330 0.0400 0.0525 0.0260 0.0261 0.0361 0.0479 0.0613 0.0303 0.0283 0.03140.0568 0.0568 0.0568 0.0568 0.0568 0.0568 0.0549 0.0568 0.0568 0.0549 0.0568 0.0568 0.05680.4401 0.5399 0.5809 0.7036 0.9235 0.4568 0.4755 0.6345 0.8420 1.1160 0.5338 0.4978 0.5530
0.5693 0.6217 0.6304 0.8976 0.8982 0.9878 0.9972 1.0200 1.0230 1.0380 1.0490 1.0890 1.10100.0699 0.0563 0.0816 0.0260 0.0149 0.0482 0.0284 0.0384 0.0482 0.0468 0.0416 0.0399 0.04800.4594 0.6416 0.6117 0.5592 0.2604 0.7889 0.6028 0.6571 0.6362 0.3382 0.6228 0.7121 0.60430.05901 0.0495 0.0509 0.0481 0.0832 0.0544 0.0592 0.0542 0.0678 0.0875 0.0526 0.0863 0.07260.04339 0.0297 0.0317 0.0319 0.0716 0.0250 0.0373 0.0318 0.0409 0.0712 0.0323 0.0463 0.04560.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0567 0.0548 0.0567 0.05480.7652 0.5231 0.5591 0.5631 1.2620 0.4405 0.6583 0.5601 0.7207 1.2550 0.5891 0.8169 0.8331
1 1 1 1 1 1 1 1 1 1 1 1
0.6849 0.7125 0.7397 0.8273 0.9317 0.9394 0.9782 0.9830 0.9864 0.9921 1.0360 1.0400 1.05500.1051 0.0893 0.0447 0.0527 0.0659 0.0548 0.0503 0.0399 0.0312 0.0307 0.0417 0.0325 0.03530.3654 0.3523 0.5918 0.5097 0.5708 0.7124 0.7168 0.5956 0.5599 0.6552 0.7332 0.6233 0.49240.03032 0.0349 0.0410 0.0446 0.0596 0.0435 0.0419 0.0643 0.0495 0.0552 0.0507 0.0554 0.05770.02416 0.0281 0.0262 0.0312 0.0391 0.0233 0.0223 0.0409 0.0328 0.0324 0.0262 0.0340 0.04110.0405 0.0405 0.0405 0.0405 0.0405 0.0405 0.0508 0.0405 0.0405 0.0508 0.0405 0.0405 0.05080.5970 0.6942 0.6466 0.7721 0.9651 0.5766 0.4384 1.0100 0.8107 0.6373 0.6476 0.8406 0.8091
1 1 1 1 1 1 1 1 1 1 1 1
0.4070 0.5278 0.5906 0.6876 0.7468 0.8203 0.8437 0.9501 0.9575 0.9742 1.0330 1.0430 1.07600.0729 0.0592 0.0399 0.0797 0.1184 0.1089 0.0975 0.0850 0.0713 0.0404 0.0284 0.0222 0.01980.3238 0.3482 0.3427 0.6814 0.4674 0.6404 0.5992 0.2712 0.4709 0.3714 0.4689 0.5548 0.41160.02739 0.0322 0.0323 0.0330 0.0422 0.0377 0.0478 0.0619 0.0540 0.0602 0.0531 0.0541 0.06890.02252 0.0260 0.0262 0.0186 0.0308 0.0226 0.0302 0.0529 0.0393 0.0478 0.0387 0.0361 0.05290.0309 0.0309 0.0309 0.0309 0.0309 0.0415 0.0309 0.0309 0.0415 0.0309 0.0309 0.0309 0.03090.7279 0.8408 0.8469 0.6013 0.9959 0.5458 0.9774 1.7090 0.9470 1.5430 1.2500 1.1660 1.7090
1 1 1 1 1 1 1 1 1 1 1 1
0.3272 0.4392 0.4611 0.5011 0.6101 0.6710 0.7954 0.8357 0.8499 0.8874 0.8938 0.9211 0.94640.0686 0.0790 0.0568 0.0714 0.0462 0.0407 0.0681 0.0796 0.0547 0.0365 0.0310 0.0291 0.01850.0348 0.1797 0.1600 0.1763 0.1946 0.5741 0.2949 0.3972 0.3540 0.2386 0.4799 0.3274 0.48370.02105 0.0406 0.0500 0.0563 0.0724 0.0503 0.0541 0.0556 0.0831 0.0861 0.0567 0.0604 0.06660.02068 0.0368 0.0458 0.0511 0.0650 0.0328 0.0454 0.0432 0.0668 0.0751 0.0409 0.0496 0.04790.0256 0.0257 0.0256 0.0256 0.0256 0.0256 0.0256 0.0256 0.0256 0.0245 0.0245 0.0240 0.02560.8067 1.4320 1.7860 1.9940 2.5360 1.2800 1.7710 1.6860 2.6080 3.0600 1.6670 2.0680 1.8690
1 1 1 1 1 1 1 1 1 1 1 1
0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0381 0.0634 0.0273 0.0250 0.0010 0.0216 0.0123 0.0349 0.0144 0.0049 0.0286 0.0448 0.00820.0001 0.1046 0.2943 0.5202 0.2919 0.5427 0.3186 0.4310 0.4856 0.2918 0.6270 0.4646 0.52820.02425 0.0274 0.0338 0.0462 0.0597 0.0337 0.0356 0.0409 0.0663 0.0579 0.0356 0.0464 0.05250.02425 0.0259 0.0284 0.0320 0.0502 0.0228 0.0294 0.0308 0.0475 0.0487 0.0217 0.0340 0.03610.0252 0.0252 0.0252 0.0250 0.0252 0.0252 0.0251 0.0250 0.0250 0.0250 0.0250 0.0250 0.03030.9636 1.0300 1.1280 1.2780 1.9950 0.9061 1.1710 1.2320 1.8990 1.9450 0.8682 1.3570 1.1910
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12h:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
11
1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 1 1 1 1 1 1 1
0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.2182 0.2165 0.2396 0.2351 0.2510 0.2374 0.2175 0.2340 0.2355 0.3163 0.3473 0.53710.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.4401 0.44010.1470 0.1510 0.0854 0.0982 0.1589 0.1349 0.1567 0.1043 0.1381 0.1385 0.1505 0.13700.0893 0.0996 0.0425 0.0585 0.0774 0.0892 0.1022 0.0474 0.0740 0.0884 0.0893 0.07280.0593 0.0593 0.0593 0.0593 0.0436 0.0436 0.0593 0.0593 0.0593 0.0593 0.0593 0.07431.5050 1.6790 0.7165 0.9855 1.7750 2.0450 1.7220 0.7996 1.2460 1.4890 1.5040 0.9791
1 1 1 1 1 1 1 1 1 1 1 1
1.7020 1.7130 1.7190 1.7420 1.8540 1.8980 1.9220 1.9660 1.9960 2.0950 2.0990 2.13200.1000 0.0784 0.0687 0.0523 0.0946 0.0875 0.0739 0.0782 0.0726 0.0845 0.0945 0.11420.3510 0.4049 0.4960 0.5708 0.4910 0.4234 0.6489 0.6448 0.5338 0.3046 0.3594 0.40720.1023 0.0978 0.0756 0.0894 0.0758 0.0890 0.0868 0.0760 0.0981 0.1470 0.1295 0.10130.0824 0.0755 0.0537 0.0585 0.0541 0.0676 0.0515 0.0453 0.0670 0.1226 0.1037 0.07800.0540 0.0441 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0540 0.0522 0.05401.5260 1.7110 0.9941 1.0850 1.0020 1.2520 0.9532 0.8392 1.2400 2.2710 1.9850 1.4450
1 1 1 1 1 1 1 1 1 1 1 1
1.3070 1.4260 1.4760 1.4890 1.5240 1.7680 1.8000 1.9220 1.9520 2.0230 2.0530 2.13200.0466 0.0876 0.0683 0.0465 0.0582 0.1348 0.1314 0.1634 0.1593 0.1705 0.1395 0.14520.5516 0.4357 0.7375 0.5744 0.5572 0.5547 0.3723 0.4832 0.6462 0.4709 0.2259 0.25750.0521 0.0493 0.0575 0.0542 0.0468 0.0579 0.0639 0.0578 0.0581 0.0618 0.0776 0.08790.0349 0.0371 0.0295 0.0353 0.0311 0.0386 0.0506 0.0415 0.0345 0.0450 0.0682 0.07580.0440 0.0440 0.0406 0.0440 0.0406 0.0406 0.0406 0.0406 0.0440 0.0406 0.0406 0.04060.7925 0.8413 0.7257 0.8025 0.7663 0.9515 1.2460 1.0220 0.7841 1.1070 1.6810 1.8660
1 1 1 1 1 1 1 1 1 1 1 1
1.0380 1.0910 1.1030 1.1130 1.1410 1.1510 1.1980 1.2030 1.3030 1.4260 1.4430 1.46300.0438 0.0374 0.0310 0.0326 0.0298 0.0171 0.0291 0.0294 0.0506 0.0816 0.0645 0.06150.6395 0.6017 0.6944 0.5125 0.6516 0.5838 0.4858 0.6830 0.5883 0.6716 0.5748 0.33100.0562 0.0637 0.0465 0.0611 0.0597 0.0685 0.0675 0.0516 0.0515 0.0586 0.0670 0.07010.0337 0.0402 0.0257 0.0427 0.0352 0.0442 0.0484 0.0290 0.0331 0.0336 0.0437 0.05730.0407 0.0407 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0445 0.0407 0.0445 0.05600.8281 0.9862 0.5779 0.9599 0.7920 0.9945 1.0890 0.6528 0.7437 0.8248 0.9824 1.0240
1 1 1 1 1 1 1 1 1 1 1 1
1.0810 1.0930 1.1290 1.2070 1.2490 1.2700 1.3000 1.3450 1.3660 1.4690 1.5040 1.53400.0392 0.0680 0.0622 0.0593 0.0578 0.0431 0.1072 0.0960 0.1081 0.1094 0.0933 0.09550.6716 0.5970 0.7995 0.7340 0.7619 0.6604 0.6130 0.7049 0.6437 0.7007 0.7474 0.55720.0708 0.0873 0.0578 0.0509 0.0605 0.0712 0.0904 0.0583 0.0625 0.0616 0.0657 0.08470.0406 0.0554 0.0259 0.0262 0.0295 0.0415 0.0562 0.0317 0.0373 0.0337 0.0330 0.05640.0549 0.0549 0.0549 0.0568 0.0549 0.0549 0.0549 0.0549 0.0549 0.0549 0.0549 0.05250.7396 1.0100 0.4713 0.4617 0.5377 0.7553 1.0240 0.5766 0.6792 0.6135 0.6013 1.0750
1.1600 1.1690 1.2170 1.3280 1.3940 1.4710 1.5130 1.5250 1.5710 1.7110 1.7440 1.75500.0445 0.0462 0.0416 0.0669 0.0810 0.0740 0.0775 0.0795 0.0601 0.0890 0.0950 0.05630.7271 0.5043 0.6860 0.6883 0.6612 0.7030 0.6547 0.6864 0.6290 0.4254 0.4166 0.54020.0724 0.1175 0.0611 0.0732 0.0822 0.0842 0.0886 0.0832 0.0811 0.0935 0.0935 0.09000.0378 0.0827 0.0342 0.0409 0.0479 0.0459 0.0521 0.0466 0.0494 0.0709 0.0714 0.06100.0548 0.0548 0.0548 0.0548 0.0548 0.0567 0.0548 0.0548 0.0548 0.0548 0.0548 0.05680.6906 1.5100 0.6248 0.7461 0.8736 0.8097 0.9503 0.8501 0.9015 1.2930 1.3030 1.0730
1 1 1 1 1 1 1 1 1 1 1 1
1.0610 1.0980 1.1120 1.1130 1.1830 1.2090 1.2680 1.3120 1.3400 1.3610 1.3800 1.42300.0354 0.0296 0.0437 0.0397 0.0187 0.0194 0.0396 0.0414 0.0743 0.1160 0.0860 0.09890.6705 0.4526 0.8265 0.5721 0.6735 0.5463 0.4173 0.5034 0.6800 0.5098 0.4208 0.39110.0503 0.0567 0.0542 0.0608 0.0556 0.0580 0.0628 0.0501 0.0716 0.0777 0.0691 0.09400.0289 0.0420 0.0226 0.0398 0.0318 0.0391 0.0479 0.0353 0.0405 0.0544 0.0526 0.07330.0508 0.0508 0.0508 0.0508 0.0405 0.0508 0.0508 0.0405 0.0508 0.0508 0.0508 0.04680.5681 0.8255 0.4446 0.7821 0.7851 0.7686 0.9426 0.8721 0.7974 1.0710 1.0340 1.5660
1 1 1 1 1 1 1 1 1 1 1 1
1.0950 1.0980 1.1340 1.1350 1.1540 1.1560 1.1580 1.1890 1.2500 1.2690 1.2940 1.33400.0150 0.0153 0.0111 0.0110 0.0198 0.0257 0.0339 0.0378 0.0204 0.0282 0.0563 0.13920.2586 0.3421 0.6510 0.2634 0.4532 0.2873 0.2210 0.6472 0.4352 0.2504 0.0811 0.19520.0582 0.0826 0.0579 0.0665 0.0643 0.0633 0.0875 0.0547 0.0625 0.0636 0.1025 0.08380.0501 0.0670 0.0342 0.0571 0.0475 0.0535 0.0772 0.0325 0.0470 0.0551 0.0982 0.07520.0309 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0415 0.0418 0.0415 0.04151.6200 1.6160 0.8244 1.3760 1.1460 1.2890 1.8610 0.7826 1.1330 1.3170 2.3680 1.8120
1 1 1 1 1 1 1 1 1 1 1 1
0.9817 0.9846 1.0790 1.0950 1.1150 1.1150 1.2020 1.2170 1.2700 1.3380 1.3430 1.38100.0265 0.0246 0.0394 0.0369 0.0493 0.0447 0.0550 0.0611 0.0631 0.0740 0.0823 0.11390.3217 0.1768 0.4313 0.6852 0.4890 0.2336 0.3710 0.4983 0.4563 0.3599 0.4320 0.20630.0671 0.0900 0.0637 0.0773 0.0764 0.1055 0.0877 0.0816 0.0742 0.1010 0.0973 0.11610.0553 0.0817 0.0480 0.0434 0.0546 0.0924 0.0696 0.0578 0.0547 0.0808 0.0733 0.10340.0240 0.0256 0.0240 0.0256 0.0245 0.0245 0.0240 0.0245 0.0245 0.0519 0.0245 0.02452.3080 3.1870 2.0050 1.6930 2.2240 3.7650 2.9040 2.3540 2.2280 1.5560 2.9870 4.2130
1 1 1 1 1 1 1 1 1 1 1 1
0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0204 0.0239 0.0535 0.0509 0.0070 0.0480 0.0603 0.0614 0.0613 0.0612 0.0546 0.18720.2256 0.2877 0.6932 0.6889 0.5344 0.4177 0.3149 0.6017 0.5947 0.6524 0.5531 0.34970.0576 0.0546 0.0358 0.0576 0.0545 0.0524 0.0604 0.0421 0.0511 0.0578 0.0670 0.06960.0507 0.0461 0.0199 0.0321 0.0372 0.0400 0.0500 0.0266 0.0325 0.0341 0.0448 0.05610.0303 0.0303 0.0303 0.0303 0.0303 0.0303 0.0303 0.0305 0.0303 0.0486 0.0303 0.03051.6730 1.5210 0.6550 1.0600 1.2270 1.3200 1.6470 0.8716 1.0730 0.7014 1.4780 1.8390
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12h:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
12
3.2 Cross-sectional regressions
The most important table of Fama-Macbeth (1973) is arguably Table 3. I replicate theirresults below, in Table 3a. The table shows the results from the cross-sectional regression
Rp � γ0t � γ1tβp � γ2tβ2p � γ3tsppeiq � ηp
Recall that the cross-sectional regression is done each month of the testing period and theestimates displayed on the table are the corresponding averages for the testing period ofinterest. I calculate all the statistics displayed in the table using the approach of Fama andMacBeth (1973)7. Panel A displays the results from the cross-sectional regression of thetest portfolios against a constant and the proxy for the market portfolio returns. For the1935-6/1968, 7/1968-2010, and 1935-2010 testing periods I find ¯γ1 � 84bps, ¯γ1 � 36bps, and¯γ1 � 57bps (respectively). These values are all highly significant with t-statistics greaterthan 2. Overall , I find that ¯γ1, which in this practical test of the CAPM should correspondto the excess return of the market portfolio on the portfolio with zero beta with respect tothe market, is positive for almost all the testing periods. In Panel B, the first three regressorsare included in the regression specification. The aforementioned results do no change muchbut I find that ¯γ2 is negative ( ¯γ2 � �24bps for the 1935-2010 testing period) and is notsignificant (t-statistics=�1.2). Panel C uses the first two as well as the fourth regressor.Here, we can see that ¯γ0 and ¯γ1 have point estimates very similar to those in panels A andB. However, ¯γ1 seems to lose some of its significance as the t-statistics for these estimatesare rarely greater than 2. ¯γ3 is not significant in any of the testing periods. Panel D includesall four regressors and is the proposed test of the CAPM, conditional on the equal-weightedNYSE being the market portfolio, conditional on market efficiency and conditional on theassumptions laid out in the introduction (such as normality). Here, I find that ¯γ1 � 1.15% onaverage per month for the 1935-6/1968 testing period and ¯γ1 � 88bps on average per monthfor the full sample (1935-2010). In both cases the t-statistics is above 1.90. ¯γ2 and ¯γ3 areoverall not significant although ¯γ3 often has point estimates with rather large magnitudes. Inall four panels the average R2 (which is listed in the column labelled r2) remains around 0.30.
The results presented thus far are similar to those found in Fama and Macbeth (1973).With an equal-weighted NYSE portfolio as the proxy for the market portfolio and with testportfolios constructed from a beta-sort using equal-weighted underlying securities βi, I findlittle evidence of non-linear dependence on βp and little evidence that idiosyncratic risk asmeasured by sppeiq is priced. However, when I use the 5 � 5 dual sort test portfolios (whilemaintaining the same market portfolio proxy and the same method of constructing the port-folios estimates using the equal weighting of the underlying securities estimates) much ofthose results no longer hold. Indeed, on Table 3e we can first notice that in Panel A pointestimates for ¯γ1 are similar to those displayed on Table 3a, and the t-statistics are very similaras well. Indeed, for the 1935-6/1968 testing period the t-statistics is 2.61, for the 7/1968-2010testing period the t-statistics is 1.40 and for the 1935-2010 testing period the t-statistics is2.84. For these three testing periods the estimates I find are ¯γ1 � 86bps, 36bps, and 58bps(respectively). Thus, as in Panel A of Table 3a, we observe a deterioration of the significance
7In particular, ρM pγjq is the first-order autocorrelation for γjt while ρ0pγjq is the first-order autocorrela-tion for γjt with the additional assumption that the mean of γjt is zero (that is ρ0pγjt, ˆγjt�1q � Erγjt � ˆγjt�1sq
13
of the estimate for the testing periods subsequent to those used in Fama-MacBeth (1973).In Panel B of Table 3e, where I include the additional regressor, β2
p , I find that ¯γ1 loses muchof its significance. The t-statistics are 0.59, 1.56 and 1.63 for the 1935-6/1968, 7/1968-2010and 1935-2010 testing periods (respectively). Furthermore, the magnitude of the estimate ishalved for the 1935-6/1968 testing period (32bps) but trebles for the 7/1968-2010 testing pe-riod (96bps). In Panel C, the regressions include the measure of idiosyncratic risk sppeiq. Asa result, the estimates ¯γ1 lose much of their significance and the estimates for ¯γ3 are highlysignificant for the testing periods within 1935-6/1968. Indeed, the t-statistics are 0.52, 0.32,0.59 for ¯γ1 and 2.68, 0.80, 2.09 for ¯γ3 (respectively for the 1935-6/1968, 7/1968-2010 and1935-2010 testing periods). The most relevant results are in Panel D, which shows that whenI include all of the regressors, ¯γ3 remains highly significant. In particular, for the full testingperiod used in Fama-MacBeth (1973)8 the t-statistics for ¯γ1 is only 1.61 while correspondingt-statistics for ¯γ3 is 3.08. Furthermore, for the 7/1968-2010 and 1935-2010 testing periods, Ifind tp ¯γ1q � tp ¯γ3q � 1.36 and tp ¯γ1q � 2.03 tp ¯γ3q � 2.77. Conditional on market efficiency,normality of the distribution of portfolio returns, risk-aversion and common knowledge, theselast results would imply that idiosyncratic risk as measured by sppeiq is priced.
8The 1935-6/1968 testing period.
14
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193516/68
0.0063
0.0084
11
0.0049
0.0360
0.0659
11
0.0047
0.0098
11
3.4760
2.5460
11
2.7480
0.3051
0.3016
1935145
0.0041
0.0163
11
0.0040
0.0485
0.0974
11
0.0039
10.047
01
10.9753
1.9160
11
0.9417
0.2945
0.2914
1946155
0.0084
0.0028
11
0.0075
0.0258
0.0418
11
0.1244
0.0720
11
3.5890
0.7427
11
3.1900
0.3284
0.3196
195616/68
0.0064
0.0059
11
0.0038
0.0299
0.0435
11
0.2655
0.1651
11
2.6020
1.6560
11
1.5260
0.2958
0.2965
1935140
0.0016
0.0124
11
0.0015
0.0594
0.1181
11
0.1935
10.101
31
10.2278
0.8809
11
0.2168
0.2371
0.2895
1941145
0.0071
0.0210
11
0.0069
0.0311
0.0657
11
0.1830
0.1490
11
1.7700
2.4770
11
1.7180
0.3624
0.2811
1946150
0.0047
0.0033
11
0.0040
0.0309
0.0483
11
0.1967
0.0346
11
1.1690
0.5229
11
1.0020
0.4101
0.3265
1951155
0.0122
0.0024
11
0.0110
0.0189
0.0346
11
10.037
90.0953
11
5.0210
0.5401
11
4.5050
0.2466
0.2930
1956160
0.0149
10.005
91
10.0128
0.0201
0.0333
11
0.1432
0.1955
11
5.7530
11.370
01
14.9180
0.2210
0.3130
196116/68
0.0007
0.0137
11
10.002
30.0339
0.0477
11
0.2205
0.1009
11
0.1853
2.7300
11
10.635
40.3456
0.2756
7/196812010
0.0081
0.0036
11
0.0036
0.0361
0.0594
11
0.0737
0.1976
11
5.0850
1.3660
11
2.2590
0.3260
0.2861
1970180
0.0031
0.0093
11
10.002
40.0376
0.0664
11
0.1828
0.1833
11
0.9349
1.6170
11
10.737
30.3167
0.2829
1980190
0.0181
10.005
11
10.0111
0.0391
0.0581
11
10.020
30.2402
11
5.3340
11.003
01
13.2670
0.3021
0.2873
1990100
0.0093
0.0023
11
0.0052
0.0384
0.0563
11
0.0819
0.2380
11
2.7700
0.4599
11
1.5570
0.3148
0.2767
2000110
0.0063
0.0044
11
0.0042
0.0317
0.0605
11
0.0046
0.1622
11
2.2790
0.8333
11
1.5370
0.3764
0.3019
1970175
0.0052
0.0003
11
0.0004
0.0410
0.0660
11
0.1769
0.1374
11
1.0750
0.0373
11
0.0840
0.3097
0.2774
1975180
0.0030
0.0217
11
10.003
00.0357
0.0676
11
0.1726
0.2406
11
0.7100
2.7190
11
10.729
30.3126
0.2900
1980185
0.0174
0.0001
11
0.0091
0.0365
0.0551
11
0.1018
0.2006
11
4.0440
0.0123
11
2.1130
0.3452
0.2898
1985190
0.0199
10.009
41
10.0143
0.0402
0.0588
11
10.105
00.2616
11
4.2090
11.355
01
13.0330
0.2501
0.2768
1990195
0.0077
0.0035
11
0.0037
0.0395
0.0584
11
0.1317
0.3411
11
1.6560
0.5082
11
0.8074
0.2831
0.2682
1995100
0.0133
0.0003
11
0.0091
0.0359
0.0518
11
0.0483
0.1021
11
3.1480
0.0427
11
2.1490
0.3512
0.2821
2000105
0.0085
0.0033
11
0.0062
0.0345
0.0543
11
10.097
110.004
91
12.0820
0.5126
11
1.5360
0.3327
0.3018
2005110
0.0035
0.0056
11
0.0016
0.0264
0.0628
11
0.1789
0.2699
11
1.1410
0.7522
11
0.5178
0.4088
0.3008
193512010
0.0073
0.0057
11
0.0042
0.0360
0.0624
11
0.1318
0.1082
11
6.1130
2.7580
11
3.5160
0.3168
0.2930
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0054
0.0124
10.002
81
0.0041
0.0518
0.1208
0.0512
10.0038
0.0347
0.0002
12.1050
2.0490
11.102
01
1.5970
0.2998
0.2861
1935145
0.0106
0.0062
0.0030
10.0105
0.0622
0.1494
0.0662
10.0105
10.084
40.0001
11.9530
0.4787
0.5120
11.9270
0.2895
0.2840
1946155
0.0036
0.0132
10.004
81
0.0026
0.0316
0.0872
0.0317
10.0764
10.018
810.000
11
1.2320
1.6630
11.639
01
0.9041
0.3474
0.3007
195616/68
0.0024
0.0170
10.006
31
10.000
20.0546
0.1165
0.0485
10.2876
0.2330
0.0005
10.5456
1.7860
11.593
01
10.038
70.2707
0.2726
1935140
0.0076
0.0035
0.0025
10.0075
0.0712
0.1878
0.0707
10.1660
10.099
610.000
31
0.8962
0.1586
0.2922
10.8870
0.2428
0.2811
1941145
0.0142
0.0095
0.0036
10.0140
0.0499
0.0854
0.0610
10.1620
0.0022
0.0005
12.2060
0.8575
0.4524
12.1750
0.3448
0.2797
1946150
0.0026
0.0075
10.001
81
0.0020
0.0355
0.0954
0.0313
10.1653
10.007
510.000
11
0.5757
0.6109
10.453
81
0.4302
0.4079
0.3131
1951155
0.0045
0.0190
10.007
71
0.0032
0.0274
0.0785
0.0322
110.085
310.106
910.000
11
1.2630
1.8690
11.845
01
0.9161
0.2869
0.2773
1956160
0.0128
10.001
310.002
01
0.0106
0.0274
0.0665
0.0271
10.2653
0.1521
0.0002
13.6070
10.154
410.578
41
3.0030
0.2376
0.2791
196116/68
10.004
40.0292
10.009
21
10.007
40.0662
0.1394
0.0586
10.2660
0.2318
0.0007
110.636
81.9880
11.485
01
11.058
00.2928
0.2675
7/196812010
0.0070
0.0073
10.002
11
0.0025
0.0641
0.1497
0.0674
10.0538
0.0293
10.000
11
2.4800
1.0950
10.707
81
0.8815
0.3226
0.2812
1970180
0.0069
0.0005
0.0044
10.0014
0.0902
0.2032
0.0949
10.0289
10.043
810.000
91
0.8734
0.0305
0.5310
10.1780
0.3330
0.2737
1980190
0.0086
0.0182
10.011
81
0.0016
0.0748
0.1754
0.0678
10.0877
0.1517
0.0005
11.3220
1.1890
11.996
01
0.2410
0.3334
0.2929
1990100
0.0114
10.005
50.0051
10.0073
0.0462
0.1165
0.0570
10.2264
0.1768
0.0004
12.8320
10.540
01.0320
11.8220
0.3160
0.2694
2000110
0.0072
0.0075
10.003
31
0.0052
0.0350
0.0969
0.0436
10.1155
10.045
610.000
21
2.3740
0.8910
10.882
91
1.6940
0.3194
0.2963
1970175
0.0033
0.0029
10.000
61
10.001
50.0896
0.1921
0.0983
110.032
110.129
910.001
41
0.3146
0.1278
10.055
31
10.138
70.3007
0.2615
1975180
0.0119
0.0027
0.0087
10.0059
0.0984
0.2229
0.1019
10.0559
0.0041
10.000
61
1.0270
0.1021
0.7237
10.5103
0.3681
0.2831
1980185
0.0108
0.0164
10.008
41
0.0024
0.0757
0.1658
0.0624
10.1315
0.1786
0.0005
11.2070
0.8393
11.141
01
0.2765
0.3668
0.2869
1985190
0.0077
0.0208
10.015
51
0.0021
0.0720
0.1791
0.0709
10.0140
0.1031
0.0003
10.9099
0.9873
11.851
01
0.2460
0.2891
0.2997
1990195
0.0122
10.009
60.0079
10.0082
0.0507
0.1214
0.0629
10.3341
0.2788
0.0010
12.0460
10.671
51.0660
11.3860
0.2946
0.2658
1995100
0.0112
0.0032
10.000
31
0.0070
0.0401
0.1080
0.0470
10.0380
0.0291
10.000
21
2.3780
0.2504
10.062
41
1.4760
0.3566
0.2676
2000105
0.0084
0.0093
10.004
91
0.0062
0.0331
0.0881
0.0497
10.0917
10.147
410.000
41
2.1670
0.8971
10.843
11
1.5880
0.2876
0.2704
2005110
0.0052
0.0067
10.002
21
0.0032
0.0364
0.0998
0.0332
10.1432
0.0273
0.0000
11.2100
0.5687
10.574
41
0.7547
0.3302
0.3113
193512010
0.0063
0.0095
10.002
41
0.0032
0.0589
0.1377
0.0608
10.1060
0.0312
0.0000
13.2430
2.0840
11.203
01
1.6490
0.3125
0.2834
TABLE!3a:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+�3ts p
(ei)
+⌘
p
15
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0091
0.0072
110.017
80.0078
0.0431
0.0739
10.7547
0.0076
10.068
91
0.0159
4.2300
1.9630
110.472
63.6180
0.2914
0.2866
1935145
0.0103
0.0137
110.038
40.0102
0.0566
0.1070
10.6163
0.0101
10.150
01
10.004
82.0890
1.4650
110.712
72.0600
0.2828
0.2772
1946155
0.0102
0.0064
110.077
00.0093
0.0344
0.0535
10.6997
10.020
00.0238
110.055
43.2540
1.3110
111.205
02.9550
0.3403
0.3104
195616/68
0.0071
0.0023
10.0475
0.0045
0.0352
0.0482
10.8939
0.2411
0.1623
10.0934
2.4840
0.5797
10.6507
1.5720
0.2598
0.2710
1935140
0.0091
0.0102
110.064
60.0090
0.0688
0.1361
10.5118
0.0604
10.175
31
10.012
31.1160
0.6314
111.063
01.1060
0.2375
0.2797
1941145
0.0118
0.0178
110.007
40.0116
0.0379
0.0565
10.7242
0.0896
0.0273
10.0179
2.4060
2.4450
110.078
72.3610
0.3364
0.2667
1946150
0.0071
0.0073
110.089
90.0064
0.0406
0.0619
10.7454
0.0494
0.0319
110.029
41.3490
0.9186
110.934
01.2220
0.4080
0.3061
1951155
0.0134
0.0055
110.064
10.0121
0.0268
0.0441
10.6569
10.134
310.099
91
10.080
43.8680
0.9614
110.755
83.5100
0.2725
0.3021
1956160
0.0116
10.008
51
0.1002
0.0095
0.0312
0.0356
10.9775
0.2965
0.0921
10.2156
2.8740
11.855
01
0.7938
2.3530
0.2233
0.2784
196116/68
0.0042
0.0095
10.0124
0.0012
0.0374
0.0541
10.8374
0.1884
0.1497
10.0148
1.0550
1.6640
10.1401
0.3098
0.2842
0.2647
7/196812010
0.0088
0.0035
110.006
60.0042
0.0436
0.0808
11.0760
0.0063
0.0295
110.091
84.5390
0.9742
110.138
52.1940
0.2960
0.2764
1970180
10.000
10.0032
10.1222
10.005
60.0473
0.0762
11.1730
0.1540
0.0554
10.0543
10.025
00.4763
11.1970
11.356
00.2955
0.2734
1980190
0.0204
0.0026
110.122
00.0133
0.0436
0.1012
11.1440
10.016
70.0230
110.183
15.3720
0.2932
111.225
03.5200
0.2983
0.2828
1990100
0.0052
10.003
21
0.1190
0.0011
0.0396
0.0675
10.7778
10.023
40.2170
10.0722
1.5070
10.553
21
1.7570
0.3224
0.3015
0.2708
2000110
0.0102
0.0027
110.026
60.0081
0.0478
0.0823
11.2600
10.181
810.052
91
10.288
92.4480
0.3835
110.242
51.9490
0.3064
0.2862
1970175
0.0000
10.004
51
0.1419
10.004
80.0523
0.0777
11.2710
0.1183
0.0467
10.0544
0.0002
10.492
31
0.9472
10.777
60.2837
0.2630
1975180
0.0022
0.0146
10.0931
10.003
80.0445
0.0743
11.1790
0.2655
0.0039
10.1681
0.4125
1.6680
10.6701
10.738
50.3029
0.2871
1980185
0.0194
0.0009
110.037
30.0111
0.0442
0.0828
11.1700
0.0896
10.005
91
10.219
13.7290
0.0962
110.270
72.1380
0.3171
0.2801
1985190
0.0230
0.0039
110.200
30.0173
0.0416
0.1157
11.1020
10.112
50.0311
110.160
34.6870
0.2894
111.542
03.5480
0.2632
0.2854
1990195
0.0065
0.0002
10.0574
0.0025
0.0349
0.0694
10.6334
0.0448
0.3214
10.0899
1.5730
0.0268
10.7685
0.6096
0.2803
0.2671
1995100
0.0061
10.007
71
0.1863
0.0019
0.0418
0.0632
10.8563
10.052
40.0748
10.0479
1.2470
11.036
01
1.8460
0.3818
0.3323
0.2684
2000105
0.0104
10.002
41
0.0507
0.0081
0.0477
0.0629
11.1130
10.328
910.091
91
10.300
51.8470
10.327
31
0.3862
1.4430
0.2728
0.2723
2005110
0.0106
0.0102
110.145
60.0087
0.0457
0.0946
11.3570
10.054
210.050
31
10.289
91.9730
0.9146
110.910
81.6120
0.3172
0.2946
193512010
0.0089
0.0051
110.011
50.0058
0.0433
0.0778
10.9478
0.0469
10.008
51
10.044
76.2050
1.9940
110.367
44.0360
0.2940
0.2808
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0069
0.0115
10.001
710.007
90.0056
0.0663
0.1198
0.0586
0.8325
0.0053
0.0456
0.0001
10.022
22.0940
1.9250
10.584
510.189
01.6960
0.3049
0.2929
1935145
0.0159
0.0061
0.0059
10.083
00.0158
0.0848
0.1454
0.0814
0.7943
0.0157
10.068
110.000
110.054
92.1460
0.4840
0.8296
11.195
02.1270
0.2907
0.2902
1946155
0.0054
0.0135
10.004
010.037
10.0045
0.0408
0.0869
0.0317
0.6697
10.123
210.006
910.000
110.065
51.4620
1.6990
11.369
010.606
21.2070
0.3542
0.3093
195616/68
0.0003
0.0146
10.006
60.0811
10.002
30.0638
0.1184
0.0506
0.9686
0.1787
0.2218
0.0004
0.0466
0.0552
1.5140
11.586
01.0250
10.444
60.2778
0.2784
1935140
0.0134
0.0026
0.0058
10.087
30.0133
0.0904
0.1815
0.0864
0.8029
0.0212
10.078
510.000
810.065
41.2470
0.1212
0.5626
10.916
41.2400
0.2383
0.2881
1941145
0.0189
0.0103
0.0061
10.077
80.0186
0.0782
0.0864
0.0758
0.7908
0.0705
10.019
80.0007
10.019
21.8680
0.9268
0.6189
10.761
81.8470
0.3527
0.2827
1946150
0.0070
0.0077
0.0001
10.090
70.0063
0.0488
0.0961
0.0328
0.7075
10.079
90.0125
10.000
110.046
71.1100
0.6201
0.0214
10.993
21.0030
0.4133
0.3119
1951155
0.0039
0.0193
10.008
00.0166
0.0027
0.0312
0.0769
0.0304
0.6311
10.165
310.110
910.000
110.070
50.9689
1.9390
12.041
00.2036
0.6643
0.2951
0.2975
1956160
0.0080
10.005
710.002
50.1631
0.0059
0.0482
0.0660
0.0327
1.1190
0.0869
0.1753
0.0001
0.1210
1.2930
10.673
810.587
01.1290
0.9553
0.2490
0.2791
196116/68
10.004
90.0282
10.009
30.0264
10.007
80.0722
0.1419
0.0597
0.8559
0.1909
0.2127
0.0006
10.000
810.641
31.8880
11.474
00.2927
11.027
00.2971
0.2778
7/196812010
0.0057
0.0067
10.002
60.0321
0.0012
0.0732
0.1534
0.0701
0.9905
0.0516
0.0180
0.0000
10.046
41.7570
0.9844
10.851
60.7310
0.3581
0.3303
0.2844
1970180
10.000
910.000
80.0005
0.1753
10.006
40.1021
0.1961
0.0954
1.0320
0.0971
10.052
210.000
50.1679
10.106
510.044
90.0570
1.9520
10.721
80.3369
0.2755
1980190
0.0085
0.0199
10.012
910.005
20.0014
0.0768
0.1803
0.0660
0.9907
0.0988
0.1593
0.0008
10.178
11.2690
1.2700
12.241
010.060
60.2159
0.3360
0.2936
1990100
0.0092
10.010
40.0062
0.0767
0.0051
0.0554
0.1204
0.0658
0.8139
0.1407
0.0863
0.0003
0.0806
1.9000
10.989
91.0880
1.0820
1.0530
0.3239
0.2814
2000110
0.0075
0.0092
10.004
110.014
20.0054
0.0478
0.1093
0.0407
1.1280
10.060
310.097
210.000
110.217
51.7970
0.9696
11.154
010.144
91.2940
0.3343
0.2984
1970175
10.009
40.0092
10.009
00.2177
10.014
20.1054
0.1903
0.0997
1.1340
0.0748
10.131
810.000
80.3115
10.759
90.4114
10.764
91.6290
11.145
00.3116
0.2580
1975180
0.0106
10.006
80.0102
0.1043
0.0046
0.1045
0.2129
0.1003
0.9444
0.0788
10.008
010.000
70.1161
0.8634
10.272
00.8652
0.9374
0.3764
0.3649
0.2904
1980185
0.0114
0.0155
10.007
810.005
70.0030
0.0756
0.1804
0.0612
1.0540
0.1147
0.1812
0.0006
10.222
31.2750
0.7290
11.083
010.045
70.3438
0.3670
0.2899
1985190
0.0068
0.0248
10.018
10.0000
0.0011
0.0754
0.1767
0.0682
0.9093
0.0743
0.0985
0.0009
10.128
20.7622
1.1920
12.249
00.0003
0.1281
0.2934
0.3001
1990195
0.0161
10.014
00.0137
10.070
70.0121
0.0606
0.1250
0.0786
0.7700
0.1205
0.1753
0.0006
0.0441
2.2530
10.948
71.4840
10.778
71.6970
0.3036
0.2801
1995100
0.0019
10.002
310.004
80.2471
10.002
40.0453
0.1121
0.0431
0.7783
0.1132
10.026
110.000
10.1115
0.3555
10.177
710.943
02.6940
10.445
00.3616
0.2759
2000105
0.0049
0.0081
10.007
20.0971
0.0026
0.0504
0.0936
0.0459
1.0620
10.158
210.164
710.000
110.210
60.8179
0.7340
11.328
00.7753
0.4355
0.3051
0.2761
2005110
0.0102
0.0125
10.001
210.154
70.0083
0.0452
0.1175
0.0320
1.1800
10.042
610.046
80.0000
10.300
61.9150
0.8992
10.305
511.112
01.5450
0.3429
0.3111
193512010
0.0062
0.0088
10.002
20.0145
0.0031
0.0702
0.1395
0.0653
0.9240
0.0635
0.0272
0.0001
10.035
62.6820
1.9060
11.033
00.4734
1.3420
0.3191
0.2882
TABLE!3a:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+�3ts p
(ei)
+⌘
p
16
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0060
0.0086
11
0.0047
0.0356
0.0661
11
0.0045
0.0378
11
3.3930
2.6110
11
2.6530
0.2589
0.2666
1935145
0.0040
0.0165
11
0.0038
0.0466
0.0979
11
0.0038
10.013
21
10.9717
1.9310
11
0.9368
0.2677
0.2522
1946155
0.0090
0.0022
11
0.0081
0.0258
0.0392
11
0.0341
0.0758
11
3.8340
0.6220
11
3.4360
0.2654
0.2938
195616/68
0.0054
0.0068
11
0.0028
0.0310
0.0453
11
0.2620
0.1762
11
2.1460
1.8510
11
1.1080
0.2461
0.2572
1935140
0.0020
0.0119
11
0.0020
0.0566
0.1189
11
0.0533
10.056
31
10.3024
0.8452
11
0.2909
0.2276
0.2504
1941145
0.0062
0.0219
11
0.0060
0.0311
0.0654
11
0.1873
0.1390
11
1.5510
2.5960
11
1.4980
0.3152
0.2480
1946150
0.0058
0.0021
11
0.0051
0.0303
0.0441
11
0.1109
0.0334
11
1.4830
0.3642
11
1.3140
0.3477
0.3030
1951155
0.0123
0.0024
11
0.0110
0.0201
0.0339
11
10.102
40.1101
11
4.7290
0.5425
11
4.2470
0.1831
0.2616
1956160
0.0137
10.004
71
10.0116
0.0217
0.0344
11
0.1391
0.1421
11
4.8830
11.061
01
14.1200
0.1831
0.2646
196116/68
10.000
10.0145
11
10.003
00.0349
0.0499
11
0.2273
0.1426
11
10.025
02.7640
11
10.821
40.2881
0.2447
7/196812010
0.0081
0.0036
11
0.0036
0.0358
0.0583
11
0.0810
0.2038
11
5.1250
1.3980
11
2.2750
0.2830
0.2581
1970180
0.0031
0.0093
11
10.002
40.0395
0.0663
11
0.1371
0.2102
11
0.9007
1.6180
11
10.689
80.2972
0.2660
1980190
0.0172
10.004
11
10.0102
0.0385
0.0587
11
0.0139
0.2295
11
5.1380
10.799
41
13.0460
0.2616
0.2593
1990100
0.0098
0.0017
11
0.0057
0.0372
0.0537
11
0.1143
0.2472
11
3.0170
0.3619
11
1.7650
0.2515
0.2374
2000110
0.0058
0.0049
11
0.0037
0.0308
0.0578
11
0.0457
0.1592
11
2.1630
0.9819
11
1.3980
0.3021
0.2628
1970175
0.0062
10.000
81
10.0015
0.0443
0.0657
11
0.1101
0.1788
11
1.1970
10.103
11
10.2773
0.3149
0.2661
1975180
0.0023
0.0224
11
10.003
70.0366
0.0663
11
0.1530
0.2594
11
0.5427
2.8630
11
10.861
80.2734
0.2636
1980185
0.0179
10.000
41
10.0095
0.0350
0.0552
11
0.1287
0.1835
11
4.3340
10.062
81
12.3230
0.3060
0.2561
1985190
0.0183
10.007
61
10.0126
0.0409
0.0598
11
10.052
60.2593
11
3.7960
11.084
01
12.6390
0.2238
0.2602
1990195
0.0084
0.0028
11
0.0044
0.0377
0.0547
11
0.1664
0.3471
11
1.8860
0.4344
11
0.9971
0.2366
0.2303
1995100
0.0136
0.0000
11
0.0093
0.0355
0.0508
11
0.0861
0.1332
11
3.2430
10.006
91
12.2320
0.2730
0.2561
2000105
0.0079
0.0040
11
0.0056
0.0323
0.0513
11
10.057
10.0337
11
2.0640
0.6612
11
1.4810
0.2645
0.2517
2005110
0.0031
0.0060
11
0.0011
0.0270
0.0607
11
0.1823
0.2286
11
0.9688
0.8427
11
0.3598
0.3307
0.2694
193512010
0.0072
0.0058
11
0.0041
0.0357
0.0619
11
0.1041
0.1238
11
6.0890
2.8360
11
3.4650
0.2724
0.2620
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0085
0.0032
0.0025
10.0072
0.0499
0.1068
0.0516
10.0068
10.100
510.000
31
3.4230
0.5930
0.9614
12.9000
0.2610
0.2623
1935145
0.0112
0.0006
0.0072
10.0110
0.0597
0.1186
0.0653
10.0112
10.281
010.000
81
2.1440
0.0554
1.2620
12.1170
0.2407
0.2478
1946155
0.0028
0.0153
10.005
81
0.0018
0.0333
0.0955
0.0352
10.0204
10.030
210.000
11
0.9136
1.7490
11.819
01
0.6022
0.3046
0.2889
195616/68
0.0108
10.004
20.0050
10.0082
0.0515
0.1043
0.0485
10.0845
0.0479
0.0001
12.5730
10.497
91.2630
11.9530
0.2439
0.2497
1935140
0.0085
10.002
20.0066
10.0084
0.0701
0.1460
0.0763
110.091
010.283
410.001
61
1.0220
10.128
80.7257
11.0120
0.2010
0.2515
1941145
0.0143
0.0039
0.0079
10.0141
0.0446
0.0755
0.0499
10.1625
10.267
20.0001
12.4890
0.3996
1.2340
12.4530
0.2877
0.2368
1946150
0.0031
0.0071
10.001
91
0.0024
0.0333
0.0930
0.0288
10.1562
10.016
410.000
11
0.7169
0.5888
10.498
41
0.5612
0.3849
0.2896
1951155
0.0025
0.0234
10.009
81
0.0012
0.0336
0.0980
0.0405
110.158
210.110
510.000
11
0.5705
1.8520
11.883
01
0.2881
0.2243
0.2671
1956160
0.0138
10.005
10.0003
10.0117
0.0339
0.0833
0.0338
10.1939
0.0802
0.0002
13.1560
10.470
60.0575
12.6700
0.2075
0.2530
196116/68
0.0088
10.003
70.0082
10.0059
0.0606
0.1167
0.0562
10.0565
0.0344
0.0001
11.3840
10.300
41.3800
10.9242
0.2682
0.2458
7/196812010
0.0064
0.0096
10.003
51
0.0018
0.0593
0.1391
0.0623
10.0678
0.0152
10.000
21
2.4290
1.5630
11.270
01
0.7051
0.2887
0.2440
1970180
0.0047
0.0065
0.0011
110.000
80.0842
0.1824
0.0801
10.0722
10.016
110.000
51
0.6417
0.4091
0.1543
110.103
70.3023
0.2450
1980190
0.0118
0.0111
10.008
41
0.0048
0.0721
0.1618
0.0655
10.0386
0.0633
10.000
11
1.8830
0.7852
11.471
01
0.7655
0.2952
0.2489
1990100
0.0070
0.0097
10.004
11
0.0029
0.0448
0.1194
0.0625
10.0999
0.0088
10.000
11
1.7910
0.9345
10.756
31
0.7447
0.2720
0.2306
2000110
0.0058
0.0088
10.003
01
0.0038
0.0357
0.1147
0.0524
10.1117
0.0228
10.000
31
1.8780
0.8785
10.666
21
1.2150
0.2859
0.2477
1970175
0.0009
0.0116
10.006
21
10.003
90.0830
0.1709
0.0829
10.1053
10.029
910.000
41
0.0898
0.5780
10.634
71
10.399
30.3019
0.2438
1975180
0.0122
0.0009
0.0100
10.0062
0.0927
0.2003
0.0859
10.0302
10.013
010.000
71
1.1200
0.0390
0.9909
10.5719
0.3029
0.2476
1980185
0.0162
0.0035
10.001
91
0.0079
0.0806
0.1722
0.0687
10.0400
0.0929
10.000
11
1.7090
0.1733
10.238
91
0.8385
0.3344
0.2418
1985190
0.0096
0.0171
10.013
81
0.0040
0.0595
0.1434
0.0586
110.004
510.020
210.000
31
1.3690
1.0100
11.998
01
0.5664
0.2591
0.2491
1990195
0.0070
0.0074
10.002
51
0.0030
0.0461
0.1215
0.0668
10.1667
0.0022
10.000
11
1.2860
0.5178
10.316
91
0.5538
0.2340
0.2106
1995100
0.0086
0.0138
10.006
91
0.0043
0.0425
0.1117
0.0535
10.0144
0.0093
0.0000
11.7110
1.0460
11.091
01
0.8613
0.3209
0.2411
2000105
0.0083
0.0055
10.001
51
0.0060
0.0351
0.1018
0.0591
10.0685
10.165
710.000
71
2.0030
0.4574
10.215
31
1.4650
0.2790
0.2323
2005110
0.0021
0.0144
10.005
81
0.0001
0.0358
0.1209
0.0410
10.1425
0.1446
0.0002
10.4953
1.0070
11.197
01
0.0343
0.2799
0.2595
193512010
0.0073
0.0068
10.000
91
0.0042
0.0554
0.1259
0.0579
10.0542
10.021
210.000
21
3.9950
1.6260
10.454
21
2.3000
0.2765
0.2525
TABLE!3e:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
17
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0050
0.0016
10.0866
0.0037
0.0384
0.0606
10.6482
0.0034
10.090
11
0.0684
2.5980
0.5196
12.6760
1.9140
0.3175
0.2612
1935145
0.0018
0.0000
10.1641
0.0016
0.0492
0.0841
10.5208
0.0016
10.170
41
0.0454
0.4140
10.005
21
3.6070
0.3807
0.3000
0.2470
1946155
0.0103
0.0062
110.081
20.0094
0.0290
0.0492
10.4861
10.049
710.021
81
10.028
83.8960
1.3850
111.831
03.5430
0.3405
0.2855
195616/68
0.0035
10.000
71
0.1532
0.0009
0.0338
0.0415
10.8185
0.2586
0.1145
10.1666
1.2700
10.218
31
2.2930
0.3242
0.3144
0.2534
1935140
0.0021
10.002
11
0.0949
0.0021
0.0584
0.1054
10.5287
0.0060
10.179
31
10.001
20.3089
10.167
61
1.5120
0.2978
0.2775
0.2457
1941145
0.0014
0.0024
10.2461
0.0011
0.0358
0.0487
10.5034
0.1998
10.124
81
0.1019
0.2921
0.3814
13.7870
0.2444
0.3266
0.2478
1946150
0.0060
0.0042
110.032
60.0053
0.0319
0.0574
10.4778
0.0113
10.036
91
10.050
11.4580
0.5715
110.528
61.2970
0.4180
0.2793
1951155
0.0147
0.0082
110.129
90.0134
0.0254
0.0397
10.4936
10.136
010.103
91
10.006
44.4670
1.5990
112.038
04.0870
0.2631
0.2723
1956160
0.0130
10.005
91
0.0322
0.0109
0.0247
0.0371
10.5821
0.0626
0.1359
10.0319
4.0760
11.232
01
0.4290
3.4080
0.2538
0.2500
196116/68
10.002
80.0027
10.2339
10.005
80.0376
0.0441
10.9384
0.2378
0.0876
10.2569
10.710
40.5806
12.3640
11.446
00.3548
0.2488
7/196812010
0.0079
0.0009
10.0324
0.0034
0.0418
0.0598
10.9183
0.0859
0.0031
10.0840
4.2780
0.3229
10.7958
1.8370
0.3312
0.2532
1970180
0.0005
10.000
81
0.1443
10.004
90.0489
0.0605
11.2250
0.1954
10.033
41
0.2706
0.1228
10.152
91
1.3540
11.161
00.3380
0.2645
1980190
0.0190
0.0013
110.088
50.0120
0.0431
0.0688
10.8337
0.0163
10.009
61
10.026
15.0660
0.2168
111.220
03.1970
0.3062
0.2512
1990100
0.0104
0.0030
110.021
70.0063
0.0419
0.0590
10.7722
0.0728
10.018
81
0.0234
2.8560
0.5784
110.323
41.7450
0.3393
0.2469
2000110
0.0044
10.005
91
0.1501
0.0023
0.0368
0.0582
10.8075
0.0020
0.0422
10.0445
1.3680
11.165
01
2.1360
0.7276
0.3484
0.2438
1970175
0.0082
0.0052
110.099
10.0034
0.0556
0.0650
11.4120
0.0976
10.128
01
0.1974
1.2530
0.6777
110.595
90.5216
0.3346
0.2576
1975180
10.004
510.003
21
0.3783
10.010
50.0426
0.0583
10.9849
0.2945
0.0334
10.3425
10.901
410.461
01
3.2590
12.114
00.3401
0.2732
1980185
0.0180
10.000
21
10.004
20.0096
0.0400
0.0618
10.8951
0.1859
10.107
91
0.0262
3.8090
10.030
71
10.039
82.0590
0.3565
0.2556
1985190
0.0212
0.0019
110.153
60.0156
0.0449
0.0726
10.7251
10.095
10.0532
110.078
84.0090
0.2221
111.797
02.9530
0.2501
0.2304
1990195
0.0080
10.001
01
0.0514
0.0040
0.0407
0.0499
10.6570
0.1199
10.033
81
0.0079
1.6630
10.168
41
0.6641
0.8395
0.2738
0.2274
1995100
0.0154
0.0069
110.104
10.0112
0.0413
0.0647
10.8246
0.0535
10.017
81
0.0397
3.1680
0.9118
111.071
02.2990
0.4046
0.2482
2000105
0.0051
10.008
61
0.1887
0.0028
0.0394
0.0545
10.8425
10.112
710.094
21
0.0222
1.1000
11.336
01
1.9010
0.6179
0.3605
0.2374
2005110
0.0029
10.004
51
0.1295
0.0009
0.0316
0.0591
10.7624
0.1721
0.1640
10.0675
0.7666
10.639
21
1.4410
0.2464
0.3407
0.2515
193512010
0.0066
0.0012
10.0562
0.0035
0.0404
0.0601
10.8106
0.0948
10.038
01
0.0769
4.9570
0.5878
12.0940
2.6360
0.3252
0.2567
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0011
0.0086
10.004
00.1056
10.000
20.0562
0.1066
0.0520
0.6859
10.000
60.0120
0.0002
0.1020
0.4063
1.6090
11.525
03.0820
10.058
50.3321
0.2652
1935145
10.005
80.0152
10.008
90.1914
10.005
90.0621
0.1207
0.0685
0.5598
10.005
710.083
30.0002
0.0638
11.060
01.4400
11.485
03.9140
11.087
00.3099
0.2472
1946155
0.0061
0.0132
10.003
610.059
70.0051
0.0326
0.0892
0.0297
0.4663
0.0189
0.0192
0.0000
10.014
02.0370
1.6200
11.335
011.401
01.7190
0.3628
0.2853
195616/68
0.0032
10.000
90.0001
0.1627
0.0006
0.0648
0.1064
0.0493
0.8855
0.2237
0.1108
0.0003
0.2280
0.6093
10.104
60.0165
2.2510
0.1166
0.3268
0.2631
1935140
10.005
90.0157
10.010
70.1162
10.006
00.0725
0.1476
0.0831
0.6006
0.0897
10.033
70.0006
0.0221
10.685
30.8979
11.081
01.6300
10.694
30.2863
0.2495
1941145
10.005
60.0145
10.006
80.2804
10.005
80.0476
0.0790
0.0460
0.4976
0.0375
10.285
210.000
20.1137
10.909
31.4250
11.140
04.3650
10.946
00.3379
0.2436
1946150
0.0038
0.0068
10.001
410.012
60.0031
0.0342
0.0878
0.0257
0.4863
0.0404
0.0543
0.0000
10.030
30.8570
0.6042
10.434
610.200
60.7047
0.4462
0.2656
1951155
0.0083
0.0195
10.005
810.106
70.0071
0.0311
0.0908
0.0333
0.4446
10.070
410.085
80.0000
0.0032
2.0810
1.6650
11.348
011.859
01.7760
0.2795
0.2820
1956160
0.0126
10.005
610.000
20.0378
0.0105
0.0340
0.0827
0.0296
0.5476
10.147
40.0508
0.0000
0.0083
2.8740
10.522
210.043
90.5340
2.3930
0.2644
0.2609
196116/68
10.003
00.0022
0.0002
0.2461
10.006
00.0786
0.1200
0.0590
1.0470
0.2536
0.1260
0.0006
0.3757
10.364
90.1742
0.0358
2.2300
10.719
00.3683
0.2577
7/196812010
0.0042
0.0085
10.005
00.0597
10.000
30.0764
0.1407
0.0665
0.9919
0.1694
0.0407
0.0003
0.1560
1.2390
1.3630
11.712
01.3590
10.102
90.3710
0.2537
1970180
10.001
10.0003
10.001
20.1671
10.006
50.1059
0.1802
0.0860
1.3090
0.2410
10.023
30.0005
0.4383
10.114
50.0207
10.156
41.4670
10.707
30.3855
0.2644
1980190
0.0130
0.0137
10.008
310.048
80.0059
0.0957
0.1683
0.0818
0.9613
0.1128
0.0467
0.0004
0.0166
1.5540
0.9378
11.161
010.583
50.7114
0.3538
0.2538
1990100
0.0047
0.0151
10.008
40.0209
0.0006
0.0660
0.1213
0.0625
0.8488
0.2237
0.1624
0.0007
0.0609
0.8161
1.4250
11.538
00.2834
0.1054
0.3634
0.2492
2000110
0.0002
0.0047
10.005
80.1644
10.001
90.0388
0.1109
0.0446
0.7715
0.0594
0.0275
10.000
20.0472
0.0474
0.4913
11.507
02.4480
10.568
80.3914
0.2455
1970175
0.0042
0.0121
10.004
210.075
510.000
50.1071
0.1719
0.0858
1.5120
0.2671
10.032
70.0009
0.4573
0.3361
0.5988
10.419
110.423
810.043
40.3745
0.2595
1975180
10.001
210.011
10.0043
0.3724
10.007
20.1088
0.1975
0.0928
1.0080
0.2075
10.043
80.0000
0.3982
10.091
910.474
50.3946
3.1350
10.561
40.3960
0.2687
1980185
0.0151
0.0044
10.002
80.0139
0.0068
0.0956
0.1693
0.0748
0.9475
0.2060
0.0325
0.0005
0.1088
1.3440
0.2213
10.316
60.1245
0.6099
0.4056
0.2480
1985190
0.0126
0.0209
10.012
810.097
90.0069
0.0921
0.1589
0.0840
0.9329
10.006
50.0311
0.0000
10.071
21.1600
1.1140
11.291
010.890
20.6416
0.2966
0.2443
1990195
10.001
80.0200
10.014
20.1160
10.005
70.0753
0.1293
0.0750
0.7968
0.2403
0.2243
0.0012
0.0455
10.199
61.3140
11.606
01.2350
10.648
10.3020
0.2337
1995100
0.0126
0.0110
10.003
210.067
30.0083
0.0518
0.1077
0.0417
0.8429
0.1727
0.0528
0.0001
0.0756
2.0640
0.8657
10.646
110.677
01.3670
0.4292
0.2471
2000105
0.0007
0.0013
10.005
40.2101
10.001
60.0373
0.0952
0.0454
0.7878
0.0708
10.198
210.000
60.0583
0.1582
0.1188
11.017
02.2630
10.360
10.3992
0.2394
2005110
10.002
40.0096
10.007
80.1408
10.004
30.0404
0.1190
0.0422
0.7598
0.0213
0.1672
0.0001
0.0387
10.493
90.6825
11.562
01.5730
10.899
70.3918
0.2497
193512010
0.0028
0.0085
10.004
60.0799
10.000
30.0682
0.1268
0.0605
0.8704
0.1637
0.0317
0.0003
0.1326
1.2600
2.0300
12.277
02.7700
10.118
20.3538
0.2594
TABLE!3e:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
18
3.3 Behavior of the market
For completeness I replicate and extend the last two tables of Fama-MacBeth (1973) anddescribe the results below. First in Table 4a we note that the average monthly return on themarket portfolio proxy (the equal-weighted NYSE portfolio) is Rm � 1.25% for 1935-2010but it is greater for the 1935-6/1968 testing period (Rm � 1.45%) than for the 7/1968-2010testing period (Rm � 1.10%). On the other hand, the return in excess of the three-monthTreasury Bill9 is halved from 1935-6/1968 to 7/1968-2010 because Rf increases from an av-erage monthly return of 13bps for 1935-6/1968 to 45bps for the 7/1968-2010 testing period.These results may not be so surprising because the post-1968 period includes several notice-able downturns (in the late 1980s, the early 2000’s and more recently in the late 2000’s).However, the equal-weighted NYSE is slightly less volatile for the 7/1968-2010 testing period(spRmq � 5.41%) than for the 1935-6/1968 period (spRmq � 6.12%); this is a bit surprisinggiven the previous observation. ¯γ0 and ¯γ1 are the estimates from the regression specificationin Panel A of Table 3a. Recall that for the Sharpe-Lintner model Epγ0tq � Rf while in theBlack model Epγ0tq is the expected return on the portfolio with zero beta with respect to themarket portfolio proxy. In both models, Epγ1tq is the excess return of the market portfolio(proxy) on γ0t. I find that ¯γ0 is fairly large10 and more volatile relative to the proxy forthe risk-free rate, Rf . Furthermore ¯γ0 is significantly less autocorrelated than Rf ; indeedρMpγ0q � 0.1361 and ρMpRf q � 0.9763 for the 1935-2010 testing period. Nonetheless, I doalso find that ¯γ1 � ¯γ0 � Rm in all testing periods.
When I use the value-weighted NYSE portfolio returns as a proxy for the market portfolioreturn I find that Rm decreases and is less volatile. Indeed, from Table 4h, Rm � 1.09%,88bps, and 97bps for the 1935-6/1968, 7/1968-2010, and 1935-2010 testing periods (respec-tively). In addition, the standard deviation of the monthly returns (spRmq) is much lowerand is (close to) 4.50% for the three aforementioned testing periods. The resulting Sharpe
ratios�Rm�Rf
spRmq
are also lower with the value-weighted NYSE portfolio returns compared to
the equal-weighted NYSE portfolio returns. In Table 4h, I also use the 5 � 5 dual-sort testportfolios where the portfolio betas are the value-weighted averages of the underlying secu-rity betas. I find that ¯γ1 tends to have much lower magnitude compared the correspondingvalues in Table 4a. More specifically, with the 5 � 5 test portfolios ¯γ1 is about half the cor-responding values if I use the 20 Fama-MacBeth (1973) test portfolios for the 1935-6/1968,7/1968-2010, and 1935-2010 testing periods. Nonetheless, I still find ¯γ1 � ¯γ0 � Rm and theautocorrelation of ¯γ0 is much lower than that of Rf (ρMpγ0q ρMpRf q). However, ρMpγ0qtends to be lower in Table 4h than in Table 4a.
9I obtain the monthly returns of the three-month Treasury Bill from the Fama-French data library10γ0 tends to be significantly larger than Rf . From Panel A of Table 3a, tpγ0 � Rf q tends to be larger
than the relevant critical values for statistical significance.
19
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0145 0.0132 0.0084 0.0063 0.0013 0.2154 0.1369 0.0612 0.0613 ! !
1935,45 0.0201 0.0200 0.0163 0.0041 0.0001 0.2246 0.1832 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0028 0.0084 0.0009 0.2370 0.0653 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0059 0.0064 0.0026 0.2392 0.1474 0.0399 0.0400 ! !
1935,40 0.0141 0.0141 0.0124 0.0016 0.0001 0.1292 0.1136 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0210 0.0071 0.0002 0.4669 0.3627 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0033 0.0047 0.0007 0.1355 0.0626 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0024 0.0122 0.0012 0.4144 0.0739 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0059 0.0149 0.0021 0.2069 ,0.1735 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0137 0.0007 0.0029 0.2581 0.3158 0.0435 0.0435 ! !
7/1968,2010 0.0110 0.0065 0.0036 0.0081 0.0045 0.1193 0.0665 0.0541 0.0543 ! !
1970,80 0.0116 0.0061 0.0093 0.0031 0.0055 0.0947 0.1447 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0051 0.0181 0.0071 0.098 ,0.0967 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0023 0.0093 0.0041 0.1486 0.0562 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0044 0.0063 0.0021 0.1560 0.0770 0.0570 0.0571 ! !
1970,75 0.0036 ,0.0012 0.0003 0.0052 0.0048 ,0.0172 0.0041 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0217 0.0030 0.0060 0.3040 0.3463 0.0625 0.0628 ! !1980,85 0.0173 0.0089 0.0001 0.0174 0.0083 0.185 0.0016 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0094 0.0199 0.0056 0.061 ,0.1714 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0035 0.0077 0.0040 0.1616 0.0897 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0003 0.0133 0.0043 0.181 0.0067 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0033 0.0085 0.0023 0.2474 0.0780 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0056 0.0035 0.0019 0.1017 0.0843 0.0661 0.0662 ! !
1935,2010 0.0125 0.0094 0.0057 0.0073 0.0031 0.1642 0.0994 0.0573 0.0575 ! !
Period
1935,6/68 0.0360 0.0012 4.7400 4.309 2.5460 3.4760 ,0.0063 ,0.0040 0.0098 0.2008 0.9661
1935,45 0.0485 0.0002 2.5890 2.5710 1.9160 0.9753 ,0.0664 ,0.0663 ,0.0470 0.1935 0.63721946,55 0.0258 0.0004 2.8350 2.597 0.7427 3.5890 0.0875 0.0864 0.0720 0.1261 0.89231956,6/68 0.0299 0.0009 3.7290 2.926 1.6560 2.6020 0.1357 0.1380 0.1651 0.2567 0.8512
1935,40 0.0594 0.0002 1.0950 1.0890 0.8809 0.2278 ,0.1260 ,0.1255 ,0.1013 0.1927 0.43611941,45 0.0311 0.0001 3.6460 3.6200 2.4770 1.7700 0.1493 0.1485 0.1490 0.1841 0.72331946,50 0.0309 0.0003 1.1480 1.0510 0.5229 1.1690 0.0922 0.0898 0.0346 0.1969 0.91021951,55 0.0189 0.0004 3.5000 3.196 0.5401 5.0210 ,0.0244 ,0.0172 0.0953 ,0.0417 0.75561956,60 0.0201 0.0007 2.0840 1.592 ,1.3700 5.7530 0.1145 0.1309 0.1955 0.1439 0.65991961,6/68 0.0339 0.0008 3.0890 2.449 2.7300 0.1853 0.1318 0.1294 0.1009 0.2153 0.8900
7/1968,2010 0.0361 0.0025 4.5880 2.685 1.3660 5.0850 0.1864 0.1905 0.1976 0.0832 0.9605
1970,80 0.0376 0.0020 2.0600 1.086 1.6170 0.9349 0.1129 0.1148 0.1833 0.1834 0.89311980,90 0.0391 0.0023 2.6750 1.124 ,1.0030 5.3340 0.1826 0.1887 0.2402 ,0.0190 0.89031990,00 0.0384 0.0011 2.8790 1.702 0.4599 2.7700 0.2137 0.2177 0.2380 0.0919 0.90552000,10 0.0317 0.0016 2.2100 1.788 0.8333 2.2790 0.2689 0.2726 0.1622 0.0165 0.9778
1970,75 0.0410 0.0013 0.4335 ,0.146 0.0373 1.0750 0.1535 0.1577 0.1374 0.1702 0.82951975,80 0.0357 0.0023 3.3950 2.570 2.7190 0.7100 0.0478 0.0543 0.2406 0.1846 0.89641980,85 0.0365 0.0022 3.0340 1.548 0.0123 4.0440 0.1518 0.1729 0.2006 0.0984 0.83061985,90 0.0402 0.0010 1.3930 0.518 ,1.3550 4.2090 0.1979 0.1980 0.2616 ,0.0928 0.77271990,95 0.0395 0.0014 2.2370 1.364 0.5082 1.6560 0.2632 0.2685 0.3411 0.1432 0.94591995,00 0.0359 0.0005 2.4730 1.540 0.0427 3.1480 0.1544 0.1551 0.1021 0.0547 0.47972000,05 0.0345 0.0015 2.5550 2.094 0.5126 2.0820 0.1855 0.1898 ,0.0049 ,0.0802 0.97282005,10 0.0264 0.0016 1.1120 0.8607 0.7522 1.1410 0.2890 0.2927 0.2699 0.1800 0.9795
1935,2010 0.0360 0.0026 6.5970 4.941 2.7580 6.1130 0.0905 0.0962 0.1082 0.1361 0.9763
TABLE!4a:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
20
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0109 0.0096 0.0044 0.0080 0.0013 0.2138 0.0986 0.0449 0.0450 ! !
1935,45 0.0115 0.0114 0.0077 0.0080 0.0001 0.1899 0.1282 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0024 0.0091 0.0009 0.3078 0.0650 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0032 0.0072 0.0026 0.1925 0.0930 0.0344 0.0345 ! !
1935,40 0.0092 0.0092 0.0039 0.0071 0.0001 0.1238 0.0534 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0121 0.0090 0.0002 0.3709 0.3203 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0048 0.0028 0.0007 0.1819 0.1167 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0000 0.0155 0.0012 0.4794 ,0.0008 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0024 0.0107 0.0021 0.1905 ,0.0708 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0069 0.0048 0.0029 0.1928 0.1974 0.0350 0.0351 ! !
7/1968,2010 0.0088 0.0043 0.0019 0.0093 0.0045 0.0959 0.0419 0.0444 0.0444 ! !
1970,80 0.0078 0.0023 0.0030 0.0086 0.0055 0.0478 0.0615 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0037 0.0172 0.0071 0.126 ,0.0779 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0056 0.0056 0.0041 0.2167 0.1474 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0019 0.0073 0.0021 0.0308 0.0426 0.0443 0.0444 ! !
1970,75 0.0034 ,0.0014 0.0001 0.0072 0.0048 ,0.0271 0.0019 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0079 0.0124 0.0060 0.2122 0.1722 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0041 0.0212 0.0083 0.149 ,0.0961 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0038 0.0155 0.0056 0.150 ,0.0754 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0072 0.0037 0.0040 0.1986 0.2136 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0106 0.0043 0.302 0.0662 0.0397 0.0397 ! !2000,05 0.0032 0.0010 0.0011 0.0103 0.0023 0.0254 0.0289 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0028 0.0039 0.0019 0.0451 0.0585 0.0471 0.0471 ! !
1935,2010 0.0097 0.0066 0.0030 0.0087 0.0031 0.1482 0.0670 0.0446 0.0447 ! !
Period
1935,6/68 0.0489 0.0012 4.8620 4.276 1.8990 3.2830 ,0.0194 ,0.0164 0.0368 0.0000 0.9661
1935,45 0.0667 0.0002 2.2010 2.1750 1.5460 1.3680 ,0.0815 ,0.0814 ,0.0050 ,0.0769 0.63721946,55 0.0370 0.0004 3.6520 3.374 0.6658 2.6990 0.0116 0.0101 0.0621 ,0.0423 0.89231956,6/68 0.0380 0.0009 3.2860 2.351 0.9322 2.3130 0.1149 0.1207 0.0754 0.2354 0.8512
1935,40 0.0820 0.0002 1.0520 1.0440 0.5080 0.7304 ,0.1453 ,0.1445 ,0.0950 ,0.1019 0.43611941,45 0.0427 0.0001 2.9180 2.8770 2.0850 1.6310 0.1957 0.1941 0.1966 0.0333 0.72331946,50 0.0420 0.0003 1.5340 1.4120 0.8716 0.5075 0.0581 0.0551 0.0532 0.0578 0.91021951,55 0.0303 0.0004 4.0120 3.699 ,0.0056 3.9550 ,0.1387 ,0.1314 0.0579 ,0.2748 0.75561956,60 0.0268 0.0007 1.9610 1.467 ,0.5981 3.0950 0.1006 0.1152 0.0264 0.1372 0.65991961,6/68 0.0439 0.0008 2.6250 1.827 1.3720 1.0420 0.1061 0.1064 0.0761 0.2439 0.8900
7/1968,2010 0.0412 0.0025 4.4750 2.160 0.7919 5.0760 0.0676 0.0695 0.1453 0.1188 0.9605
1970,80 0.0509 0.0020 1.8350 0.547 0.5736 1.9410 0.0239 0.0253 0.1456 0.1092 0.89311980,90 0.0447 0.0023 3.1430 1.431 ,0.7567 4.4110 0.0647 0.0750 0.0989 0.0578 0.89031990,00 0.0366 0.0011 3.7280 2.488 1.2700 1.7470 ,0.0867 ,0.0849 0.1647 0.1145 0.90552000,10 0.0294 0.0016 0.8911 0.354 0.4685 2.8380 0.1825 0.1854 0.1688 0.0989 0.9778
1970,75 0.0569 0.0013 0.5462 ,0.228 0.0134 1.0800 0.0966 0.1058 0.1369 0.1635 0.82951975,80 0.0445 0.0023 2.9150 1.797 1.1510 2.3670 ,0.0320 ,0.0340 0.1481 ,0.0162 0.89641980,85 0.0448 0.0022 2.9040 1.240 ,0.6459 4.0050 0.0511 0.0778 0.0737 0.0419 0.83061985,90 0.0429 0.0010 2.2190 1.270 ,0.5810 3.0620 0.0862 0.0844 0.1160 0.0520 0.77271990,95 0.0357 0.0014 2.6910 1.684 1.2810 0.8816 ,0.1039 ,0.1042 0.1412 0.1149 0.94591995,00 0.0373 0.0005 3.4740 2.560 0.4309 2.4080 ,0.0801 ,0.0776 0.1804 0.1241 0.47972000,05 0.0270 0.0015 0.7153 0.215 0.2232 3.2440 0.0366 0.0436 0.0388 0.1650 0.97282005,10 0.0301 0.0016 0.7322 0.3824 0.4910 1.0940 0.2615 0.2618 0.2561 0.0340 0.9795
1935,2010 0.0447 0.0026 6.5800 4.458 1.7940 5.8790 0.0292 0.0346 0.1051 0.0559 0.9763
TABLE!4h:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
21
3.4 Variance decomposition
Following Fama-MacBeth (1973), I let φjt denote the estimation error such that φjt � γjt�γjt.Then, let spφjtq be the standard error of γjt in the cross-sectional regression at time t and
let s2pφjq denote the average of the s2pφjtq values for all t in the testing period. Lastly with
the sample variance of the monthly γjt estimates, s2pγjtq, I define s2pγjtq � s2pγjtq � s2pφjq
and F � s2pγjtq{s2pφjq (the F-statistics).
I will first describe the results in Table 5a. This is the base case with the 20 beta-sortedportfolios. As I include additional regressors in the model the F-statistics tend to decrease.This should be expected because as Fama-MacBeth (1973) explains the additional regressorsintroduce more colinearity and the error in the new regressors is likely correlated with theerror in the original regressors. Nonetheless, focusing on Panel D, the F-statistics tend tobe above the relevant critical values11 except for γ3. These results provide some reassurancethat the variation in γjt is not driven by error and likely correctly reflects variation in thetrue variable, γjt. The exception is for γ3, where the corresponding F-statistics tend to be
too low to reject the null hypothesis that s2pγ3tq � s2pφ3q. Nonetheless, I also find that theF-statistics are larger for the 7/1968-2010 testing period than for the 1935-6/1968 testingperiod.
In Table 5e, I use the value-weighted NYSE porfolio returns as a proxy for the marketportfolio returns, the 5 � 5 dual-sorted test portfolios, and regressors constructed usingequal-weighted averages of the underlying security estimates. Focusing again on Panel D, Ifind that the F-statistics are much greater. In particular, for the 1935-2010 testing period,
s2pγ0tq{s2pφ0q � 2.87, s2pγ1tq{s2pφ1q � 2.56, s2pγ2tq{s2pφ2q � 1.97. These results providesome evidence that estimates γ0, γ1 and γ2 are likely accurate (and more so than in Ta-
ble 5a). However, notice that s2pγ3tq{s2pφ3q � 4.18 , 4.44, and 4.36 for the 1935-6/1968,7/1968-2010, and 1935-2010 testing periods (respectively). Thus with the 5 � 5 dual-sorttest portfolios I find that Epγ3tq is more accurately estimated than the other coefficients andit is also more accurately estimated compared to when I use the 20 beta-sorted test porfoliosof Fama-MacBeth (1973). Given the results in Table 3e which show that ¯γ3 is significantlydifferent from zero the results on Table 5e cast additional doubt on the validity of the assetpricing model. Lastly, on Table 5e we can also see that the F-statistics are greater for the7/1968-2010 testing period than for the 1935-6/1968 testing period. This is perhaps hintingthat the coefficients in the cross-sectional regressions tend to be better estimated in latertime periods.
11The F-stat has degrees of freedom tn � 1, npP �Kqu where n is the number of months in the testingperiod, P is the number of test-portfolios, and K is the number of coefficients γj in the regression. Therelevant critical value for a test at a 5% level is between 1.25 and 1.35.
22
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0010
0.0003
0.0013
4.1530
0.0040
0.0003
0.0043
14.3600
193516/68
0.0011
0.0007
0.0019
2.5860
0.0039
0.0015
0.0055
3.5910
1935145
0.0016
0.0008
0.0023
3.1240
0.0088
0.0007
0.0095
12.9700
1935145
0.0019
0.0013
0.0032
2.4850
0.0085
0.0029
0.0114
3.9470
1946155
0.0006
0.0001
0.0007
8.4480
0.0017
0.0001
0.0017
24.2400
1946155
0.0009
0.0002
0.0012
4.9260
0.0022
0.0007
0.0029
4.3780
195616/68
0.0008
0.0001
0.0009
7.7540
0.0018
0.0001
0.0019
16.9500
195616/68
0.0006
0.0006
0.0012
2.0570
0.0013
0.0010
0.0023
2.3040
1935140
0.0024
0.0012
0.0035
3.0160
0.0128
0.0012
0.0140
12.0400
1935140
0.0030
0.0017
0.0047
2.7630
0.0147
0.0038
0.0185
4.8720
1941145
0.0007
0.0003
0.0010
3.7860
0.0041
0.0002
0.0043
19.0500
1941145
0.0006
0.0008
0.0014
1.8250
0.0014
0.0018
0.0032
1.7460
1946150
0.0009
0.0001
0.0010
11.8200
0.0023
0.0001
0.0023
31.4600
1946150
0.0014
0.0003
0.0017
5.8420
0.0029
0.0009
0.0038
4.3450
1951155
0.0003
0.0001
0.0004
4.6550
0.0011
0.0001
0.0012
17.0400
1951155
0.0005
0.0002
0.0007
3.6190
0.0015
0.0004
0.0019
4.5540
1956160
0.0003
0.0001
0.0004
4.3960
0.0010
0.0001
0.0011
13.5600
1956160
0.0004
0.0005
0.0010
1.8150
0.0003
0.0010
0.0013
1.2550
196116/68
0.0010
0.0001
0.0012
8.7520
0.0021
0.0001
0.0023
17.3200
196116/68
0.0008
0.0006
0.0014
2.1770
0.0019
0.0010
0.0029
2.8950
7/196812010
0.0011
0.0002
0.0013
7.5540
0.0034
0.0002
0.0035
19.6600
7/196812010
0.0012
0.0007
0.0019
2.7380
0.0041
0.0025
0.0065
2.6340
1970180
0.0012
0.0002
0.0014
7.1430
0.0042
0.0002
0.0044
20.4300
1970180
0.0014
0.0009
0.0022
2.5770
0.0026
0.0032
0.0058
1.8150
1980190
0.0013
0.0002
0.0015
7.8760
0.0032
0.0002
0.0034
16.7000
1980190
0.0012
0.0007
0.0019
2.7370
0.0072
0.0031
0.0103
3.3380
1990100
0.0013
0.0002
0.0015
7.1170
0.0030
0.0002
0.0032
14.9200
1990100
0.0011
0.0004
0.0016
3.5120
0.0030
0.0016
0.0046
2.9120
2000110
0.0009
0.0001
0.0010
7.5570
0.0035
0.0001
0.0037
27.6800
2000110
0.0014
0.0009
0.0023
2.6580
0.0041
0.0027
0.0068
2.4960
1970175
0.0015
0.0002
0.0017
7.4680
0.0041
0.0002
0.0044
17.8500
1970175
0.0019
0.0009
0.0027
3.1290
0.0035
0.0025
0.0060
2.3780
1975180
0.0011
0.0002
0.0013
6.6240
0.0044
0.0002
0.0046
21.5700
1975180
0.0010
0.0010
0.0020
2.0070
0.0012
0.0043
0.0055
1.2860
1980185
0.0012
0.0002
0.0013
8.8620
0.0029
0.0002
0.0030
18.9200
1980185
0.0011
0.0009
0.0020
2.2390
0.0033
0.0035
0.0069
1.9530
1985190
0.0014
0.0002
0.0016
7.2270
0.0032
0.0002
0.0035
15.0700
1985190
0.0012
0.0005
0.0017
3.4710
0.0109
0.0025
0.0134
5.2820
1990195
0.0013
0.0003
0.0016
6.0130
0.0031
0.0003
0.0034
12.8800
1990195
0.0009
0.0004
0.0012
3.4470
0.0033
0.0015
0.0048
3.1280
1995100
0.0012
0.0001
0.0013
9.5910
0.0025
0.0001
0.0027
19.2300
1995100
0.0012
0.0005
0.0017
3.3990
0.0025
0.0015
0.0040
2.7150
2000105
0.0011
0.0001
0.0012
8.7580
0.0028
0.0001
0.0030
21.5300
2000105
0.0015
0.0007
0.0023
3.0420
0.0020
0.0020
0.0040
1.9770
2005110
0.0006
0.0001
0.0007
5.9350
0.0038
0.0001
0.0039
34.4700
2005110
0.0012
0.0009
0.0021
2.2690
0.0056
0.0034
0.0089
2.6650
193512010
0.0011
0.0002
0.0013
5.5530
0.0037
0.0002
0.0039
16.6500
193512010
0.0012
0.0007
0.0019
2.6670
0.0040
0.0021
0.0061
2.9440
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0014
0.0013
0.0027
2.0370
0.0080
0.0066
0.0146
2.2190
193516/68
0.0009
0.0035
0.0044
1.2730
0.0072
0.0071
0.0144
2.0150
1935145
0.0019
0.0020
0.0039
1.9780
0.0117
0.0107
0.0223
2.0950
1935145
0.0008
0.0064
0.0072
1.1200
0.0093
0.0119
0.0211
1.7810
1946155
0.0004
0.0006
0.0010
1.6710
0.0050
0.0026
0.0076
2.9710
1946155
0.0002
0.0015
0.0017
1.1320
0.0049
0.0026
0.0075
2.8940
195616/68
0.0017
0.0013
0.0030
2.2420
0.0073
0.0062
0.0136
2.1790
195616/68
0.0016
0.0024
0.0041
1.6660
0.0074
0.0066
0.0140
2.1260
1935140
0.0022
0.0028
0.0051
1.7810
0.0200
0.0153
0.0353
2.3090
1935140
0.0003
0.0079
0.0082
1.0330
0.0159
0.0170
0.0330
1.9360
1941145
0.0016
0.0009
0.0025
2.7560
0.0021
0.0052
0.0073
1.4080
1941145
0.0015
0.0046
0.0061
1.3190
0.0017
0.0058
0.0075
1.2920
1946150
0.0007
0.0006
0.0013
2.1150
0.0066
0.0025
0.0091
3.5890
1946150
0.0006
0.0017
0.0024
1.3630
0.0066
0.0026
0.0092
3.4950
1951155
0.0002
0.0006
0.0008
1.2560
0.0036
0.0026
0.0062
2.3880
1951155
10.000
20.0012
0.0010
0.8148
0.0033
0.0026
0.0059
2.3010
1956160
0.0002
0.0005
0.0007
1.5000
0.0021
0.0023
0.0044
1.9300
1956160
0.0007
0.0016
0.0023
1.4450
0.0017
0.0026
0.0043
1.6680
196116/68
0.0025
0.0019
0.0044
2.3230
0.0106
0.0089
0.0194
2.1930
196116/68
0.0022
0.0030
0.0052
1.7350
0.0109
0.0093
0.0201
2.1750
7/196812010
0.0030
0.0011
0.0041
3.6050
0.0161
0.0063
0.0224
3.5560
7/196812010
0.0025
0.0028
0.0054
1.8960
0.0150
0.0085
0.0235
2.7670
1970180
0.0059
0.0023
0.0081
3.5990
0.0297
0.0116
0.0413
3.5480
1970180
0.0056
0.0048
0.0104
2.1830
0.0235
0.0150
0.0384
2.5690
1980190
0.0043
0.0013
0.0056
4.3010
0.0241
0.0067
0.0308
4.5900
1980190
0.0030
0.0029
0.0059
2.0240
0.0224
0.0101
0.0325
3.2090
1990100
0.0013
0.0008
0.0021
2.6320
0.0080
0.0056
0.0136
2.4150
1990100
0.0004
0.0026
0.0031
1.1630
0.0068
0.0077
0.0145
1.8930
2000110
0.0008
0.0004
0.0012
3.2420
0.0068
0.0026
0.0094
3.6610
2000110
0.0008
0.0015
0.0023
1.5360
0.0081
0.0038
0.0120
3.1060
1970175
0.0057
0.0023
0.0080
3.4220
0.0243
0.0126
0.0369
2.9190
1970175
0.0045
0.0066
0.0111
1.6910
0.0223
0.0140
0.0362
2.5940
1975180
0.0075
0.0022
0.0097
4.3560
0.0386
0.0111
0.0497
4.4970
1975180
0.0077
0.0033
0.0109
3.3580
0.0293
0.0161
0.0453
2.8230
1980185
0.0045
0.0012
0.0057
4.5910
0.0220
0.0055
0.0275
4.9910
1980185
0.0038
0.0019
0.0057
3.0400
0.0225
0.0101
0.0326
3.2380
1985190
0.0039
0.0012
0.0052
4.1590
0.0248
0.0073
0.0321
4.3900
1985190
0.0020
0.0037
0.0057
1.5380
0.0220
0.0092
0.0312
3.3850
1990195
0.0015
0.0011
0.0026
2.3740
0.0073
0.0074
0.0147
1.9930
1990195
10.000
20.0038
0.0037
0.9554
0.0049
0.0108
0.0156
1.4530
1995100
0.0012
0.0004
0.0016
3.6550
0.0085
0.0031
0.0117
3.7220
1995100
0.0010
0.0011
0.0021
1.9050
0.0090
0.0036
0.0126
3.5080
2000105
0.0007
0.0004
0.0011
2.5060
0.0046
0.0032
0.0078
2.4200
2000105
0.0011
0.0014
0.0025
1.7970
0.0049
0.0038
0.0088
2.2940
2005110
0.0010
0.0003
0.0013
4.5310
0.0083
0.0017
0.0100
5.8940
2005110
0.0006
0.0015
0.0020
1.3910
0.0102
0.0037
0.0138
3.7690
193512010
0.0023
0.0012
0.0035
2.8560
0.0125
0.0064
0.0190
2.9510
193512010
0.0018
0.0031
0.0049
1.5890
0.0116
0.0079
0.0195
2.4660
TABLE!5a:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
23
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.1079
0.4617
0.5696
1.2340
1935145
11
11
11
11
1935145
11
11
0.0324
0.3475
0.3799
1.0930
1946155
11
11
11
11
1946155
11
11
0.2059
0.2838
0.4896
1.7260
195616/68
11
11
11
11
195616/68
11
11
0.0954
0.7037
0.7991
1.1360
1935140
11
11
11
11
1935140
11
11
10.070
40.3324
0.2620
0.7882
1941145
11
11
11
11
1941145
11
11
0.1590
0.3654
0.5244
1.4350
1946150
11
11
11
11
1946150
11
11
0.2352
0.3205
0.5557
1.7340
1951155
11
11
11
11
1951155
11
11
0.1845
0.2470
0.4315
1.7470
1956160
11
11
11
11
1956160
11
11
0.2057
0.7499
0.9556
1.2740
196116/68
11
11
11
11
196116/68
11
11
0.0284
0.6729
0.7012
1.0420
7/196812010
11
11
11
11
7/196812010
11
11
0.4087
0.7498
1.1580
1.5450
1970180
11
11
11
11
1970180
11
11
0.4060
0.9703
1.3760
1.4180
1980190
11
11
11
11
1980190
11
11
0.4909
0.8171
1.3080
1.6010
1990100
11
11
11
11
1990100
11
11
0.2101
0.3949
0.6050
1.5320
2000110
11
11
11
11
2000110
11
11
0.6719
0.9154
1.5870
1.7340
1970175
11
11
11
11
1970175
11
11
0.7125
0.9025
1.6150
1.7890
1975180
11
11
11
11
1975180
11
11
0.2310
1.1590
1.3900
1.1990
1980185
11
11
11
11
1980185
11
11
0.3482
1.0210
1.3690
1.3410
1985190
11
11
11
11
1985190
11
11
0.6158
0.5996
1.2150
2.0270
1990195
11
11
11
11
1990195
11
11
0.0929
0.3083
0.4011
1.3010
1995100
11
11
11
11
1995100
11
11
0.2751
0.4581
0.7332
1.6000
2000105
11
11
11
11
2000105
11
11
0.5578
0.6815
1.2390
1.8190
2005110
11
11
11
11
2005110
11
11
0.7250
1.1160
1.8410
1.6500
193512010
11
11
11
11
193512010
11
11
0.2754
0.6230
0.8984
1.4420
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0010
0.0016
0.0026
1.6010
11
11
193516/68
0.0008
0.0027
0.0034
1.2930
0.0229
0.6701
0.6930
1.0340
1935145
0.0015
0.0029
0.0044
1.5050
11
11
1935145
0.0010
0.0056
0.0066
1.1780
10.104
80.7357
0.6309
0.8576
1946155
0.0005
0.0005
0.0010
1.9410
11
11
1946155
0.0003
0.0007
0.0010
1.3710
0.0489
0.3996
0.4485
1.1220
195616/68
0.0009
0.0014
0.0024
1.6670
11
11
195616/68
0.0010
0.0016
0.0026
1.5950
0.1089
0.8292
0.9381
1.1310
1935140
0.0007
0.0043
0.0050
1.1710
11
11
1935140
10.000
50.0079
0.0075
0.9405
10.075
30.7200
0.6447
0.8954
1941145
0.0024
0.0013
0.0037
2.8590
11
11
1941145
0.0029
0.0029
0.0057
1.9910
10.129
10.7544
0.6253
0.8289
1946150
0.0005
0.0005
0.0010
2.0980
11
11
1946150
0.0003
0.0007
0.0011
1.4330
0.0376
0.4629
0.5005
1.0810
1951155
0.0005
0.0006
0.0010
1.8120
11
11
1951155
0.0002
0.0007
0.0009
1.2840
0.0619
0.3364
0.3982
1.1840
1956160
0.0002
0.0005
0.0007
1.4770
11
11
1956160
0.0004
0.0007
0.0011
1.5230
0.2822
0.9704
1.2530
1.2910
196116/68
0.0014
0.0020
0.0034
1.6980
11
11
196116/68
0.0014
0.0022
0.0036
1.6120
10.002
40.7350
0.7326
0.9967
7/196812010
0.0029
0.0017
0.0045
2.7340
11
11
7/196812010
0.0022
0.0027
0.0049
1.8020
0.0712
0.9100
0.9812
1.0780
1970180
0.0061
0.0029
0.0090
3.1120
11
11
1970180
0.0052
0.0040
0.0091
2.3050
10.080
51.1460
1.0650
0.9297
1980190
0.0029
0.0017
0.0046
2.6490
11
11
1980190
0.0011
0.0032
0.0044
1.3460
10.049
41.0310
0.9816
0.9520
1990100
0.0015
0.0018
0.0032
1.8550
11
11
1990100
0.0002
0.0041
0.0043
1.0550
10.004
40.6669
0.6625
0.9934
2000110
0.0012
0.0007
0.0019
2.7100
11
11
2000110
0.0009
0.0008
0.0017
2.1780
0.2870
0.9845
1.2720
1.2920
1970175
0.0064
0.0032
0.0097
2.9830
11
11
1970175
0.0049
0.0051
0.0099
1.9650
0.0130
1.2730
1.2860
1.0100
1975180
0.0077
0.0027
0.0104
3.8230
11
11
1975180
0.0070
0.0030
0.0101
3.3330
10.234
01.1260
0.8919
0.7922
1980185
0.0027
0.0012
0.0039
3.2270
11
11
1980185
0.0024
0.0013
0.0037
2.8440
0.1015
1.0090
1.1110
1.1010
1985190
0.0029
0.0021
0.0050
2.3930
11
11
1985190
10.000
10.0048
0.0047
0.9796
10.170
80.9975
0.8268
0.8288
1990195
0.0016
0.0024
0.0040
1.6720
11
11
1990195
10.000
40.0066
0.0062
0.9398
10.180
70.7735
0.5928
0.7664
1995100
0.0013
0.0009
0.0022
2.4610
11
11
1995100
0.0008
0.0010
0.0019
1.8210
0.1164
0.4894
0.6058
1.2380
2000105
0.0015
0.0009
0.0025
2.6370
11
11
2000105
0.0011
0.0010
0.0021
2.0880
0.3758
0.7527
1.1280
1.4990
2005110
0.0007
0.0004
0.0011
2.7910
11
11
2005110
0.0006
0.0004
0.0010
2.3420
0.2167
1.1760
1.3920
1.1840
193512010
0.0020
0.0017
0.0037
2.2380
11
11
193512010
0.0016
0.0027
0.0043
1.5790
0.0494
0.8044
0.8538
1.0610
FF
FF
TABLE!5a:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
24
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0010
0.0003
0.0013
4.1890
0.0041
0.0003
0.0044
15.1500
193516/68
0.0012
0.0003
0.0015
4.6120
0.0030
0.0007
0.0037
5.2790
1935145
0.0015
0.0007
0.0022
3.1310
0.0089
0.0007
0.0096
14.4200
1935145
0.0017
0.0007
0.0024
3.4130
0.0056
0.0015
0.0071
4.7480
1946155
0.0006
0.0001
0.0007
7.4270
0.0015
0.0001
0.0015
18.7800
1946155
0.0007
0.0001
0.0008
8.7940
0.0022
0.0002
0.0024
11.1300
195616/68
0.0008
0.0001
0.0010
7.3540
0.0019
0.0001
0.0020
16.4000
195616/68
0.0010
0.0002
0.0011
7.1520
0.0013
0.0004
0.0017
4.4920
1935140
0.0021
0.0011
0.0032
3.0260
0.0131
0.0010
0.0141
13.6800
1935140
0.0024
0.0010
0.0034
3.3470
0.0091
0.0020
0.0111
5.5100
1941145
0.0007
0.0003
0.0010
3.7330
0.0041
0.0002
0.0043
18.8400
1941145
0.0009
0.0003
0.0013
3.7590
0.0015
0.0009
0.0024
2.7500
1946150
0.0008
0.0001
0.0009
11.4800
0.0019
0.0001
0.0019
26.8800
1946150
0.0009
0.0001
0.0010
12.7000
0.0030
0.0003
0.0033
12.9800
1951155
0.0003
0.0001
0.0004
4.0590
0.0011
0.0001
0.0012
12.6200
1951155
0.0005
0.0001
0.0006
5.7810
0.0014
0.0002
0.0016
8.7310
1956160
0.0004
0.0001
0.0005
4.2280
0.0011
0.0001
0.0012
11.7400
1956160
0.0005
0.0001
0.0006
4.3340
0.0011
0.0002
0.0014
5.9130
196116/68
0.0011
0.0001
0.0012
8.5090
0.0024
0.0001
0.0025
17.7000
196116/68
0.0012
0.0002
0.0014
8.1580
0.0015
0.0005
0.0019
4.0130
7/196812010
0.0011
0.0002
0.0013
6.9250
0.0032
0.0002
0.0034
17.9100
7/196812010
0.0015
0.0003
0.0017
6.9520
0.0027
0.0009
0.0036
4.0200
1970180
0.0014
0.0002
0.0016
8.2040
0.0042
0.0002
0.0044
21.3800
1970180
0.0021
0.0003
0.0024
7.5400
0.0023
0.0014
0.0037
2.6090
1980190
0.0013
0.0002
0.0015
7.1690
0.0032
0.0002
0.0034
16.1600
1980190
0.0016
0.0003
0.0019
6.9040
0.0036
0.0011
0.0047
4.3360
1990100
0.0011
0.0002
0.0014
5.8720
0.0026
0.0002
0.0029
12.0800
1990100
0.0015
0.0002
0.0018
7.8050
0.0030
0.0005
0.0035
6.8310
2000110
0.0008
0.0002
0.0009
5.3400
0.0032
0.0002
0.0033
19.1200
2000110
0.0011
0.0002
0.0014
5.7150
0.0028
0.0006
0.0034
5.4020
1970175
0.0018
0.0002
0.0020
10.0800
0.0041
0.0002
0.0043
20.9000
1970175
0.0027
0.0004
0.0031
8.1390
0.0025
0.0017
0.0042
2.4520
1975180
0.0011
0.0002
0.0013
6.4470
0.0042
0.0002
0.0044
19.3400
1975180
0.0015
0.0003
0.0018
6.2690
0.0022
0.0012
0.0034
2.7690
1980185
0.0011
0.0002
0.0012
7.3500
0.0029
0.0002
0.0030
17.2500
1980185
0.0014
0.0002
0.0016
6.8360
0.0027
0.0011
0.0038
3.3990
1985190
0.0014
0.0002
0.0017
7.3380
0.0033
0.0002
0.0036
15.5600
1985190
0.0017
0.0003
0.0020
6.8350
0.0042
0.0011
0.0053
4.8040
1990195
0.0011
0.0003
0.0014
5.1970
0.0027
0.0003
0.0030
10.8500
1990195
0.0014
0.0003
0.0017
6.1710
0.0019
0.0006
0.0025
4.3950
1995100
0.0011
0.0002
0.0013
7.3430
0.0024
0.0002
0.0026
14.6600
1995100
0.0015
0.0002
0.0017
10.6100
0.0038
0.0004
0.0042
10.2600
2000105
0.0009
0.0002
0.0010
5.6120
0.0024
0.0002
0.0026
14.1700
2000105
0.0013
0.0002
0.0015
7.1430
0.0025
0.0005
0.0030
5.8600
2005110
0.0006
0.0002
0.0007
4.7680
0.0035
0.0001
0.0037
24.8800
2005110
0.0008
0.0002
0.0010
4.2790
0.0028
0.0007
0.0035
5.0710
193512010
0.0010
0.0002
0.0013
5.3860
0.0036
0.0002
0.0038
16.4200
193512010
0.0013
0.0003
0.0016
5.7820
0.0028
0.0008
0.0036
4.4950
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0009
0.0016
0.0025
1.5600
0.0036
0.0078
0.0114
1.4610
193516/68
0.0013
0.0019
0.0032
1.6900
0.0042
0.0071
0.0114
1.5940
1935145
0.0009
0.0026
0.0036
1.3510
0.0003
0.0138
0.0141
1.0190
1935145
0.0008
0.0031
0.0039
1.2530
0.0018
0.0128
0.0146
1.1380
1946155
0.0005
0.0006
0.0011
1.8260
0.0066
0.0025
0.0091
3.6020
1946155
0.0003
0.0008
0.0011
1.3530
0.0056
0.0024
0.0080
3.3140
195616/68
0.0012
0.0015
0.0027
1.7930
0.0041
0.0068
0.0109
1.6050
195616/68
0.0025
0.0017
0.0042
2.5020
0.0054
0.0060
0.0113
1.8970
1935140
0.0010
0.0039
0.0049
1.2540
0.0008
0.0206
0.0213
1.0370
1935140
0.0010
0.0043
0.0053
1.2220
0.0029
0.0189
0.0218
1.1550
1941145
0.0009
0.0011
0.0020
1.7870
10.000
10.0058
0.0057
0.9761
1941145
0.0006
0.0016
0.0023
1.3870
0.0006
0.0056
0.0062
1.1100
1946150
0.0007
0.0004
0.0011
2.7790
0.0071
0.0015
0.0086
5.6640
1946150
0.0005
0.0007
0.0012
1.7660
0.0062
0.0015
0.0077
5.0630
1951155
0.0003
0.0008
0.0011
1.3840
0.0061
0.0035
0.0096
2.7170
1951155
0.0001
0.0009
0.0010
1.0610
0.0050
0.0033
0.0082
2.5170
1956160
0.0005
0.0007
0.0011
1.7170
0.0039
0.0030
0.0069
2.2970
1956160
0.0004
0.0008
0.0012
1.5140
0.0041
0.0027
0.0068
2.4970
196116/68
0.0017
0.0020
0.0037
1.8160
0.0043
0.0093
0.0136
1.4660
196116/68
0.0039
0.0023
0.0062
2.6930
0.0063
0.0081
0.0144
1.7730
7/196812010
0.0024
0.0012
0.0035
3.0350
0.0131
0.0062
0.0194
3.1040
7/196812010
0.0044
0.0014
0.0058
4.0740
0.0142
0.0056
0.0198
3.5380
1970180
0.0049
0.0022
0.0071
3.1830
0.0225
0.0108
0.0333
3.0940
1970180
0.0087
0.0026
0.0112
4.3820
0.0232
0.0093
0.0325
3.5000
1980190
0.0038
0.0014
0.0052
3.7920
0.0192
0.0070
0.0262
3.7650
1980190
0.0075
0.0016
0.0092
5.6610
0.0220
0.0063
0.0283
4.4820
1990100
0.0012
0.0008
0.0020
2.3820
0.0084
0.0059
0.0143
2.4360
1990100
0.0033
0.0011
0.0044
4.1060
0.0096
0.0051
0.0147
2.8720
2000110
0.0008
0.0005
0.0013
2.7170
0.0102
0.0030
0.0132
4.3900
2000110
0.0009
0.0006
0.0015
2.5480
0.0096
0.0027
0.0123
4.6050
1970175
0.0047
0.0022
0.0069
3.1850
0.0183
0.0109
0.0292
2.6790
1970175
0.0084
0.0031
0.0115
3.7280
0.0199
0.0097
0.0296
3.0500
1975180
0.0062
0.0023
0.0086
3.6670
0.0291
0.0110
0.0401
3.6370
1975180
0.0097
0.0022
0.0118
5.4270
0.0296
0.0094
0.0390
4.1520
1980185
0.0049
0.0016
0.0065
4.0380
0.0225
0.0072
0.0297
4.1190
1980185
0.0076
0.0016
0.0091
5.8510
0.0225
0.0061
0.0287
4.6850
1985190
0.0026
0.0010
0.0035
3.6040
0.0146
0.0059
0.0206
3.4690
1985190
0.0069
0.0015
0.0085
5.4760
0.0194
0.0059
0.0253
4.2850
1990195
0.0010
0.0012
0.0021
1.8280
0.0065
0.0083
0.0148
1.7780
1990195
0.0042
0.0014
0.0057
3.9890
0.0093
0.0074
0.0167
2.2430
1995100
0.0014
0.0004
0.0018
4.3300
0.0099
0.0026
0.0125
4.7740
1995100
0.0021
0.0006
0.0027
4.5600
0.0095
0.0021
0.0116
5.4140
2000105
0.0008
0.0005
0.0012
2.7170
0.0072
0.0031
0.0104
3.2950
2000105
0.0008
0.0006
0.0014
2.3820
0.0064
0.0027
0.0091
3.3960
2005110
0.0008
0.0005
0.0013
2.7960
0.0120
0.0026
0.0146
5.5590
2005110
0.0011
0.0005
0.0016
3.0360
0.0118
0.0024
0.0142
5.8660
193512010
0.0017
0.0014
0.0031
2.2670
0.0089
0.0069
0.0159
2.2880
193512010
0.0030
0.0016
0.0047
2.8650
0.0098
0.0063
0.0161
2.5620
TABLE!5e:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
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s2(�
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s2(�
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s2(�
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s2(�
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s2(�
0)
s2(�
0)
s2(�
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s2(�
1)
s2(�
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�j,
t
25
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.3271
0.0930
0.4201
4.5160
1935145
11
11
11
11
1935145
11
11
0.1770
0.0943
0.2713
2.8770
1946155
11
11
11
11
1946155
11
11
0.1846
0.0517
0.2363
4.5710
195616/68
11
11
11
11
195616/68
11
11
0.5450
0.1250
0.6700
5.3600
1935140
11
11
11
11
1935140
11
11
0.2016
0.0780
0.2795
3.5850
1941145
11
11
11
11
1941145
11
11
0.1398
0.1136
0.2534
2.2310
1946150
11
11
11
11
1946150
11
11
0.1817
0.0466
0.2283
4.8960
1951155
11
11
11
11
1951155
11
11
0.1868
0.0568
0.2436
4.2900
1956160
11
11
11
11
1956160
11
11
0.2496
0.0893
0.3388
3.7950
196116/68
11
11
11
11
196116/68
11
11
0.7318
0.1488
0.8806
5.9180
7/196812010
11
11
11
11
7/196812010
11
11
0.6471
0.1961
0.8432
4.3000
1970180
11
11
11
11
1970180
11
11
1.1600
0.3399
1.5000
4.4140
1980190
11
11
11
11
1980190
11
11
0.4805
0.2146
0.6951
3.2390
1990100
11
11
11
11
1990100
11
11
0.5193
0.0770
0.5963
7.7440
2000110
11
11
11
11
2000110
11
11
0.5151
0.1371
0.6521
4.7580
1970175
11
11
11
11
1970175
11
11
1.5310
0.4620
1.9920
4.3130
1975180
11
11
11
11
1975180
11
11
0.7214
0.2485
0.9700
3.9030
1980185
11
11
11
11
1980185
11
11
0.5700
0.2312
0.8011
3.4650
1985190
11
11
11
11
1985190
11
11
0.3111
0.2147
0.5258
2.4490
1990195
11
11
11
11
1990195
11
11
0.3553
0.0764
0.4316
5.6520
1995100
11
11
11
11
1995100
11
11
0.6097
0.0703
0.6800
9.6720
2000105
11
11
11
11
2000105
11
11
0.6063
0.1036
0.7098
6.8540
2005110
11
11
11
11
2005110
11
11
0.4238
0.1575
0.5813
3.6910
193512010
11
11
11
11
193512010
11
11
0.5063
0.1507
0.6571
4.3590
!!
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!!
!!
!!
!!
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!!
Pane
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!!
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!193516/68
0.0008
0.0019
0.0027
1.4250
11
11
193516/68
0.0006
0.0021
0.0027
1.3160
0.3581
0.1124
0.4704
4.1860
1935145
0.0008
0.0035
0.0043
1.2150
11
11
1935145
0.0007
0.0040
0.0047
1.1710
0.1972
0.1161
0.3134
2.6990
1946155
0.0007
0.0005
0.0012
2.3700
11
11
1946155
0.0003
0.0006
0.0009
1.5170
0.1498
0.0677
0.2175
3.2130
195616/68
0.0008
0.0015
0.0024
1.5600
11
11
195616/68
0.0009
0.0015
0.0024
1.5850
0.6392
0.1449
0.7841
5.4120
1935140
0.0005
0.0053
0.0058
1.0930
11
11
1935140
0.0009
0.0060
0.0069
1.1450
0.2627
0.0980
0.3607
3.6800
1941145
0.0011
0.0014
0.0025
1.8250
11
11
1941145
0.0005
0.0016
0.0021
1.3290
0.1101
0.1376
0.2476
1.8000
1946150
0.0006
0.0003
0.0008
3.1290
11
11
1946150
0.0003
0.0004
0.0007
1.7340
0.1623
0.0742
0.2365
3.1880
1951155
0.0009
0.0008
0.0016
2.0990
11
11
1951155
0.0003
0.0008
0.0011
1.4190
0.1364
0.0612
0.1977
3.2280
1956160
0.0005
0.0006
0.0011
1.7650
11
11
1956160
0.0002
0.0006
0.0009
1.3810
0.2045
0.0953
0.2999
3.1460
196116/68
0.0011
0.0021
0.0032
1.5160
11
11
196116/68
0.0014
0.0021
0.0035
1.6360
0.9185
0.1779
1.0960
6.1620
7/196812010
0.0022
0.0016
0.0039
2.3790
11
11
7/196812010
0.0027
0.0017
0.0044
2.5860
0.7621
0.2217
0.9838
4.4370
1970180
0.0039
0.0025
0.0064
2.5280
11
11
1970180
0.0049
0.0025
0.0074
3.0070
1.3350
0.3769
1.7120
4.5430
1980190
0.0025
0.0018
0.0043
2.3880
11
11
1980190
0.0047
0.0020
0.0067
3.4000
0.6821
0.2420
0.9241
3.8190
1990100
0.0020
0.0019
0.0039
2.0790
11
11
1990100
0.0019
0.0021
0.0039
1.8990
0.6143
0.1061
0.7204
6.7900
2000110
0.0019
0.0008
0.0027
3.4340
11
11
2000110
0.0012
0.0008
0.0020
2.6120
0.4606
0.1347
0.5953
4.4200
1970175
0.0042
0.0027
0.0069
2.5800
11
11
1970175
0.0045
0.0029
0.0074
2.5350
1.7440
0.5428
2.2870
4.2140
1975180
0.0048
0.0026
0.0074
2.8710
11
11
1975180
0.0064
0.0022
0.0086
3.9000
0.7769
0.2393
1.0160
4.2470
1980185
0.0031
0.0016
0.0047
2.9280
11
11
1980185
0.0042
0.0014
0.0056
4.0340
0.6642
0.2335
0.8977
3.8440
1985190
0.0017
0.0018
0.0034
1.9320
11
11
1985190
0.0047
0.0023
0.0071
3.0300
0.6026
0.2676
0.8702
3.2520
1990195
0.0017
0.0028
0.0045
1.6110
11
11
1990195
0.0026
0.0030
0.0056
1.8490
0.5300
0.1048
0.6349
6.0560
1995100
0.0021
0.0007
0.0029
3.9520
11
11
1995100
0.0009
0.0008
0.0017
2.1490
0.6114
0.0991
0.7105
7.1680
2000105
0.0026
0.0009
0.0035
3.8540
11
11
2000105
0.0012
0.0009
0.0021
2.3420
0.5121
0.1086
0.6207
5.7180
2005110
0.0011
0.0006
0.0017
2.6750
11
11
2005110
0.0012
0.0006
0.0018
3.1720
0.4300
0.1474
0.5773
3.9170
193512010
0.0016
0.0017
0.0034
1.9300
11
11
193512010
0.0018
0.0019
0.0037
1.9670
0.5840
0.1736
0.7576
4.3640
FF
FF
TABLE!5e:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
26
4 Conclusion
I extend the calculations of Fama and MacBeth (1973) to include data for 7/1968 through2010. I also reproduce the calculations with 5�5 dual-sorted test portfolios and compare theresults to those with the original 20 beta-sorted portfolios of Fama-MacBeth (1973). In ad-dition, I alternate between the use of a value-weighted and equal-weighted NYSE portfolioas the market portfolio proxy. I also alternate between using equal-weighted and value-weighted averages of underlying security betas and standard deviations of residuals fromsecurity-level market model regressions to construct the corresponding portfolio-level regres-sors for the cross-sectional regression (1).
I find some evidence that the results from Fama-MacBeth (1973) have weakened over time.More importantly I find that using the 5 � 5 test portfolios constructed with a dual-sorton beta and standard deviation of residuals for the underlying securities leads to resultswhich disagree with those from Fama-MacBeth (1973). In particular, I find that the coeffi-cient on the regressor measuring idiosyncratic risk in (1) is significantly different from zerofor testing periods in both 1935-6/1968 (the full sample period of Fama-MacBeth; 1973)and 7/1968-2010. Using some of the other aforementioned variations to the Fama-MacBeth(1973) approach again lead to results inconsistent with those in Fama-MacBeth (1973). Thissuggests that some of the Fama-MacBeth (1973) results may not be robust and casts somedoubt on the relatively good performance of the CAPM12. Overall the results suggest thatadditional robustness inspections would have helped reveal some of the flaws of the CAPMusing the regression specification of Fama-MacBeth (1973) without the need for more ad-vanced statistical tests. More generally, these results hint that for empirical work it maysometimes be important to reproduce the calculations with some variations in the methodused as a means of verifying the robustness of results.
12As mentioned before, this is not a “true” test of the CAPM but rather a test of some practical implicationsof the CAPM conditional on several assumptions.
27
References
[1] Black, Fischer. Capital Market Equilibrium with Restricted Borrowing, Journal of Busi-ness 45 (July 1972): 444-455.
[2] The Center for Research in Security Prices (CRSP).http://www.crsp.com .
[3] Fama, Eugene F. Foundations of Finance, 1976.
[4] Fama, Eugene F.; MacBeth, James D. Risk, Return and Equilibrium: Empirical Tests,Journal of Political Economy, Vol. 81, No. 3 (May - Jun 1973), pp 607-636.
[5] Fama, Eugene F. ; French, KennethMultifactor Explanation of Asset Pricing Anomalies,Journal of Finance, Volume 61, Issue 5, (Oct., 2006).
[6] Fama, Eugene F. ; French, KennethValue Premium and The CAPM, Journal of Finance,Volume 51, Issue 1, (Mar., 1996), 55-84.
[7] French, Kenneth. Fama-French data library.http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html.
[8] Lintner, John. The Valuation of Risk Assets and the Selection of Risky Investments inStock Portfolios and Capital Budgets, Revue of Economics and Statistics 47 (February1965): 13-37.
[9] Sharpe, William F. Capital Asset Prices: A Theory of Market Equilibrium uner Condi-tions of Risk, Journal of Finance 19 (September 1964): 425-442.
28
5 Appendix
Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11
0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.1670 0.1910 0.1732 0.0714 0.0597 0.0430 0.0266 0.0098 0.0138 0.02440.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.57980.0948 0.1058 0.1212 0.1010 0.1085 0.1014 0.1335 0.1080 0.1119 0.13300.0614 0.0645 0.0672 0.0556 0.0476 0.0589 0.0696 0.0587 0.0740 0.07330.0952 0.0952 0.0952 0.0952 0.0952 0.0952 0.0952 0.0904 0.0845 0.08450.6451 0.6775 0.7055 0.5833 0.5000 0.6180 0.7309 0.6493 0.8759 0.8668
1 1 1 1 1 1 1 1 1
0.2668 0.3387 0.6050 0.6437 0.7233 0.7665 0.7711 0.8176 0.8491 1.06000.0752 0.0332 0.0232 0.0204 0.0293 0.0385 0.0280 0.0421 0.0634 0.05120.6756 0.3854 0.4084 0.6536 0.7629 0.7734 0.7550 0.7257 0.7036 0.70410.03682 0.0747 0.0824 0.0442 0.0518 0.0617 0.0617 0.0535 0.0643 0.05910.02097 0.0586 0.0634 0.0260 0.0252 0.0294 0.0306 0.0280 0.0350 0.03220.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.0481 0.05470.4359 1.2170 1.3170 0.5403 0.5243 0.6102 0.6349 0.5818 0.7278 0.5885
1 1 1 1 1 1 1 1 1
0.3293 0.3905 0.5648 0.6610 0.7493 0.7529 0.7964 0.8250 0.8816 0.91440.0933 0.1033 0.0503 0.0449 0.0248 0.0378 0.0247 0.0347 0.0180 0.02120.2693 0.5691 0.5072 0.5770 0.5906 0.5423 0.6103 0.6881 0.7282 0.68780.03592 0.0199 0.0318 0.0351 0.0370 0.0405 0.0401 0.0412 0.0408 0.04170.0307 0.0131 0.0223 0.0228 0.0237 0.0274 0.0250 0.0230 0.0213 0.02330.0400 0.0400 0.0400 0.0400 0.0468 0.0400 0.0400 0.0400 0.0400 0.04000.7680 0.3267 0.5585 0.5708 0.5056 0.6860 0.6265 0.5748 0.5321 0.5822
1 1 1 1 1 1 1 1 1
0.3084 0.6031 0.6223 0.7743 0.7955 0.8285 0.8751 0.9072 0.9196 1.00100.0935 0.0887 0.0228 0.0649 0.0625 0.0286 0.0393 0.0451 0.0414 0.02040.7566 0.5757 0.7028 0.5930 0.6010 0.7511 0.7984 0.7489 0.6986 0.54100.03888 0.0383 0.0406 0.0444 0.0511 0.0372 0.0483 0.0478 0.0532 0.05400.01918 0.0250 0.0221 0.0283 0.0323 0.0186 0.0217 0.0239 0.0292 0.03660.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.0507 0.05070.3781 0.4921 0.4359 0.5577 0.6360 0.3659 0.4270 0.4716 0.5753 0.7205
1 1 1 1 1 1 1 1 1
0.5577 0.5824 0.6698 0.7220 0.7227 0.7386 0.7784 0.9208 0.9478 0.98250.0696 0.0358 0.0170 0.0291 0.0197 0.0236 0.0381 0.0514 0.0426 0.04350.5299 0.5245 0.5554 0.6317 0.7497 0.6908 0.7312 0.7502 0.6734 0.69040.05095 0.0489 0.0582 0.0508 0.0545 0.0561 0.0594 0.0528 0.0729 0.05210.03493 0.0337 0.0388 0.0309 0.0272 0.0312 0.0308 0.0264 0.0417 0.02900.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.05590.6244 0.6025 0.6934 0.5515 0.4870 0.5572 0.5507 0.4713 0.7446 0.5179
0.4740 0.5052 0.5535 0.6491 0.7107 0.7495 0.7911 0.8149 0.8261 0.89670.0519 0.0435 0.0219 0.0299 0.0428 0.0361 0.0669 0.0590 0.0475 0.03770.5390 0.6285 0.6055 0.6926 0.4894 0.6959 0.7222 0.6973 0.7140 0.52020.06375 0.0508 0.0474 0.0588 0.0485 0.0670 0.0647 0.0640 0.0725 0.08920.04328 0.0310 0.0298 0.0326 0.0347 0.0370 0.0341 0.0352 0.0388 0.06180.0685 0.0685 0.0685 0.0539 0.0685 0.0685 0.0685 0.0685 0.0685 0.06850.6319 0.4520 0.4346 0.6048 0.5059 0.5398 0.4982 0.5143 0.5662 0.9026
1 1 1 1 1 1 1 1 1
0.5268 0.6173 0.6201 0.6722 0.6926 0.7643 0.8083 0.8420 0.8538 0.88040.0505 0.0429 0.0297 0.0239 0.0508 0.0457 0.0464 0.0413 0.0370 0.02780.3358 0.5076 0.5185 0.5370 0.6284 0.6899 0.6255 0.6965 0.7178 0.58350.04451 0.0318 0.0428 0.0421 0.0414 0.0480 0.0563 0.0471 0.0509 0.05510.03627 0.0223 0.0297 0.0286 0.0253 0.0267 0.0344 0.0260 0.0270 0.03560.0428 0.0428 0.0428 0.0428 0.0428 0.0428 0.0428 0.0540 0.0428 0.04280.8474 0.5204 0.6940 0.6688 0.5900 0.6240 0.8047 0.4807 0.6316 0.8308
1 1 1 1 1 1 1 1 1
0.3647 0.5153 0.5914 0.6054 0.6711 0.8440 0.8632 0.9015 0.9535 0.97440.0689 0.0958 0.0698 0.0611 0.0509 0.0468 0.0325 0.0238 0.0152 0.02260.1919 0.3264 0.4397 0.4914 0.3682 0.4804 0.6637 0.5441 0.5344 0.61330.02505 0.0322 0.0300 0.0340 0.0648 0.0486 0.0446 0.0463 0.0481 0.05690.02252 0.0264 0.0225 0.0242 0.0515 0.0350 0.0259 0.0313 0.0328 0.03540.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.03470.6483 0.7598 0.6463 0.6979 1.4820 1.0080 0.7442 0.9009 0.9441 1.0180
1 1 1 1 1 1 1 1 1
0.2298 0.2360 0.2894 0.3523 0.7516 0.8021 0.8065 0.8204 0.8401 0.85780.0262 0.0762 0.0705 0.1157 0.0957 0.0800 0.0640 0.0437 0.0681 0.06740.2305 0.1471 0.3252 0.3575 0.4904 0.2743 0.3770 0.5940 0.6077 0.52080.03828 0.0388 0.0394 0.0626 0.0629 0.0611 0.0595 0.0559 0.0507 0.07870.03358 0.0358 0.0324 0.0501 0.0449 0.0520 0.0469 0.0356 0.0317 0.05450.0649 0.0649 0.0649 0.0649 0.0626 0.0626 0.0626 0.0404 0.0626 0.06270.5171 0.5516 0.4983 0.7729 0.7167 0.8308 0.7495 0.8822 0.5066 0.8684
1 1 1 1 1 1 1 1 1
0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0163 0.0848 0.0818 0.0341 0.0122 0.0096 0.0373 0.0525 0.0126 0.01940.3743 0.2956 0.3653 0.4138 0.5038 0.6303 0.2965 0.6764 0.6362 0.68060.03035 0.0254 0.0368 0.0366 0.0510 0.0364 0.0373 0.0447 0.0397 0.04510.024 0.0213 0.0294 0.0280 0.0360 0.0221 0.0313 0.0254 0.0240 0.02550.0450 0.0450 0.0450 0.0450 0.0450 0.0441 0.0450 0.0450 0.0450 0.04410.5340 0.4743 0.6530 0.6235 0.7999 0.5020 0.6963 0.5648 0.5325 0.5775
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12b:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 1 1 1 1
0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.0283 0.0198 0.0259 0.0530 0.0574 0.0583 0.0591 0.0785 0.0902 0.26830.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.5798 0.57980.1506 0.1306 0.1169 0.1360 0.1494 0.1237 0.1413 0.1335 0.1096 0.14540.0815 0.0657 0.0647 0.0815 0.0751 0.0644 0.0789 0.0606 0.0525 0.07050.0904 0.0904 0.0845 0.0904 0.0845 0.0904 0.0845 0.0845 0.0845 0.08450.9011 0.7266 0.7652 0.9010 0.8884 0.7125 0.9334 0.7175 0.6208 0.8336
1 1 1 1 1 1 1 1 1
1.0670 1.1130 1.2400 1.2900 1.2930 1.3230 1.3280 1.3300 1.4310 1.44000.0481 0.0437 0.0679 0.0458 0.0448 0.0533 0.0295 0.0592 0.0620 0.25540.7311 0.6581 0.6973 0.6882 0.7027 0.7055 0.6147 0.6351 0.7762 0.53980.0713 0.0890 0.0963 0.1009 0.0817 0.0844 0.1011 0.0928 0.0806 0.14750.0370 0.0520 0.0530 0.0564 0.0446 0.0458 0.0628 0.0561 0.0381 0.10000.0481 0.0547 0.0481 0.0481 0.0547 0.0547 0.0547 0.0547 0.0547 0.05470.7686 0.9518 1.1020 1.1710 0.8152 0.8380 1.1490 1.0260 0.6978 1.8300
1 1 1 1 1 1 1 1 1
0.9179 1.0770 1.1510 1.1910 1.2020 1.3690 1.3940 1.5160 1.5820 2.08400.0330 0.0480 0.0627 0.0505 0.0290 0.0610 0.0586 0.0732 0.0475 0.20090.6580 0.7794 0.6666 0.5686 0.5103 0.6591 0.7141 0.3799 0.7965 0.57640.0491 0.0484 0.0538 0.0527 0.0486 0.0552 0.0674 0.0738 0.0592 0.07330.0287 0.0227 0.0311 0.0346 0.0340 0.0322 0.0361 0.0581 0.0267 0.04770.0468 0.0400 0.0400 0.0468 0.0468 0.0468 0.0400 0.0468 0.0468 0.04680.6133 0.5689 0.7768 0.7392 0.7264 0.6889 0.9017 1.2420 0.5702 1.0200
1 1 1 1 1 1 1 1 1
1.0540 1.0870 1.1440 1.1820 1.1870 1.2580 1.2670 1.4850 1.5260 1.88400.0190 0.0518 0.0531 0.0577 0.0525 0.0520 0.0286 0.0536 0.0590 0.16690.7913 0.6931 0.6910 0.7351 0.7024 0.7319 0.6285 0.7422 0.5808 0.65970.0586 0.0543 0.0593 0.0569 0.0642 0.0589 0.0603 0.0711 0.0549 0.06120.0268 0.0301 0.0330 0.0293 0.0350 0.0305 0.0368 0.0361 0.0356 0.03570.0507 0.0582 0.0582 0.0507 0.0580 0.0582 0.0582 0.0580 0.0580 0.05800.5276 0.5167 0.5661 0.5774 0.6036 0.5238 0.6315 0.6218 0.6128 0.6151
1 1 1 1 1 1 1 1 1
0.9893 0.9974 1.0170 1.0190 1.0270 1.0620 1.0660 1.0900 1.3280 1.41800.0467 0.0509 0.0510 0.0595 0.0661 0.0736 0.0811 0.1053 0.0857 0.06570.6304 0.8520 0.8041 0.8538 0.6594 0.7420 0.6875 0.8346 0.8022 0.67900.0678 0.0610 0.0651 0.0700 0.0545 0.0764 0.0795 0.0730 0.0681 0.07190.0412 0.0235 0.0288 0.0268 0.0318 0.0388 0.0445 0.0297 0.0303 0.04070.0559 0.0653 0.0653 0.0559 0.0653 0.0653 0.0653 0.0650 0.0653 0.06500.7370 0.3597 0.4413 0.4783 0.4870 0.5948 0.6812 0.4567 0.4638 0.6265
0.9119 0.9925 1.0040 1.0240 1.0240 1.2080 1.2240 1.3400 1.3450 1.45400.0395 0.0809 0.0810 0.0628 0.0561 0.0604 0.0711 0.1002 0.1040 0.02160.7724 0.7283 0.8525 0.7324 0.7033 0.7958 0.8480 0.6657 0.7276 0.74050.0735 0.0665 0.0850 0.0889 0.0743 0.0970 0.0790 0.0931 0.0969 0.08760.0351 0.0346 0.0326 0.0460 0.0405 0.0439 0.0308 0.0538 0.0506 0.04460.0685 0.0539 0.0685 0.0539 0.0539 0.0539 0.0539 0.0685 0.0539 0.05390.5117 0.6423 0.4765 0.8522 0.7507 0.8129 0.5706 0.7857 0.9372 0.8274
1 1 1 1 1 1 1 1 1
0.9455 0.9898 1.0030 1.0380 1.0530 1.1030 1.1120 1.1870 1.2690 1.56800.0393 0.0139 0.0175 0.0304 0.0245 0.0353 0.0428 0.0501 0.1090 0.06140.7385 0.6304 0.6533 0.7723 0.5250 0.6694 0.7144 0.6682 0.4629 0.51320.0590 0.0532 0.0511 0.0583 0.0687 0.0499 0.0650 0.0610 0.0821 0.09110.0302 0.0324 0.0301 0.0278 0.0473 0.0287 0.0348 0.0352 0.0602 0.06350.0428 0.0540 0.0540 0.0540 0.0540 0.0540 0.0428 0.0428 0.0540 0.05400.7046 0.5994 0.5573 0.5148 0.8764 0.5321 0.8119 0.8213 1.1140 1.1770
1 1 1 1 1 1 1 1 1
0.9746 0.9797 1.0500 1.0740 1.1180 1.1300 1.1470 1.1680 1.2400 1.24600.0273 0.0361 0.0242 0.0355 0.0179 0.0274 0.0383 0.0474 0.1104 0.13100.5765 0.5451 0.5824 0.6045 0.1389 0.4995 0.5808 0.2737 0.5450 0.37720.0655 0.0692 0.0558 0.0637 0.0508 0.0714 0.0668 0.1207 0.0778 0.08750.0426 0.0467 0.0360 0.0400 0.0472 0.0505 0.0433 0.1028 0.0525 0.06910.0347 0.0347 0.0444 0.0444 0.0444 0.0444 0.0444 0.0444 0.0444 0.04441.2260 1.3440 0.8124 0.9024 1.0630 1.1380 0.9754 2.3190 1.1830 1.5570
1 1 1 1 1 1 1 1 1
0.9436 1.0240 1.0780 1.2360 1.2750 1.2820 1.3020 1.4220 1.4300 1.67000.0573 0.0461 0.0331 0.0776 0.0684 0.0426 0.0533 0.0780 0.0968 0.22040.5525 0.5833 0.5839 0.4964 0.6446 0.6085 0.6742 0.6555 0.6070 0.57820.0595 0.0603 0.0710 0.0652 0.0940 0.1102 0.0863 0.0827 0.0938 0.10170.0398 0.0389 0.0458 0.0463 0.0560 0.0689 0.0493 0.0486 0.0588 0.06610.0627 0.0628 0.0404 0.0404 0.0404 0.0628 0.0404 0.0404 0.0404 0.04040.6347 0.6192 1.1350 1.1460 1.3880 1.0970 1.2200 1.2030 1.4570 1.6360
1 1 1 1 1 1 1 1 1
0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0203 0.0197 0.0163 0.0351 0.0223 0.0328 0.0158 0.0066 0.0332 0.01820.6425 0.5224 0.6469 0.5710 0.6738 0.7202 0.6638 0.6686 0.6580 0.57990.0394 0.0546 0.0536 0.0493 0.0555 0.0525 0.0583 0.0577 0.0576 0.06450.0236 0.0377 0.0319 0.0323 0.0317 0.0278 0.0338 0.0332 0.0337 0.04180.0450 0.0320 0.0450 0.0320 0.0320 0.0320 0.0320 0.0320 0.0320 0.03200.5232 1.1780 0.7078 1.0090 0.9900 0.8674 1.0550 1.0380 1.0510 1.3070
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12b:1Equal=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
30
Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11
0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.2370 0.3565 0.3356 0.2189 0.1936 0.1798 0.1760 0.1712 0.2201 0.22800.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.64090.0798 0.1009 0.0935 0.0965 0.1111 0.1023 0.0998 0.1009 0.1010 0.10870.0478 0.0338 0.0363 0.0310 0.0486 0.0486 0.0358 0.0334 0.0374 0.03400.0907 0.0907 0.0907 0.0907 0.0907 0.0907 0.0907 0.0808 0.0808 0.08080.5275 0.3732 0.4005 0.3418 0.5355 0.5359 0.3945 0.4128 0.4624 0.4210
1 1 1 1 1 1 1 1 1
0.5290 0.8304 0.9300 1.0190 1.0480 1.1270 1.3160 1.4110 1.4840 1.50500.0163 0.0157 0.0289 0.0314 0.0060 0.0208 0.0157 0.0229 0.0350 0.03590.5719 0.7561 0.8473 0.9053 0.9344 0.8725 0.8049 0.8533 0.6512 0.70620.03975 0.0499 0.0427 0.0435 0.0440 0.0486 0.0575 0.0596 0.0630 0.06880.02601 0.0246 0.0167 0.0134 0.0113 0.0173 0.0254 0.0228 0.0372 0.03730.0541 0.0541 0.0544 0.0541 0.0544 0.0544 0.0544 0.0544 0.0544 0.05440.4811 0.4555 0.3068 0.2476 0.2070 0.3186 0.4664 0.4191 0.6835 0.6851
1 1 1 1 1 1 1 1 1
0.6639 0.8237 0.8852 0.8949 1.0530 1.0570 1.0720 1.1230 1.1680 1.28700.0189 0.0409 0.0382 0.0168 0.0474 0.0114 0.0054 0.0204 0.0191 0.04360.6283 0.7373 0.7789 0.8566 0.8291 0.9115 0.9055 0.8451 0.8364 0.87620.02298 0.0251 0.0232 0.0274 0.0338 0.0331 0.0368 0.0333 0.0393 0.03630.01401 0.0129 0.0109 0.0104 0.0140 0.0098 0.0113 0.0131 0.0159 0.01280.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.0404 0.04040.3469 0.3186 0.2697 0.2565 0.3461 0.2435 0.2800 0.3240 0.3932 0.3163
1 1 1 1 1 1 1 1 1
0.4917 0.5419 0.7179 0.7376 0.7852 0.8959 0.9459 0.9474 0.9681 0.98980.0375 0.0237 0.0818 0.0306 0.0307 0.0523 0.0614 0.0235 0.0301 0.03330.7813 0.8043 0.8517 0.8915 0.8830 0.7752 0.8350 0.8133 0.8059 0.84380.03373 0.0341 0.0345 0.0359 0.0374 0.0408 0.0410 0.0398 0.0441 0.04490.01577 0.0151 0.0133 0.0118 0.0128 0.0193 0.0167 0.0172 0.0194 0.01770.0552 0.0552 0.0552 0.0552 0.0552 0.0552 0.0552 0.0506 0.0552 0.05060.2859 0.2732 0.2406 0.2140 0.2320 0.3505 0.3017 0.3401 0.3521 0.3505
1 1 1 1 1 1 1 1 1
0.6953 0.7497 0.8465 0.8541 0.8703 0.9791 1.0060 1.0150 1.0440 1.08700.0312 0.0240 0.0117 0.0236 0.0172 0.0279 0.0238 0.0226 0.0240 0.02950.7238 0.7875 0.7877 0.8072 0.8487 0.8646 0.8814 0.8217 0.8696 0.80920.04368 0.0407 0.0436 0.0469 0.0486 0.0453 0.0517 0.0578 0.0509 0.06140.02295 0.0187 0.0201 0.0206 0.0189 0.0167 0.0178 0.0244 0.0184 0.02680.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.0759 0.05730.3025 0.2470 0.2649 0.2714 0.2491 0.2199 0.2348 0.3216 0.2420 0.4676
0.7939 0.8983 0.9204 0.9619 0.9936 0.9944 1.0360 1.1140 1.1540 1.22400.0702 0.0546 0.0219 0.0197 0.0279 0.0153 0.0136 0.0259 0.0352 0.04410.5474 0.6395 0.7570 0.7154 0.7896 0.7917 0.8052 0.8313 0.8506 0.87440.05356 0.0520 0.0461 0.0499 0.0511 0.0559 0.0525 0.0579 0.0609 0.05580.03603 0.0312 0.0228 0.0266 0.0234 0.0255 0.0232 0.0238 0.0236 0.01980.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.0694 0.05730.5189 0.4497 0.3276 0.3833 0.3372 0.3672 0.3339 0.3425 0.3393 0.3453
1 1 1 1 1 1 1 1 1
0.6761 0.7001 0.8386 0.8839 0.9171 0.9599 1.0020 1.0170 1.0250 1.08100.0193 0.0255 0.0483 0.0540 0.0079 0.0131 0.0110 0.0098 0.0094 0.01410.6736 0.6442 0.8487 0.8661 0.8926 0.8462 0.8583 0.8888 0.8850 0.82390.02831 0.0300 0.0360 0.0390 0.0395 0.0389 0.0403 0.0422 0.0486 0.04700.01618 0.0179 0.0140 0.0143 0.0129 0.0152 0.0152 0.0141 0.0165 0.01970.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.0448 0.05350.3609 0.3986 0.3125 0.3181 0.2885 0.3401 0.3387 0.3140 0.3679 0.3693
1 1 1 1 1 1 1 1 1
0.4389 0.5208 0.6935 0.7940 0.7989 0.9664 1.0210 1.0260 1.0530 1.07900.0143 0.0162 0.0485 0.0082 0.0606 0.0215 0.0041 0.0034 0.0082 0.01380.5295 0.5258 0.6500 0.7772 0.6086 0.7697 0.8501 0.8392 0.6635 0.62610.02586 0.0299 0.0287 0.0337 0.0369 0.0410 0.0421 0.0393 0.0438 0.04810.01774 0.0206 0.0170 0.0159 0.0231 0.0197 0.0163 0.0158 0.0254 0.02940.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0498 0.0458 0.0458 0.04580.3565 0.4143 0.3414 0.3200 0.4637 0.3950 0.3275 0.3437 0.5541 0.6422
1 1 1 1 1 1 1 1 1
0.3921 0.4585 0.5013 0.6583 0.7675 0.8564 0.8583 0.8936 0.9670 0.97970.0616 0.0631 0.0438 0.0728 0.0173 0.0352 0.0414 0.0394 0.0518 0.04580.0895 0.1464 0.1993 0.3379 0.5999 0.7332 0.5816 0.6168 0.6026 0.72630.01992 0.0298 0.0371 0.0453 0.0485 0.0432 0.0455 0.0461 0.0466 0.05230.01901 0.0275 0.0332 0.0369 0.0307 0.0223 0.0294 0.0285 0.0294 0.02730.1023 0.1023 0.1032 0.1007 0.1020 0.1010 0.1010 0.1013 0.0982 0.09840.1859 0.2690 0.3212 0.3665 0.3008 0.2208 0.2912 0.2817 0.2988 0.2779
1 1 1 1 1 1 1 1 1
0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0123 0.0144 0.0352 0.0156 0.0672 0.0522 0.0495 0.0367 0.0371 0.03810.2621 0.3597 0.3541 0.5611 0.6257 0.6987 0.6983 0.6988 0.7286 0.77240.03163 0.0246 0.0305 0.0297 0.0368 0.0341 0.0328 0.0326 0.0371 0.03950.02717 0.0197 0.0245 0.0197 0.0225 0.0187 0.0180 0.0179 0.0193 0.01880.0542 0.0542 0.0542 0.0542 0.0541 0.0541 0.0545 0.0545 0.0545 0.05450.5011 0.3630 0.4517 0.3624 0.4154 0.3456 0.3304 0.3277 0.3542 0.3458
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12c:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(�p,t�1)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
31
1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 1 1 1 1
0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.2397 0.2268 0.2138 0.2025 0.1905 0.2091 0.2051 0.1946 0.1897 0.23460.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.6409 0.64090.1162 0.1178 0.1176 0.1185 0.0998 0.1169 0.1231 0.1178 0.1265 0.12920.0427 0.0335 0.0486 0.0459 0.0353 0.0389 0.0525 0.0392 0.0406 0.04130.0808 0.0878 0.0878 0.0808 0.0878 0.0878 0.0878 0.0878 0.0878 0.08780.5286 0.3815 0.5536 0.5673 0.4025 0.4428 0.5976 0.4467 0.4626 0.4705
1 1 1 1 1 1 1 1 1
1.5420 1.5720 1.5930 1.6850 1.8110 1.9060 1.9210 1.9700 2.0320 2.11600.0194 0.0238 0.0178 0.0177 0.0587 0.0397 0.0213 0.0307 0.0208 0.04890.7189 0.7290 0.7719 0.6975 0.7670 0.5981 0.7052 0.6380 0.5798 0.61150.0686 0.0672 0.0670 0.0701 0.0715 0.0871 0.0793 0.1008 0.0986 0.10590.0363 0.0350 0.0320 0.0385 0.0345 0.0552 0.0430 0.0607 0.0639 0.06600.0544 0.0544 0.0561 0.0561 0.0561 0.0561 0.0561 0.0561 0.0561 0.05610.6676 0.6431 0.5708 0.6874 0.6158 0.9848 0.7675 1.0820 1.1400 1.1770
1 1 1 1 1 1 1 1 1
1.3320 1.3520 1.4090 1.4290 1.5350 1.7040 1.7040 1.7510 1.8230 1.85700.0538 0.0427 0.0580 0.0442 0.0694 0.0983 0.0870 0.0725 0.0921 0.09310.8244 0.8385 0.7454 0.7816 0.7566 0.8506 0.7901 0.6184 0.7302 0.57700.0392 0.0402 0.0414 0.0437 0.0466 0.0479 0.0490 0.0532 0.0549 0.05650.0164 0.0162 0.0209 0.0204 0.0230 0.0185 0.0224 0.0329 0.0285 0.03680.0404 0.0443 0.0443 0.0443 0.0404 0.0443 0.0443 0.0443 0.0443 0.04430.4065 0.3649 0.4717 0.4615 0.5688 0.4187 0.5066 0.7426 0.6435 0.8304
1 1 1 1 1 1 1 1 1
1.0560 1.0640 1.0750 1.0910 1.1180 1.1340 1.1370 1.1620 1.2450 1.33100.0398 0.0314 0.0132 0.0144 0.0164 0.0162 0.0127 0.0228 0.0190 0.02980.8210 0.8637 0.8030 0.8316 0.8103 0.8010 0.7964 0.8149 0.7631 0.73740.0439 0.0449 0.0481 0.0473 0.0476 0.0466 0.0482 0.0516 0.0579 0.05630.0186 0.0166 0.0213 0.0194 0.0207 0.0208 0.0218 0.0222 0.0282 0.02880.0552 0.0506 0.0552 0.0506 0.0506 0.0552 0.0552 0.0506 0.0506 0.05060.3366 0.3276 0.3868 0.3838 0.4093 0.3763 0.3943 0.4389 0.5573 0.5697
1 1 1 1 1 1 1 1 1
1.1040 1.1160 1.1250 1.1530 1.1540 1.1610 1.2220 1.3100 1.3270 1.40900.0294 0.0268 0.0300 0.0318 0.0375 0.0399 0.0319 0.0491 0.0562 0.05150.8662 0.8317 0.8716 0.8280 0.8959 0.8700 0.8485 0.8515 0.8464 0.82680.0568 0.0532 0.0548 0.0576 0.0589 0.0590 0.0586 0.0593 0.0663 0.06260.0208 0.0218 0.0196 0.0239 0.0190 0.0213 0.0228 0.0229 0.0260 0.02610.0759 0.0759 0.0573 0.0573 0.0759 0.0573 0.0573 0.0573 0.0563 0.05630.2739 0.2878 0.3424 0.4169 0.2505 0.3711 0.3981 0.3987 0.4622 0.4630
1.2600 1.2830 1.2890 1.3010 1.3180 1.3650 1.4250 1.4570 1.6480 1.75200.0537 0.0588 0.0524 0.0536 0.0389 0.0469 0.0519 0.0541 0.0916 0.09330.7906 0.7829 0.7752 0.8239 0.7682 0.7988 0.7861 0.7491 0.6596 0.66570.0675 0.0671 0.0660 0.0673 0.0689 0.0755 0.0723 0.0773 0.0850 0.09480.0309 0.0313 0.0313 0.0282 0.0332 0.0339 0.0334 0.0387 0.0496 0.05480.0694 0.0694 0.0694 0.0573 0.0573 0.0573 0.0573 0.0573 0.0573 0.05730.4450 0.4501 0.4509 0.4932 0.5794 0.5913 0.5835 0.6763 0.8659 0.9571
1 1 1 1 1 1 1 1 1
1.1030 1.1170 1.1270 1.1660 1.2140 1.2200 1.2730 1.3260 1.3600 1.55800.0140 0.0084 0.0069 0.0184 0.0129 0.0100 0.0158 0.0265 0.0355 0.02190.8952 0.8975 0.8460 0.8246 0.8718 0.8138 0.7459 0.7626 0.8038 0.75330.0483 0.0450 0.0469 0.0483 0.0479 0.0508 0.0521 0.0513 0.0578 0.06070.0156 0.0144 0.0184 0.0202 0.0172 0.0219 0.0263 0.0250 0.0256 0.03020.0448 0.0535 0.0448 0.0448 0.0535 0.0535 0.0535 0.0535 0.0535 0.05350.3487 0.2696 0.4110 0.4511 0.3210 0.4103 0.4913 0.4675 0.4786 0.5643
1 1 1 1 1 1 1 1 1
1.1070 1.1140 1.1210 1.1240 1.1800 1.1870 1.2320 1.2380 1.2570 1.31000.0239 0.0225 0.0231 0.0088 0.0150 0.0143 0.0244 0.0199 0.0288 0.02700.7705 0.7266 0.6294 0.6039 0.1712 0.7101 0.5851 0.6291 0.5460 0.48560.0415 0.0456 0.0478 0.0489 0.0587 0.0488 0.0499 0.0528 0.0548 0.06750.0199 0.0239 0.0291 0.0308 0.0534 0.0263 0.0322 0.0322 0.0369 0.04840.0458 0.0458 0.0458 0.0458 0.0444 0.0458 0.0444 0.0444 0.0444 0.04440.4333 0.5205 0.6350 0.6724 1.2030 0.5734 0.7244 0.7241 0.8312 1.0900
1 1 1 1 1 1 1 1 1
0.9868 0.9912 1.0120 1.0800 1.1630 1.1800 1.2010 1.2270 1.2410 1.42800.0370 0.0210 0.0259 0.0357 0.0500 0.0486 0.0480 0.0466 0.0123 0.03390.7317 0.6747 0.6446 0.6843 0.6848 0.6764 0.6974 0.6340 0.6353 0.67580.0539 0.0472 0.0586 0.0624 0.0720 0.0659 0.0620 0.0654 0.0734 0.08040.0279 0.0269 0.0350 0.0351 0.0404 0.0375 0.0341 0.0396 0.0443 0.04580.1014 0.0594 0.0594 0.1014 0.0594 0.0580 0.0588 0.0588 0.0588 0.05880.2754 0.4537 0.5886 0.3456 0.6810 0.6466 0.5794 0.6723 0.7532 0.7780
1 1 1 1 1 1 1 1 1
0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0393 0.0522 0.0646 0.0454 0.0605 0.0637 0.0977 0.1123 0.0587 0.05440.8442 0.7029 0.7349 0.8028 0.8241 0.7042 0.7414 0.8081 0.7778 0.77950.0421 0.0379 0.0400 0.0413 0.0449 0.0459 0.0441 0.0473 0.0487 0.05640.0166 0.0207 0.0206 0.0184 0.0188 0.0250 0.0224 0.0207 0.0229 0.02650.0533 0.0533 0.0409 0.0411 0.0405 0.0405 0.0405 0.0405 0.0405 0.04040.3118 0.3881 0.5033 0.4466 0.4645 0.6154 0.5536 0.5105 0.5657 0.6560
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12c:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
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32
Statistics 1 2 3 4 5 6 7 8 9 101 1 1 1 1 1 1 1 1 11
0.2429 0.2938 0.3493 0.5820 0.6477 0.7326 0.7416 0.8639 0.8960 0.89700.1763 0.2919 0.2994 0.1914 0.1908 0.2014 0.1780 0.1756 0.1832 0.18940.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.54750.0949 0.1112 0.1055 0.1161 0.1185 0.1106 0.1249 0.1148 0.1134 0.13140.0638 0.0703 0.0702 0.0585 0.0654 0.0735 0.0754 0.0613 0.0720 0.07610.1152 0.1152 0.1152 0.1152 0.1152 0.1089 0.1152 0.1152 0.0885 0.10890.5542 0.6105 0.6093 0.5078 0.5675 0.6754 0.6545 0.5319 0.8136 0.6995
1 1 1 1 1 1 1 1 1
0.6907 0.7579 0.7992 1.0160 1.0280 1.2490 1.2990 1.3500 1.4260 1.44500.1303 0.0402 0.0315 0.0708 0.0724 0.0813 0.0550 0.0562 0.0552 0.05730.3996 0.3970 0.5800 0.6321 0.6258 0.7861 0.6356 0.7520 0.5351 0.51310.04332 0.0821 0.0512 0.0507 0.0582 0.0521 0.0612 0.0615 0.0649 0.07410.03357 0.0637 0.0332 0.0307 0.0356 0.0241 0.0369 0.0306 0.0443 0.05170.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.0464 0.04640.7241 1.3750 0.7157 0.6627 0.7679 0.5200 0.7964 0.6607 0.9546 1.1150
1 1 1 1 1 1 1 1 1
0.4036 0.7557 0.8834 0.9378 0.9882 1.0020 1.1100 1.1270 1.2070 1.29200.0895 0.0883 0.0503 0.0496 0.0606 0.0154 0.0395 0.0317 0.0464 0.06430.3093 0.4507 0.5238 0.6160 0.6631 0.7381 0.4884 0.5486 0.6369 0.67710.03506 0.0251 0.0276 0.0337 0.0420 0.0402 0.0407 0.0377 0.0457 0.04110.02914 0.0186 0.0191 0.0209 0.0244 0.0206 0.0291 0.0253 0.0276 0.02340.0451 0.0451 0.0451 0.0451 0.0451 0.0479 0.0451 0.0478 0.0451 0.04510.6460 0.4125 0.4229 0.4635 0.5405 0.4295 0.6450 0.5295 0.6108 0.5178
1 1 1 1 1 1 1 1 1
0.3692 0.5439 0.5548 0.7022 0.7401 0.8784 0.8991 1.0010 1.0080 1.00900.1063 0.0407 0.0326 0.0502 0.0137 0.0503 0.0571 0.0809 0.0702 0.06670.6838 0.6043 0.6176 0.7301 0.5911 0.5519 0.6817 0.6059 0.5960 0.66540.04185 0.0384 0.0476 0.0361 0.0429 0.0531 0.0497 0.0468 0.0518 0.05770.02353 0.0241 0.0295 0.0187 0.0274 0.0356 0.0281 0.0294 0.0329 0.03340.0581 0.0581 0.0581 0.0581 0.0581 0.0581 0.0581 0.0552 0.0552 0.05810.4049 0.4151 0.5067 0.3224 0.4716 0.6120 0.4828 0.5319 0.5959 0.5744
1 1 1 1 1 1 1 1 1
0.5734 0.6521 0.8431 0.8757 0.9168 0.9565 1.0080 1.0220 1.0260 1.06400.0729 0.0538 0.0282 0.0258 0.0423 0.0444 0.0307 0.0242 0.0257 0.01480.6108 0.5302 0.5707 0.6686 0.6316 0.7285 0.6185 0.5459 0.7113 0.54690.05569 0.0586 0.0525 0.0535 0.0586 0.0535 0.0573 0.0690 0.0642 0.06660.03474 0.0402 0.0344 0.0308 0.0356 0.0279 0.0354 0.0465 0.0345 0.04490.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.0719 0.07190.4834 0.5589 0.4787 0.4288 0.4948 0.3880 0.4928 0.6465 0.4801 0.6241
0.6564 0.8040 0.8971 0.9254 0.9677 1.0400 1.0690 1.0930 1.1270 1.20200.0315 0.0666 0.0343 0.0320 0.0310 0.0248 0.0289 0.0322 0.0423 0.04780.3181 0.5747 0.6134 0.5198 0.5941 0.5150 0.6161 0.7174 0.6042 0.62100.0696 0.0525 0.0467 0.0610 0.0590 0.0738 0.0544 0.0631 0.0907 0.08200.05748 0.0342 0.0291 0.0422 0.0376 0.0514 0.0337 0.0336 0.0571 0.05050.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0696 0.0599 0.06960.9600 0.5713 0.4854 0.7056 0.6281 0.8583 0.5628 0.4820 0.9536 0.7250
1 1 1 1 1 1 1 1 1
0.7104 0.7611 0.8536 0.9193 0.9682 0.9778 0.9893 0.9980 1.0020 1.08700.0640 0.0253 0.0496 0.0351 0.0674 0.0401 0.0479 0.0493 0.0406 0.04030.3757 0.3402 0.6337 0.7240 0.6013 0.6164 0.6932 0.7031 0.5678 0.55820.04095 0.0355 0.0416 0.0443 0.0531 0.0473 0.0455 0.0528 0.0527 0.05790.03235 0.0289 0.0252 0.0233 0.0335 0.0293 0.0252 0.0288 0.0346 0.03850.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0391 0.0570 0.03910.8271 0.7378 0.6439 0.5953 0.8565 0.7492 0.6437 0.7360 0.6072 0.9832
1 1 1 1 1 1 1 1 1
0.4015 0.5794 0.6091 0.7069 0.8113 0.8413 0.9452 0.9677 0.9770 1.06700.0503 0.0706 0.0689 0.0345 0.0899 0.0849 0.0746 0.0337 0.0443 0.01660.3030 0.4550 0.5382 0.5049 0.2510 0.4264 0.6303 0.6387 0.5314 0.49920.02638 0.0338 0.0281 0.0377 0.0517 0.0578 0.0484 0.0456 0.0539 0.05890.02202 0.0250 0.0191 0.0265 0.0447 0.0438 0.0294 0.0274 0.0369 0.04170.0429 0.0429 0.0429 0.0429 0.0355 0.0429 0.0429 0.0429 0.0355 0.04630.5133 0.5823 0.4454 0.6180 1.2580 1.0210 0.6853 0.6382 1.0370 0.9003
1 1 1 1 1 1 1 1 1
0.3242 0.3928 0.4614 0.5923 0.6126 0.6610 0.7742 0.7779 0.8698 0.97860.0656 0.0437 0.0528 0.0403 0.0699 0.0475 0.0498 0.0505 0.0185 0.04280.1058 0.1889 0.1453 0.2601 0.3717 0.4622 0.3615 0.4389 0.3134 0.41840.03297 0.0430 0.0618 0.0529 0.0707 0.0577 0.0493 0.0571 0.0668 0.06200.03117 0.0387 0.0571 0.0455 0.0561 0.0423 0.0394 0.0428 0.0554 0.04730.0858 0.0822 0.0853 0.0853 0.0740 0.0856 0.0823 0.0823 0.0765 0.08210.3635 0.4710 0.6698 0.5333 0.7578 0.4944 0.4791 0.5200 0.7235 0.5759
1 1 1 1 1 1 1 1 1
0.2320 0.2843 0.3283 0.4210 0.6107 0.6318 0.6396 0.7380 0.8787 0.92050.0374 0.0307 0.0117 0.0513 0.0331 0.0028 0.1039 0.0671 0.0170 0.01610.1926 0.2473 0.2113 0.4225 0.4154 0.5501 0.4451 0.3997 0.3470 0.43850.03871 0.0301 0.0385 0.0339 0.0420 0.0479 0.0342 0.0393 0.0424 0.04750.03478 0.0261 0.0342 0.0257 0.0321 0.0321 0.0255 0.0304 0.0343 0.03560.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0461 0.0452 0.0443 0.04610.7557 0.5672 0.7433 0.5594 0.6978 0.6985 0.5533 0.6737 0.7748 0.7723
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12d:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=10)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
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33
1 1 1 1 1 1 1 1 1Statistics 11 12 13 14 15 16 17 18 19 20
1 1 1 1 1 1 1 1 1
0.9502 1.0090 1.0970 1.1640 1.1920 1.2490 1.3510 1.3570 1.3880 1.46100.2156 0.2127 0.2058 0.2172 0.2292 0.2414 0.2177 0.3308 0.4062 0.85380.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.5475 0.54750.1413 0.1210 0.1227 0.1207 0.1011 0.1544 0.1149 0.1235 0.1222 0.13870.0728 0.0618 0.0559 0.0668 0.0475 0.0939 0.0625 0.0605 0.0660 0.06750.0885 0.1089 0.1089 0.0885 0.0885 0.0885 0.0885 0.1089 0.0885 0.08850.8228 0.5677 0.5137 0.7550 0.5373 1.0620 0.7064 0.5554 0.7457 0.7631
1 1 1 1 1 1 1 1 1
1.4870 1.6080 1.6980 1.7210 1.7550 1.7680 1.7910 1.8160 2.0810 2.15700.0405 0.0350 0.0461 0.0501 0.0667 0.0754 0.0609 0.0876 0.0630 0.09870.3442 0.3915 0.4504 0.6082 0.5329 0.5017 0.4693 0.4700 0.6505 0.35420.0944 0.0753 0.0873 0.0833 0.0687 0.0900 0.0963 0.1029 0.0878 0.13610.0764 0.0587 0.0647 0.0521 0.0470 0.0635 0.0702 0.0750 0.0519 0.10940.0464 0.0541 0.0541 0.0464 0.0541 0.0541 0.0541 0.0541 0.0541 0.05411.6490 1.0870 1.1980 1.1240 0.8686 1.1750 1.2980 1.3870 0.9599 2.0230
1 1 1 1 1 1 1 1 1
1.3050 1.3490 1.4580 1.4820 1.6730 1.7020 1.7910 1.8840 1.8900 1.96600.0313 0.0323 0.0629 0.0708 0.1028 0.1077 0.1271 0.1505 0.1305 0.07420.6004 0.7015 0.4378 0.6820 0.5855 0.6008 0.3641 0.3005 0.5035 0.43070.0422 0.0453 0.0488 0.0568 0.0556 0.0544 0.0691 0.0679 0.0580 0.06680.0267 0.0247 0.0366 0.0320 0.0358 0.0344 0.0551 0.0568 0.0409 0.05040.0451 0.0451 0.0478 0.0451 0.0479 0.0478 0.0478 0.0451 0.0478 0.04790.5919 0.5483 0.7649 0.7101 0.7476 0.7181 1.1520 1.2580 0.8539 1.0530
1 1 1 1 1 1 1 1 1
1.0180 1.0280 1.0330 1.0440 1.0800 1.1530 1.3170 1.3390 1.4220 1.61700.0452 0.0528 0.0474 0.0529 0.0480 0.0468 0.0559 0.0554 0.0802 0.14040.5765 0.6170 0.6668 0.6704 0.6153 0.4737 0.6798 0.6021 0.5173 0.56060.0594 0.0517 0.0555 0.0611 0.0535 0.0725 0.0479 0.0622 0.0608 0.06350.0387 0.0320 0.0321 0.0351 0.0332 0.0526 0.0271 0.0392 0.0422 0.04210.0552 0.0581 0.0552 0.0581 0.0581 0.0581 0.0552 0.0552 0.0552 0.05520.6999 0.5508 0.5803 0.6033 0.5709 0.9045 0.4907 0.7099 0.7645 0.7615
1 1 1 1 1 1 1 1 1
1.0840 1.0900 1.0900 1.1050 1.1250 1.1890 1.2210 1.4170 1.4190 1.42500.0442 0.0432 0.0416 0.0355 0.0765 0.0759 0.0652 0.0492 0.0671 0.07760.6996 0.7167 0.7357 0.6918 0.7030 0.7529 0.7188 0.6459 0.6806 0.67150.0718 0.0612 0.0583 0.0727 0.0598 0.0660 0.0702 0.0586 0.0650 0.06780.0393 0.0326 0.0300 0.0404 0.0326 0.0328 0.0372 0.0349 0.0367 0.03890.0719 0.0564 0.0564 0.0554 0.0564 0.0564 0.0564 0.0564 0.0719 0.05540.5473 0.5782 0.5320 0.7290 0.5784 0.5824 0.6608 0.6191 0.5112 0.7021
1.2290 1.3280 1.3650 1.3710 1.3910 1.4630 1.4720 1.6250 1.6970 1.75900.0379 0.0491 0.0577 0.0635 0.0633 0.0806 0.0603 0.0917 0.1352 0.05440.5655 0.5657 0.6568 0.6481 0.7381 0.6845 0.6439 0.5189 0.6905 0.49270.0893 0.0800 0.0645 0.0775 0.0773 0.0839 0.0812 0.0830 0.0832 0.09770.0589 0.0527 0.0378 0.0460 0.0396 0.0471 0.0485 0.0576 0.0463 0.06960.0696 0.0599 0.0696 0.0599 0.0599 0.0696 0.0599 0.0696 0.0696 0.06960.8454 0.8800 0.5430 0.7684 0.6610 0.6771 0.8097 0.8271 0.6650 0.9992
1 1 1 1 1 1 1 1 1
1.1070 1.1190 1.1200 1.1760 1.1760 1.1780 1.3170 1.3310 1.3980 1.40900.0349 0.0219 0.0100 0.0190 0.0333 0.0320 0.0512 0.0894 0.0998 0.12850.5428 0.5819 0.6524 0.5426 0.7114 0.7325 0.5689 0.3774 0.5859 0.51690.0585 0.0491 0.0632 0.0531 0.0519 0.0586 0.0617 0.0704 0.0656 0.09080.0396 0.0318 0.0373 0.0359 0.0279 0.0303 0.0405 0.0555 0.0422 0.06310.0570 0.0570 0.0391 0.0391 0.0570 0.0570 0.0391 0.0570 0.0570 0.05700.6942 0.5572 0.9527 0.9188 0.4889 0.5315 1.0360 0.9737 0.7405 1.1070
1 1 1 1 1 1 1 1 1
1.0930 1.1030 1.1190 1.1350 1.1650 1.1750 1.2050 1.2120 1.2410 1.32000.0187 0.0154 0.0217 0.0160 0.0139 0.0242 0.0246 0.0333 0.0584 0.15180.5328 0.2693 0.4001 0.4531 0.0756 0.4872 0.2704 0.3962 0.1908 0.36130.0606 0.0651 0.0590 0.0603 0.1061 0.0630 0.0542 0.0705 0.0602 0.07550.0415 0.0556 0.0457 0.0446 0.1020 0.0451 0.0463 0.0548 0.0542 0.06030.0355 0.0463 0.0355 0.0464 0.0464 0.0355 0.0464 0.0463 0.0463 0.04631.1660 1.2010 1.2860 0.9609 2.1980 1.2690 0.9971 1.1840 1.1700 1.3030
1 1 1 1 1 1 1 1 1
1.0320 1.0940 1.1270 1.1280 1.1400 1.1500 1.1880 1.3350 1.3820 1.41800.0590 0.0668 0.0585 0.0539 0.0446 0.0463 0.0537 0.0925 0.0633 0.08360.5637 0.2128 0.4912 0.4206 0.5153 0.5285 0.3798 0.3056 0.3472 0.44960.0621 0.0624 0.0761 0.0663 0.0931 0.0752 0.0843 0.0946 0.0830 0.09700.0410 0.0554 0.0543 0.0505 0.0648 0.0517 0.0664 0.0789 0.0671 0.07200.0376 0.0376 0.0376 0.0740 0.0402 0.0765 0.0402 0.0375 0.0402 0.04021.0910 1.4720 1.4420 0.6819 1.6110 0.6750 1.6500 2.1010 1.6680 1.7890
1 1 1 1 1 1 1 1 1
0.9931 1.0500 1.0870 1.1060 1.1490 1.2170 1.2770 1.3360 1.3710 1.42900.0353 0.0437 0.0532 0.0396 0.0481 0.0580 0.1027 0.1102 0.0388 0.05100.5152 0.4914 0.6708 0.5798 0.6411 0.3481 0.6240 0.5120 0.5132 0.55680.0472 0.0476 0.0527 0.0465 0.0472 0.0504 0.0482 0.0572 0.0482 0.06390.0329 0.0340 0.0303 0.0301 0.0283 0.0407 0.0296 0.0399 0.0336 0.04260.0443 0.0461 0.0452 0.0461 0.0443 0.0443 0.0444 0.0443 0.0443 0.04430.7412 0.7370 0.6702 0.6536 0.6387 0.9191 0.6660 0.9023 0.7590 0.9613
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12d:1Value=Weighted1NYSE1Market1Portfolio111111111+1111111201Single=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios111=20)1
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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sp,t�1(ei)s(ep)/sp,t�1(ei)
34
Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11
0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.1655 0.1886 0.2127 0.1740 0.0517 0.0345 0.0289 0.0208 0.0150 0.0119 0.0088 0.0099 0.00720.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1164 0.0835 0.0637 0.0834 0.1104 0.0890 0.0958 0.1034 0.1084 0.1285 0.0978 0.1113 0.10470.0545 0.0242 0.0196 0.0243 0.0509 0.0169 0.0277 0.0226 0.0289 0.0579 0.0348 0.0332 0.02290.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0598 0.05981.0140 0.4500 0.3650 0.4520 0.9472 0.3138 0.5155 0.4213 0.5374 1.0770 0.6478 0.5552 0.3833
1 1 1 1 1 1 1 1 1 1 1 1
0.2612 0.4558 0.4567 0.6069 0.6995 0.6996 0.7051 0.7606 0.9002 0.9152 0.9486 0.9797 1.14200.0440 0.0040 0.0034 0.0112 0.0384 0.0043 0.0248 0.0179 0.0302 0.0069 0.0177 0.0261 0.04220.6997 0.8142 0.7765 0.7839 0.8552 0.9186 0.8782 0.8538 0.8844 0.8599 0.8863 0.9125 0.94460.03643 0.0411 0.0364 0.0482 0.0533 0.0443 0.0507 0.0459 0.0569 0.0594 0.0554 0.0550 0.06410.01996 0.0177 0.0172 0.0224 0.0203 0.0127 0.0177 0.0175 0.0194 0.0222 0.0187 0.0163 0.01510.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0483 0.0460 0.04830.4340 0.3849 0.3745 0.4867 0.4409 0.2748 0.3846 0.3811 0.4204 0.4829 0.3870 0.3536 0.3122
1 1 1 1 1 1 1 1 1 1 1 1
0.4506 0.4838 0.5846 0.5904 0.6644 0.6909 0.7289 0.7746 0.8179 0.8277 0.8549 0.9368 0.93830.0384 0.0370 0.0138 0.0336 0.0367 0.0307 0.0330 0.0372 0.0232 0.0304 0.0488 0.0275 0.02950.7100 0.6700 0.7000 0.8189 0.7896 0.8062 0.8623 0.8876 0.8449 0.8678 0.9234 0.9153 0.93900.02253 0.0229 0.0251 0.0235 0.0339 0.0348 0.0356 0.0351 0.0309 0.0388 0.0391 0.0372 0.03960.01213 0.0131 0.0137 0.0100 0.0156 0.0153 0.0132 0.0118 0.0122 0.0141 0.0108 0.0108 0.00980.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0389 0.0331 0.03890.3670 0.3972 0.4151 0.3024 0.4708 0.4630 0.3999 0.3565 0.3680 0.4269 0.2788 0.3274 0.2521
1 1 1 1 1 1 1 1 1 1 1 1
0.5790 0.5960 0.6217 0.6464 0.7447 0.8657 0.8691 0.8721 0.9045 0.9316 0.9847 1.0230 1.08200.0767 0.0283 0.0321 0.0145 0.0245 0.0121 0.0093 0.0156 0.0072 0.0144 0.0099 0.0168 0.03640.7842 0.8143 0.8425 0.8224 0.8730 0.9125 0.9326 0.9256 0.9235 0.8813 0.9089 0.9202 0.92140.03031 0.0345 0.0370 0.0334 0.0400 0.0348 0.0385 0.0421 0.0388 0.0419 0.0396 0.0440 0.04590.01408 0.0149 0.0147 0.0141 0.0143 0.0103 0.0100 0.0115 0.0107 0.0144 0.0119 0.0124 0.01290.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0435 0.0406 0.0406 0.0406 0.04350.3466 0.3659 0.3616 0.3464 0.3512 0.2537 0.2464 0.2824 0.2466 0.3550 0.2939 0.3064 0.2962
1 1 1 1 1 1 1 1 1 1 1 1
0.5769 0.5919 0.6742 0.6768 0.6784 0.8338 0.8363 0.8601 0.8678 0.8856 0.8879 0.9121 0.98820.0324 0.0153 0.0324 0.0248 0.0149 0.0529 0.0443 0.0420 0.0299 0.0243 0.0127 0.0154 0.01060.6408 0.6920 0.6702 0.8007 0.8441 0.7977 0.8517 0.9170 0.9269 0.9102 0.8841 0.9175 0.92990.03835 0.0409 0.0377 0.0436 0.0553 0.0388 0.0416 0.0470 0.0539 0.0704 0.0461 0.0505 0.05340.02298 0.0227 0.0216 0.0195 0.0218 0.0175 0.0160 0.0136 0.0146 0.0211 0.0157 0.0145 0.01410.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0515 0.0453 0.0515 0.04530.5076 0.5010 0.4778 0.4302 0.4820 0.3858 0.3540 0.2992 0.3214 0.4095 0.3466 0.2814 0.3120
0.4459 0.4848 0.6120 0.6449 0.6502 0.6589 0.6869 0.7484 0.8191 0.8378 0.8512 0.8781 0.88420.0503 0.0343 0.0169 0.0121 0.0197 0.0226 0.0249 0.0265 0.0149 0.0110 0.0147 0.0278 0.02120.6986 0.7524 0.8268 0.8196 0.8361 0.8506 0.9079 0.8742 0.9142 0.9472 0.9093 0.9236 0.91160.0524 0.0480 0.0482 0.0466 0.0580 0.0492 0.0523 0.0528 0.0577 0.0543 0.0575 0.0571 0.06010.02877 0.0239 0.0201 0.0198 0.0235 0.0190 0.0159 0.0187 0.0169 0.0125 0.0173 0.0158 0.01790.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.05180.5868 0.4868 0.4091 0.4032 0.4788 0.3878 0.3234 0.3821 0.3449 0.2544 0.3529 0.3220 0.3453
1 1 1 1 1 1 1 1 1 1 1 1
0.5663 0.5685 0.6048 0.6368 0.6989 0.7365 0.7461 0.7755 0.8123 0.8321 0.8338 0.8868 0.89440.0831 0.0623 0.0253 0.0164 0.0167 0.0147 0.0063 0.0153 0.0045 0.0281 0.0337 0.0306 0.03360.3503 0.3700 0.7861 0.7844 0.7333 0.6313 0.8779 0.8708 0.9046 0.8660 0.8839 0.8995 0.89190.02978 0.0304 0.0341 0.0393 0.0495 0.0359 0.0365 0.0402 0.0470 0.0474 0.0447 0.0456 0.04900.02401 0.0241 0.0158 0.0182 0.0255 0.0218 0.0128 0.0144 0.0145 0.0174 0.0152 0.0145 0.01610.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0467 0.0465 0.04650.5162 0.5183 0.3396 0.3922 0.5491 0.4690 0.2745 0.3105 0.3117 0.3730 0.3262 0.3112 0.3466
1 1 1 1 1 1 1 1 1 1 1 1
0.3768 0.3826 0.4595 0.6799 0.7064 0.7243 0.8467 0.9220 0.9564 0.9692 1.0120 1.0530 1.06300.0441 0.0239 0.0273 0.0443 0.0196 0.0574 0.0257 0.0138 0.0168 0.0128 0.0277 0.0334 0.01480.2734 0.3217 0.3434 0.5562 0.6450 0.7639 0.7830 0.7747 0.7310 0.7161 0.7984 0.8558 0.82070.02403 0.0269 0.0296 0.0330 0.0351 0.0347 0.0391 0.0403 0.0381 0.0407 0.0437 0.0432 0.04610.02048 0.0221 0.0240 0.0220 0.0209 0.0168 0.0182 0.0191 0.0198 0.0217 0.0196 0.0164 0.01950.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0436 0.0341 0.03410.6010 0.6487 0.7048 0.6444 0.6144 0.4942 0.5341 0.5612 0.5796 0.6360 0.4500 0.4808 0.5732
1 1 1 1 1 1 1 1 1 1 1 1
0.2724 0.3200 0.3237 0.4746 0.6061 0.7194 0.7586 0.7935 0.7987 0.8390 0.9370 0.9388 0.94690.0433 0.0420 0.0240 0.0428 0.0575 0.0289 0.0276 0.0413 0.0322 0.0365 0.0206 0.0243 0.02420.1808 0.2887 0.1527 0.2102 0.4903 0.7030 0.5486 0.7944 0.7368 0.5715 0.7143 0.8191 0.78820.0212 0.0370 0.0419 0.0416 0.0455 0.0421 0.0433 0.0470 0.0490 0.0551 0.0512 0.0477 0.05400.01919 0.0312 0.0386 0.0370 0.0325 0.0229 0.0291 0.0213 0.0251 0.0361 0.0274 0.0203 0.02490.0299 0.0301 0.0299 0.0299 0.0299 0.0299 0.0299 0.0300 0.0299 0.0300 0.0307 0.0300 0.03070.6409 1.0370 1.2880 1.2340 1.0860 0.7662 0.9726 0.7115 0.8390 1.2040 0.8935 0.6781 0.8108
1 1 1 1 1 1 1 1 1 1 1 1
0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0663 0.0598 0.0528 0.0240 0.0531 0.0791 0.0687 0.0348 0.0714 0.0405 0.0183 0.0085 0.00770.0419 0.2880 0.4842 0.4720 0.8177 0.6577 0.7578 0.8084 0.8059 0.6534 0.7833 0.8820 0.81030.02255 0.0272 0.0313 0.0350 0.0331 0.0295 0.0302 0.0355 0.0355 0.0425 0.0328 0.0387 0.03640.02208 0.0229 0.0225 0.0254 0.0141 0.0173 0.0149 0.0155 0.0157 0.0250 0.0153 0.0133 0.01590.0282 0.0282 0.0282 0.0281 0.0282 0.0280 0.0282 0.0281 0.0280 0.0280 0.0281 0.0315 0.02800.7823 0.8132 0.7974 0.9052 0.5004 0.6171 0.5272 0.5527 0.5598 0.8938 0.5433 0.4212 0.5674
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12e:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(ep)s(Rp)
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r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
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r(Rp, Rm)2
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sp,t�1(ei)s(ep)/sp,t�1(ei)
35
1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 1 1 1 1 1 1 1
0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0126 0.0203 0.0348 0.0436 0.0471 0.0291 0.0307 0.0337 0.0319 0.0621 0.0670 0.02790.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1174 0.1332 0.0870 0.1033 0.1396 0.1458 0.1244 0.1155 0.1232 0.1385 0.1368 0.13000.0372 0.0524 0.0286 0.0269 0.0512 0.0480 0.0506 0.0321 0.0329 0.0403 0.0396 0.04690.0537 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0615 0.05980.6930 0.8762 0.4787 0.4505 0.8563 0.8025 0.8457 0.5373 0.5496 0.6745 0.6434 0.7839
1 1 1 1 1 1 1 1 1 1 1 1
1.1690 1.1700 1.1710 1.2380 1.2500 1.2580 1.3070 1.3130 1.3470 1.4420 1.4570 1.53600.0414 0.0090 0.0156 0.0139 0.0046 0.0021 0.0172 0.0449 0.0374 0.0285 0.0365 0.03020.9067 0.8655 0.9008 0.9297 0.9178 0.8738 0.8251 0.9191 0.8072 0.8357 0.8654 0.94430.0677 0.0834 0.0764 0.0683 0.0728 0.0894 0.0913 0.0774 0.1124 0.1097 0.1099 0.08600.0207 0.0306 0.0241 0.0181 0.0209 0.0317 0.0382 0.0220 0.0493 0.0445 0.0403 0.02030.0460 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0548 0.04830.4491 0.6332 0.4984 0.3751 0.4323 0.6571 0.7906 0.4555 1.0220 0.9204 0.7365 0.4201
1 1 1 1 1 1 1 1 1 1 1 1
0.9428 1.0200 1.0510 1.0640 1.0700 1.0920 1.2640 1.3590 1.5440 1.5880 1.6180 1.62700.0305 0.0013 0.0243 0.0288 0.0328 0.0379 0.0190 0.0185 0.0742 0.0750 0.0819 0.07170.8832 0.8985 0.9538 0.9281 0.9185 0.9117 0.8472 0.9135 0.9170 0.9079 0.8377 0.72250.0365 0.0407 0.0458 0.0441 0.0462 0.0453 0.0439 0.0565 0.0547 0.0568 0.0546 0.05330.0125 0.0130 0.0098 0.0118 0.0132 0.0135 0.0172 0.0166 0.0158 0.0172 0.0220 0.02810.0331 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0433 0.0389 0.0389 0.03890.3778 0.3336 0.2534 0.3046 0.3393 0.3469 0.4418 0.4274 0.3637 0.4434 0.5659 0.7225
1 1 1 1 1 1 1 1 1 1 1 1
1.0990 1.1260 1.1590 1.1740 1.1910 1.1940 1.1950 1.3250 1.3310 1.3320 1.3360 1.36200.0318 0.0232 0.0325 0.0233 0.0161 0.0125 0.0274 0.0129 0.0245 0.0255 0.0285 0.12220.9174 0.8455 0.9003 0.9024 0.8930 0.9253 0.8874 0.8998 0.8947 0.9273 0.9129 0.80210.0447 0.0501 0.0465 0.0442 0.0465 0.0555 0.0526 0.0522 0.0579 0.0545 0.0528 0.06010.0129 0.0197 0.0147 0.0138 0.0152 0.0152 0.0177 0.0165 0.0188 0.0147 0.0156 0.02670.0435 0.0434 0.0435 0.0435 0.0435 0.0435 0.0406 0.0435 0.0435 0.0435 0.0434 0.05110.2957 0.4533 0.3379 0.3174 0.3499 0.3488 0.4344 0.3799 0.4320 0.3379 0.3588 0.5225
1 1 1 1 1 1 1 1 1 1 1 1
0.9958 1.0040 1.1150 1.1350 1.1480 1.1500 1.1730 1.1780 1.1950 1.2620 1.3200 1.37200.0111 0.0114 0.0384 0.0236 0.0109 0.0163 0.0261 0.0380 0.0344 0.0482 0.0519 0.05670.9390 0.9251 0.9185 0.9378 0.9389 0.9151 0.8907 0.8945 0.9202 0.9308 0.9212 0.91410.0562 0.0653 0.0494 0.0591 0.0552 0.0679 0.0728 0.0611 0.0623 0.0645 0.0661 0.08530.0139 0.0179 0.0141 0.0147 0.0137 0.0198 0.0241 0.0199 0.0176 0.0170 0.0186 0.02500.0515 0.0515 0.0515 0.0515 0.0453 0.0515 0.0515 0.0515 0.0515 0.0515 0.0515 0.05960.2695 0.3465 0.2737 0.2861 0.3014 0.3841 0.4669 0.3853 0.3419 0.3292 0.3601 0.4196
0.9132 0.9216 1.0090 1.0380 1.0550 1.1270 1.1550 1.1720 1.2630 1.3490 1.3560 1.40100.0151 0.0218 0.0141 0.0215 0.0154 0.0290 0.0283 0.0264 0.0218 0.0451 0.0248 0.03310.9194 0.9133 0.9175 0.9225 0.9500 0.9596 0.8927 0.9319 0.9433 0.9206 0.9205 0.86740.0691 0.0720 0.0644 0.0688 0.0684 0.0759 0.0795 0.0776 0.0826 0.0825 0.0981 0.09030.0196 0.0212 0.0185 0.0192 0.0153 0.0153 0.0260 0.0203 0.0197 0.0232 0.0277 0.03290.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.05800.3790 0.4097 0.3575 0.3699 0.2956 0.2947 0.5029 0.3913 0.3798 0.4488 0.5345 0.5670
1 1 1 1 1 1 1 1 1 1 1 1
0.9534 0.9700 0.9831 1.0010 1.0560 1.0630 1.1800 1.1830 1.2470 1.2510 1.3130 1.47700.0215 0.0199 0.0232 0.0245 0.0153 0.0425 0.0077 0.0135 0.0064 0.0303 0.0284 0.05630.9158 0.9024 0.9144 0.9238 0.9172 0.8773 0.8885 0.8873 0.9168 0.7976 0.8603 0.85760.0479 0.0484 0.0491 0.0456 0.0466 0.0491 0.0516 0.0491 0.0548 0.0532 0.0562 0.07350.0139 0.0151 0.0144 0.0126 0.0134 0.0172 0.0172 0.0165 0.0158 0.0239 0.0210 0.02770.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.05430.2976 0.3244 0.3077 0.2696 0.2873 0.3688 0.3691 0.3531 0.3388 0.5131 0.4506 0.5106
1 1 1 1 1 1 1 1 1 1 1 1
1.0730 1.0800 1.0810 1.0980 1.1000 1.1040 1.1340 1.1710 1.1890 1.2810 1.2890 1.30700.0202 0.0201 0.0188 0.0102 0.0099 0.0130 0.0076 0.0169 0.0135 0.0278 0.0248 0.03600.8080 0.8183 0.8234 0.8309 0.7904 0.8261 0.6210 0.8839 0.8346 0.7953 0.3198 0.69490.0473 0.0509 0.0500 0.0489 0.0438 0.0521 0.0631 0.0576 0.0581 0.0654 0.0690 0.06910.0207 0.0217 0.0210 0.0201 0.0201 0.0218 0.0389 0.0196 0.0236 0.0296 0.0569 0.03810.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0438 0.0438 0.0438 0.0438 0.0438 0.04350.4753 0.4976 0.4811 0.4603 0.4594 0.4983 0.8875 0.4481 0.5399 0.6752 1.3000 0.8767
1 1 1 1 1 1 1 1 1 1 1 1
0.9583 0.9779 1.0060 1.0280 1.1340 1.1710 1.2190 1.2580 1.3030 1.3210 1.4670 1.53800.0308 0.0324 0.0506 0.0482 0.0380 0.0361 0.0300 0.0323 0.0283 0.0208 0.0536 0.05290.8517 0.8205 0.7949 0.8326 0.8120 0.8547 0.7467 0.8685 0.8354 0.8698 0.8049 0.74490.0492 0.0557 0.0642 0.0656 0.0699 0.0627 0.0715 0.0707 0.0666 0.0767 0.0787 0.08680.0190 0.0236 0.0291 0.0269 0.0303 0.0239 0.0360 0.0257 0.0270 0.0277 0.0348 0.04380.0307 0.0300 0.0311 0.0311 0.0311 0.0311 0.0311 0.0311 0.0307 0.0311 0.0311 0.05050.6184 0.7881 0.9354 0.8642 0.9748 0.7693 1.1580 0.8256 0.8816 0.8911 1.1190 0.8680
1 1 1 1 1 1 1 1 1 1 1 1
0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0193 0.0207 0.0103 0.0062 0.0044 0.0190 0.0193 0.0232 0.0216 0.0240 0.0254 0.11590.8766 0.8306 0.7733 0.8334 0.8747 0.8831 0.8094 0.8624 0.8533 0.8384 0.8522 0.78390.0423 0.0499 0.0386 0.0503 0.0496 0.0476 0.0512 0.0511 0.0467 0.0506 0.0508 0.06690.0149 0.0205 0.0184 0.0205 0.0176 0.0163 0.0224 0.0190 0.0179 0.0203 0.0195 0.03110.0317 0.0315 0.0315 0.0317 0.0317 0.0317 0.0318 0.0318 0.0318 0.0318 0.0318 0.04370.4688 0.6514 0.5828 0.6473 0.5537 0.5127 0.7028 0.5956 0.5613 0.6390 0.6135 0.7125
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12e:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)1111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
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36
Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11
0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.1374 0.1690 0.1809 0.1454 0.0473 0.0437 0.0456 0.0501 0.0416 0.0459 0.0476 0.0103 0.00720.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.47410.1519 0.0857 0.0708 0.1063 0.1113 0.0994 0.0896 0.1232 0.1131 0.1273 0.1043 0.1198 0.12170.1102 0.0429 0.0390 0.0562 0.0748 0.0507 0.0446 0.0535 0.0643 0.0686 0.0554 0.0586 0.06680.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0487 0.0604 0.0487 0.0604 0.0487 0.04872.2640 0.8812 0.8015 1.1540 1.5360 1.0410 0.9158 1.1000 1.0640 1.4090 0.9158 1.2050 1.3730
1 1 1 1 1 1 1 1 1 1 1 1
0.3084 0.4479 0.4954 0.6335 0.6474 0.6586 0.7597 0.8310 0.9167 0.9431 0.9929 1.0300 1.03100.0700 0.0425 0.0475 0.0518 0.0263 0.0409 0.0555 0.0613 0.0511 0.0449 0.0625 0.0695 0.07250.5500 0.3767 0.3692 0.3066 0.6410 0.7781 0.7405 0.5739 0.7157 0.6293 0.8318 0.4657 0.66870.04385 0.0783 0.0482 0.1254 0.0664 0.0579 0.0588 0.0496 0.0596 0.0713 0.0567 0.0780 0.06900.02941 0.0619 0.0383 0.1044 0.0398 0.0273 0.0300 0.0324 0.0318 0.0434 0.0233 0.0570 0.03970.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0559 0.0559 0.05590.6589 1.3860 0.8582 2.3390 0.8911 0.6111 0.6716 0.7259 0.7122 0.9730 0.4160 1.0200 0.7100
1 1 1 1 1 1 1 1 1 1 1 1
0.3289 0.3910 0.5092 0.6315 0.6773 0.7063 0.7634 0.7835 0.7898 0.8305 0.8733 0.8821 0.94980.0841 0.0881 0.0592 0.0220 0.0280 0.0374 0.0261 0.0296 0.0459 0.0450 0.0337 0.0397 0.02410.3800 0.2926 0.4585 0.4819 0.5108 0.6088 0.6329 0.6523 0.4673 0.5205 0.6944 0.7020 0.63810.02956 0.0296 0.0360 0.0294 0.0430 0.0405 0.0421 0.0444 0.0362 0.0395 0.0447 0.0454 0.05060.02328 0.0249 0.0265 0.0212 0.0301 0.0254 0.0255 0.0262 0.0264 0.0274 0.0247 0.0248 0.03050.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0454 0.0409 0.0454 0.0454 0.0454 0.04090.5124 0.5474 0.5828 0.4665 0.6616 0.5581 0.5611 0.5760 0.6453 0.6027 0.5436 0.5450 0.7451
1 1 1 1 1 1 1 1 1 1 1 1
0.3473 0.5078 0.6460 0.6498 0.6888 0.7229 0.9016 0.9147 0.9469 0.9627 0.9906 1.0240 1.04400.0744 0.0784 0.0803 0.0457 0.0521 0.0376 0.0484 0.0449 0.0341 0.0355 0.0185 0.0218 0.01940.6004 0.6712 0.5733 0.5605 0.6745 0.7109 0.7289 0.6992 0.6553 0.6163 0.7062 0.5894 0.56690.03479 0.0388 0.0404 0.0420 0.0494 0.0397 0.0484 0.0461 0.0488 0.0509 0.0466 0.0491 0.06410.02199 0.0223 0.0264 0.0278 0.0282 0.0214 0.0252 0.0253 0.0287 0.0316 0.0253 0.0314 0.04220.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0402 0.0442 0.0442 0.0402 0.0442 0.04020.5476 0.5541 0.6573 0.6930 0.7015 0.5319 0.6278 0.6292 0.6487 0.7142 0.6291 0.7116 1.0510
1 1 1 1 1 1 1 1 1 1 1 1
0.4853 0.5941 0.6209 0.6800 0.7138 0.7627 0.7858 0.7865 0.9102 0.9275 0.9290 0.9562 0.96420.0693 0.0342 0.0320 0.0303 0.0262 0.0351 0.0330 0.0201 0.0513 0.0543 0.0398 0.0368 0.02450.5585 0.5145 0.4710 0.7113 0.6419 0.5885 0.6577 0.6263 0.7245 0.6969 0.6892 0.7027 0.65010.04131 0.0457 0.0443 0.0511 0.0684 0.0432 0.0557 0.0537 0.0645 0.0780 0.0531 0.0644 0.06060.02745 0.0318 0.0322 0.0275 0.0410 0.0277 0.0326 0.0328 0.0339 0.0429 0.0296 0.0351 0.03580.0537 0.0537 0.0537 0.0537 0.0537 0.0537 0.0607 0.0537 0.0537 0.0537 0.0537 0.0607 0.06070.5109 0.5921 0.6000 0.5108 0.7622 0.5161 0.5367 0.6104 0.6305 0.7986 0.5505 0.5784 0.5898
0.3812 0.4045 0.4218 0.5669 0.6105 0.6900 0.7045 0.7284 0.7759 0.8313 0.8332 0.8848 0.91010.0560 0.0640 0.0720 0.0420 0.0390 0.0203 0.0477 0.0633 0.0835 0.0813 0.0827 0.0616 0.05980.6495 0.6109 0.6176 0.6372 0.4542 0.7614 0.6953 0.5537 0.7790 0.7233 0.7401 0.6174 0.57420.05952 0.0533 0.0522 0.0509 0.0687 0.0511 0.0601 0.0496 0.0757 0.0713 0.0558 0.0883 0.05940.03524 0.0333 0.0323 0.0307 0.0507 0.0250 0.0332 0.0331 0.0356 0.0375 0.0284 0.0546 0.03880.0492 0.0492 0.0492 0.0492 0.0492 0.0492 0.0492 0.0535 0.0492 0.0492 0.0492 0.0535 0.04920.7167 0.6763 0.6566 0.6241 1.0320 0.5076 0.6749 0.6195 0.7235 0.7628 0.5782 1.0210 0.7883
1 1 1 1 1 1 1 1 1 1 1 1
0.5588 0.5817 0.5931 0.6048 0.6853 0.7189 0.7325 0.7326 0.7430 0.8472 0.8697 0.8771 0.90940.0814 0.0801 0.0453 0.0469 0.0348 0.0249 0.0163 0.0314 0.0541 0.0432 0.0306 0.0280 0.03220.2291 0.2879 0.5126 0.5573 0.4842 0.4753 0.5658 0.6294 0.6018 0.6754 0.7487 0.6505 0.52740.0318 0.0325 0.0443 0.0462 0.0605 0.0408 0.0466 0.0511 0.0570 0.0533 0.0528 0.0533 0.06050.02793 0.0274 0.0309 0.0308 0.0435 0.0296 0.0307 0.0311 0.0360 0.0304 0.0265 0.0315 0.04160.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0456 0.0409 0.0409 0.04560.6120 0.6012 0.6777 0.6741 0.9523 0.6483 0.6726 0.6820 0.7889 0.6654 0.6472 0.7699 0.9108
1 1 1 1 1 1 1 1 1 1 1 1
0.3462 0.3947 0.4087 0.5533 0.6697 0.7832 0.8210 0.8251 0.9501 0.9591 0.9706 1.0170 1.02700.0592 0.0525 0.0507 0.0603 0.0461 0.0465 0.0646 0.0366 0.0516 0.0452 0.0270 0.0303 0.03580.2722 0.2517 0.2295 0.5224 0.4601 0.4360 0.6436 0.5893 0.3385 0.4518 0.5783 0.6128 0.59500.02669 0.0307 0.0304 0.0324 0.0382 0.0413 0.0465 0.0543 0.0484 0.0564 0.0534 0.0686 0.04860.02277 0.0266 0.0267 0.0224 0.0281 0.0310 0.0278 0.0348 0.0394 0.0417 0.0347 0.0427 0.03090.0326 0.0326 0.0326 0.0326 0.0326 0.0423 0.0326 0.0326 0.0326 0.0326 0.0326 0.0326 0.03260.6982 0.8142 0.8180 0.6869 0.8614 0.7330 0.8516 1.0670 1.2070 1.2800 1.0640 1.3090 0.9478
1 1 1 1 1 1 1 1 1 1 1 1
0.1992 0.2303 0.3039 0.3070 0.3135 0.6854 0.7208 0.7504 0.7550 0.8862 0.8888 0.9281 0.93060.0401 0.0521 0.0491 0.0640 0.1516 0.0602 0.0753 0.0833 0.0762 0.0521 0.0400 0.0256 0.03470.1500 0.2428 0.1662 0.1102 0.3860 0.5079 0.2293 0.4512 0.3801 0.2516 0.5662 0.6066 0.61820.02178 0.0402 0.0497 0.0473 0.0788 0.0641 0.0569 0.0581 0.0787 0.0821 0.0537 0.0661 0.06950.02008 0.0350 0.0454 0.0446 0.0617 0.0449 0.0500 0.0431 0.0620 0.0710 0.0354 0.0415 0.04300.0255 0.0255 0.0255 0.0255 0.0255 0.0255 0.0255 0.0254 0.0255 0.0254 0.0254 0.0236 0.02360.7885 1.3700 1.7830 1.7530 2.4250 1.7650 1.9630 1.6930 2.4330 2.7930 1.3910 1.7580 1.8210
1 1 1 1 1 1 1 1 1 1 1 1
0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0512 0.0437 0.0392 0.0208 0.0106 0.0186 0.0327 0.0185 0.0195 0.0090 0.0453 0.0180 0.02030.0274 0.1574 0.3596 0.4008 0.6299 0.4834 0.5618 0.4167 0.4317 0.3190 0.7289 0.6799 0.58510.02457 0.0261 0.0352 0.0412 0.0454 0.0381 0.0356 0.0443 0.0610 0.0544 0.0346 0.0460 0.04690.02423 0.0240 0.0282 0.0319 0.0276 0.0274 0.0236 0.0339 0.0460 0.0449 0.0180 0.0260 0.03020.0252 0.0252 0.0252 0.0252 0.0251 0.0252 0.0252 0.0304 0.0252 0.0251 0.0251 0.0252 0.03040.9599 0.9504 1.1160 1.2640 1.1010 1.0850 0.9365 1.1120 1.8250 1.7880 0.7179 1.0340 0.9913
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12f:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
37
1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 1 1 1 1 1 1 1
0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0355 0.0237 0.0367 0.0409 0.0466 0.0303 0.0265 0.0430 0.0533 0.0726 0.1293 0.46070.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.4741 0.47410.1397 0.1681 0.0809 0.1150 0.1580 0.1470 0.1520 0.1340 0.1319 0.1514 0.1371 0.12630.0857 0.1098 0.0424 0.0673 0.0689 0.0748 0.1074 0.0674 0.0743 0.0875 0.0632 0.05930.0604 0.0604 0.0604 0.0604 0.0487 0.0604 0.0604 0.0604 0.0604 0.0604 0.0604 0.06041.4170 1.8180 0.7014 1.1130 1.4150 1.2380 1.7780 1.1150 1.2300 1.4490 1.0460 0.9814
1 1 1 1 1 1 1 1 1 1 1 1
1.0780 1.0990 1.2190 1.2420 1.2950 1.3380 1.3830 1.4210 1.4920 1.5190 1.5300 1.56600.0434 0.0403 0.0391 0.0341 0.0407 0.0566 0.0648 0.0864 0.1226 0.0700 0.1041 0.15380.5820 0.5683 0.7085 0.6561 0.5793 0.6759 0.6306 0.7507 0.5858 0.5792 0.6255 0.77430.0755 0.0902 0.0847 0.0955 0.0956 0.1050 0.0872 0.0744 0.1310 0.1293 0.0964 0.09860.0488 0.0593 0.0457 0.0560 0.0620 0.0598 0.0530 0.0371 0.0843 0.0839 0.0590 0.04690.0446 0.0446 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0559 0.0584 0.05591.0940 1.3280 0.8177 1.0020 1.1090 1.0690 0.9476 0.6644 1.5080 1.5000 1.0090 0.8381
1 1 1 1 1 1 1 1 1 1 1 1
1.0450 1.1070 1.1310 1.1340 1.1860 1.3940 1.4700 1.4750 1.5310 1.5620 1.7490 2.17300.0405 0.0324 0.0373 0.0409 0.0311 0.0784 0.1001 0.0814 0.0919 0.0776 0.1325 0.25180.4492 0.7404 0.7790 0.6893 0.6548 0.5581 0.5088 0.6959 0.8154 0.5272 0.4860 0.40730.0398 0.0540 0.0567 0.0485 0.0492 0.0506 0.0583 0.0586 0.0631 0.0703 0.0694 0.08570.0296 0.0275 0.0267 0.0270 0.0289 0.0336 0.0409 0.0323 0.0271 0.0484 0.0498 0.06600.0418 0.0409 0.0409 0.0409 0.0409 0.0409 0.0454 0.0409 0.0409 0.0409 0.0409 0.04090.7073 0.6726 0.6518 0.6612 0.7064 0.8222 0.8994 0.7906 0.6628 1.1820 1.2170 1.6140
1 1 1 1 1 1 1 1 1 1 1 1
1.0760 1.1490 1.1760 1.1840 1.2060 1.2230 1.2470 1.3480 1.3550 1.3670 1.4670 1.88000.0254 0.0429 0.0503 0.0521 0.0528 0.0182 0.0190 0.0316 0.0231 0.0346 0.1239 0.12620.7820 0.6404 0.7774 0.6868 0.5764 0.7393 0.7252 0.7051 0.6957 0.5673 0.7171 0.49750.0514 0.0719 0.0547 0.0662 0.0581 0.0663 0.0661 0.0533 0.0655 0.0652 0.0660 0.06810.0240 0.0431 0.0258 0.0370 0.0378 0.0339 0.0347 0.0290 0.0361 0.0429 0.0351 0.04830.0442 0.0442 0.0442 0.0442 0.0402 0.0442 0.0442 0.0402 0.0442 0.0442 0.0442 0.05740.5428 0.9759 0.5845 0.8385 0.9407 0.7667 0.7848 0.7207 0.8173 0.9709 0.7945 0.8417
1 1 1 1 1 1 1 1 1 1 1 1
0.9680 1.0190 1.0560 1.0640 1.0780 1.1580 1.1900 1.2490 1.2550 1.3090 1.3520 1.39800.0126 0.0303 0.0355 0.0439 0.0477 0.0274 0.0411 0.0864 0.0715 0.0611 0.0970 0.13410.6855 0.6861 0.7573 0.7774 0.6913 0.7151 0.7143 0.7251 0.7411 0.6526 0.7498 0.75250.0617 0.0874 0.0601 0.0659 0.0583 0.0778 0.0846 0.0736 0.0649 0.0703 0.0706 0.08610.0346 0.0490 0.0296 0.0311 0.0324 0.0415 0.0452 0.0386 0.0330 0.0415 0.0353 0.04280.0537 0.0607 0.0537 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0607 0.0498 0.06070.6438 0.8062 0.5513 0.5119 0.5329 0.6837 0.7446 0.6350 0.5436 0.6826 0.7098 0.7050
0.9360 0.9674 0.9684 1.0200 1.0310 1.0550 1.1560 1.1820 1.3030 1.3280 1.3370 1.58400.0711 0.0597 0.0648 0.0640 0.0448 0.0293 0.0541 0.0784 0.0792 0.0653 0.0911 0.06760.6958 0.7152 0.8217 0.8266 0.6652 0.7718 0.7471 0.7677 0.8067 0.7223 0.6925 0.75240.0869 0.0814 0.0760 0.0918 0.0702 0.0787 0.1389 0.0848 0.0864 0.0903 0.0960 0.09160.0480 0.0434 0.0321 0.0382 0.0406 0.0376 0.0699 0.0409 0.0380 0.0476 0.0532 0.04560.0535 0.0535 0.0535 0.0492 0.0535 0.0535 0.0535 0.0535 0.0535 0.0535 0.0535 0.05410.8969 0.8125 0.6003 0.7776 0.7596 0.7034 1.3070 0.7643 0.7101 0.8903 0.9953 0.8417
1 1 1 1 1 1 1 1 1 1 1 1
0.9155 0.9318 0.9506 0.9649 0.9993 1.1440 1.1670 1.1690 1.2180 1.2550 1.3490 1.45100.0320 0.0382 0.0373 0.0400 0.0484 0.0388 0.0333 0.0621 0.0734 0.0708 0.0719 0.07720.6051 0.5569 0.5782 0.6823 0.7851 0.6610 0.5956 0.7083 0.7309 0.4103 0.6267 0.47570.0495 0.0637 0.0627 0.0520 0.0582 0.0543 0.0542 0.0642 0.0702 0.0744 0.0632 0.10040.0311 0.0424 0.0407 0.0293 0.0270 0.0316 0.0344 0.0347 0.0364 0.0571 0.0386 0.07270.0409 0.0409 0.0409 0.0409 0.0456 0.0409 0.0409 0.0409 0.0409 0.0409 0.0409 0.05590.7608 1.0370 0.9957 0.7163 0.5916 0.7732 0.8423 0.8478 0.8908 1.3970 0.9443 1.3010
1 1 1 1 1 1 1 1 1 1 1 1
1.0330 1.0360 1.0490 1.0660 1.0730 1.0890 1.1000 1.1120 1.2380 1.2660 1.2680 1.33100.0362 0.0094 0.0245 0.0307 0.0273 0.0277 0.0326 0.0381 0.0158 0.0178 0.0799 0.12130.3820 0.4980 0.5356 0.4681 0.2847 0.4575 0.1059 0.5410 0.2727 0.4037 0.2231 0.42770.0603 0.0734 0.0603 0.0742 0.0528 0.0675 0.0796 0.0678 0.1352 0.0917 0.0783 0.08070.0474 0.0520 0.0411 0.0541 0.0447 0.0497 0.0753 0.0459 0.1153 0.0708 0.0690 0.06100.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0423 0.0450 0.04231.1210 1.2300 0.9729 1.2810 1.0570 1.1770 1.7800 1.0860 2.7270 1.6740 1.5330 1.4430
1 1 1 1 1 1 1 1 1 1 1 1
0.9658 0.9659 1.0370 1.1310 1.1510 1.1560 1.2260 1.2470 1.2890 1.4950 1.5200 1.75200.0285 0.0339 0.0414 0.0311 0.0393 0.0631 0.0552 0.0527 0.0742 0.0943 0.0490 0.21880.4774 0.3912 0.5852 0.6431 0.4807 0.5078 0.4573 0.6318 0.6583 0.6218 0.4864 0.50430.0592 0.0829 0.0724 0.0747 0.0840 0.1011 0.1159 0.0819 0.0834 0.0895 0.0953 0.12690.0428 0.0646 0.0466 0.0446 0.0605 0.0709 0.0854 0.0497 0.0487 0.0550 0.0683 0.08940.0240 0.0236 0.0254 0.0240 0.0240 0.0240 0.0236 0.0240 0.0240 0.0240 0.0432 0.02401.7850 2.7390 1.8340 1.8620 2.5270 2.9610 3.6180 2.0750 2.0350 2.2980 1.5800 3.7300
1 1 1 1 1 1 1 1 1 1 1 1
0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0218 0.0196 0.0179 0.0195 0.0287 0.0137 0.0294 0.0290 0.0448 0.0443 0.0531 0.09630.4092 0.6291 0.7061 0.6650 0.5819 0.6250 0.4964 0.5935 0.7056 0.6266 0.6071 0.50630.0472 0.0562 0.0489 0.0573 0.0593 0.0498 0.0636 0.0538 0.0531 0.0628 0.0639 0.06950.0363 0.0342 0.0265 0.0332 0.0384 0.0305 0.0452 0.0343 0.0288 0.0384 0.0401 0.04880.0304 0.0251 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.0305 0.04311.1920 1.3640 0.8704 1.0890 1.2600 1.0010 1.4820 1.1260 0.9459 1.2600 1.3160 1.1330
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12f:1Equal=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Value=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
38
Statistics 1 2 3 4 5 6 7 8 9 10 11 12 131 1 1 1 1 1 1 1 1 1 1 1 11
0.1982 0.2179 0.3416 0.3583 0.5905 0.6921 0.7318 0.7658 0.8538 0.8645 0.9063 0.9174 0.94490.2895 0.2822 0.3083 0.3186 0.2218 0.2056 0.2037 0.1869 0.1853 0.1765 0.1725 0.1716 0.18310.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.7242 0.72420.1076 0.0781 0.0708 0.0867 0.1351 0.1020 0.0998 0.0913 0.1011 0.1398 0.0958 0.0999 0.12000.0565 0.0219 0.0224 0.0324 0.0803 0.0335 0.0347 0.0224 0.0403 0.0928 0.0242 0.0250 0.04430.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0488 0.0592 0.05921.1590 0.4490 0.4602 0.6638 1.6460 0.6865 0.7123 0.4592 0.8273 1.9030 0.4952 0.4217 0.7493
1 1 1 1 1 1 1 1 1 1 1 1
0.4600 0.6638 0.7427 0.9694 1.0190 1.0500 1.0990 1.2700 1.3290 1.3760 1.4120 1.5520 1.59000.0692 0.0229 0.0094 0.0935 0.0273 0.0367 0.0265 0.0406 0.0423 0.0439 0.0480 0.0616 0.02790.6997 0.8142 0.7765 0.7839 0.8552 0.9186 0.8782 0.8538 0.8844 0.8599 0.8863 0.9125 0.94460.03643 0.0411 0.0364 0.0482 0.0533 0.0443 0.0507 0.0459 0.0569 0.0594 0.0554 0.0550 0.06410.01996 0.0177 0.0172 0.0224 0.0203 0.0127 0.0177 0.0175 0.0194 0.0222 0.0187 0.0163 0.01510.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0460 0.0483 0.0460 0.04830.4340 0.3849 0.3745 0.4867 0.4409 0.2748 0.3846 0.3811 0.4204 0.4829 0.3870 0.3536 0.3122
1 1 1 1 1 1 1 1 1 1 1 1
0.4506 0.4838 0.5846 0.5904 0.6644 0.6909 0.7289 0.7746 0.8179 0.8277 0.8549 0.9368 0.93830.0384 0.0370 0.0138 0.0336 0.0367 0.0307 0.0330 0.0372 0.0232 0.0304 0.0488 0.0275 0.02950.7100 0.6700 0.7000 0.8189 0.7896 0.8062 0.8623 0.8876 0.8449 0.8678 0.9234 0.9153 0.93900.02253 0.0229 0.0251 0.0235 0.0339 0.0348 0.0356 0.0351 0.0309 0.0388 0.0391 0.0372 0.03960.01213 0.0131 0.0137 0.0100 0.0156 0.0153 0.0132 0.0118 0.0122 0.0141 0.0108 0.0108 0.00980.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0331 0.0389 0.0331 0.03890.3670 0.3972 0.4151 0.3024 0.4708 0.4630 0.3999 0.3565 0.3680 0.4269 0.2788 0.3274 0.2521
1 1 1 1 1 1 1 1 1 1 1 1
0.5790 0.5960 0.6217 0.6464 0.7447 0.8657 0.8691 0.8721 0.9045 0.9316 0.9847 1.0230 1.08200.0767 0.0283 0.0321 0.0145 0.0245 0.0121 0.0093 0.0156 0.0072 0.0144 0.0099 0.0168 0.03640.7842 0.8143 0.8425 0.8224 0.8730 0.9125 0.9326 0.9256 0.9235 0.8813 0.9089 0.9202 0.92140.03031 0.0345 0.0370 0.0334 0.0400 0.0348 0.0385 0.0421 0.0388 0.0419 0.0396 0.0440 0.04590.01408 0.0149 0.0147 0.0141 0.0143 0.0103 0.0100 0.0115 0.0107 0.0144 0.0119 0.0124 0.01290.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0406 0.0435 0.0406 0.0406 0.0406 0.04350.3466 0.3659 0.3616 0.3464 0.3512 0.2537 0.2464 0.2824 0.2466 0.3550 0.2939 0.3064 0.2962
1 1 1 1 1 1 1 1 1 1 1 1
0.5769 0.5919 0.6742 0.6768 0.6784 0.8338 0.8363 0.8601 0.8678 0.8856 0.8879 0.9121 0.98820.0324 0.0153 0.0324 0.0248 0.0149 0.0529 0.0443 0.0420 0.0299 0.0243 0.0127 0.0154 0.01060.6408 0.6920 0.6702 0.8007 0.8441 0.7977 0.8517 0.9170 0.9269 0.9102 0.8841 0.9175 0.92990.03835 0.0409 0.0377 0.0436 0.0553 0.0388 0.0416 0.0470 0.0539 0.0704 0.0461 0.0505 0.05340.02298 0.0227 0.0216 0.0195 0.0218 0.0175 0.0160 0.0136 0.0146 0.0211 0.0157 0.0145 0.01410.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0453 0.0515 0.0453 0.0515 0.04530.5076 0.5010 0.4778 0.4302 0.4820 0.3858 0.3540 0.2992 0.3214 0.4095 0.3466 0.2814 0.3120
0.4459 0.4848 0.6120 0.6449 0.6502 0.6589 0.6869 0.7484 0.8191 0.8378 0.8512 0.8781 0.88420.0503 0.0343 0.0169 0.0121 0.0197 0.0226 0.0249 0.0265 0.0149 0.0110 0.0147 0.0278 0.02120.6986 0.7524 0.8268 0.8196 0.8361 0.8506 0.9079 0.8742 0.9142 0.9472 0.9093 0.9236 0.91160.0524 0.0480 0.0482 0.0466 0.0580 0.0492 0.0523 0.0528 0.0577 0.0543 0.0575 0.0571 0.06010.02877 0.0239 0.0201 0.0198 0.0235 0.0190 0.0159 0.0187 0.0169 0.0125 0.0173 0.0158 0.01790.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.0490 0.05180.5868 0.4868 0.4091 0.4032 0.4788 0.3878 0.3234 0.3821 0.3449 0.2544 0.3529 0.3220 0.3453
1 1 1 1 1 1 1 1 1 1 1 1
0.5663 0.5685 0.6048 0.6368 0.6989 0.7365 0.7461 0.7755 0.8123 0.8321 0.8338 0.8868 0.89440.0831 0.0623 0.0253 0.0164 0.0167 0.0147 0.0063 0.0153 0.0045 0.0281 0.0337 0.0306 0.03360.3503 0.3700 0.7861 0.7844 0.7333 0.6313 0.8779 0.8708 0.9046 0.8660 0.8839 0.8995 0.89190.02978 0.0304 0.0341 0.0393 0.0495 0.0359 0.0365 0.0402 0.0470 0.0474 0.0447 0.0456 0.04900.02401 0.0241 0.0158 0.0182 0.0255 0.0218 0.0128 0.0144 0.0145 0.0174 0.0152 0.0145 0.01610.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0465 0.0467 0.0465 0.04650.5162 0.5183 0.3396 0.3922 0.5491 0.4690 0.2745 0.3105 0.3117 0.3730 0.3262 0.3112 0.3466
1 1 1 1 1 1 1 1 1 1 1 1
0.3768 0.3826 0.4595 0.6799 0.7064 0.7243 0.8467 0.9220 0.9564 0.9692 1.0120 1.0530 1.06300.0441 0.0239 0.0273 0.0443 0.0196 0.0574 0.0257 0.0138 0.0168 0.0128 0.0277 0.0334 0.01480.2734 0.3217 0.3434 0.5562 0.6450 0.7639 0.7830 0.7747 0.7310 0.7161 0.7984 0.8558 0.82070.02403 0.0269 0.0296 0.0330 0.0351 0.0347 0.0391 0.0403 0.0381 0.0407 0.0437 0.0432 0.04610.02048 0.0221 0.0240 0.0220 0.0209 0.0168 0.0182 0.0191 0.0198 0.0217 0.0196 0.0164 0.01950.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0341 0.0436 0.0341 0.03410.6010 0.6487 0.7048 0.6444 0.6144 0.4942 0.5341 0.5612 0.5796 0.6360 0.4500 0.4808 0.5732
1 1 1 1 1 1 1 1 1 1 1 1
0.2724 0.3200 0.3237 0.4746 0.6061 0.7194 0.7586 0.7935 0.7987 0.8390 0.9370 0.9388 0.94690.0433 0.0420 0.0240 0.0428 0.0575 0.0289 0.0276 0.0413 0.0322 0.0365 0.0206 0.0243 0.02420.1808 0.2887 0.1527 0.2102 0.4903 0.7030 0.5486 0.7944 0.7368 0.5715 0.7143 0.8191 0.78820.0212 0.0370 0.0419 0.0416 0.0455 0.0421 0.0433 0.0470 0.0490 0.0551 0.0512 0.0477 0.05400.01919 0.0312 0.0386 0.0370 0.0325 0.0229 0.0291 0.0213 0.0251 0.0361 0.0274 0.0203 0.02490.0299 0.0301 0.0299 0.0299 0.0299 0.0299 0.0299 0.0300 0.0299 0.0300 0.0307 0.0300 0.03070.6409 1.0370 1.2880 1.2340 1.0860 0.7662 0.9726 0.7115 0.8390 1.2040 0.8935 0.6781 0.8108
1 1 1 1 1 1 1 1 1 1 1 1
0.0828 0.1077 0.2610 0.4231 0.4888 0.5512 0.6108 0.7213 0.7237 0.7857 0.8590 0.9238 0.92610.0663 0.0598 0.0528 0.0240 0.0531 0.0791 0.0687 0.0348 0.0714 0.0405 0.0183 0.0085 0.00770.0419 0.2880 0.4842 0.4720 0.8177 0.6577 0.7578 0.8084 0.8059 0.6534 0.7833 0.8820 0.81030.02255 0.0272 0.0313 0.0350 0.0331 0.0295 0.0302 0.0355 0.0355 0.0425 0.0328 0.0387 0.03640.02208 0.0229 0.0225 0.0254 0.0141 0.0173 0.0149 0.0155 0.0157 0.0250 0.0153 0.0133 0.01590.0282 0.0282 0.0282 0.0281 0.0282 0.0280 0.0282 0.0281 0.0280 0.0280 0.0281 0.0315 0.02800.7823 0.8132 0.7974 0.9052 0.5004 0.6171 0.5272 0.5527 0.5598 0.8938 0.5433 0.4212 0.5674
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
TABLE12g:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios11=13)
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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39
1 1 1 1 1 1 1 1 1 1 1 1Statistics 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 1 1 1 1 1 1 1
0.9547 1.0390 1.1280 1.1440 1.1450 1.2580 1.2950 1.3200 1.3360 1.3570 1.3810 1.44600.0126 0.0203 0.0348 0.0436 0.0471 0.0291 0.0307 0.0337 0.0319 0.0621 0.0670 0.02790.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.7807 0.78070.1174 0.1332 0.0870 0.1033 0.1396 0.1458 0.1244 0.1155 0.1232 0.1385 0.1368 0.13000.0372 0.0524 0.0286 0.0269 0.0512 0.0480 0.0506 0.0321 0.0329 0.0403 0.0396 0.04690.0537 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0598 0.0615 0.05980.6930 0.8762 0.4787 0.4505 0.8563 0.8025 0.8457 0.5373 0.5496 0.6745 0.6434 0.7839
1 1 1 1 1 1 1 1 1 1 1 1
1.1690 1.1700 1.1710 1.2380 1.2500 1.2580 1.3070 1.3130 1.3470 1.4420 1.4570 1.53600.0414 0.0090 0.0156 0.0139 0.0046 0.0021 0.0172 0.0449 0.0374 0.0285 0.0365 0.03020.9067 0.8655 0.9008 0.9297 0.9178 0.8738 0.8251 0.9191 0.8072 0.8357 0.8654 0.94430.0677 0.0834 0.0764 0.0683 0.0728 0.0894 0.0913 0.0774 0.1124 0.1097 0.1099 0.08600.0207 0.0306 0.0241 0.0181 0.0209 0.0317 0.0382 0.0220 0.0493 0.0445 0.0403 0.02030.0460 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0483 0.0548 0.04830.4491 0.6332 0.4984 0.3751 0.4323 0.6571 0.7906 0.4555 1.0220 0.9204 0.7365 0.4201
1 1 1 1 1 1 1 1 1 1 1 1
0.9428 1.0200 1.0510 1.0640 1.0700 1.0920 1.2640 1.3590 1.5440 1.5880 1.6180 1.62700.0305 0.0013 0.0243 0.0288 0.0328 0.0379 0.0190 0.0185 0.0742 0.0750 0.0819 0.07170.8832 0.8985 0.9538 0.9281 0.9185 0.9117 0.8472 0.9135 0.9170 0.9079 0.8377 0.72250.0365 0.0407 0.0458 0.0441 0.0462 0.0453 0.0439 0.0565 0.0547 0.0568 0.0546 0.05330.0125 0.0130 0.0098 0.0118 0.0132 0.0135 0.0172 0.0166 0.0158 0.0172 0.0220 0.02810.0331 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0389 0.0433 0.0389 0.0389 0.03890.3778 0.3336 0.2534 0.3046 0.3393 0.3469 0.4418 0.4274 0.3637 0.4434 0.5659 0.7225
1 1 1 1 1 1 1 1 1 1 1 1
1.0990 1.1260 1.1590 1.1740 1.1910 1.1940 1.1950 1.3250 1.3310 1.3320 1.3360 1.36200.0318 0.0232 0.0325 0.0233 0.0161 0.0125 0.0274 0.0129 0.0245 0.0255 0.0285 0.12220.9174 0.8455 0.9003 0.9024 0.8930 0.9253 0.8874 0.8998 0.8947 0.9273 0.9129 0.80210.0447 0.0501 0.0465 0.0442 0.0465 0.0555 0.0526 0.0522 0.0579 0.0545 0.0528 0.06010.0129 0.0197 0.0147 0.0138 0.0152 0.0152 0.0177 0.0165 0.0188 0.0147 0.0156 0.02670.0435 0.0434 0.0435 0.0435 0.0435 0.0435 0.0406 0.0435 0.0435 0.0435 0.0434 0.05110.2957 0.4533 0.3379 0.3174 0.3499 0.3488 0.4344 0.3799 0.4320 0.3379 0.3588 0.5225
1 1 1 1 1 1 1 1 1 1 1 1
0.9958 1.0040 1.1150 1.1350 1.1480 1.1500 1.1730 1.1780 1.1950 1.2620 1.3200 1.37200.0111 0.0114 0.0384 0.0236 0.0109 0.0163 0.0261 0.0380 0.0344 0.0482 0.0519 0.05670.9390 0.9251 0.9185 0.9378 0.9389 0.9151 0.8907 0.8945 0.9202 0.9308 0.9212 0.91410.0562 0.0653 0.0494 0.0591 0.0552 0.0679 0.0728 0.0611 0.0623 0.0645 0.0661 0.08530.0139 0.0179 0.0141 0.0147 0.0137 0.0198 0.0241 0.0199 0.0176 0.0170 0.0186 0.02500.0515 0.0515 0.0515 0.0515 0.0453 0.0515 0.0515 0.0515 0.0515 0.0515 0.0515 0.05960.2695 0.3465 0.2737 0.2861 0.3014 0.3841 0.4669 0.3853 0.3419 0.3292 0.3601 0.4196
0.9132 0.9216 1.0090 1.0380 1.0550 1.1270 1.1550 1.1720 1.2630 1.3490 1.3560 1.40100.0151 0.0218 0.0141 0.0215 0.0154 0.0290 0.0283 0.0264 0.0218 0.0451 0.0248 0.03310.9194 0.9133 0.9175 0.9225 0.9500 0.9596 0.8927 0.9319 0.9433 0.9206 0.9205 0.86740.0691 0.0720 0.0644 0.0688 0.0684 0.0759 0.0795 0.0776 0.0826 0.0825 0.0981 0.09030.0196 0.0212 0.0185 0.0192 0.0153 0.0153 0.0260 0.0203 0.0197 0.0232 0.0277 0.03290.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.0518 0.05800.3790 0.4097 0.3575 0.3699 0.2956 0.2947 0.5029 0.3913 0.3798 0.4488 0.5345 0.5670
1 1 1 1 1 1 1 1 1 1 1 1
0.9534 0.9700 0.9831 1.0010 1.0560 1.0630 1.1800 1.1830 1.2470 1.2510 1.3130 1.47700.0215 0.0199 0.0232 0.0245 0.0153 0.0425 0.0077 0.0135 0.0064 0.0303 0.0284 0.05630.9158 0.9024 0.9144 0.9238 0.9172 0.8773 0.8885 0.8873 0.9168 0.7976 0.8603 0.85760.0479 0.0484 0.0491 0.0456 0.0466 0.0491 0.0516 0.0491 0.0548 0.0532 0.0562 0.07350.0139 0.0151 0.0144 0.0126 0.0134 0.0172 0.0172 0.0165 0.0158 0.0239 0.0210 0.02770.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.0467 0.05430.2976 0.3244 0.3077 0.2696 0.2873 0.3688 0.3691 0.3531 0.3388 0.5131 0.4506 0.5106
1 1 1 1 1 1 1 1 1 1 1 1
1.0730 1.0800 1.0810 1.0980 1.1000 1.1040 1.1340 1.1710 1.1890 1.2810 1.2890 1.30700.0202 0.0201 0.0188 0.0102 0.0099 0.0130 0.0076 0.0169 0.0135 0.0278 0.0248 0.03600.8080 0.8183 0.8234 0.8309 0.7904 0.8261 0.6210 0.8839 0.8346 0.7953 0.3198 0.69490.0473 0.0509 0.0500 0.0489 0.0438 0.0521 0.0631 0.0576 0.0581 0.0654 0.0690 0.06910.0207 0.0217 0.0210 0.0201 0.0201 0.0218 0.0389 0.0196 0.0236 0.0296 0.0569 0.03810.0436 0.0436 0.0436 0.0436 0.0436 0.0436 0.0438 0.0438 0.0438 0.0438 0.0438 0.04350.4753 0.4976 0.4811 0.4603 0.4594 0.4983 0.8875 0.4481 0.5399 0.6752 1.3000 0.8767
1 1 1 1 1 1 1 1 1 1 1 1
0.9583 0.9779 1.0060 1.0280 1.1340 1.1710 1.2190 1.2580 1.3030 1.3210 1.4670 1.53800.0308 0.0324 0.0506 0.0482 0.0380 0.0361 0.0300 0.0323 0.0283 0.0208 0.0536 0.05290.8517 0.8205 0.7949 0.8326 0.8120 0.8547 0.7467 0.8685 0.8354 0.8698 0.8049 0.74490.0492 0.0557 0.0642 0.0656 0.0699 0.0627 0.0715 0.0707 0.0666 0.0767 0.0787 0.08680.0190 0.0236 0.0291 0.0269 0.0303 0.0239 0.0360 0.0257 0.0270 0.0277 0.0348 0.04380.0307 0.0300 0.0311 0.0311 0.0311 0.0311 0.0311 0.0311 0.0307 0.0311 0.0311 0.05050.6184 0.7881 0.9354 0.8642 0.9748 0.7693 1.1580 0.8256 0.8816 0.8911 1.1190 0.8680
1 1 1 1 1 1 1 1 1 1 1 1
0.9979 1.0300 1.1240 1.1390 1.1470 1.2340 1.2400 1.2700 1.2780 1.2930 1.3220 1.63100.0193 0.0207 0.0103 0.0062 0.0044 0.0190 0.0193 0.0232 0.0216 0.0240 0.0254 0.11590.8766 0.8306 0.7733 0.8334 0.8747 0.8831 0.8094 0.8624 0.8533 0.8384 0.8522 0.78390.0423 0.0499 0.0386 0.0503 0.0496 0.0476 0.0512 0.0511 0.0467 0.0506 0.0508 0.06690.0149 0.0205 0.0184 0.0205 0.0176 0.0163 0.0224 0.0190 0.0179 0.0203 0.0195 0.03110.0317 0.0315 0.0315 0.0317 0.0317 0.0317 0.0318 0.0318 0.0318 0.0318 0.0318 0.04370.4688 0.6514 0.5828 0.6473 0.5537 0.5127 0.7028 0.5956 0.5613 0.6390 0.6135 0.7125
Portfolios1for1Estimation1Period11982=86
Portfolios1for1Estimation1Period11990=94
Portfolios1for1Estimation1Period11998=02
Portfolios1for1Estimation1Period12002=06
Portfolios1for1Estimation1Period11950=54
Portfolios1for1Estimation1Period11958=62
Portfolios1for1Estimation1Period11966=70
Portfolios1for1Estimation1Period11974=78
TABLE12g:1Value=Weighted1NYSE1Market1Portfolio111111111+11111115x51Double=Sort1Test1Portfolios1Built1Using1Equal=Weighted1SecuritiesSAMPLE1STATISTICS1FOR1FOUR1SECLECTED1ESTIMATION1PERIODS1(test1portfolios114=25)111
Portfolios1for1Estimation1Period11934=38
Portfolios1for1Estimation1Period11942=46
�p,t�1
s(�p,t�1)
r(Rp, Rm)2
s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(ep)s(Rp)
sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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sp,t�1(ei)s(ep)/sp,t�1(ei)
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s(�p,t�1)
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s(�p,t�1)
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s(�p,t�1)
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s(�p,t�1)
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s(ep)s(Rp)
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s(�p,t�1)
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40
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193516/68
0.0097
0.0043
11
0.0084
0.0486
0.0550
11
0.0082
0.0727
11
4.0070
1.5630
11
3.4690
0.3051
0.3016
1935145
0.0079
0.0114
11
0.0077
0.0687
0.0757
11
0.0078
0.0795
11
1.3130
1.7300
11
1.2890
0.2945
0.2914
1946155
0.0089
0.0028
11
0.0080
0.0333
0.0418
11
0.0443
0.0611
11
2.9270
0.7215
11
2.6170
0.3284
0.3196
195616/68
0.0120
10.000
71
10.0094
0.0363
0.0407
11
0.1369
0.0139
11
4.0390
10.216
01
13.1490
0.2958
0.2965
1935140
0.0052
0.0084
11
0.0051
0.0864
0.0872
11
10.080
50.0615
11
0.5032
0.8146
11
0.4956
0.2371
0.2895
1941145
0.0111
0.0150
11
0.0109
0.0388
0.0597
11
0.0950
0.1096
11
2.2130
1.9440
11
2.1710
0.3624
0.2811
1946150
0.0052
0.0034
11
0.0045
0.0377
0.0457
11
0.1602
0.0692
11
1.0660
0.5686
11
0.9293
0.4101
0.3265
1951155
0.0126
0.0022
11
0.0114
0.0281
0.0379
11
10.168
50.0462
11
3.4790
0.4400
11
3.1340
0.2466
0.2930
1956160
0.0158
10.007
71
10.0137
0.0277
0.0285
11
0.0960
0.0746
11
4.4140
12.097
01
13.8050
0.2210
0.3130
196116/68
0.0094
0.0039
11
0.0065
0.0410
0.0467
11
0.1263
10.019
71
12.1800
0.8012
11
1.4980
0.3456
0.2756
7/196812010
0.0103
0.0009
11
0.0057
0.0421
0.0573
11
0.0617
0.1131
11
5.5030
0.3614
11
3.0870
0.3260
0.2861
1970180
0.0062
0.0057
11
0.0008
0.0481
0.0614
11
0.0339
0.1379
11
1.4840
1.0690
11
0.1815
0.3167
0.2829
1980190
0.0206
10.007
91
10.0135
0.0477
0.0632
11
0.0654
0.0575
11
4.9580
11.434
01
13.2590
0.3021
0.2873
1990100
0.0096
0.0014
11
0.0055
0.0368
0.0525
11
0.0545
0.1907
11
3.0000
0.3010
11
1.7350
0.3148
0.2767
2000110
0.0076
0.0022
11
0.0055
0.0339
0.0550
11
10.016
40.1598
11
2.5780
0.4678
11
1.8820
0.3764
0.3019
1970175
0.0052
0.0017
11
0.0004
0.0541
0.0609
11
0.0268
0.0991
11
0.8114
0.2361
11
0.0602
0.3097
0.2774
1975180
0.0093
0.0127
11
0.0033
0.0422
0.0623
11
0.0286
0.1477
11
1.8690
1.7250
11
0.6678
0.3126
0.2900
1980185
0.0232
10.006
61
10.0149
0.0511
0.0607
11
0.0818
0.0294
11
3.8460
10.923
31
12.4570
0.3452
0.2898
1985190
0.0186
10.008
11
10.0130
0.0418
0.0628
11
0.0188
0.0789
11
3.7750
11.090
01
12.6380
0.2501
0.2768
1990195
0.0092
0.0014
11
0.0052
0.0363
0.0559
11
0.0779
0.2624
11
2.1570
0.2123
11
1.2380
0.2831
0.2682
1995100
0.0129
0.0002
11
0.0086
0.0372
0.0477
11
0.0690
0.1012
11
2.9480
0.0444
11
1.9810
0.3512
0.2821
2000105
0.0098
0.0015
11
0.0075
0.0357
0.0504
11
10.122
210.068
41
12.3310
0.2588
11
1.7970
0.3327
0.3018
2005110
0.0044
0.0037
11
0.0024
0.0294
0.0562
11
0.1450
0.3337
11
1.2600
0.5633
11
0.7028
0.4088
0.3008
193512010
0.0100
0.0024
11
0.0069
0.0450
0.0563
11
0.0303
0.0978
11
6.7170
1.2880
11
4.6400
0.3168
0.2930
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0035
0.0185
10.006
71
0.0022
0.0740
0.1511
0.0650
10.0019
0.0902
0.0003
10.9582
2.4470
12.070
01
0.6047
0.0911
0.1841
1935145
0.0039
0.0226
10.005
91
0.0038
0.0887
0.1720
0.0740
10.0033
0.1702
0.0007
10.5065
1.5010
10.909
31
0.4881
0.0896
0.1868
1946155
0.0032
0.0148
10.005
31
0.0022
0.0564
0.1280
0.0531
10.0425
0.1632
0.0003
10.6164
1.2710
11.096
01
0.4329
0.1233
0.1997
195616/68
0.0035
0.0178
10.008
61
0.0009
0.0727
0.1495
0.0656
10.0135
10.056
710.000
21
0.5888
1.4570
11.602
01
0.1493
0.0666
0.1652
1935140
0.0041
0.0135
10.003
51
0.0040
0.1102
0.2006
0.0774
10.0197
0.2201
0.0009
10.3139
0.5656
10.375
71
0.3080
0.0630
0.1861
1941145
0.0037
0.0333
10.008
81
0.0035
0.0542
0.1314
0.0703
10.3537
0.0239
0.0006
10.5307
1.9640
10.964
21
0.4995
0.1211
0.1841
1946150
0.0009
0.0119
10.003
51
0.0002
0.0505
0.1206
0.0470
110.109
50.1628
0.0004
10.1327
0.7613
10.573
51
0.0307
0.1715
0.2104
1951155
0.0055
0.0178
10.007
21
0.0043
0.0621
0.1359
0.0590
10.1534
0.1568
0.0003
10.6841
1.0160
10.939
31
0.5313
0.0751
0.1773
1956160
0.0017
0.0251
10.015
61
10.000
40.0466
0.1072
0.0467
110.201
210.364
410.000
51
0.2818
1.8100
12.589
01
10.068
90.0477
0.1570
196116/68
0.0047
0.0130
10.003
91
0.0018
0.0860
0.1725
0.0755
10.0512
0.0200
0.0000
10.5176
0.7124
10.488
91
0.1933
0.0792
0.1701
7/196812010
0.0049
0.0136
10.006
61
0.0003
0.0798
0.1913
0.0929
10.0726
0.0897
0.0003
11.3790
1.6010
11.599
01
0.0958
0.1196
0.1931
1970180
10.005
70.0318
10.012
51
10.011
10.1012
0.2201
0.1012
10.1898
0.1693
0.0016
110.642
31.6610
11.423
01
11.261
00.0923
0.1762
1980190
0.0097
0.0196
10.015
11
0.0027
0.1001
0.2457
0.1248
110.090
20.0053
10.000
91
1.1140
0.9183
11.393
01
0.3047
0.1342
0.2109
1990100
0.0076
0.0091
10.005
31
0.0035
0.0563
0.1573
0.0855
10.0533
0.0171
10.000
21
1.5530
0.6674
10.707
11
0.7204
0.0993
0.1666
2000110
0.0084
10.000
70.0017
10.0063
0.0384
0.1168
0.0499
10.0333
10.011
210.000
31
2.5120
10.068
70.3981
11.9000
0.1451
0.1996
1970175
0.0033
0.0054
10.001
41
10.001
50.1058
0.2091
0.1004
10.1875
0.1753
0.0013
10.2614
0.2175
10.122
01
10.122
60.0784
0.1532
1975180
10.009
20.0535
10.019
81
10.015
20.1010
0.2318
0.1057
10.0980
0.0816
0.0008
110.776
01.9590
11.590
01
11.284
00.0999
0.1884
1980185
0.0095
0.0233
10.014
61
0.0012
0.0999
0.2309
0.1121
110.065
10.0532
0.0002
10.8060
0.8579
11.108
01
0.0992
0.1370
0.2073
1985190
0.0133
0.0105
10.012
21
0.0076
0.1003
0.2576
0.1345
110.126
610.058
110.002
31
1.1240
0.3455
10.771
41
0.6466
0.1426
0.2217
1990195
0.0056
0.0140
10.008
11
0.0016
0.0635
0.1828
0.1008
110.008
610.000
510.000
41
0.7489
0.6500
10.685
41
0.2170
0.0974
0.1615
1995100
0.0131
0.0013
10.001
21
0.0088
0.0467
0.1200
0.0621
10.1885
0.0626
0.0001
12.3820
0.0898
10.157
51
1.6100
0.1108
0.1757
2000105
0.0088
0.0039
10.001
01
0.0066
0.0353
0.0901
0.0487
10.0503
10.152
210.000
61
2.1250
0.3655
10.176
41
1.5880
0.1101
0.1716
2005110
0.0064
10.003
00.0036
10.0045
0.0400
0.1325
0.0478
10.0358
0.0479
0.0000
11.3670
10.192
80.6448
10.9573
0.1754
0.2170
193512010
0.0043
0.0157
10.006
61
0.0012
0.0773
0.1746
0.0818
10.0624
0.0895
0.0003
11.6750
2.7170
12.451
01
0.4582
0.1070
0.1896
TABLE!3b
:!Equ
al1W
eighted!NYSE!Market!Po
rtfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!Po
rtfolios!Bu
ilt!Using!Value
1Weighted!Securities
SUMMARY
!RESULTS!FO
R!TH
E!RE
GRE
SSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+�3ts p
(ei)
+⌘
p
41
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Period
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0107
0.0070
110.055
30.0094
0.0560
0.0689
10.9425
0.0091
0.0795
110.000
43.8210
2.0350
111.174
03.3540
0.0933
0.1845
1935145
0.0080
0.0115
110.017
90.0079
0.0763
0.0890
10.8588
0.0082
0.0645
110.058
61.2030
1.4810
110.238
81.1810
0.1011
0.1922
1946155
0.0117
0.0093
110.124
40.0108
0.0420
0.0620
10.9021
0.0456
0.0638
10.0172
3.0590
1.6350
111.511
02.8100
0.1180
0.2037
195616/68
0.0122
0.0013
110.032
60.0096
0.0437
0.0520
11.0420
0.0893
0.1202
10.0309
3.4120
0.2953
110.382
92.6770
0.0668
0.1574
1935140
0.0032
0.0023
10.0544
0.0031
0.0900
0.1042
10.6782
10.072
80.1678
110.075
30.2968
0.1858
10.6755
0.2896
0.0610
0.1744
1941145
0.0138
0.0224
110.103
50.0135
0.0563
0.0659
11.0320
0.0153
10.298
61
10.039
81.8940
2.6360
110.776
21.8640
0.1485
0.2027
1946150
0.0097
0.0123
110.167
40.0090
0.0471
0.0656
10.8237
0.1974
10.018
21
0.0820
1.5950
1.4560
111.574
01.4850
0.1443
0.2002
1951155
0.0138
0.0062
110.081
40.0125
0.0365
0.0587
10.9794
10.213
50.1575
110.050
52.9190
0.8183
110.643
72.6530
0.0917
0.2055
1956160
0.0119
10.011
21
0.1215
0.0098
0.0351
0.0405
11.0900
0.0794
0.0134
110.074
92.6300
12.135
01
0.8631
2.1590
0.0476
0.1317
196116/68
0.0123
0.0095
110.135
30.0094
0.0487
0.0572
11.0020
0.0932
0.1027
10.0753
2.4010
1.5800
111.281
01.8270
0.0796
0.1719
7/196812010
0.0124
0.0050
110.082
50.0078
0.0509
0.0842
11.1370
0.0821
10.029
21
0.0355
5.4810
1.3290
111.638
03.4900
0.1127
0.1875
1970180
0.0074
0.0073
110.053
10.0020
0.0589
0.0805
11.2500
10.017
010.097
01
10.132
51.4460
1.0380
110.487
80.3830
0.0939
0.1815
1980190
0.0265
0.0033
110.206
40.0194
0.0514
0.1010
11.1800
0.1568
10.053
11
0.1226
5.9220
0.3770
112.009
04.3490
0.1096
0.1859
1990100
0.0080
0.0007
10.0263
0.0039
0.0443
0.0705
10.9101
0.0872
0.0317
110.016
72.0680
0.1091
10.3319
1.0130
0.1008
0.1690
2000110
0.0083
0.0023
110.010
60.0063
0.0474
0.0836
11.1560
0.0396
0.1210
10.1420
2.0230
0.3102
110.105
41.5240
0.1399
0.1991
1970175
0.0094
0.0129
110.213
70.0046
0.0650
0.0901
11.3780
10.017
310.184
41
10.195
71.2260
1.2120
111.316
00.6010
0.0874
0.1664
1975180
0.0074
0.0047
10.1107
0.0014
0.0523
0.0702
11.0290
10.033
510.068
91
10.097
31.2040
0.5631
10.9130
0.2330
0.0882
0.1899
1980185
0.0258
10.004
41
10.054
60.0175
0.0514
0.0949
11.0110
0.1265
0.0249
10.0521
4.2560
10.393
11
10.458
02.8810
0.1144
0.1827
1985190
0.0247
0.0061
110.247
10.0191
0.0492
0.1051
11.3290
0.1764
10.114
61
0.1512
4.2630
0.4906
111.578
03.3010
0.1044
0.1962
1990195
0.0112
0.0085
110.110
40.0072
0.0437
0.0672
10.8653
0.1590
0.0324
10.0074
2.1790
1.0770
111.082
01.4180
0.1084
0.1727
1995100
0.0087
10.006
71
0.1321
0.0044
0.0457
0.0691
10.8913
0.0493
0.0109
110.041
61.6100
10.822
61
1.2570
0.8178
0.0945
0.1694
2000105
0.0144
0.0076
110.139
70.0121
0.0504
0.0831
11.2010
0.0006
0.0954
10.3374
2.4220
0.7747
110.987
72.0390
0.1293
0.1897
2005110
0.0005
10.003
71
0.1473
10.001
40.0393
0.0794
11.0330
0.0522
0.1505
110.031
00.1086
10.397
71
1.2100
10.313
10.1494
0.2036
193512010
0.0116
0.0059
110.070
50.0085
0.0532
0.0778
11.0560
0.0431
0.0088
10.0198
6.5950
2.2720
112.016
04.8430
0.1042
0.1863
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0053
0.0160
10.005
310.019
70.0040
0.0923
0.1556
0.0720
1.0110
0.0037
0.0593
10.000
110.076
71.1480
2.0580
11.465
010.391
20.8648
0.0963
0.2064
1935145
0.0032
0.0206
10.006
30.0129
0.0031
0.1169
0.1878
0.0902
0.9925
0.0028
0.0957
0.0000
10.159
50.3128
1.2560
10.801
80.1492
0.2988
0.0967
0.2131
1946155
0.0098
0.0115
10.001
310.105
10.0088
0.0599
0.1232
0.0492
0.8559
10.018
00.1524
0.0002
10.022
11.7890
1.0240
10.279
511.346
01.6150
0.1278
0.2205
195616/68
0.0035
0.0156
10.007
60.0200
0.0009
0.0898
0.1487
0.0697
1.1350
10.045
810.052
610.000
410.048
70.4811
1.2820
11.327
00.2160
0.1254
0.0706
0.1855
1935140
10.003
50.0150
10.009
80.1031
10.003
60.1447
0.2268
0.1047
0.9544
10.052
40.1037
10.000
110.162
210.203
30.5575
10.785
60.9099
10.207
80.0542
0.2054
1941145
0.0111
0.0272
10.002
210.093
70.0109
0.0718
0.1286
0.0699
1.0340
0.0159
0.0676
0.0000
10.159
21.1970
1.6390
10.248
610.702
11.1740
0.1471
0.2126
1946150
0.0088
0.0110
0.0004
10.140
30.0081
0.0602
0.1175
0.0459
0.7444
10.099
60.1689
0.0004
0.0283
1.1320
0.7247
0.0685
11.460
01.0450
0.1675
0.2242
1951155
0.0108
0.0120
10.002
910.070
00.0095
0.0601
0.1295
0.0526
0.9597
0.0586
0.1325
0.0001
10.073
71.3880
0.7190
10.429
710.565
01.2290
0.0881
0.2112
1956160
10.003
50.0188
10.015
40.1876
10.005
60.0598
0.1077
0.0500
1.1580
10.240
710.308
310.000
710.164
910.457
31.3530
12.389
01.2540
10.729
60.0608
0.1741
196116/68
0.0082
0.0134
10.002
310.091
70.0053
0.1052
0.1712
0.0800
1.1120
10.007
40.0140
10.000
210.009
10.7424
0.7421
10.273
710.782
40.4773
0.0771
0.1935
7/196812010
0.0090
0.0141
10.004
210.099
80.0045
0.0912
0.1951
0.0963
1.1620
0.0300
0.0722
0.0001
10.010
02.2390
1.6260
10.972
811.938
01.1170
0.1328
0.2075
1970180
10.000
20.0265
10.008
310.080
210.005
60.1174
0.2187
0.1045
1.3060
0.0655
0.1415
0.0011
10.223
810.017
51.3910
10.911
610.705
010.551
80.1015
0.1971
1980190
0.0141
0.0278
10.014
710.156
50.0071
0.1112
0.2528
0.1318
1.1990
10.061
910.001
310.001
10.1411
1.4590
1.2610
11.279
011.499
00.7318
0.1520
0.2177
1990100
0.0089
0.0011
10.000
50.0129
0.0049
0.0660
0.1628
0.0904
0.9514
0.0742
10.024
210.000
410.032
11.5560
0.0770
10.067
20.1556
0.8458
0.1189
0.1905
2000110
0.0118
10.000
40.0032
10.072
30.0097
0.0511
0.1311
0.0511
1.1680
10.092
10.0638
10.000
40.0467
2.6520
10.031
70.7284
10.710
52.1900
0.1552
0.2131
1970175
0.0125
0.0057
0.0041
10.222
50.0077
0.1274
0.2120
0.1064
1.4640
0.0276
0.1590
0.0009
10.297
00.8315
0.2287
0.3267
11.289
00.5117
0.0917
0.1711
1975180
10.008
30.0438
10.017
60.0692
10.014
30.1078
0.2285
0.1053
1.0400
0.0339
0.0549
0.0005
10.155
510.651
41.6280
11.419
00.5647
11.128
00.0996
0.2118
1980185
0.0095
0.0283
10.017
010.024
90.0012
0.1107
0.2308
0.1166
1.0710
10.073
70.0319
10.000
20.0016
0.7319
1.0410
11.235
010.197
20.0942
0.1509
0.2103
1985190
0.0174
0.0197
10.011
110.177
40.0117
0.1132
0.2708
0.1441
1.3320
10.091
810.044
410.002
60.2213
1.3030
0.6183
10.652
811.130
00.8808
0.1663
0.2303
1990195
0.0116
0.0084
10.001
010.104
50.0076
0.0764
0.1825
0.1086
0.9688
0.0632
10.043
410.000
60.0066
1.2860
0.3921
10.074
810.915
40.8451
0.1270
0.1885
1995100
0.0110
10.007
30.0012
0.0904
0.0067
0.0544
0.1324
0.0629
0.8887
0.1212
0.0123
0.0000
10.075
61.7140
10.469
40.1659
0.8635
1.0500
0.1138
0.1955
2000105
0.0161
0.0035
0.0027
10.152
90.0139
0.0516
0.1170
0.0507
1.2400
0.0698
10.020
610.000
50.3871
2.6530
0.2520
0.4466
11.046
02.2790
0.1321
0.1961
2005110
0.0044
10.003
10.0024
0.0521
0.0025
0.0471
0.1368
0.0481
1.0220
10.308
70.1235
10.000
210.258
10.7932
10.191
80.4254
0.4327
0.4443
0.1712
0.2234
193512010
0.0074
0.0149
10.004
610.064
50.0043
0.0917
0.1787
0.0864
1.0980
10.000
50.0674
0.0000
10.039
32.4340
2.5170
11.621
011.774
01.4100
0.1167
0.2077
TABLE!3b
:!Equ
al1W
eighted!NYSE!Market!Po
rtfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!Po
rtfolios!Bu
ilt!Using!Value
1Weighted!Securities
SUMMARY
!RESULTS!FO
R!TH
E!RE
GRE
SSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
42
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0077
0.0053
11
0.0064
0.0394
0.0519
11
0.0061
10.011
41
13.9190
2.0330
11
3.2510
0.3051
0.3016
1935145
0.0083
0.0084
11
0.0082
0.0545
0.0686
11
0.0082
10.111
71
11.7500
1.4060
11
1.7200
0.2945
0.2914
1946155
0.0078
0.0029
11
0.0069
0.0259
0.0373
11
0.1394
0.0682
11
3.3180
0.8582
11
2.9200
0.3284
0.3196
195616/68
0.0071
0.0044
11
0.0045
0.0324
0.0446
11
0.2607
0.1452
11
2.6770
1.2010
11
1.6840
0.2958
0.2965
1935140
0.0082
0.0038
11
0.0081
0.0683
0.0819
11
0.0997
10.194
81
11.0150
0.3957
11
1.0050
0.2371
0.2895
1941145
0.0085
0.0139
11
0.0082
0.0317
0.0484
11
0.1363
0.1414
11
2.0620
2.2150
11
2.0100
0.3624
0.2811
1946150
0.0044
0.0028
11
0.0038
0.0312
0.0423
11
0.2255
0.0334
11
1.1000
0.5097
11
0.9342
0.4101
0.3265
1951155
0.0113
0.0031
11
0.0100
0.0188
0.0319
11
10.055
30.0701
11
4.6360
0.7435
11
4.1280
0.2466
0.2930
1956160
0.0154
10.006
81
10.0133
0.0208
0.0406
11
0.1759
0.1503
11
5.7230
11.299
01
14.9340
0.2210
0.3130
196116/68
0.0015
0.0118
11
10.001
40.0372
0.0458
11
0.2184
0.0865
11
0.3885
2.4530
11
10.359
80.3456
0.2756
7/196812010
0.0082
0.0029
11
0.0037
0.0385
0.0575
11
0.1320
0.1811
11
4.8140
1.1350
11
2.1630
0.3260
0.2861
1970180
0.0014
0.0092
11
10.004
00.0423
0.0633
11
0.2181
0.1851
11
0.3892
1.6700
11
11.098
00.3167
0.2829
1980190
0.0184
10.005
01
10.0113
0.0424
0.0619
11
0.0569
0.2157
11
4.9720
10.919
71
13.0840
0.3021
0.2873
1990100
0.0082
0.0031
11
0.0042
0.0392
0.0579
11
0.1096
0.1778
11
2.4180
0.6192
11
1.2270
0.3148
0.2767
2000110
0.0088
0.0008
11
0.0067
0.0308
0.0518
11
0.0267
0.1156
11
3.2810
0.1806
11
2.5170
0.3764
0.3019
1970175
0.0045
0.0009
11
10.000
30.0418
0.0587
11
0.1852
0.1544
11
0.9150
0.1332
11
10.057
60.3097
0.2774
1975180
10.000
50.0209
11
10.006
50.0436
0.0680
11
0.2443
0.2274
11
10.096
82.6040
11
11.282
00.3126
0.2900
1980185
0.0193
10.001
81
10.0110
0.0427
0.0578
11
0.0936
0.1761
11
3.8410
10.260
21
12.2020
0.3452
0.2898
1985190
0.0192
10.008
01
10.0135
0.0406
0.0631
11
0.0335
0.2430
11
4.0030
11.076
01
12.8430
0.2501
0.2768
1990195
0.0080
0.0030
11
0.0041
0.0394
0.0562
11
0.1931
0.2868
11
1.7320
0.4523
11
0.8818
0.2831
0.2682
1995100
0.0110
0.0026
11
0.0067
0.0382
0.0575
11
0.0474
0.0713
11
2.4320
0.3790
11
1.4900
0.3512
0.2821
2000105
0.0113
10.000
11
10.0091
0.0308
0.0527
11
10.086
610.040
01
13.1210
10.010
41
12.5070
0.3327
0.3018
2005110
0.0059
0.0017
11
0.0039
0.0294
0.0473
11
0.1521
0.2953
11
1.6990
0.3031
11
1.1390
0.4088
0.3008
193512010
0.0080
0.0039
11
0.0049
0.0389
0.0551
11
0.1417
0.1083
11
6.2010
2.1570
11
3.7900
0.3168
0.2930
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0029
0.0154
10.004
71
0.0016
0.0584
0.1102
0.0441
10.0012
0.0632
0.0002
11.0000
2.8040
12.126
01
0.5521
0.3076
0.2954
1935145
0.0097
0.0061
0.0009
10.0095
0.0653
0.1093
0.0386
10.0095
10.162
310.000
11
1.6990
0.6402
0.2552
11.6750
0.2999
0.3069
1946155
10.001
30.0191
10.006
31
10.002
20.0401
0.0840
0.0289
10.0684
0.0004
0.0000
110.353
32.4930
12.393
01
10.611
40.3532
0.3083
195616/68
0.0004
0.0206
10.008
21
10.002
20.0640
0.1282
0.0567
10.3073
0.2250
0.0007
10.0707
1.9690
11.775
01
10.427
60.2779
0.2711
1935140
0.0086
0.0032
0.0003
10.0085
0.0717
0.1299
0.0378
10.0481
10.190
210.000
31
1.0110
0.2077
0.0651
11.0020
0.2437
0.3062
1941145
0.0110
0.0096
0.0015
10.0108
0.0573
0.0792
0.0397
10.0832
10.083
00.0001
11.4830
0.9345
0.2987
11.4540
0.3665
0.2967
1946150
10.004
30.0171
10.005
11
10.005
00.0456
0.0891
0.0250
10.1131
0.0714
0.0001
110.729
11.4840
11.572
01
10.841
20.4167
0.3256
1951155
0.0017
0.0212
10.007
61
0.0005
0.0337
0.0792
0.0325
110.018
410.105
60.0000
10.3925
2.0700
11.800
01
0.1112
0.2896
0.2784
1956160
0.0067
0.0153
10.011
41
0.0046
0.0312
0.0780
0.0398
10.2253
0.0774
0.0005
11.6570
1.5210
12.220
01
1.1290
0.2579
0.2857
196116/68
10.003
80.0241
10.006
11
10.006
80.0786
0.1531
0.0657
10.3058
0.2487
0.0008
110.461
91.4960
10.879
21
10.816
80.2912
0.2617
7/196812010
0.0058
0.0092
10.003
11
0.0013
0.0715
0.1438
0.0621
10.0434
0.0081
10.000
11
1.8360
1.4470
11.145
01
0.4037
0.3335
0.2866
1970180
0.0067
10.000
30.0039
10.0012
0.1024
0.1829
0.0747
10.0131
10.062
110.000
31
0.7511
10.016
20.5965
10.1386
0.3419
0.2726
1980190
0.0066
0.0239
10.014
61
10.000
40.0826
0.1655
0.0614
10.0533
0.0631
0.0000
10.9230
1.6570
12.732
01
10.058
50.3453
0.3015
1990100
0.0092
10.000
20.0023
10.0051
0.0575
0.1386
0.0714
10.1622
0.0939
0.0002
11.8430
10.020
70.3700
11.0280
0.3216
0.2688
2000110
0.0071
0.0056
10.002
31
0.0051
0.0353
0.0935
0.0450
10.1136
10.007
410.000
31
2.3230
0.6849
10.594
71
1.6520
0.3473
0.3022
1970175
10.000
30.0108
10.004
51
10.005
10.1050
0.1872
0.0812
110.033
910.124
110.000
71
10.023
30.4913
10.466
31
10.410
00.3195
0.2616
1975180
0.0148
10.007
00.0113
10.0088
0.1053
0.1883
0.0769
10.0387
10.027
010.000
21
1.1910
10.313
41.2470
10.7092
0.3639
0.2832
1980185
0.0142
0.0096
10.005
21
0.0059
0.0873
0.1574
0.0553
10.1045
0.1200
0.0001
11.3810
0.5182
10.794
91
0.5756
0.3821
0.2928
1985190
0.0007
0.0380
10.023
71
10.004
90.0744
0.1670
0.0637
110.046
010.018
610.000
11
0.0828
1.9310
13.155
01
10.561
40.3005
0.3112
1990195
0.0078
0.0035
0.0001
10.0038
0.0627
0.1415
0.0758
10.2046
0.1084
0.0006
11.0550
0.2088
0.0118
10.5164
0.2920
0.2628
1995100
0.0106
0.0022
0.0011
10.0063
0.0504
0.1309
0.0630
10.0712
0.0733
10.000
11
1.7810
0.1438
0.1435
11.0630
0.3752
0.2694
2000105
0.0099
0.0044
10.002
51
0.0077
0.0339
0.0935
0.0568
10.0997
10.099
910.000
61
2.4850
0.4021
10.368
61
1.9260
0.3231
0.2779
2005110
0.0035
0.0076
10.002
51
0.0016
0.0359
0.0877
0.0235
10.1275
0.0922
0.0000
10.8340
0.7322
10.908
91
0.3742
0.3497
0.3180
193512010
0.0045
0.0120
10.003
81
0.0014
0.0661
0.1301
0.0549
10.0896
0.0261
0.0000
12.0740
2.7730
12.102
01
0.6514
0.3221
0.2906
TABLE!3c:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
43
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0093
0.0082
110.072
90.0080
0.0499
0.0518
10.7504
0.0077
10.095
91
0.0121
3.7340
3.1680
111.946
03.2090
0.3098
0.2988
1935145
0.0082
0.0077
10.0088
0.0080
0.0709
0.0621
10.7051
0.0082
10.233
61
10.077
61.3220
1.4220
10.1422
1.2990
0.2995
0.3053
1946155
0.0095
0.0085
110.122
00.0085
0.0306
0.0440
10.6012
0.0642
10.103
81
10.044
93.3890
2.1300
112.224
03.0520
0.3600
0.3161
195616/68
0.0102
0.0083
110.104
90.0076
0.0395
0.0480
10.8834
0.1732
0.1148
10.1328
3.1540
2.1280
111.455
02.3370
0.2785
0.2747
1935140
0.0098
0.0064
110.052
10.0097
0.0861
0.0740
10.5839
10.043
810.257
31
10.075
30.9567
0.7243
110.751
80.9490
0.2438
0.3067
1941145
0.0063
0.0093
10.0808
0.0061
0.0477
0.0445
10.8254
0.0857
10.144
61
10.054
01.0260
1.6190
10.7580
0.9902
0.3655
0.2927
1946150
0.0057
0.0093
110.125
20.0050
0.0346
0.0487
10.5616
0.1704
10.110
21
10.021
41.2710
1.4760
111.727
01.1210
0.4294
0.3233
1951155
0.0133
0.0078
110.118
90.0120
0.0257
0.0391
10.6431
10.092
910.147
31
10.059
33.9930
1.5490
111.431
03.6220
0.2906
0.2953
1956160
0.0196
0.0010
110.189
60.0175
0.0311
0.0413
10.9049
0.2621
0.0764
10.2536
4.8850
0.1827
111.623
04.3660
0.2512
0.2898
196116/68
0.0039
0.0133
110.048
50.0009
0.0432
0.0517
10.8692
0.0806
0.1165
10.0536
0.8482
2.4340
110.529
30.2021
0.2967
0.2642
7/196812010
0.0079
0.0003
10.0376
0.0033
0.0460
0.0713
10.8925
0.0840
0.0419
110.016
43.8640
0.0992
10.9504
1.6440
0.3182
0.2816
1970180
10.001
110.002
01
0.1857
10.006
50.0497
0.0731
11.0340
0.1503
10.055
11
0.0229
10.251
710.308
31
2.0630
11.522
00.3404
0.2749
1980190
0.0198
10.001
51
10.064
70.0128
0.0467
0.0852
10.7812
10.023
40.0310
110.114
34.8770
10.199
61
10.950
93.1560
0.3152
0.2885
1990100
0.0062
10.000
91
0.0708
0.0021
0.0434
0.0606
10.6678
0.0822
0.1050
10.0365
1.6360
10.172
31
1.2190
0.5562
0.3012
0.2732
2000110
0.0078
10.000
41
0.0303
0.0057
0.0447
0.0762
10.9884
0.0409
0.0900
110.029
52.0070
10.064
11
0.3521
1.4710
0.3218
0.2908
1970175
0.0016
10.002
21
0.0916
10.003
20.0531
0.0640
11.1350
0.0873
0.0345
110.002
40.2582
10.297
71
0.6851
10.506
80.3171
0.2694
1975180
10.003
20.0036
10.2652
10.009
20.0468
0.0826
11.0050
0.2568
10.104
81
0.1128
10.577
70.3718
12.2390
11.688
00.3666
0.2818
1980185
0.0190
10.008
01
0.0838
0.0107
0.0471
0.0830
10.8482
0.0404
10.052
31
10.140
93.4270
10.822
31
0.8380
1.9360
0.3512
0.2860
1985190
0.0222
0.0047
110.203
10.0166
0.0442
0.0851
10.6847
10.076
10.0843
110.094
04.2560
0.4679
112.517
03.1910
0.2663
0.2867
1990195
0.0076
0.0001
10.0411
0.0036
0.0410
0.0537
10.5840
0.1750
0.2369
10.0699
1.5690
0.0121
10.5964
0.7514
0.2841
0.2654
1995100
0.0076
10.001
81
0.0872
0.0033
0.0445
0.0646
10.7058
0.0219
0.0192
110.007
41.4470
10.230
41
1.0480
0.6347
0.3330
0.2780
2000105
0.0098
10.002
81
0.0539
0.0075
0.0377
0.0735
10.8449
10.174
810.026
31
10.064
52.1990
10.326
41
0.5414
1.6870
0.2820
0.2821
2005110
0.0050
0.0015
10.0179
0.0031
0.0486
0.0741
11.0730
0.1728
0.2041
10.0247
0.8778
0.1733
10.1418
0.5368
0.3397
0.2917
193512010
0.0085
0.0038
110.011
10.0054
0.0478
0.0636
10.8343
0.0651
0.0059
110.003
15.3760
1.7970
110.400
53.4090
0.3145
0.2892
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0050
0.0147
10.003
710.038
30.0037
0.0764
0.1110
0.0455
0.7757
0.0032
0.0791
0.0002
10.026
61.3180
2.6470
11.635
010.987
90.9757
0.3195
0.3043
1935145
0.0075
0.0073
10.000
40.0352
0.0073
0.0979
0.1127
0.0412
0.7479
0.0077
10.097
010.000
110.104
40.8713
0.7402
10.107
40.5385
0.8547
0.3115
0.3125
1946155
0.0040
0.0163
10.003
610.090
90.0030
0.0475
0.0819
0.0293
0.6156
0.0351
0.0570
0.0001
10.034
90.9184
2.1850
11.353
011.618
00.6998
0.3661
0.3216
195616/68
0.0038
0.0198
10.006
710.060
30.0011
0.0742
0.1288
0.0581
0.9040
0.2008
0.2049
0.0005
0.0467
0.6191
1.8830
11.413
010.817
20.1887
0.2891
0.2793
1935140
0.0135
0.0009
0.0018
10.043
90.0134
0.1101
0.1383
0.0433
0.6429
0.0255
10.085
610.000
110.046
61.0330
0.0529
0.3571
10.575
41.0270
0.2489
0.3162
1941145
0.0003
0.0149
10.003
00.1288
0.0001
0.0816
0.0721
0.0387
0.8519
10.108
310.178
810.000
210.133
10.0298
1.5990
10.603
11.1710
0.0088
0.3856
0.2937
1946150
0.0023
0.0141
10.002
110.108
60.0016
0.0575
0.0905
0.0273
0.5920
0.1327
0.1441
0.0001
10.013
50.3071
1.2060
10.599
711.420
00.2172
0.4313
0.3321
1951155
0.0057
0.0186
10.005
110.073
20.0045
0.0353
0.0730
0.0313
0.6428
10.115
110.088
40.0000
10.039
31.2490
1.9720
11.268
010.882
60.9786
0.3009
0.2995
1956160
0.0107
0.0150
10.009
410.091
80.0085
0.0443
0.0817
0.0406
0.9351
10.156
90.0006
0.0000
0.0093
1.8640
1.4210
11.790
010.760
41.4970
0.2525
0.2952
196116/68
10.000
90.0230
10.004
910.039
310.003
80.0887
0.1527
0.0674
0.8874
0.2519
0.2417
0.0008
0.0716
10.091
31.4300
10.691
110.420
510.405
70.3135
0.2671
7/196812010
10.001
30.0142
10.008
20.1044
10.005
80.0892
0.1520
0.0698
0.9407
0.1055
0.0150
10.000
10.0326
10.325
82.1070
12.654
02.5060
11.474
00.3535
0.2922
1970180
10.014
60.0160
10.009
60.2805
10.020
10.1302
0.1923
0.0865
1.1690
0.1672
10.006
00.0003
0.2879
11.290
00.9540
11.271
02.7560
11.775
00.3733
0.2791
1980190
0.0037
0.0227
10.016
40.0778
10.003
40.0947
0.1759
0.0761
0.7946
0.0490
0.0549
10.000
110.109
00.4492
1.4810
12.475
01.1250
10.408
60.3478
0.3097
1990100
0.0057
0.0007
10.000
50.0671
0.0016
0.0713
0.1488
0.0806
0.7340
0.0881
0.0293
10.000
610.018
30.9185
0.0559
10.064
41.0500
0.2604
0.3355
0.2752
2000110
0.0055
0.0050
10.002
90.0385
0.0034
0.0477
0.1038
0.0448
0.9713
0.0131
0.0391
10.000
410.069
91.3200
0.5516
10.737
00.4554
0.8175
0.3704
0.3019
1970175
10.023
00.0297
10.016
50.2600
10.027
80.1336
0.1926
0.0880
1.1810
0.1943
10.030
30.0007
0.3707
11.460
01.3060
11.596
01.8680
11.763
00.3529
0.2691
1975180
10.001
40.0029
10.000
90.2605
10.007
40.1303
0.1979
0.0906
1.1770
0.1023
10.043
210.000
70.3063
10.093
50.1227
10.083
41.8780
10.486
00.3944
0.2952
1980185
0.0063
0.0078
10.009
70.1904
10.002
10.0889
0.1583
0.0554
0.7527
0.1994
0.1145
0.0004
10.042
00.5981
0.4188
11.482
02.1460
10.197
40.3852
0.3022
1985190
0.0019
0.0371
10.023
010.015
510.003
70.0966
0.1850
0.0886
0.7998
10.089
810.015
610.000
610.167
40.1687
1.7010
12.200
010.164
110.327
20.3009
0.3151
1990195
0.0049
0.0068
10.003
60.0457
0.0009
0.0812
0.1584
0.0907
0.7231
0.0816
0.0292
10.000
90.0361
0.5110
0.3661
10.334
00.5362
0.0957
0.3112
0.2743
1995100
0.0069
10.000
10.0000
0.0832
0.0026
0.0568
0.1325
0.0639
0.6991
0.0818
0.0256
10.000
210.074
11.0300
10.005
20.0063
1.0100
0.3919
0.3822
0.2709
2000105
0.0077
0.0033
10.003
40.0560
0.0055
0.0392
0.1024
0.0565
0.8238
10.072
210.057
510.000
710.077
41.6680
0.2762
10.513
30.5763
1.1780
0.3359
0.2828
2005110
0.0017
0.0068
10.002
60.0386
10.000
20.0534
0.0989
0.0235
1.0610
0.0732
0.1399
0.0000
10.033
40.2771
0.5825
10.953
10.3091
10.031
40.3819
0.3110
193512010
0.0015
0.0144
10.006
20.0416
10.001
60.0839
0.1355
0.0604
0.8743
0.0936
0.0333
0.0000
0.0073
0.5377
3.2090
13.115
01.4360
10.582
60.3385
0.2979
TABLE!3c:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
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Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
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t(¯ �0)
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r2s(
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Rp
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�1t�
p+�2t�
2 p+
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(ei)
+⌘
p
44
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!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0096
0.0026
11
0.0083
0.0528
0.0472
11
0.0080
0.0339
11
3.6250
1.1050
11
3.1330
0.3051
0.3016
1935145
0.0061
0.0088
11
0.0060
0.0730
0.0586
11
0.0060
10.024
41
10.9563
1.7170
11
0.9339
0.2945
0.2914
1946155
0.0082
0.0031
11
0.0072
0.0376
0.0396
11
0.0480
0.0870
11
2.3780
0.8448
11
2.1030
0.3284
0.3196
195616/68
0.0137
10.003
11
10.0111
0.0410
0.0410
11
0.2004
0.0572
11
4.0900
10.941
01
13.3090
0.2958
0.2965
1935140
0.0057
0.0049
11
0.0056
0.0900
0.0676
11
0.0153
10.068
01
10.5316
0.6171
11
0.5243
0.2371
0.2895
1941145
0.0066
0.0133
11
0.0064
0.0461
0.0458
11
10.008
80.0616
11
1.1070
2.2520
11
1.0710
0.3624
0.2811
1946150
0.0028
0.0048
11
0.0022
0.0446
0.0454
11
0.1849
0.0751
11
0.4909
0.8178
11
0.3751
0.4101
0.3265
1951155
0.0135
0.0013
11
0.0123
0.0284
0.0331
11
10.289
90.0947
11
3.6850
0.3079
11
3.3470
0.2466
0.2930
1956160
0.0148
10.007
11
10.0127
0.0262
0.0322
11
0.2778
0.0337
11
4.3790
11.694
01
13.7420
0.2210
0.3130
196116/68
0.0130
10.000
51
10.0100
0.0486
0.0459
11
0.1801
0.0581
11
2.5320
10.112
71
11.9590
0.3456
0.2756
7/196812010
0.0110
0.0000
11
0.0064
0.0451
0.0544
11
0.0764
0.1031
11
5.4830
10.006
21
13.2250
0.3260
0.2861
1970180
0.0071
0.0043
11
0.0016
0.0531
0.0552
11
0.1025
0.2262
11
1.5290
0.8900
11
0.3495
0.3167
0.2829
1980190
0.0193
10.006
11
10.0123
0.0481
0.0640
11
0.0116
0.0786
11
4.6110
11.101
01
12.9360
0.3021
0.2873
1990100
0.0096
0.0016
11
0.0055
0.0377
0.0526
11
0.0824
0.0614
11
2.9220
0.3412
11
1.6870
0.3148
0.2767
2000110
0.0111
10.002
31
10.0090
0.0355
0.0488
11
0.0163
0.0983
11
3.5730
10.552
41
12.9080
0.3764
0.3019
1970175
0.0085
10.001
41
10.0038
0.0622
0.0520
11
0.1359
0.2678
11
1.1650
10.226
71
10.5120
0.3097
0.2774
1975180
0.0074
0.0125
11
0.0014
0.0482
0.0569
11
0.0137
0.1922
11
1.2970
1.8680
11
0.2428
0.3126
0.2900
1980185
0.0216
10.004
81
10.0133
0.0486
0.0591
11
0.0023
0.0895
11
3.7750
10.684
61
12.3200
0.3452
0.2898
1985190
0.0204
10.009
01
10.0147
0.0456
0.0649
11
0.0302
0.0694
11
3.7920
11.173
01
12.7540
0.2501
0.2768
1990195
0.0116
10.000
81
10.0076
0.0349
0.0492
11
0.0817
0.0415
11
2.8270
10.131
71
11.8740
0.2831
0.2682
1995100
0.0113
0.0019
11
0.0070
0.0411
0.0547
11
0.1258
0.0971
11
2.3220
0.3004
11
1.4450
0.3512
0.2821
2000105
0.0162
10.004
91
10.0139
0.0323
0.0457
11
10.099
710.064
51
14.2510
10.904
71
13.6590
0.3327
0.3018
2005110
0.0058
0.0002
11
0.0038
0.0362
0.0489
11
0.0795
0.2202
11
1.3580
0.0431
11
0.9031
0.4088
0.3008
193512010
0.0103
0.0011
11
0.0072
0.0486
0.0514
11
0.0679
0.0787
11
6.4180
0.6693
11
4.4960
0.3168
0.2930
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0055
0.0111
10.003
91
0.0042
0.0807
0.1557
0.0661
10.0041
10.068
310.000
41
1.3760
1.4250
11.187
01
1.0530
0.0844
0.1824
1935145
0.0042
0.0115
10.000
71
0.0040
0.0940
0.1546
0.0515
10.0040
10.058
410.000
11
0.5088
0.8497
10.162
11
0.4914
0.0852
0.1790
1946155
0.0051
0.0090
10.002
51
0.0041
0.0648
0.1247
0.0496
110.150
610.131
410.000
61
0.8584
0.7925
10.556
71
0.6988
0.1164
0.2132
195616/68
0.0071
0.0124
10.007
81
0.0045
0.0802
0.1782
0.0861
10.0462
10.053
210.000
51
1.0880
0.8495
11.112
01
0.6892
0.0582
0.1535
1935140
0.0049
0.0064
10.000
51
0.0049
0.1109
0.1771
0.0557
10.0138
10.079
710.000
41
0.3759
0.3037
10.080
51
0.3700
0.0725
0.1717
1941145
0.0033
0.0175
10.001
01
0.0030
0.0697
0.1240
0.0465
10.1272
10.021
20.0001
10.3629
1.0940
10.160
41
0.3385
0.1003
0.1875
1946150
0.0020
0.0055
10.000
11
0.0014
0.0611
0.1019
0.0344
110.160
810.026
40.0000
10.2573
0.4203
10.014
41
0.1730
0.1494
0.2207
1951155
0.0081
0.0125
10.005
01
0.0069
0.0686
0.1447
0.0613
110.131
310.193
610.001
21
0.9170
0.6695
10.628
21
0.7788
0.0834
0.2019
1956160
0.0017
0.0287
10.019
81
10.000
40.0574
0.1461
0.0721
110.110
110.244
910.000
61
0.2319
1.5240
12.124
01
10.052
60.0170
0.1205
196116/68
0.0107
0.0015
0.0002
10.0078
0.0924
0.1968
0.0938
10.0732
10.001
910.000
51
1.1000
0.0699
0.0153
10.7983
0.0856
0.1671
7/196812010
0.0078
0.0084
10.004
51
0.0032
0.0960
0.1920
0.0869
10.1216
0.0940
0.0003
11.8270
0.9822
11.169
01
0.7603
0.0942
0.1787
1970180
0.0015
0.0148
10.004
41
10.003
90.1504
0.2683
0.1061
10.1876
0.1559
0.0018
10.1167
0.6351
10.481
31
10.300
20.0822
0.1706
1980190
0.0124
0.0119
10.009
71
0.0053
0.0912
0.1970
0.0896
10.0196
0.0867
0.0003
11.5580
0.6948
11.248
01
0.6718
0.0945
0.1798
1990100
0.0118
10.004
20.0029
10.0078
0.0578
0.1585
0.0920
10.0041
10.063
910.000
81
2.3530
10.305
10.3639
11.5410
0.0789
0.1637
2000110
0.0057
0.0164
10.011
41
0.0036
0.0411
0.1036
0.0516
10.0218
0.0069
0.0001
11.5850
1.8170
12.532
01
1.0070
0.1176
0.1913
1970175
0.0106
10.004
70.0012
10.0058
0.1668
0.2886
0.1187
10.2909
0.2477
0.0034
10.5380
10.138
40.0870
10.2939
0.0786
0.1660
1975180
10.000
30.0263
10.005
51
10.006
30.1354
0.2480
0.0945
110.039
910.025
110.000
51
10.015
80.8987
10.496
31
10.392
30.0808
0.1699
1980185
0.0152
0.0092
10.006
51
0.0069
0.1017
0.2046
0.0875
110.091
80.0092
10.000
31
1.2670
0.3820
10.633
71
0.5752
0.1087
0.1790
1985190
0.0103
0.0179
10.014
71
0.0046
0.0803
0.1942
0.0936
10.1986
0.1565
0.0008
11.0870
0.7804
11.332
01
0.4914
0.0802
0.1765
1990195
0.0105
0.0027
10.002
11
0.0066
0.0625
0.1624
0.0943
110.137
910.201
710.001
81
1.4300
0.1406
10.188
11
0.8907
0.0733
0.1434
1995100
0.0164
10.011
90.0074
10.0121
0.0525
0.1500
0.0849
10.1888
0.0579
0.0000
12.6450
10.672
80.7360
11.9530
0.0895
0.1844
2000105
0.0043
0.0342
10.022
81
0.0020
0.0398
0.1025
0.0617
10.0064
10.033
10.0003
10.9113
2.8310
13.133
01
0.4289
0.0908
0.1647
2005110
0.0063
10.000
70.0003
10.0044
0.0411
0.0961
0.0299
10.0343
10.037
010.000
11
1.2990
10.066
00.0756
10.9008
0.1436
0.2114
193512010
0.0068
0.0096
10.004
21
0.0037
0.0895
0.1769
0.0784
10.0808
0.0389
0.0000
12.2890
1.6300
11.633
01
1.2390
0.0899
0.1803
TABLE!3d
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+�3ts p
(ei)
+⌘
p
45
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0114
0.0062
110.081
40.0101
0.0586
0.0548
10.8072
0.0099
0.0182
110.099
93.8840
2.2530
112.019
03.4420
0.0905
0.1856
1935145
0.0075
0.0107
110.030
70.0074
0.0781
0.0626
10.4746
0.0075
10.012
91
10.015
31.1040
1.9540
110.740
51.0830
0.0811
0.1719
1946155
0.0091
0.0072
110.096
10.0082
0.0395
0.0515
10.8120
0.0276
0.0790
110.103
32.5360
1.5400
111.297
02.2740
0.1247
0.2208
195616/68
0.0165
0.0014
110.113
80.0139
0.0510
0.0498
11.0110
0.0351
10.006
21
10.172
73.9550
0.3323
111.378
03.3300
0.0715
0.1624
1935140
0.0077
0.0062
110.015
50.0077
0.0952
0.0689
10.4469
10.059
710.000
81
10.009
50.6850
0.7563
110.293
00.6781
0.0678
0.1584
1941145
0.0073
0.0160
110.048
70.0071
0.0518
0.0543
10.5087
10.079
610.061
41
10.022
71.0900
2.2860
110.740
81.0580
0.0969
0.1867
1946150
0.0026
0.0073
110.048
70.0020
0.0437
0.0568
10.7199
0.2025
0.0494
110.044
90.4671
0.9939
110.524
10.3490
0.1641
0.2247
1951155
0.0156
0.0072
110.143
60.0144
0.0339
0.0462
10.8983
10.257
10.1264
110.171
13.5780
1.2080
111.238
03.2950
0.0852
0.2114
1956160
0.0187
10.001
21
10.146
80.0166
0.0334
0.0514
11.2910
10.141
610.044
51
10.256
84.3450
10.184
51
10.880
83.8590
0.0575
0.1427
196116/68
0.0150
0.0031
110.091
80.0121
0.0602
0.0490
10.7780
0.0624
0.0164
110.113
62.3660
0.5947
111.119
01.9030
0.0807
0.1744
7/196812010
0.0103
10.002
01
0.0378
0.0058
0.0536
0.0637
10.8938
0.0721
0.0143
110.038
24.3380
10.704
41
0.9561
2.4330
0.0892
0.1666
1970180
0.0040
10.004
01
0.1644
10.001
50.0638
0.0685
11.1850
0.1083
0.0348
110.007
20.7198
10.675
71
1.5930
10.263
60.0834
0.1639
1980190
0.0189
10.006
71
0.0131
0.0119
0.0507
0.0756
10.7363
0.0154
10.020
91
10.118
14.2880
11.013
01
0.2039
2.6980
0.0836
0.1788
1990100
0.0097
0.0026
110.016
90.0056
0.0481
0.0553
10.6540
0.0057
10.013
21
10.017
32.3200
0.5399
110.296
31.3490
0.0848
0.1492
2000110
0.0115
10.003
21
0.0012
0.0095
0.0456
0.0558
10.7781
0.0437
0.0330
110.054
62.9060
10.659
21
0.0178
2.3880
0.1021
0.1713
1970175
0.0054
10.006
61
0.1382
0.0006
0.0742
0.0742
11.3380
0.0913
0.0851
110.032
60.6197
10.755
41
0.8765
0.0714
0.0684
0.1437
1975180
0.0079
0.0088
10.0363
0.0019
0.0624
0.0691
11.1510
0.1048
10.054
91
0.0319
1.0780
1.0770
10.2673
0.2621
0.0945
0.1750
1980185
0.0217
10.007
11
0.0284
0.0134
0.0495
0.0805
10.8095
0.0271
10.059
31
10.148
53.7240
10.749
91
0.2973
2.2990
0.0925
0.1847
1985190
0.0196
10.007
61
10.004
80.0139
0.0502
0.0672
10.6511
0.0119
0.0284
110.093
13.3030
10.961
51
10.062
82.3590
0.0712
0.1668
1990195
0.0123
0.0018
110.040
20.0083
0.0402
0.0478
10.5349
10.008
510.005
51
0.0047
2.5930
0.3183
110.637
11.7680
0.0777
0.1369
1995100
0.0105
0.0013
10.0135
0.0062
0.0549
0.0605
10.7295
0.0287
0.0011
110.039
51.6150
0.1785
10.1570
0.9567
0.1005
0.1623
2000105
0.0124
10.010
11
0.1006
0.0101
0.0371
0.0519
10.6943
0.0139
10.297
71
10.044
32.8320
11.653
01
1.2290
2.3140
0.0821
0.1521
2005110
0.0100
0.0035
110.086
80.0081
0.0510
0.0549
10.8017
0.0680
0.2887
110.053
51.6650
0.5417
110.919
01.3440
0.1167
0.1907
193512010
0.0108
0.0016
110.014
60.0077
0.0558
0.0600
10.8583
0.0298
0.0188
110.067
65.8210
0.8054
110.514
54.1420
0.0898
0.1751
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0101
0.0090
10.001
610.073
60.0088
0.0958
0.1609
0.0690
0.8374
0.0087
10.052
310.000
210.087
72.1020
1.1200
10.461
111.760
01.8300
0.0892
0.1993
1935145
0.0113
0.0057
0.0023
10.042
60.0111
0.1173
0.1658
0.0589
0.5858
0.0110
10.060
510.000
210.038
51.0990
0.3932
0.4531
10.832
11.0850
0.0791
0.1935
1946155
0.0079
0.0088
10.000
410.095
40.0070
0.0692
0.1218
0.0490
0.8268
0.0117
10.095
810.000
210.063
01.2500
0.7953
10.100
111.263
01.1010
0.1268
0.2278
195616/68
0.0107
0.0120
10.005
910.083
30.0081
0.0937
0.1834
0.0884
1.0180
0.0586
10.033
510.000
310.148
51.4010
0.8016
10.821
011.002
01.0610
0.0679
0.1757
1935140
0.0109
0.0038
0.0012
10.024
70.0108
0.1405
0.1950
0.0657
0.6137
10.019
510.074
110.000
310.029
00.6541
0.1628
0.1591
10.339
00.6494
0.0719
0.1842
1941145
0.0117
0.0080
0.0036
10.063
80.0115
0.0832
0.1242
0.0500
0.5554
10.088
810.031
410.000
110.050
61.0890
0.4974
0.5601
10.889
41.0690
0.0877
0.2051
1946150
0.0008
0.0089
10.000
510.038
60.0001
0.0672
0.0992
0.0355
0.7604
10.005
60.0122
0.0001
10.021
60.0891
0.6939
10.108
210.393
60.0124
0.1649
0.2368
1951155
0.0150
0.0088
10.000
410.152
10.0138
0.0711
0.1417
0.0599
0.8911
0.0291
10.153
610.000
510.113
91.6370
0.4810
10.051
711.322
01.5040
0.0888
0.2137
1956160
0.0064
0.0304
10.017
710.128
00.0043
0.0609
0.1450
0.0699
1.2800
10.224
310.162
110.000
410.224
60.8148
1.6210
11.965
010.774
30.5470
0.0461
0.1537
196116/68
0.0136
10.000
20.0019
10.053
50.0107
0.1106
0.2049
0.0984
0.8031
0.1019
10.007
910.000
410.096
51.1670
10.010
80.1876
10.632
10.9153
0.0825
0.1884
7/196812010
0.0067
0.0056
10.004
20.0489
0.0022
0.1061
0.1940
0.0917
0.9209
0.1287
0.1039
0.0006
10.010
61.4340
0.6473
11.042
01.2000
0.4686
0.1002
0.1917
1970180
10.000
90.0064
10.004
00.1455
10.006
30.1637
0.2623
0.1101
1.2040
0.1895
0.1765
0.0022
0.0043
10.061
10.2805
10.420
91.3880
10.444
10.1038
0.1911
1980190
0.0107
0.0066
10.008
40.0694
0.0037
0.0998
0.2058
0.1006
0.7939
0.0718
0.1180
0.0011
10.045
41.2330
0.3681
10.960
01.0050
0.4231
0.0920
0.2014
1990100
0.0151
10.010
00.0074
10.032
90.0110
0.0719
0.1687
0.1001
0.6770
10.001
010.066
010.000
810.002
72.4050
10.682
40.8461
10.558
11.7550
0.0865
0.1755
2000110
0.0049
0.0176
10.012
20.0099
0.0028
0.0498
0.1127
0.0522
0.8228
0.0198
0.0409
0.0002
10.025
21.1310
1.7930
12.697
00.1380
0.6547
0.1125
0.1916
1970175
0.0097
10.010
20.0024
0.0838
0.0049
0.1821
0.2893
0.1230
1.3540
0.2473
0.2526
0.0037
10.070
00.4526
10.299
70.1685
0.5249
0.2291
0.0999
0.1794
1975180
10.002
50.0254
10.007
30.0618
10.008
50.1456
0.2348
0.0968
1.1580
0.0335
10.007
70.0000
0.1010
10.147
00.9195
10.643
30.4529
10.497
30.1042
0.1962
1980185
0.0093
0.0121
10.011
20.1035
0.0010
0.1104
0.2048
0.0929
0.8707
10.017
90.0445
0.0005
10.054
00.7147
0.5021
11.023
01.0090
0.0751
0.1094
0.2088
1985190
0.0133
0.0049
10.007
50.0245
0.0077
0.0924
0.2087
0.1090
0.7100
0.1696
0.1734
0.0014
10.053
81.2220
0.1977
10.580
30.2922
0.7041
0.0789
0.1882
1990195
0.0166
10.008
30.0065
10.059
80.0127
0.0775
0.1791
0.1091
0.5989
10.124
610.165
210.001
90.0255
1.8200
10.395
20.5065
10.847
81.3890
0.0811
0.1616
1995100
0.0161
10.012
00.0074
0.0008
0.0118
0.0652
0.1521
0.0848
0.7209
0.1601
0.0369
0.0002
10.034
42.0900
10.671
60.7383
0.0096
1.5330
0.1022
0.1889
2000105
0.0014
0.0297
10.022
60.0813
10.000
90.0430
0.1105
0.0621
0.7358
10.011
60.0113
0.0004
10.033
50.2775
2.2800
13.090
00.9378
10.168
10.0886
0.1673
2005110
0.0080
0.0066
10.001
610.072
60.0061
0.0536
0.1083
0.0318
0.8559
0.0368
0.0277
0.0000
10.006
01.2710
0.5151
10.430
610.719
50.9664
0.1297
0.2136
193512010
0.0082
0.0071
10.003
110.005
00.0051
0.1017
0.1801
0.0825
0.8867
0.0819
0.0493
0.0002
10.046
92.4340
1.1850
11.123
010.170
51.5100
0.0954
0.1951
TABLE!3d
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Equal1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
46
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0096
0.0043
11
0.0083
0.0451
0.0545
11
0.0080
0.0187
11
4.2460
1.5860
11
3.6620
0.2589
0.2666
1935145
0.0103
0.0088
11
0.0101
0.0610
0.0737
11
0.0103
10.044
81
11.9250
1.3600
11
1.8990
0.2677
0.2522
1946155
0.0093
0.0024
11
0.0083
0.0344
0.0432
11
10.050
50.0653
11
2.9550
0.6019
11
2.6530
0.2654
0.2938
195616/68
0.0092
0.0020
11
0.0066
0.0356
0.0416
11
0.2036
0.1328
11
3.1590
0.5888
11
2.2520
0.2461
0.2572
1935140
0.0098
0.0031
11
0.0097
0.0751
0.0877
11
10.057
010.106
61
11.0940
0.2986
11
1.0850
0.2276
0.2504
1941145
0.0109
0.0154
11
0.0107
0.0389
0.0524
11
0.1401
0.1098
11
2.1680
2.2810
11
2.1260
0.3152
0.2480
1946150
0.0059
0.0024
11
0.0052
0.0389
0.0475
11
0.0563
0.0703
11
1.1660
0.3969
11
1.0330
0.3477
0.3030
1951155
0.0127
0.0023
11
0.0115
0.0291
0.0387
11
10.201
80.0543
11
3.3760
0.4617
11
3.0460
0.1831
0.2616
1956160
0.0158
10.007
51
10.0137
0.0283
0.0316
11
0.0481
0.0255
11
4.3280
11.832
01
13.7380
0.1831
0.2646
196116/68
0.0048
0.0083
11
0.0018
0.0393
0.0461
11
0.2178
0.1292
11
1.1500
1.7110
11
0.4394
0.2881
0.2447
7/196812010
0.0092
0.0022
11
0.0047
0.0378
0.0544
11
0.0465
0.1277
11
5.5070
0.9199
11
2.8060
0.2830
0.2581
1970180
0.0069
0.0052
11
0.0014
0.0451
0.0648
11
0.0218
0.1182
11
1.7450
0.9262
11
0.3553
0.2972
0.2660
1980190
0.0155
10.002
51
10.0085
0.0401
0.0563
11
0.0264
0.0502
11
4.4530
10.505
01
12.4340
0.2616
0.2593
1990100
0.0096
0.0017
11
0.0055
0.0346
0.0469
11
0.0348
0.2096
11
3.1920
0.4184
11
1.8460
0.2515
0.2374
2000110
0.0067
0.0034
11
0.0046
0.0310
0.0509
11
0.0659
0.1848
11
2.4690
0.7671
11
1.7090
0.3021
0.2628
1970175
0.0066
0.0002
11
0.0018
0.0510
0.0654
11
0.0562
0.0970
11
1.0990
0.0239
11
0.3004
0.3149
0.2661
1975180
0.0086
0.0140
11
0.0026
0.0394
0.0684
11
10.091
80.1436
11
1.8570
1.7360
11
0.5690
0.2734
0.2636
1980185
0.0190
10.002
41
10.0107
0.0398
0.0526
11
0.0772
0.0138
11
4.0550
10.382
41
12.2700
0.3060
0.2561
1985190
0.0135
10.002
31
10.0079
0.0387
0.0575
11
10.043
20.0853
11
2.9610
10.338
11
11.7290
0.2238
0.2602
1990195
0.0096
0.0017
11
0.0056
0.0319
0.0468
11
0.0258
0.2612
11
2.5510
0.3107
11
1.5020
0.2366
0.2303
1995100
0.0120
0.0013
11
0.0077
0.0368
0.0461
11
0.0707
0.1688
11
2.7660
0.2483
11
1.7860
0.2730
0.2561
2000105
0.0089
0.0033
11
0.0066
0.0327
0.0446
11
0.0156
0.0282
11
2.3010
0.6270
11
1.7200
0.2645
0.2517
2005110
0.0038
0.0039
11
0.0019
0.0272
0.0543
11
0.1308
0.2791
11
1.1990
0.6140
11
0.5936
0.3307
0.2694
193512010
0.0094
0.0031
11
0.0063
0.0411
0.0544
11
0.0392
0.0815
11
6.8720
1.7420
11
4.5890
0.2724
0.2620
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
10.001
90.0301
10.012
11
10.003
20.0671
0.1584
0.0700
110.003
410.033
810.000
21
10.553
23.8040
13.475
01
10.941
70.0930
0.1658
1935145
10.001
10.0359
10.013
01
10.001
20.0685
0.1841
0.0831
110.001
510.000
110.000
21
10.184
52.2290
11.785
01
10.208
60.0719
0.1509
1946155
10.002
00.0267
10.011
21
10.002
90.0681
0.1502
0.0659
110.106
410.086
410.000
51
10.316
91.9450
11.863
01
10.469
10.1353
0.1974
195616/68
10.002
40.0278
10.012
21
10.005
00.0656
0.1403
0.0604
10.1384
10.036
810.000
11
10.451
32.4250
12.468
01
10.935
80.0778
0.1442
1935140
10.008
30.0474
10.021
91
10.008
40.0751
0.2151
0.0956
10.1757
10.055
810.000
61
10.931
71.8580
11.926
01
10.940
60.0551
0.1401
1941145
0.0074
0.0222
10.002
41
0.0072
0.0592
0.1395
0.0644
10.0478
0.1358
0.0003
10.9696
1.2310
10.292
01
0.9411
0.0917
0.1616
1946150
10.000
40.0162
10.006
11
10.001
10.0519
0.1171
0.0460
10.0609
0.1826
0.0003
110.060
31.0700
11.030
01
10.159
50.1866
0.2029
1951155
10.003
50.0372
10.016
31
10.004
80.0815
0.1777
0.0812
110.177
910.208
610.001
41
10.335
91.6210
11.554
01
10.452
60.0839
0.1790
1956160
0.0025
0.0246
10.015
71
0.0004
0.0465
0.1095
0.0526
110.164
010.439
110.000
61
0.4103
1.7390
12.307
01
0.0586
0.0648
0.1448
196116/68
10.005
70.0299
10.009
81
10.008
60.0758
0.1581
0.0653
10.2105
0.0907
0.0003
110.709
61.7940
11.430
01
11.076
00.0864
0.1439
7/196812010
0.0052
0.0125
10.005
61
0.0007
0.0714
0.1753
0.0836
10.0633
0.0772
0.0002
11.6560
1.6040
11.503
01
0.2208
0.1091
0.1661
1970180
10.002
30.0249
10.009
31
10.007
70.1000
0.2267
0.1050
10.0361
0.0048
10.000
51
10.258
41.2630
11.022
01
10.887
20.1166
0.1684
1980190
0.0120
0.0074
10.005
91
0.0050
0.0842
0.2016
0.1000
10.0109
0.0888
0.0004
11.6380
0.4220
10.676
01
0.6763
0.1061
0.1651
1990100
0.0074
0.0094
10.005
21
0.0033
0.0523
0.1502
0.0812
10.2103
0.1457
0.0009
11.6310
0.7225
10.732
81
0.7337
0.0879
0.1532
2000110
0.0049
0.0083
10.002
51
0.0029
0.0359
0.1264
0.0553
10.0295
0.0160
10.000
21
1.5790
0.7587
10.512
31
0.9189
0.1228
0.1753
1970175
0.0021
0.0097
10.004
31
10.002
70.0904
0.1921
0.0939
110.005
310.067
210.001
11
0.1972
0.4271
10.390
61
10.252
50.1105
0.1712
1975180
10.001
90.0363
10.010
51
10.007
90.1181
0.2661
0.1263
10.0524
0.0302
10.000
11
10.138
71.1580
10.703
91
10.572
10.1228
0.1679
1980185
0.0128
0.0102
10.005
71
0.0045
0.0870
0.1980
0.0944
110.145
110.024
610.000
51
1.2480
0.4366
10.508
21
0.4369
0.1102
0.1525
1985190
0.0124
0.0053
10.006
11
0.0067
0.0795
0.1987
0.1014
10.1534
0.1644
0.0011
11.3190
0.2249
10.511
91
0.7173
0.1067
0.1794
1990195
0.0038
0.0203
10.011
51
10.000
20.0585
0.1739
0.0939
10.2618
0.1881
0.0019
10.5451
0.9911
11.042
01
10.032
00.0629
0.1377
1995100
0.0146
10.005
40.0032
10.0103
0.0429
0.1107
0.0589
10.0907
10.010
610.000
21
2.8900
10.415
00.4585
12.0510
0.1161
0.1663
2000105
0.0055
0.0127
10.004
61
0.0032
0.0358
0.1132
0.0583
10.0768
10.010
910.000
21
1.3020
0.9547
10.666
71
0.7718
0.1054
0.1651
2005110
0.0039
0.0042
10.000
41
0.0019
0.0345
0.1320
0.0488
110.017
50.0165
10.000
11
0.9478
0.2701
10.072
41
0.4685
0.1377
0.1812
193512010
0.0021
0.0202
10.008
51
10.001
00.0696
0.1682
0.0779
10.0648
0.0365
0.0000
10.9171
3.6270
13.276
01
10.434
60.1020
0.1661
TABLE!3f:!Equ
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eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
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est!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
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!!
!!
!!
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!!
!!
!!
!!
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!!
!!
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!!
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193516/68
0.0089
0.0046
10.0105
0.0076
0.0472
0.0647
10.6843
0.0074
0.0363
110.018
73.7690
1.4090
10.3058
3.2110
0.1036
0.1715
1935145
0.0088
0.0087
10.0223
0.0086
0.0625
0.0834
10.5319
0.0087
10.005
61
10.036
01.6110
1.1880
10.4795
1.5860
0.0865
0.1567
1946155
0.0108
0.0058
110.073
90.0099
0.0380
0.0558
10.6840
10.164
70.0610
110.057
03.1230
1.1300
111.184
02.8490
0.1360
0.2024
195616/68
0.0074
0.0000
10.0676
0.0048
0.0376
0.0514
10.7920
0.1632
0.0846
10.0280
2.4100
0.0002
11.0460
1.5540
0.0926
0.1535
1935140
0.0080
0.0050
10.0132
0.0079
0.0760
0.0954
10.5202
10.065
80.0048
110.024
40.8877
0.4431
10.2143
0.8792
0.0749
0.1497
1941145
0.0097
0.0130
10.0330
0.0095
0.0416
0.0671
10.5496
10.031
710.049
01
10.049
71.8080
1.4980
10.4651
1.7690
0.1003
0.1647
1946150
0.0068
0.0045
110.042
10.0062
0.0404
0.0631
10.6603
10.020
10.0924
110.026
91.3120
0.5566
110.494
31.1840
0.1848
0.2027
1951155
0.0148
0.0070
110.105
70.0136
0.0353
0.0480
10.7111
10.333
40.0008
110.084
43.2520
1.1280
111.152
02.9770
0.0873
0.1916
1956160
0.0125
10.010
71
0.1178
0.0104
0.0333
0.0386
10.7273
0.0099
0.1083
10.0397
2.9030
12.144
01
1.2550
2.4110
0.0680
0.1417
196116/68
0.0040
0.0071
10.0341
0.0011
0.0400
0.0576
10.8346
0.1934
0.0361
10.0109
0.9502
1.1730
10.3881
0.2521
0.1089
0.1595
7/196812010
0.0093
0.0024
110.007
50.0048
0.0447
0.0671
10.8981
0.0026
0.0219
110.017
94.7110
0.8086
110.188
72.4320
0.1128
0.1661
1970180
0.0069
0.0050
110.007
50.0014
0.0541
0.0687
11.0780
10.040
610.008
51
0.0347
1.4640
0.8350
110.080
40.3046
0.1228
0.1675
1980190
0.0179
0.0025
110.087
20.0108
0.0462
0.0801
10.9636
0.0626
10.025
01
10.059
24.4520
0.3584
111.040
02.7040
0.0937
0.1655
1990100
0.0090
0.0007
10.0171
0.0049
0.0416
0.0553
10.7208
0.0175
0.0675
110.003
62.4760
0.1521
10.2722
1.3560
0.1089
0.1538
2000110
0.0050
10.000
61
0.0724
0.0030
0.0398
0.0650
10.8666
0.0390
0.0971
110.024
61.4500
10.102
31
0.9601
0.8572
0.1337
0.1769
1970175
0.0117
0.0126
110.218
90.0069
0.0612
0.0729
11.2070
10.132
210.038
41
10.037
41.6140
1.4630
111.540
00.9504
0.1202
0.1710
1975180
0.0043
0.0019
10.1892
10.001
70.0495
0.0670
10.9062
0.0072
10.023
41
0.0955
0.7451
0.2386
11.7720
10.287
10.1215
0.1584
1980185
0.0194
10.001
81
10.010
70.0111
0.0436
0.0698
10.7641
0.1478
10.074
31
10.058
63.7780
10.215
41
10.118
32.1640
0.0968
0.1631
1985190
0.0176
0.0062
110.151
20.0119
0.0464
0.0855
11.0870
10.004
00.0020
110.070
03.2130
0.6157
111.181
02.1880
0.0867
0.1693
1990195
0.0100
0.0016
110.007
50.0060
0.0380
0.0542
10.6810
10.063
70.1573
10.0153
2.2250
0.2458
110.092
91.3500
0.0919
0.1469
1995100
0.0098
10.001
51
0.0583
0.0056
0.0442
0.0540
10.7308
0.0992
10.026
31
10.022
01.8880
10.230
01
0.6769
1.0710
0.1282
0.1614
2000105
0.0084
0.0016
10.0277
0.0061
0.0419
0.0493
10.8496
0.0180
0.0286
10.0746
1.6960
0.2733
10.2770
1.2420
0.1264
0.1770
2005110
0.0009
10.002
41
0.1197
10.001
00.0355
0.0739
10.8561
0.0440
0.1279
110.126
40.2157
10.280
81
1.1860
10.250
00.1406
0.1838
193512010
0.0091
0.0033
10.0004
0.0060
0.0458
0.0660
10.8106
10.006
90.0280
110.019
46.0190
1.5310
10.0148
3.9730
0.1088
0.1685
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
10.002
50.0273
10.012
00.0408
10.003
80.0745
0.1549
0.0738
0.7096
10.003
910.003
30.0000
10.007
510.666
43.5300
13.253
01.1530
11.016
00.1144
0.1849
1935145
10.005
50.0375
10.016
40.0644
10.005
70.0864
0.1854
0.0966
0.6297
10.006
20.0319
0.0002
10.021
410.730
72.3150
11.939
01.1700
10.749
90.0974
0.1693
1946155
0.0032
0.0210
10.007
610.055
70.0023
0.0650
0.1385
0.0596
0.6567
10.159
410.072
310.000
310.043
70.5417
1.6600
11.392
010.929
10.3825
0.1575
0.2138
195616/68
10.004
40.0235
10.011
70.0975
10.007
00.0707
0.1378
0.0601
0.8064
0.1454
10.009
20.0000
0.0332
10.760
22.0850
12.385
01.4810
11.209
00.0948
0.1678
1935140
10.012
50.0483
10.024
80.0599
10.012
60.0886
0.2130
0.1059
0.5775
0.1656
10.025
210.000
410.026
411.190
01.9100
11.973
00.8740
11.197
00.0832
0.1617
1941145
0.0028
0.0248
10.006
40.0697
0.0026
0.0836
0.1469
0.0842
0.6913
0.0251
0.1585
0.0009
10.015
00.2571
1.3050
10.589
30.7807
0.2366
0.1143
0.1778
1946150
0.0042
0.0117
10.003
610.047
00.0035
0.0516
0.1139
0.0442
0.6354
10.019
50.1369
0.0003
10.034
60.6266
0.7985
10.635
010.572
50.5268
0.2176
0.2158
1951155
0.0023
0.0302
10.011
510.064
40.0010
0.0765
0.1598
0.0720
0.6826
10.224
210.186
210.001
010.061
20.2280
1.4660
11.241
010.731
20.1040
0.0975
0.1956
1956160
10.000
30.0164
10.013
90.1558
10.002
40.0509
0.1039
0.0513
0.7042
10.264
410.448
010.000
80.0142
10.046
21.2220
12.099
01.7140
10.366
00.0799
0.1604
196116/68
10.007
10.0282
10.010
20.0587
10.010
10.0814
0.1568
0.0656
0.8695
0.2492
0.1163
0.0006
0.0393
10.828
31.7050
11.481
00.6402
11.169
00.1047
0.1727
7/196812010
0.0045
0.0138
10.006
40.0030
10.000
10.0819
0.1795
0.0885
0.9553
0.0793
0.0535
0.0005
0.0087
1.2310
1.7300
11.626
00.0714
10.020
20.1325
0.1834
1970180
10.003
70.0283
10.011
010.006
910.009
20.1122
0.2315
0.1110
1.1640
0.0618
10.028
410.000
30.0810
10.380
41.4050
11.135
010.068
210.941
20.1390
0.1833
1980190
0.0141
0.0086
10.004
710.054
10.0071
0.1000
0.2033
0.1092
1.0620
0.0719
0.0986
0.0011
10.040
91.6220
0.4845
10.492
410.585
50.8138
0.1206
0.1802
1990100
0.0057
0.0106
10.006
40.0242
0.0017
0.0630
0.1550
0.0833
0.7836
0.1987
0.1422
0.0012
0.0207
1.0470
0.7849
10.885
80.3547
0.3023
0.1298
0.1793
2000110
0.0027
0.0064
10.003
50.0717
0.0006
0.0405
0.1360
0.0531
0.8316
0.0803
10.046
710.000
210.005
50.7523
0.5397
10.755
70.9899
0.1659
0.1540
0.1949
1970175
0.0068
0.0226
10.004
610.211
30.0020
0.1038
0.2193
0.1050
1.3360
10.021
410.094
210.000
90.0363
0.5520
0.8751
10.374
011.342
00.1604
0.1292
0.1844
1975180
10.008
70.0342
10.014
30.1515
10.014
70.1264
0.2663
0.1302
0.9575
0.0987
10.024
810.000
10.0188
10.584
71.0890
10.930
11.3420
10.991
20.1525
0.1802
1980185
0.0123
0.0119
10.006
70.0013
0.0040
0.0964
0.2006
0.0978
0.8104
10.060
710.007
010.000
310.056
21.0840
0.5019
10.577
20.0139
0.3527
0.1183
0.1721
1985190
0.0159
0.0071
10.004
010.093
00.0102
0.1024
0.2004
0.1164
1.2300
0.1507
0.1706
0.0020
10.049
31.3160
0.3022
10.289
510.641
40.8491
0.1258
0.1906
1990195
0.0027
0.0222
10.012
80.0067
10.001
30.0669
0.1747
0.0958
0.7096
0.2440
0.1912
0.0022
0.0376
0.3380
1.0780
11.131
00.0802
10.166
90.1036
0.1708
1995100
0.0110
10.003
70.0008
0.0594
0.0067
0.0579
0.1221
0.0621
0.8294
0.1435
0.0058
10.000
10.0143
1.6090
10.257
00.1064
0.6081
0.9857
0.1550
0.1888
2000105
0.0040
0.0135
10.006
00.0341
0.0017
0.0420
0.1183
0.0541
0.8265
0.0922
10.047
710.000
30.0863
0.8011
0.9653
10.946
60.3504
0.3470
0.1458
0.1916
2005110
0.0011
10.001
110.000
60.1066
10.000
90.0380
0.1425
0.0487
0.8147
0.0396
10.055
410.000
210.103
90.2364
10.066
510.100
11.1100
10.197
20.1591
0.2022
193512010
0.0014
0.0197
10.008
80.0197
10.001
70.0788
0.1691
0.0824
0.8557
0.0753
0.0343
0.0003
0.0001
0.5391
3.5190
13.242
00.6938
10.655
20.1245
0.1842
TABLE!3f:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
48
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0053
0.0071
11
0.0040
0.0371
0.0545
11
0.0037
0.0385
11
2.8610
2.6130
11
2.1530
0.2589
0.2666
1935145
0.0029
0.0123
11
0.0027
0.0482
0.0730
11
0.0027
10.044
71
10.6796
1.9300
11
0.6457
0.2677
0.2522
1946155
0.0080
0.0028
11
0.0070
0.0260
0.0368
11
0.0767
0.0727
11
3.3650
0.8473
11
2.9680
0.2654
0.2938
195616/68
0.0053
0.0060
11
0.0027
0.0334
0.0470
11
0.2914
0.1807
11
1.9360
1.5620
11
0.9749
0.2461
0.2572
1935140
0.0017
0.0085
11
0.0017
0.0571
0.0873
11
10.010
610.109
61
10.2566
0.8214
11
0.2452
0.2276
0.2504
1941145
0.0042
0.0168
11
0.0040
0.0353
0.0518
11
0.1891
0.1567
11
0.9199
2.5150
11
0.8721
0.3152
0.2480
1946150
0.0046
0.0027
11
0.0039
0.0312
0.0416
11
0.1523
0.0352
11
1.1400
0.4984
11
0.9740
0.3477
0.3030
1951155
0.0114
0.0030
11
0.0101
0.0191
0.0316
11
10.065
50.0893
11
4.6160
0.7384
11
4.1130
0.1831
0.2616
1956160
0.0146
10.006
11
10.0125
0.0190
0.0372
11
0.3003
0.1473
11
5.9630
11.263
01
15.0840
0.1831
0.2646
196116/68
10.000
90.0140
11
10.003
90.0392
0.0511
11
0.2260
0.1437
11
10.229
02.6030
11
10.938
30.2881
0.2447
7/196812010
0.0077
0.0034
11
0.0031
0.0395
0.0591
11
0.1250
0.1968
11
4.3780
1.3050
11
1.7960
0.2830
0.2581
1970180
0.0005
0.0100
11
10.004
90.0472
0.0667
11
0.2074
0.2249
11
0.1312
1.7260
11
11.201
00.2972
0.2660
1980190
0.0183
10.004
81
10.0112
0.0434
0.0622
11
0.0711
0.2373
11
4.8320
10.895
01
12.9850
0.2616
0.2593
1990100
0.0084
0.0030
11
0.0043
0.0386
0.0578
11
0.1047
0.1857
11
2.4910
0.5882
11
1.2830
0.2515
0.2374
2000110
0.0069
0.0027
11
0.0048
0.0299
0.0542
11
0.0607
0.1263
11
2.6400
0.5685
11
1.8540
0.3021
0.2628
1970175
0.0065
10.000
81
10.0017
0.0490
0.0633
11
0.1329
0.2010
11
1.1310
10.113
01
10.3006
0.3149
0.2661
1975180
10.003
30.0234
11
10.009
30.0464
0.0691
11
0.2684
0.2614
11
10.598
72.8700
11
11.714
00.2734
0.2636
1980185
0.0179
10.000
51
10.0096
0.0423
0.0580
11
0.1673
0.2079
11
3.5900
10.072
71
11.9400
0.3060
0.2561
1985190
0.0202
10.008
91
10.0146
0.0434
0.0634
11
10.015
60.2491
11
3.9500
11.195
01
12.8620
0.2238
0.2602
1990195
0.0084
0.0027
11
0.0044
0.0381
0.0551
11
0.1881
0.2861
11
1.8670
0.4138
11
0.9889
0.2366
0.2303
1995100
0.0108
0.0026
11
0.0065
0.0388
0.0585
11
0.0449
0.0906
11
2.3620
0.3781
11
1.4340
0.2730
0.2561
2000105
0.0094
0.0018
11
0.0071
0.0299
0.0544
11
10.077
210.008
41
12.6650
0.2794
11
2.0390
0.2645
0.2517
2005110
0.0036
0.0039
11
0.0016
0.0280
0.0507
11
0.2149
0.2612
11
1.0880
0.6466
11
0.4996
0.3307
0.2694
193512010
0.0066
0.0050
11
0.0035
0.0385
0.0572
11
0.1263
0.1364
11
5.1950
2.6640
11
2.7610
0.2724
0.2620
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0060
0.0059
0.0003
10.0047
0.0657
0.1213
0.0497
10.0043
10.009
60.0001
11.8410
0.9705
0.1207
11.4430
0.2777
0.2691
1935145
0.0111
10.002
20.0053
10.0109
0.0818
0.1391
0.0538
10.0111
10.101
410.000
11
1.5500
10.184
81.1270
11.5300
0.2675
0.2691
1946155
10.000
60.0177
10.005
71
10.001
50.0501
0.1046
0.0371
10.0071
10.039
710.000
11
10.123
11.8490
11.689
01
10.329
60.3199
0.2918
195616/68
0.0069
0.0036
0.0008
10.0043
0.0606
0.1171
0.0545
10.1630
0.1162
0.0003
11.3980
0.3721
0.1691
10.8708
0.2527
0.2472
1935140
0.0116
10.009
50.0067
10.0116
0.0990
0.1723
0.0635
10.0463
10.085
010.000
21
0.9901
10.463
60.8859
10.9835
0.2201
0.2680
1941145
0.0104
0.0063
0.0037
10.0102
0.0558
0.0853
0.0399
10.1600
10.194
00.0001
11.4460
0.5734
0.7132
11.4170
0.3237
0.2616
1946150
0.0001
0.0096
10.002
41
10.000
60.0530
0.1008
0.0299
10.0298
10.015
310.000
11
0.0158
0.7400
10.625
61
10.081
20.4011
0.2972
1951155
10.001
20.0257
10.009
01
10.002
50.0474
0.1085
0.0431
110.054
910.094
010.000
11
10.201
61.8330
11.621
01
10.401
90.2387
0.2646
1956160
0.0111
0.0025
10.004
21
0.0089
0.0407
0.0987
0.0482
10.3218
0.2000
0.0006
12.1030
0.1936
10.676
11
1.6990
0.2051
0.2375
196116/68
0.0042
0.0043
0.0041
10.0012
0.0709
0.1284
0.0583
10.1210
0.0842
0.0001
10.5563
0.3165
0.6599
10.1634
0.2845
0.2498
7/196812010
0.0056
0.0087
10.002
61
0.0011
0.0727
0.1495
0.0683
10.0657
10.028
510.000
31
1.7430
1.3160
10.862
21
0.3344
0.3050
0.2536
1970180
0.0022
0.0073
0.0011
110.003
30.1086
0.1947
0.0744
10.0805
10.015
610.000
41
0.2290
0.4327
0.1732
110.349
10.3377
0.2589
1980190
0.0084
0.0194
10.012
31
0.0014
0.0926
0.1792
0.0673
10.0381
0.0127
10.000
31
1.0430
1.2410
12.098
01
0.1695
0.3150
0.2577
1990100
0.0071
0.0053
10.000
81
0.0031
0.0548
0.1478
0.0870
10.0119
10.070
610.000
11
1.4990
0.4104
10.105
51
0.6425
0.2549
0.2219
2000110
0.0063
0.0045
10.000
91
0.0043
0.0362
0.1115
0.0613
10.1579
10.032
310.000
41
2.0120
0.4617
10.166
71
1.3560
0.3126
0.2652
1970175
10.001
50.0141
10.006
11
10.006
30.0979
0.1749
0.0716
10.0782
10.084
010.000
51
10.131
50.6829
10.717
91
10.546
70.3428
0.2549
1975180
0.0085
0.0027
0.0082
10.0025
0.1210
0.2157
0.0817
10.0638
0.0017
10.000
51
0.5968
0.1045
0.8510
10.1760
0.3274
0.2638
1980185
0.0157
0.0042
10.002
01
0.0074
0.1056
0.1907
0.0689
10.0732
0.0667
10.000
31
1.2620
0.1850
10.242
31
0.5979
0.3655
0.2525
1985190
0.0038
0.0319
10.021
11
10.001
80.0720
0.1556
0.0603
110.075
510.108
910.000
31
0.4522
1.7410
12.969
01
10.213
40.2696
0.2549
1990195
0.0082
0.0016
0.0013
10.0042
0.0597
0.1573
0.0931
110.000
310.127
910.000
41
1.1690
0.0850
0.1159
10.6028
0.2164
0.1985
1995100
0.0072
0.0121
10.004
71
0.0029
0.0468
0.1271
0.0735
10.0208
0.0163
0.0004
11.3010
0.8054
10.548
31
0.5269
0.2961
0.2313
2000105
0.0088
0.0038
10.001
11
0.0066
0.0377
0.1193
0.0774
10.1165
10.113
110.000
91
1.9910
0.2709
10.122
31
1.4900
0.2865
0.2467
2005110
0.0028
0.0062
10.001
01
0.0008
0.0332
0.0953
0.0313
10.1908
0.0839
0.0001
10.7021
0.5557
10.275
51
0.2054
0.3264
0.2811
193512010
0.0058
0.0075
10.001
31
0.0027
0.0696
0.1377
0.0608
10.0767
10.021
710.000
11
2.5130
1.6360
10.659
01
1.1640
0.2930
0.2607
TABLE!3g:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
49
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!C:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0047
0.0032
10.0574
0.0034
0.0386
0.0507
10.5088
0.0031
10.067
91
0.0357
2.4570
1.2440
12.2600
1.7780
0.3455
0.2734
1935145
0.0016
0.0026
10.1264
0.0015
0.0497
0.0656
10.4548
0.0014
10.174
31
0.0115
0.3704
0.4530
13.1800
0.3374
0.3396
0.2713
1946155
0.0085
0.0055
110.056
10.0075
0.0275
0.0417
10.3915
0.0631
10.019
71
10.013
83.3850
1.4340
111.569
03.0100
0.3579
0.2958
195616/68
0.0045
0.0018
10.0880
0.0019
0.0349
0.0421
10.6137
0.2784
0.1228
10.0957
1.5660
0.5238
11.7560
0.6474
0.3407
0.2577
1935140
0.0005
0.0006
10.0858
0.0005
0.0587
0.0801
10.4831
10.014
010.188
11
10.005
20.0764
0.0659
11.4960
0.0653
0.3204
0.2769
1941145
0.0029
0.0049
10.1744
0.0027
0.0369
0.0429
10.4177
0.1926
10.126
01
0.0334
0.6059
0.8894
13.2340
0.5598
0.3623
0.2651
1946150
0.0044
0.0037
110.015
00.0037
0.0305
0.0472
10.3236
0.1673
10.040
91
10.029
31.1110
0.5995
110.359
30.9412
0.4346
0.2956
1951155
0.0126
0.0073
110.097
10.0114
0.0237
0.0356
10.4483
10.097
710.068
81
0.0052
4.1240
1.5790
111.678
03.7200
0.2812
0.2777
1956160
0.0143
10.006
31
0.0099
0.0122
0.0240
0.0354
10.4679
0.1459
0.1398
10.0173
4.6220
11.381
01
0.1645
3.9390
0.2675
0.2572
196116/68
10.002
10.0072
10.1400
10.005
00.0394
0.0453
10.6917
0.2408
0.0830
10.1492
10.508
11.5080
11.9200
11.213
00.3895
0.2476
7/196812010
0.0076
0.0012
10.0261
0.0031
0.0425
0.0603
10.6659
0.0997
0.0108
10.0165
4.0530
0.4309
10.8851
1.6550
0.3497
0.2582
1970180
0.0020
0.0016
10.0849
10.003
40.0481
0.0686
10.8647
0.1637
10.084
81
0.0690
0.4809
0.2735
11.1280
10.825
20.3550
0.2672
1980190
0.0190
10.002
11
10.044
50.0119
0.0452
0.0686
10.6263
0.0395
0.0196
110.056
44.8250
10.354
51
10.816
03.0470
0.3218
0.2548
1990100
0.0089
0.0020
10.0068
0.0048
0.0445
0.0553
10.6216
0.1241
10.014
91
0.0280
2.2930
0.4192
10.1251
1.2440
0.3437
0.2517
2000110
0.0045
10.001
61
0.0828
0.0024
0.0363
0.0568
10.5668
0.0281
0.0930
10.0105
1.4130
10.317
01
1.6780
0.7627
0.3701
0.2517
1970175
0.0071
0.0048
110.097
10.0023
0.0509
0.0682
10.9935
0.1247
10.124
41
0.0570
1.1880
0.6012
110.829
40.3881
0.3714
0.2664
1975180
10.001
10.0031
10.2411
10.007
10.0460
0.0741
10.7035
0.1998
10.060
71
0.0641
10.210
20.3523
12.9080
11.333
00.3382
0.2685
1980185
0.0183
10.001
81
0.0132
0.0100
0.0426
0.0657
10.6204
0.1451
0.0065
110.044
43.6440
10.238
71
0.1808
2.0030
0.3647
0.2592
1985190
0.0211
10.002
61
10.094
10.0155
0.0464
0.0689
10.6016
10.031
50.0147
110.063
33.8580
10.323
71
11.327
02.8400
0.2809
0.2392
1990195
0.0076
10.001
71
0.0659
0.0036
0.0427
0.0494
10.6218
0.1909
10.006
21
0.0281
1.5040
10.300
11
0.8998
0.7172
0.2847
0.2392
1995100
0.0127
0.0060
110.064
30.0084
0.0454
0.0582
10.5778
0.0903
10.028
21
0.0284
2.3740
0.8802
110.943
71.5810
0.4071
0.2516
2000105
0.0056
10.004
91
0.1278
0.0033
0.0387
0.0526
10.5929
10.091
110.103
41
0.0130
1.2240
10.786
91
1.8280
0.7338
0.3697
0.2461
2005110
0.0022
0.0011
10.0553
0.0003
0.0313
0.0570
10.5315
0.2000
0.2507
10.0104
0.6050
0.1678
10.8824
0.0796
0.3708
0.2595
193512010
0.0064
0.0020
10.0399
0.0032
0.0409
0.0563
10.6017
0.1096
10.015
61
0.0248
4.6970
1.0900
12.0010
2.4070
0.3479
0.2649
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
10.002
20.0145
10.004
90.0777
10.003
50.0644
0.1110
0.0419
0.5296
10.003
90.0858
0.0002
0.0544
10.679
72.6110
12.355
02.9390
11.085
00.3592
0.2743
1935145
10.008
00.0174
10.006
00.1526
10.008
10.0734
0.1187
0.0409
0.4712
10.007
810.023
60.0001
0.0246
11.243
01.6800
11.672
03.7070
11.265
00.3506
0.2728
1946155
0.0029
0.0140
10.003
510.039
70.0019
0.0451
0.0922
0.0304
0.3765
0.1471
0.1096
0.0000
10.010
50.6999
1.6590
11.267
011.154
00.4700
0.3778
0.2902
195616/68
10.001
20.0123
10.005
10.1062
10.003
80.0691
0.1181
0.0500
0.6552
0.2760
0.1789
0.0004
0.1321
10.211
01.2730
11.255
01.9860
10.672
20.3517
0.2635
1935140
10.005
30.0100
10.003
80.1007
10.005
30.0882
0.1469
0.0471
0.5251
0.1681
0.0189
0.0001
0.0071
10.503
10.5715
10.682
31.6160
10.510
50.3217
0.2830
1941145
10.011
20.0263
10.008
50.2140
10.011
40.0511
0.0728
0.0323
0.3937
0.1296
10.250
80.0000
0.0466
11.693
02.7920
12.049
04.2110
11.728
00.3847
0.2584
1946150
10.000
20.0103
10.002
70.0009
10.000
90.0512
0.0929
0.0273
0.3416
0.1986
0.2164
0.0001
10.027
410.033
30.8553
10.766
70.0201
10.133
70.4620
0.2761
1951155
0.0060
0.0177
10.004
310.080
20.0048
0.0382
0.0923
0.0334
0.4073
10.053
310.057
410.000
10.0084
1.2140
1.4850
11.004
011.525
00.9657
0.2937
0.2814
1956160
0.0107
0.0011
10.003
90.0243
0.0086
0.0397
0.0947
0.0417
0.4570
10.039
00.0773
0.0001
0.0013
2.0880
0.0909
10.732
20.4119
1.6760
0.2777
0.2603
196116/68
10.009
10.0197
10.005
90.1609
10.012
10.0824
0.1314
0.0551
0.7567
0.3018
0.2073
0.0006
0.2207
11.049
01.4240
11.019
02.0170
11.387
00.4011
0.2552
7/196812010
0.0027
0.0118
10.005
90.0431
10.001
80.0865
0.1542
0.0682
0.7143
0.1781
0.0702
0.0003
0.0499
0.7080
1.7210
11.954
01.3610
10.477
10.3819
0.2626
1970180
10.005
90.0164
10.007
10.1014
10.011
30.1296
0.2063
0.0853
0.9497
0.2298
0.0876
0.0009
0.1749
10.520
40.9113
10.962
61.2270
11.005
00.3987
0.2712
1980190
0.0076
0.0214
10.013
40.0000
0.0006
0.1167
0.2031
0.0883
0.7457
0.1538
0.1013
0.0009
10.007
90.7517
1.2100
11.739
010.000
20.0581
0.3696
0.2643
1990100
0.0045
0.0119
10.005
80.0240
0.0004
0.0668
0.1332
0.0697
0.6597
0.1889
0.0949
0.0005
0.0384
0.7694
1.0290
10.963
60.4175
0.0664
0.3557
0.2589
2000110
0.0028
0.0031
10.002
50.0877
0.0007
0.0346
0.1087
0.0510
0.5342
0.1305
10.026
810.000
40.0028
0.9355
0.3279
10.573
81.8860
0.2491
0.4090
0.2566
1970175
0.0033
0.0114
10.003
510.081
410.001
50.1134
0.1703
0.0669
1.0350
0.2012
0.0056
0.0001
0.1789
0.2483
0.5681
10.441
710.667
210.110
30.3968
0.2665
1975180
10.009
60.0212
10.008
90.2422
10.015
60.1477
0.2373
0.1030
0.8717
0.2276
0.1124
0.0014
0.1553
10.549
90.7562
10.732
52.3580
10.896
10.3965
0.2759
1980185
0.0149
0.0047
10.002
70.0173
0.0065
0.1233
0.2066
0.0846
0.7035
0.2440
0.1507
0.0013
0.0398
1.0220
0.1918
10.269
50.2085
0.4526
0.4156
0.2630
1985190
0.0031
0.0351
10.022
510.012
710.002
50.1027
0.1862
0.0853
0.7483
0.0151
0.0075
0.0003
10.047
80.2570
1.6000
12.237
010.143
710.209
50.3237
0.2559
1990195
10.002
20.0207
10.013
10.1006
10.006
20.0792
0.1405
0.0768
0.7063
0.1869
0.1030
0.0007
0.0530
10.240
21.2480
11.451
01.2090
10.666
60.2924
0.2497
1995100
0.0134
0.0037
0.0016
10.062
90.0091
0.0484
0.1184
0.0566
0.5591
0.1390
0.0503
0.0001
0.0212
2.3470
0.2659
0.2395
10.954
71.5990
0.4227
0.2553
2000105
0.0033
0.0018
10.003
80.1341
0.0010
0.0337
0.1122
0.0625
0.5553
0.1417
10.140
310.000
80.0170
0.8290
0.1379
10.516
12.0490
0.2633
0.4012
0.2486
2005110
0.0006
0.0049
10.001
80.0608
10.001
30.0351
0.0977
0.0306
0.5125
0.0842
0.1163
0.0001
10.007
40.1530
0.4264
10.503
81.0060
10.314
40.4150
0.2609
193512010
0.0006
0.0130
10.005
50.0583
10.002
60.0776
0.1368
0.0581
0.6395
0.1882
0.0755
0.0003
0.0518
0.2165
2.8570
12.844
02.7520
10.997
10.3719
0.2679
TABLE!3g:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
50
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!A:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0080
0.0044
11
0.0067
0.0489
0.0467
11
0.0065
0.0368
11
3.2830
1.8990
11
2.7460
0.2589
0.2666
1935145
0.0080
0.0077
11
0.0078
0.0667
0.0570
11
0.0080
10.005
01
11.3680
1.5460
11
1.3430
0.2677
0.2522
1946155
0.0091
0.0024
11
0.0082
0.0370
0.0395
11
10.043
30.0621
11
2.6990
0.6658
11
2.4200
0.2654
0.2938
195616/68
0.0072
0.0032
11
0.0046
0.0380
0.0420
11
0.2419
0.0754
11
2.3130
0.9322
11
1.4690
0.2461
0.2572
1935140
0.0071
0.0039
11
0.0070
0.0820
0.0654
11
10.101
410.095
01
10.7304
0.5080
11
0.7226
0.2276
0.2504
1941145
0.0090
0.0121
11
0.0088
0.0427
0.0451
11
0.0327
0.1966
11
1.6310
2.0850
11
1.5930
0.3152
0.2480
1946150
0.0028
0.0048
11
0.0021
0.0420
0.0429
11
0.0592
0.0532
11
0.5075
0.8716
11
0.3845
0.3477
0.3030
1951155
0.0155
0.0000
11
0.0143
0.0303
0.0360
11
10.272
90.0579
11
3.9550
10.005
61
13.6380
0.1831
0.2616
1956160
0.0107
10.002
41
10.0086
0.0268
0.0309
11
0.1467
0.0264
11
3.0950
10.598
11
12.4810
0.1831
0.2646
196116/68
0.0048
0.0069
11
0.0019
0.0439
0.0478
11
0.2477
0.0761
11
1.0420
1.3720
11
0.4066
0.2881
0.2447
7/196812010
0.0093
0.0019
11
0.0047
0.0412
0.0530
11
0.1089
0.1453
11
5.0760
0.7919
11
2.6050
0.2830
0.2581
1970180
0.0086
0.0030
11
0.0031
0.0509
0.0601
11
0.1061
0.1456
11
1.9410
0.5736
11
0.7104
0.2972
0.2660
1980190
0.0172
10.003
71
10.0101
0.0447
0.0564
11
0.0500
0.0989
11
4.4110
10.756
71
12.6120
0.2616
0.2593
1990100
0.0056
0.0056
11
0.0015
0.0366
0.0506
11
0.1070
0.1647
11
1.7470
1.2700
11
0.4678
0.2515
0.2374
2000110
0.0073
0.0019
11
0.0052
0.0294
0.0463
11
0.0914
0.1688
11
2.8380
0.4685
11
2.0390
0.3021
0.2628
1970175
0.0072
0.0001
11
0.0025
0.0569
0.0628
11
0.1635
0.1369
11
1.0800
0.0134
11
0.3656
0.3149
0.2661
1975180
0.0124
0.0079
11
0.0064
0.0445
0.0580
11
10.022
10.1481
11
2.3670
1.1510
11
1.2300
0.2734
0.2636
1980185
0.0212
10.004
11
10.0128
0.0448
0.0543
11
0.0399
0.0737
11
4.0050
10.645
91
12.4380
0.3060
0.2561
1985190
0.0155
10.003
81
10.0099
0.0429
0.0557
11
0.0452
0.1160
11
3.0620
10.581
01
11.9500
0.2238
0.2602
1990195
0.0037
0.0072
11
10.000
30.0357
0.0475
11
0.1036
0.1412
11
0.8816
1.2810
11
10.065
70.2366
0.2303
1995100
0.0106
0.0026
11
0.0063
0.0373
0.0518
11
0.1218
0.1804
11
2.4080
0.4309
11
1.4400
0.2730
0.2561
2000105
0.0103
0.0011
11
0.0080
0.0270
0.0422
11
0.1559
0.0388
11
3.2440
0.2232
11
2.5450
0.2645
0.2517
2005110
0.0039
0.0028
11
0.0019
0.0301
0.0476
11
0.0311
0.2561
11
1.0940
0.4910
11
0.5476
0.3307
0.2694
193512010
0.0087
0.0030
11
0.0056
0.0447
0.0503
11
0.0525
0.1051
11
5.8790
1.7940
11
3.7860
0.2724
0.2620
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0016
0.0160
10.004
61
0.0003
0.0784
0.1498
0.0613
110.000
210.123
410.000
61
0.4172
2.1350
11.511
01
0.0840
0.0835
0.1559
1935145
10.002
00.0226
10.004
71
10.002
10.0885
0.1492
0.0498
110.002
310.206
810.000
51
10.253
41.7360
11.082
01
10.272
00.0718
0.1542
1946155
0.0052
0.0094
10.002
71
0.0042
0.0678
0.1306
0.0505
10.0101
0.0201
10.000
21
0.8334
0.7926
10.580
51
0.6811
0.1156
0.1751
195616/68
0.0020
0.0154
10.006
11
10.000
70.0774
0.1648
0.0767
110.005
310.140
010.001
11
0.3094
1.1440
10.976
91
10.103
20.0680
0.1373
1935140
10.002
40.0175
10.004
11
10.002
50.1055
0.1765
0.0550
110.050
910.217
510.000
71
10.193
20.8358
10.632
41
10.199
40.0499
0.1357
1941145
10.001
40.0287
10.005
41
10.001
60.0636
0.1096
0.0434
110.014
810.181
110.000
21
10.172
22.0270
10.964
11
10.199
30.0976
0.1711
1946150
0.0025
0.0052
10.000
11
0.0018
0.0663
0.1138
0.0352
10.0105
0.0765
0.0000
10.2903
0.3568
10.012
31
0.2124
0.1544
0.1831
1951155
0.0078
0.0137
10.005
31
0.0066
0.0696
0.1463
0.0624
10.0060
10.025
510.000
31
0.8704
0.7229
10.657
71
0.7352
0.0768
0.1590
1956160
0.0048
0.0136
10.008
71
0.0027
0.0547
0.1536
0.0800
110.284
910.401
810.001
91
0.6802
0.6856
10.842
91
0.3805
0.0419
0.0936
196116/68
0.0001
0.0166
10.004
41
10.002
90.0896
0.1727
0.0749
10.0639
0.0013
10.000
51
0.0060
0.9117
10.557
01
10.305
30.0854
0.1581
7/196812010
0.0061
0.0073
10.002
11
0.0016
0.0810
0.1732
0.0806
10.0418
0.0481
0.0004
11.7100
0.9562
10.580
01
0.4448
0.0880
0.1576
1970180
10.003
70.0262
10.009
71
10.009
20.1120
0.2073
0.0829
110.024
910.025
410.000
31
10.384
51.4500
11.345
01
10.944
60.0915
0.1625
1980190
0.0040
0.0260
10.014
81
10.003
10.0912
0.1958
0.0898
10.0308
0.0605
0.0004
10.5007
1.5260
11.891
01
10.388
00.0835
0.1435
1990100
0.0143
10.018
60.0134
10.0103
0.0650
0.1737
0.0979
10.1349
0.0589
0.0017
12.5370
11.228
01.5710
11.8130
0.0657
0.1493
2000110
0.0066
0.0029
0.0002
10.0045
0.0343
0.1063
0.0551
10.0947
0.0020
10.000
11
2.2010
0.3147
0.0393
11.5150
0.0952
0.1649
1970175
0.0016
0.0107
10.004
41
10.003
20.1102
0.1918
0.0768
110.007
810.049
810.000
51
0.1248
0.4727
10.490
51
10.244
00.0975
0.1797
1975180
10.003
20.0376
10.012
71
10.009
20.1234
0.2310
0.0956
110.058
710.041
310.000
61
10.221
41.3810
11.124
01
10.634
60.0806
0.1388
1980185
0.0024
0.0340
10.017
41
10.005
90.0991
0.2058
0.0920
10.0363
0.1450
0.0013
10.2055
1.4020
11.601
01
10.508
30.0974
0.1515
1985190
0.0099
0.0128
10.009
81
0.0043
0.0803
0.1770
0.0834
10.0233
10.055
410.000
41
1.0520
0.6118
10.999
61
0.4554
0.0701
0.1356
1990195
0.0212
10.039
10.0250
10.0172
0.0721
0.1870
0.1042
10.1550
0.0819
0.0025
12.4980
11.774
02.0380
12.0260
0.0616
0.1327
1995100
0.0090
0.0052
10.000
81
0.0047
0.0516
0.1429
0.0817
10.0636
10.027
20.0007
11.4770
0.3081
10.086
11
0.7763
0.0647
0.1592
2000105
0.0083
0.0048
10.000
61
0.0061
0.0351
0.1158
0.0684
10.0644
10.007
210.000
21
2.0180
0.3524
10.069
21
1.4850
0.0760
0.1482
2005110
0.0037
0.0032
10.000
11
0.0018
0.0317
0.0889
0.0310
10.1188
0.0081
0.0000
10.9908
0.3044
10.038
61
0.4708
0.1121
0.1838
193512010
0.0042
0.0111
10.003
21
0.0010
0.0799
0.1633
0.0727
10.0148
10.015
90.0000
11.5690
2.0580
11.326
01
0.3924
0.0860
0.1568
TABLE!3h
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
51
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Perio
d!
!!
!!
!!
!!
!!
!!
!!
!!
!!
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!!
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Pane
l!C:
!!
!!
!!
!!
!!
!!
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!!
!!
!!
193516/68
0.0080
0.0035
10.0195
0.0067
0.0499
0.0522
10.5454
0.0065
10.027
31
10.001
63.2130
1.3280
10.7161
2.6870
0.1051
0.1668
1935145
0.0075
0.0071
10.0223
0.0073
0.0673
0.0667
10.4140
0.0075
10.020
61
10.018
21.2720
1.2100
10.6162
1.2470
0.0932
0.1605
1946155
0.0101
0.0035
110.034
40.0092
0.0386
0.0451
10.5357
10.095
410.023
31
10.057
52.8710
0.8426
110.702
82.6030
0.1369
0.1961
195616/68
0.0068
0.0003
10.0602
0.0042
0.0391
0.0423
10.6450
0.2403
10.066
51
0.0574
2.1200
0.0927
11.1430
1.2990
0.0901
0.1427
1935140
0.0071
0.0070
110.026
30.0071
0.0829
0.0815
10.4156
10.079
010.028
41
10.012
30.7250
0.7233
110.533
60.7172
0.0784
0.1486
1941145
0.0079
0.0071
10.0798
0.0077
0.0428
0.0437
10.4080
0.0472
0.0079
110.025
51.4270
1.2620
11.5150
1.3880
0.1108
0.1732
1946150
0.0043
0.0026
10.0202
0.0036
0.0410
0.0509
10.5145
0.0447
10.019
91
10.058
70.8042
0.3995
10.3041
0.6781
0.1893
0.2055
1951155
0.0160
0.0043
110.088
90.0148
0.0355
0.0389
10.5549
10.300
710.040
71
10.056
53.4930
0.8590
111.241
03.2210
0.0845
0.1724
1956160
0.0106
10.002
11
0.0018
0.0085
0.0295
0.0352
10.5972
0.1759
0.0193
10.0236
2.7800
10.457
21
0.0235
2.2270
0.0595
0.1113
196116/68
0.0042
0.0019
10.0991
0.0013
0.0443
0.0466
10.6754
0.2387
10.101
81
0.0843
0.9017
0.3906
11.3920
0.2715
0.1106
0.1575
7/196812010
0.0088
0.0002
10.0252
0.0042
0.0450
0.0556
10.7536
0.1159
0.0642
10.0552
4.3940
0.0908
10.7537
2.1320
0.1182
0.1738
1970180
0.0082
10.004
11
0.0885
0.0028
0.0543
0.0611
11.0410
0.1243
0.0560
10.1317
1.7390
10.776
21
0.9763
0.5849
0.1343
0.1935
1980190
0.0180
10.002
31
10.028
20.0110
0.0466
0.0640
10.7171
0.0457
0.1134
10.0315
4.4460
10.410
81
10.452
52.7200
0.0947
0.1568
1990100
0.0054
0.0060
110.002
90.0013
0.0427
0.0501
10.5821
0.1626
10.024
51
0.0427
1.4480
1.3700
110.057
80.3503
0.1081
0.1589
2000110
0.0054
10.001
21
0.0714
0.0034
0.0360
0.0495
10.6482
0.1033
10.020
11
0.0233
1.7300
10.272
31
1.2650
1.0760
0.1338
0.1785
1970175
0.0096
0.0088
110.162
30.0048
0.0603
0.0643
11.0060
0.1212
0.0211
110.014
31.3500
1.1570
111.369
00.6745
0.1392
0.2076
1975180
0.0098
10.013
11
0.3125
0.0038
0.0489
0.0549
11.0290
0.0783
10.019
41
0.3051
1.6990
12.020
01
2.5760
0.6604
0.1240
0.1795
1980185
0.0198
10.008
51
0.0749
0.0114
0.0463
0.0659
10.7240
0.0758
0.1387
10.0818
3.6170
11.095
01
0.8781
2.1040
0.1061
0.1585
1985190
0.0176
0.0008
110.085
70.0120
0.0449
0.0605
10.6914
0.0032
0.0907
110.002
13.3300
0.1176
111.051
02.2710
0.0784
0.1539
1990195
0.0033
0.0071
10.0034
10.000
70.0395
0.0466
10.5454
0.0875
10.000
71
0.0181
0.7038
1.2960
10.0527
10.152
70.0932
0.1388
1995100
0.0104
0.0040
110.013
40.0061
0.0454
0.0506
10.5964
0.2356
10.044
21
0.0684
1.9460
0.6656
110.189
91.1500
0.1240
0.1766
2000105
0.0093
10.000
21
0.0425
0.0070
0.0355
0.0428
10.6850
0.0907
10.104
81
0.0354
2.2230
10.037
61
0.5264
1.6880
0.1222
0.1666
2005110
0.0005
10.003
41
0.1269
10.001
50.0339
0.0536
10.5823
0.0814
0.0112
10.0020
0.1205
10.534
71
1.8490
10.367
00.1443
0.1890
193512010
0.0084
0.0016
10.0227
0.0053
0.0472
0.0541
10.6697
0.0630
0.0271
10.0307
5.3890
0.9199
11.0220
3.4060
0.1124
0.1708
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!D:
!!
!!
!!
!!
!!
!!
!!
!!
!!
!!
193516/68
0.0010
0.0155
10.004
70.0207
10.000
30.0805
0.1478
0.0627
0.5708
10.000
910.086
410.000
40.0189
0.2507
2.0980
11.487
00.7244
10.074
10.1118
0.1779
1935145
10.004
50.0246
10.006
30.0402
10.004
70.0853
0.1463
0.0528
0.4519
10.005
110.217
810.000
610.017
710.610
31.9240
11.355
01.0180
10.629
60.0989
0.1733
1946155
0.0078
0.0075
10.001
310.039
10.0068
0.0759
0.1334
0.0538
0.5677
0.1088
0.1180
0.0001
10.036
61.1230
0.6149
10.259
710.755
10.9878
0.1498
0.2010
195616/68
0.0004
0.0139
10.006
00.0514
10.002
20.0798
0.1602
0.0762
0.6595
0.1027
10.112
110.000
60.0934
0.0665
1.0650
10.960
60.9547
10.333
40.0925
0.1575
1935140
10.002
20.0199
10.004
510.015
510.002
20.0976
0.1711
0.0583
0.4584
10.121
110.224
810.000
910.011
310.187
10.9809
10.649
210.285
310.193
70.0867
0.1645
1941145
10.007
40.0301
10.008
30.1061
10.007
60.0687
0.1112
0.0459
0.4387
10.080
510.205
810.000
310.025
710.830
72.0980
11.407
01.8740
10.856
10.1134
0.1836
1946150
10.002
60.0130
10.004
10.0347
10.003
20.0712
0.1164
0.0391
0.5499
0.0120
0.1577
0.0001
10.054
810.279
20.8645
10.805
70.4894
10.351
30.2041
0.2189
1951155
0.0181
0.0020
0.0015
10.113
00.0169
0.0797
0.1493
0.0656
0.5802
0.1486
0.0799
0.0001
10.019
71.7640
0.1028
0.1785
11.509
01.6460
0.0956
0.1660
1956160
0.0062
0.0099
10.006
210.003
60.0041
0.0542
0.1483
0.0770
0.5815
10.277
310.365
510.001
60.0314
0.8835
0.5150
10.624
210.047
60.5807
0.0631
0.1137
196116/68
10.003
40.0167
10.005
80.0881
10.006
30.0931
0.1684
0.0761
0.7076
0.1834
0.0211
0.0000
0.1386
10.346
30.9381
10.726
11.1810
10.645
70.1121
0.1788
7/196812010
0.0026
0.0106
10.004
70.0413
10.001
90.0883
0.1757
0.0836
0.7800
0.0761
0.0235
0.0004
0.0691
0.6691
1.3660
11.281
01.1960
10.491
00.1271
0.1881
1970180
10.012
40.0326
10.016
30.1144
10.017
90.1260
0.2067
0.0896
1.0980
0.0374
10.066
610.000
10.1583
11.132
01.8100
12.083
01.1970
11.629
00.1412
0.1995
1980190
0.0032
0.0262
10.014
80.0105
10.003
90.0974
0.1971
0.0929
0.7621
0.0924
0.0489
0.0007
0.0696
0.3759
1.5240
11.831
00.1589
10.457
00.1053
0.1672
1990100
0.0107
10.009
60.0088
0.0016
0.0066
0.0707
0.1797
0.0978
0.6078
0.1330
0.0908
0.0015
0.0493
1.7440
10.611
11.0320
0.0306
1.0800
0.1180
0.1863
2000110
0.0037
0.0018
10.001
00.0801
0.0017
0.0347
0.1183
0.0582
0.6299
0.0888
10.007
510.000
10.0253
1.2360
0.1761
10.193
11.4600
0.5559
0.1419
0.1930
1970175
0.0057
0.0171
10.003
210.175
80.0009
0.1160
0.1966
0.0811
1.0310
10.044
410.094
910.000
910.063
10.4163
0.7392
10.340
011.447
00.0658
0.1389
0.2085
1975180
10.023
10.0452
10.026
20.3614
10.029
10.1399
0.2287
0.1018
1.0860
0.0480
10.091
30.0002
0.3838
11.401
01.6770
12.186
02.8230
11.766
00.1403
0.1910
1980185
10.006
00.0394
10.023
50.1314
10.014
30.1070
0.2033
0.0929
0.7809
0.1144
0.1660
0.0017
0.1298
10.476
81.6430
12.149
01.4280
11.142
00.1172
0.1735
1985190
0.0154
0.0067
10.004
410.070
20.0097
0.0842
0.1809
0.0885
0.7256
0.0380
10.106
210.000
40.0280
1.5500
0.3156
10.418
910.820
60.9834
0.0927
0.1623
1990195
0.0182
10.030
40.0208
10.013
00.0142
0.0738
0.1861
0.1022
0.5515
0.1505
0.1257
0.0026
0.0221
2.0900
11.385
01.7270
10.199
31.6320
0.1066
0.1723
1995100
0.0052
0.0130
10.004
60.0120
0.0010
0.0655
0.1594
0.0851
0.6438
0.1179
0.0140
0.0003
0.0800
0.6784
0.6930
10.462
30.1580
0.1252
0.1275
0.2007
2000105
0.0062
0.0049
10.001
60.0597
0.0039
0.0355
0.1338
0.0739
0.6998
0.0771
10.022
510.000
20.0421
1.4820
0.3118
10.188
40.7234
0.9518
0.1318
0.1745
2005110
10.000
90.0000
10.001
60.1299
10.002
80.0323
0.0915
0.0292
0.5294
0.0721
0.0071
0.0000
0.0008
10.225
010.004
310.470
32.0820
10.736
80.1481
0.2119
193512010
0.0019
0.0128
10.004
70.0322
10.001
20.0849
0.1640
0.0751
0.6954
0.0580
10.016
70.0001
0.0478
0.6784
2.3500
11.892
01.3980
10.428
70.1203
0.1837
TABLE!3h
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Do
uble1Sort!T
est!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
SUMMAR
Y!RE
SULTS!FO
R!TH
E!RE
GRESSION!(con
t.)
Statistics
¯ �0
¯ � 1¯ �2
¯ � 3�0�
Rf
s(�0)
s(�
1)
s(�2)
s(�3)
⇢ 0(�
0�R
f)⇢
M(�
1)
⇢0(�
2)
⇢0(�3)
t(¯ �0)
t(¯ �1)
t(¯ �2)
t(¯ �3)
t(�0�
Rf)
r2s(
r2)
Rp
=�0t+
�1t�
p+�2t�
2 p+
�3ts p
(ei)
+⌘
p
52
53
[htp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0145 0.0132 0.0043 0.0097 0.0013 0.2154 0.0701 0.0612 0.0613 ! !
1935,45 0.0201 0.0200 0.0114 0.0079 0.0001 0.2246 0.1285 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0028 0.0089 0.0009 0.2370 0.0635 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 ,0.0007 0.0120 0.0026 0.2392 ,0.0180 0.0399 0.0400 ! !
1935,40 0.0141 0.0141 0.0084 0.0052 0.0001 0.1292 0.0776 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0150 0.0111 0.0002 0.4669 0.2589 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0034 0.0052 0.0007 0.1355 0.0645 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0022 0.0126 0.0012 0.4144 0.0660 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0077 0.0158 0.0021 0.2069 ,0.2268 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0039 0.0094 0.0029 0.2581 0.0906 0.0435 0.0435 ! !
7/1968,2010 0.0110 0.0065 0.0009 0.0103 0.0045 0.1193 0.0170 0.0541 0.0543 ! !
1970,80 0.0116 0.0061 0.0057 0.0062 0.0055 0.0947 0.0884 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0079 0.0206 0.0071 0.098 ,0.1503 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0014 0.0096 0.0041 0.1486 0.0343 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0022 0.0076 0.0021 0.1560 0.0393 0.0570 0.0571 ! !
1970,75 0.0036 ,0.0012 0.0017 0.0052 0.0048 ,0.0172 0.0241 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0127 0.0093 0.0060 0.3040 0.2025 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0066 0.0232 0.0083 0.185 ,0.1368 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0081 0.0186 0.0056 0.061 ,0.1474 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0014 0.0092 0.0040 0.1616 0.0359 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0002 0.0129 0.0043 0.181 0.0064 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0015 0.0098 0.0023 0.2474 0.0365 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0037 0.0044 0.0019 0.1017 0.0564 0.0661 0.0662 ! !
1935,2010 0.0125 0.0094 0.0024 0.0100 0.0031 0.1642 0.0419 0.0573 0.0575 ! !
Period
1935,6/68 0.0486 0.0012 4.7400 4.309 1.5630 4.0070 ,0.0063 ,0.0040 0.0727 ,0.0002 0.9661
1935,45 0.0687 0.0002 2.5890 2.5710 1.7300 1.3130 ,0.0664 ,0.0663 0.0795 ,0.0535 0.63721946,55 0.0333 0.0004 2.8350 2.597 0.7215 2.9270 0.0875 0.0864 0.0611 0.0441 0.89231956,6/68 0.0363 0.0009 3.7290 2.926 ,0.2160 4.0390 0.1357 0.1380 0.0139 0.1317 0.8512
1935,40 0.0864 0.0002 1.0950 1.0890 0.8146 0.5032 ,0.1260 ,0.1255 0.0615 ,0.0812 0.43611941,45 0.0388 0.0001 3.6460 3.6200 1.9440 2.2130 0.1493 0.1485 0.1096 0.0961 0.72331946,50 0.0377 0.0003 1.1480 1.0510 0.5686 1.0660 0.0922 0.0898 0.0692 0.1594 0.91021951,55 0.0281 0.0004 3.5000 3.196 0.4400 3.4790 ,0.0244 ,0.0172 0.0462 ,0.1733 0.75561956,60 0.0277 0.0007 2.0840 1.592 ,2.0970 4.4140 0.1145 0.1309 0.0746 0.0870 0.65991961,6/68 0.0410 0.0008 3.0890 2.449 0.8012 2.1800 0.1318 0.1294 ,0.0197 0.1249 0.8900
7/1968,2010 0.0421 0.0025 4.5880 2.685 0.3614 5.5030 0.1864 0.1905 0.1131 0.0711 0.9605
1970,80 0.0481 0.0020 2.0600 1.086 1.0690 1.4840 0.1129 0.1148 0.1379 0.0407 0.89311980,90 0.0477 0.0023 2.6750 1.124 ,1.4340 4.9580 0.1826 0.1887 0.0575 0.0629 0.89031990,00 0.0368 0.0011 2.8790 1.702 0.3010 3.0000 0.2137 0.2177 0.1907 0.0645 0.90552000,10 0.0339 0.0016 2.2100 1.788 0.4678 2.5780 0.2689 0.2726 0.1598 ,0.0085 0.9778
1970,75 0.0541 0.0013 0.4335 ,0.146 0.2361 0.8114 0.1535 0.1577 0.0991 0.0262 0.82951975,80 0.0422 0.0023 3.3950 2.570 1.7250 1.8690 0.0478 0.0543 0.1477 0.0445 0.89641980,85 0.0511 0.0022 3.0340 1.548 ,0.9233 3.8460 0.1518 0.1729 0.0294 0.0713 0.83061985,90 0.0418 0.0010 1.3930 0.518 ,1.0900 3.7750 0.1979 0.1980 0.0789 0.0248 0.77271990,95 0.0363 0.0014 2.2370 1.364 0.2123 2.1570 0.2632 0.2685 0.2624 0.0933 0.94591995,00 0.0372 0.0005 2.4730 1.540 0.0444 2.9480 0.1544 0.1551 0.1012 0.0719 0.47972000,05 0.0357 0.0015 2.5550 2.094 0.2588 2.3310 0.1855 0.1898 ,0.0684 ,0.1138 0.97282005,10 0.0294 0.0016 1.1120 0.8607 0.5633 1.2600 0.2890 0.2927 0.3337 0.1482 0.9795
1935,2010 0.0450 0.0026 6.5970 4.941 1.2880 6.7170 0.0905 0.0962 0.0978 0.0342 0.9763
TABLE!4b:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
54
[htp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0109 0.0096 0.0053 0.0077 0.0013 0.2138 0.1171 0.0449 0.0450 ! !
1935,45 0.0115 0.0114 0.0084 0.0083 0.0001 0.1899 0.1405 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0029 0.0078 0.0009 0.3078 0.0791 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0044 0.0071 0.0026 0.1925 0.1271 0.0344 0.0345 ! !
1935,40 0.0092 0.0092 0.0038 0.0082 0.0001 0.1238 0.0521 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0139 0.0085 0.0002 0.3709 0.3656 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0028 0.0044 0.0007 0.1819 0.0673 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0031 0.0113 0.0012 0.4794 0.0964 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0068 0.0154 0.0021 0.1905 ,0.2022 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0118 0.0015 0.0029 0.1928 0.3376 0.0350 0.0351 ! !
7/1968,2010 0.0088 0.0043 0.0029 0.0082 0.0045 0.0959 0.0651 0.0444 0.0444 ! !
1970,80 0.0078 0.0023 0.0092 0.0014 0.0055 0.0478 0.1886 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0050 0.0184 0.0071 0.126 ,0.1039 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0031 0.0082 0.0041 0.2167 0.0824 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0008 0.0088 0.0021 0.0308 0.0184 0.0443 0.0444 ! !
1970,75 0.0034 ,0.0014 0.0009 0.0045 0.0048 ,0.0271 0.0176 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0209 ,0.0005 0.0060 0.2122 0.4569 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0018 0.0193 0.0083 0.149 ,0.0412 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0080 0.0192 0.0056 0.150 ,0.1585 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0030 0.0080 0.0040 0.1986 0.0892 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0110 0.0043 0.302 0.0647 0.0397 0.0397 ! !2000,05 0.0032 0.0010 ,0.0001 0.0113 0.0023 0.0254 ,0.0017 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0017 0.0059 0.0019 0.0451 0.0358 0.0471 0.0471 ! !
1935,2010 0.0097 0.0066 0.0039 0.0080 0.0031 0.1482 0.0882 0.0446 0.0447 ! !
Period
1935,6/68 0.0394 0.0012 4.8620 4.276 2.0330 3.9190 ,0.0194 ,0.0164 ,0.0114 0.1460 0.9661
1935,45 0.0545 0.0002 2.2010 2.1750 1.4060 1.7500 ,0.0815 ,0.0814 ,0.1117 0.1049 0.63721946,55 0.0259 0.0004 3.6520 3.374 0.8582 3.3180 0.0116 0.0101 0.0682 0.1404 0.89231956,6/68 0.0324 0.0009 3.2860 2.351 1.2010 2.6770 0.1149 0.1207 0.1452 0.2549 0.8512
1935,40 0.0683 0.0002 1.0520 1.0440 0.3957 1.0150 ,0.1453 ,0.1445 ,0.1948 0.0991 0.43611941,45 0.0317 0.0001 2.9180 2.8770 2.2150 2.0620 0.1957 0.1941 0.1414 0.1371 0.72331946,50 0.0312 0.0003 1.5340 1.4120 0.5097 1.1000 0.0581 0.0551 0.0334 0.2247 0.91021951,55 0.0188 0.0004 4.0120 3.699 0.7435 4.6360 ,0.1387 ,0.1314 0.0701 ,0.0566 0.75561956,60 0.0208 0.0007 1.9610 1.467 ,1.2990 5.7230 0.1006 0.1152 0.1503 0.1832 0.65991961,6/68 0.0372 0.0008 2.6250 1.827 2.4530 0.3885 0.1061 0.1064 0.0865 0.2150 0.8900
7/1968,2010 0.0385 0.0025 4.4750 2.160 1.1350 4.8140 0.0676 0.0695 0.1811 0.1388 0.9605
1970,80 0.0423 0.0020 1.8350 0.547 1.6700 0.3892 0.0239 0.0253 0.1851 0.2184 0.89311980,90 0.0424 0.0023 3.1430 1.431 ,0.9197 4.9720 0.0647 0.0750 0.2157 0.0645 0.89031990,00 0.0392 0.0011 3.7280 2.488 0.6192 2.4180 ,0.0867 ,0.0849 0.1778 0.1185 0.90552000,10 0.0308 0.0016 0.8911 0.354 0.1806 3.2810 0.1825 0.1854 0.1156 0.0324 0.9778
1970,75 0.0418 0.0013 0.5462 ,0.228 0.1332 0.9150 0.0966 0.1058 0.1544 0.1808 0.82951975,80 0.0436 0.0023 2.9150 1.797 2.6040 ,0.0968 ,0.0320 ,0.0340 0.2274 0.2510 0.89641980,85 0.0427 0.0022 2.9040 1.240 ,0.2602 3.8410 0.0511 0.0778 0.1761 0.0973 0.83061985,90 0.0406 0.0010 2.2190 1.270 ,1.0760 4.0030 0.0862 0.0844 0.2430 0.0455 0.77271990,95 0.0394 0.0014 2.6910 1.684 0.4523 1.7320 ,0.1039 ,0.1042 0.2868 0.2031 0.94591995,00 0.0382 0.0005 3.4740 2.560 0.3790 2.4320 ,0.0801 ,0.0776 0.0713 0.0530 0.47972000,05 0.0308 0.0015 0.7153 0.215 ,0.0104 3.1210 0.0366 0.0436 ,0.0400 ,0.0763 0.97282005,10 0.0294 0.0016 0.7322 0.3824 0.3031 1.6990 0.2615 0.2618 0.2953 0.1505 0.9795
1935,2010 0.0389 0.0026 6.5800 4.458 2.1570 6.2010 0.0292 0.0346 0.1083 0.1433 0.9763
TABLE!4c:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
55
[hp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0109 0.0096 0.0026 0.0096 0.0013 0.2138 0.0580 0.0449 0.0450 ! !
1935,45 0.0115 0.0114 0.0088 0.0061 0.0001 0.1899 0.1464 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0031 0.0082 0.0009 0.3078 0.0826 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 ,0.0031 0.0137 0.0026 0.1925 ,0.0915 0.0344 0.0345 ! !
1935,40 0.0092 0.0092 0.0049 0.0057 0.0001 0.1238 0.0669 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0133 0.0066 0.0002 0.3709 0.3519 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0048 0.0028 0.0007 0.1819 0.1157 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0013 0.0135 0.0012 0.4794 0.0414 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0071 0.0148 0.0021 0.1905 ,0.2094 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 ,0.0005 0.0130 0.0029 0.1928 ,0.0156 0.0350 0.0351 ! !
7/1968,2010 0.0088 0.0043 0.0000 0.0110 0.0045 0.0959 ,0.0003 0.0444 0.0444 ! !
1970,80 0.0078 0.0023 0.0043 0.0071 0.0055 0.0478 0.0876 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0061 0.0193 0.0071 0.126 ,0.1286 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0016 0.0096 0.0041 0.2167 0.0412 0.0379 0.0379 ! !2000,10 0.0034 0.0014 ,0.0023 0.0111 0.0021 0.0308 ,0.0530 0.0443 0.0444 ! !
1970,75 0.0034 ,0.0014 ,0.0014 0.0085 0.0048 ,0.0271 ,0.0265 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0125 0.0074 0.0060 0.2122 0.2741 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0048 0.0216 0.0083 0.149 ,0.1109 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0090 0.0204 0.0056 0.150 ,0.1776 0.0505 0.0506 ! !1990,95 0.0106 0.0067 ,0.0008 0.0116 0.0040 0.1986 ,0.0228 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0019 0.0113 0.0043 0.302 0.0488 0.0397 0.0397 ! !2000,05 0.0032 0.0010 ,0.0049 0.0162 0.0023 0.0254 ,0.1268 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0002 0.0058 0.0019 0.0451 0.0053 0.0471 0.0471 ! !
1935,2010 0.0097 0.0066 0.0011 0.0103 0.0031 0.1482 0.0255 0.0446 0.0447 ! !
Period
1935,6/68 0.0528 0.0012 4.8620 4.276 1.1050 3.6250 ,0.0194 ,0.0164 0.0339 0.0620 0.9661
1935,45 0.0730 0.0002 2.2010 2.1750 1.7170 0.9563 ,0.0815 ,0.0814 ,0.0244 0.0108 0.63721946,55 0.0376 0.0004 3.6520 3.374 0.8448 2.3780 0.0116 0.0101 0.0870 0.0476 0.89231956,6/68 0.0410 0.0009 3.2860 2.351 ,0.9410 4.0900 0.1149 0.1207 0.0572 0.1985 0.8512
1935,40 0.0900 0.0002 1.0520 1.0440 0.6171 0.5316 ,0.1453 ,0.1445 ,0.0680 0.0149 0.43611941,45 0.0461 0.0001 2.9180 2.8770 2.2520 1.1070 0.1957 0.1941 0.0616 ,0.0083 0.72331946,50 0.0446 0.0003 1.5340 1.4120 0.8178 0.4909 0.0581 0.0551 0.0751 0.1831 0.91021951,55 0.0284 0.0004 4.0120 3.699 0.3079 3.6850 ,0.1387 ,0.1314 0.0947 ,0.2932 0.75561956,60 0.0262 0.0007 1.9610 1.467 ,1.6940 4.3790 0.1006 0.1152 0.0337 0.2703 0.65991961,6/68 0.0486 0.0008 2.6250 1.827 ,0.1127 2.5320 0.1061 0.1064 0.0581 0.1803 0.8900
7/1968,2010 0.0451 0.0025 4.4750 2.160 ,0.0062 5.4830 0.0676 0.0695 0.1031 0.0826 0.9605
1970,80 0.0531 0.0020 1.8350 0.547 0.8900 1.5290 0.0239 0.0253 0.2262 0.1086 0.89311980,90 0.0481 0.0023 3.1430 1.431 ,1.1010 4.6110 0.0647 0.0750 0.0786 0.0124 0.89031990,00 0.0377 0.0011 3.7280 2.488 0.3412 2.9220 ,0.0867 ,0.0849 0.0614 0.0904 0.90552000,10 0.0355 0.0016 0.8911 0.354 ,0.5524 3.5730 0.1825 0.1854 0.0983 0.0200 0.9778
1970,75 0.0622 0.0013 0.5462 ,0.228 ,0.2267 1.1650 0.0966 0.1058 0.2678 0.1395 0.82951975,80 0.0482 0.0023 2.9150 1.797 1.8680 1.2970 ,0.0320 ,0.0340 0.1922 0.0255 0.89641980,85 0.0486 0.0022 2.9040 1.240 ,0.6846 3.7750 0.0511 0.0778 0.0895 ,0.0047 0.83061985,90 0.0456 0.0010 2.2190 1.270 ,1.1730 3.7920 0.0862 0.0844 0.0694 0.0377 0.77271990,95 0.0349 0.0014 2.6910 1.684 ,0.1317 2.8270 ,0.1039 ,0.1042 0.0415 0.0948 0.94591995,00 0.0411 0.0005 3.4740 2.560 0.3004 2.3220 ,0.0801 ,0.0776 0.0971 0.1295 0.47972000,05 0.0323 0.0015 0.7153 0.215 ,0.9047 4.2510 0.0366 0.0436 ,0.0645 ,0.0948 0.97282005,10 0.0362 0.0016 0.7322 0.3824 0.0431 1.3580 0.2615 0.2618 0.2202 0.0796 0.9795
1935,2010 0.0486 0.0026 6.5800 4.458 0.6693 6.4180 0.0292 0.0346 0.0787 0.0716 0.9763
TABLE!4d:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!20!Single,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
56
[hp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0145 0.0132 0.0086 0.0060 0.0013 0.2154 0.1408 0.0612 0.0613 ! !
1935,45 0.0201 0.0200 0.0165 0.0040 0.0001 0.2246 0.1854 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0022 0.0090 0.0009 0.2370 0.0513 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0068 0.0054 0.0026 0.2392 0.1713 0.0399 0.0400 ! !
1935,40 0.0141 0.0141 0.0119 0.0020 0.0001 0.1292 0.1097 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0219 0.0062 0.0002 0.4669 0.3788 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0021 0.0058 0.0007 0.1355 0.0399 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0024 0.0123 0.0012 0.4144 0.0729 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0047 0.0137 0.0021 0.2069 ,0.1389 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0145 ,0.0001 0.0029 0.2581 0.3343 0.0435 0.0435 ! !
7/1968,2010 0.0110 0.0065 0.0036 0.0081 0.0045 0.1193 0.0667 0.0541 0.0543 ! !
1970,80 0.0116 0.0061 0.0093 0.0031 0.0055 0.0947 0.1445 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0041 0.0172 0.0071 0.098 ,0.0778 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0017 0.0098 0.0041 0.1486 0.0423 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0049 0.0058 0.0021 0.1560 0.0866 0.0570 0.0571 ! !
1970,75 0.0036 ,0.0012 ,0.0008 0.0062 0.0048 ,0.0172 ,0.0114 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0224 0.0023 0.0060 0.3040 0.3577 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0004 0.0179 0.0083 0.185 ,0.0085 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0076 0.0183 0.0056 0.061 ,0.1395 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0028 0.0084 0.0040 0.1616 0.0718 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0000 0.0136 0.0043 0.181 ,0.0011 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0040 0.0079 0.0023 0.2474 0.0950 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0060 0.0031 0.0019 0.1017 0.0913 0.0661 0.0662 ! !
1935,2010 0.0125 0.0094 0.0058 0.0072 0.0031 0.1642 0.1014 0.0573 0.0575 ! !
Period
1935,6/68 0.0356 0.0012 4.7400 4.309 2.6110 3.3930 ,0.0063 ,0.0040 0.0378 0.1256 0.9661
1935,45 0.0466 0.0002 2.5890 2.5710 1.9310 0.9717 ,0.0664 ,0.0663 ,0.0132 0.0826 0.63721946,55 0.0258 0.0004 2.8350 2.597 0.6220 3.8340 0.0875 0.0864 0.0758 0.0359 0.89231956,6/68 0.0310 0.0009 3.7290 2.926 1.8510 2.1460 0.1357 0.1380 0.1762 0.2518 0.8512
1935,40 0.0566 0.0002 1.0950 1.0890 0.8452 0.3024 ,0.1260 ,0.1255 ,0.0563 0.0528 0.43611941,45 0.0311 0.0001 3.6460 3.6200 2.5960 1.5510 0.1493 0.1485 0.1390 0.1884 0.72331946,50 0.0303 0.0003 1.1480 1.0510 0.3642 1.4830 0.0922 0.0898 0.0334 0.1115 0.91021951,55 0.0201 0.0004 3.5000 3.196 0.5425 4.7290 ,0.0244 ,0.0172 0.1101 ,0.1058 0.75561956,60 0.0217 0.0007 2.0840 1.592 ,1.0610 4.8830 0.1145 0.1309 0.1421 0.1404 0.65991961,6/68 0.0349 0.0008 3.0890 2.449 2.7640 ,0.0250 0.1318 0.1294 0.1426 0.2193 0.8900
7/1968,2010 0.0358 0.0025 4.5880 2.685 1.3980 5.1250 0.1864 0.1905 0.2038 0.0909 0.9605
1970,80 0.0395 0.0020 2.0600 1.086 1.6180 0.9007 0.1129 0.1148 0.2102 0.1365 0.89311980,90 0.0385 0.0023 2.6750 1.124 ,0.7994 5.1380 0.1826 0.1887 0.2295 0.0189 0.89031990,00 0.0372 0.0011 2.8790 1.702 0.3619 3.0170 0.2137 0.2177 0.2472 0.1243 0.90552000,10 0.0308 0.0016 2.2100 1.788 0.9819 2.1630 0.2689 0.2726 0.1592 0.0580 0.9778
1970,75 0.0443 0.0013 0.4335 ,0.146 ,0.1031 1.1970 0.1535 0.1577 0.1788 0.1045 0.82951975,80 0.0366 0.0023 3.3950 2.570 2.8630 0.5427 0.0478 0.0543 0.2594 0.1625 0.89641980,85 0.0350 0.0022 3.0340 1.548 ,0.0628 4.3340 0.1518 0.1729 0.1835 0.1268 0.83061985,90 0.0409 0.0010 1.3930 0.518 ,1.0840 3.7960 0.1979 0.1980 0.2593 ,0.0404 0.77271990,95 0.0377 0.0014 2.2370 1.364 0.4344 1.8860 0.2632 0.2685 0.3471 0.1780 0.94591995,00 0.0355 0.0005 2.4730 1.540 ,0.0069 3.2430 0.1544 0.1551 0.1332 0.0924 0.47972000,05 0.0323 0.0015 2.5550 2.094 0.6612 2.0640 0.1855 0.1898 0.0337 ,0.0384 0.97282005,10 0.0270 0.0016 1.1120 0.8607 0.8427 0.9688 0.2890 0.2927 0.2286 0.1837 0.9795
1935,2010 0.0357 0.0026 6.5970 4.941 2.8360 6.0890 0.0905 0.0962 0.1238 0.1088 0.9763
TABLE!4e:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
t(Rm)
57
[hp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0145 0.0132 0.0043 0.0096 0.0013 0.2154 0.0706 0.0612 0.0613 ! !
1935,45 0.0201 0.0200 0.0088 0.0103 0.0001 0.2246 0.0984 0.0890 0.0890 ! !1946,55 0.0112 0.0103 0.0024 0.0093 0.0009 0.2370 0.0547 0.0434 0.0434 ! !1956,6/68 0.0122 0.0095 0.0020 0.0092 0.0026 0.2392 0.0501 0.0399 0.0400 ! !
1935,40 0.0141 0.0141 0.0031 0.0098 0.0001 0.1292 0.0286 0.1087 0.1087 ! !1941,45 0.0273 0.0270 0.0154 0.0109 0.0002 0.4669 0.2667 0.0579 0.0578 ! !1946,50 0.0077 0.0070 0.0024 0.0059 0.0007 0.1355 0.0468 0.0520 0.0520 ! !1951,55 0.0147 0.0135 0.0023 0.0127 0.0012 0.4144 0.0708 0.0326 0.0328 ! !1956,60 0.0091 0.0070 ,0.0075 0.0158 0.0021 0.2069 ,0.2202 0.0340 0.0342 ! !1961,6/68 0.0142 0.0112 0.0083 0.0048 0.0029 0.2581 0.1912 0.0435 0.0435 ! !
7/1968,2010 0.0110 0.0065 0.0022 0.0092 0.0045 0.1193 0.0410 0.0541 0.0543 ! !
1970,80 0.0116 0.0061 0.0052 0.0069 0.0055 0.0947 0.0809 0.0646 0.0647 ! !1980,90 0.0122 0.0052 ,0.0025 0.0155 0.0071 0.098 ,0.0472 0.0525 0.0528 ! !1990,00 0.0100 0.0060 0.0017 0.0096 0.0041 0.1486 0.0427 0.0401 0.0402 ! !2000,10 0.0110 0.0089 0.0034 0.0067 0.0021 0.1560 0.0597 0.0570 0.0571 ! !
1970,75 0.0036 ,0.0012 0.0002 0.0066 0.0048 ,0.0172 0.0026 0.0702 0.0704 ! !1975,80 0.0250 0.0190 0.0140 0.0086 0.0060 0.3040 0.2238 0.0625 0.0628 ! !1980,85 0.0173 0.0089 ,0.0024 0.0190 0.0083 0.185 ,0.0491 0.0483 0.0490 ! !1985,90 0.0090 0.0034 ,0.0023 0.0135 0.0056 0.061 ,0.0419 0.0548 0.0549 ! !1990,95 0.0103 0.0063 0.0017 0.0096 0.0040 0.1616 0.0439 0.0390 0.0392 ! !1995,00 0.0113 0.0070 0.0013 0.0120 0.0043 0.181 0.0348 0.0388 0.0388 ! !2000,05 0.0127 0.0104 0.0033 0.0089 0.0023 0.2474 0.0783 0.0421 0.0422 ! !2005,10 0.0087 0.0067 0.0039 0.0038 0.0019 0.1017 0.0595 0.0661 0.0662 ! !
1935,2010 0.0125 0.0094 0.0031 0.0094 0.0031 0.1642 0.0548 0.0573 0.0575 ! !
Period
1935,6/68 0.0451 0.0012 4.7400 4.309 1.5860 4.2460 ,0.0063 ,0.0040 0.0187 0.0245 0.9661
1935,45 0.0610 0.0002 2.5890 2.5710 1.3600 1.9250 ,0.0664 ,0.0663 ,0.0448 ,0.0206 0.63721946,55 0.0344 0.0004 2.8350 2.597 0.6019 2.9550 0.0875 0.0864 0.0653 ,0.0507 0.89231956,6/68 0.0356 0.0009 3.7290 2.926 0.5888 3.1590 0.1357 0.1380 0.1328 0.1961 0.8512
1935,40 0.0751 0.0002 1.0950 1.0890 0.2986 1.0940 ,0.1260 ,0.1255 ,0.1066 ,0.0574 0.43611941,45 0.0389 0.0001 3.6460 3.6200 2.2810 2.1680 0.1493 0.1485 0.1098 0.1410 0.72331946,50 0.0389 0.0003 1.1480 1.0510 0.3969 1.1660 0.0922 0.0898 0.0703 0.0556 0.91021951,55 0.0291 0.0004 3.5000 3.196 0.4617 3.3760 ,0.0244 ,0.0172 0.0543 ,0.2054 0.75561956,60 0.0283 0.0007 2.0840 1.592 ,1.8320 4.3280 0.1145 0.1309 0.0255 0.0416 0.65991961,6/68 0.0393 0.0008 3.0890 2.449 1.7110 1.1500 0.1318 0.1294 0.1292 0.2139 0.8900
7/1968,2010 0.0378 0.0025 4.5880 2.685 0.9199 5.5070 0.1864 0.1905 0.1277 0.0542 0.9605
1970,80 0.0451 0.0020 2.0600 1.086 0.9262 1.7450 0.1129 0.1148 0.1182 0.0264 0.89311980,90 0.0401 0.0023 2.6750 1.124 ,0.5050 4.4530 0.1826 0.1887 0.0502 0.0291 0.89031990,00 0.0346 0.0011 2.8790 1.702 0.4184 3.1920 0.2137 0.2177 0.2096 0.0428 0.90552000,10 0.0310 0.0016 2.2100 1.788 0.7671 2.4690 0.2689 0.2726 0.1848 0.0715 0.9778
1970,75 0.0510 0.0013 0.4335 ,0.146 0.0239 1.0990 0.1535 0.1577 0.0970 0.0545 0.82951975,80 0.0394 0.0023 3.3950 2.570 1.7360 1.8570 0.0478 0.0543 0.1436 ,0.0767 0.89641980,85 0.0398 0.0022 3.0340 1.548 ,0.3824 4.0550 0.1518 0.1729 0.0138 0.0661 0.83061985,90 0.0387 0.0010 1.3930 0.518 ,0.3381 2.9610 0.1979 0.1980 0.0853 ,0.0330 0.77271990,95 0.0319 0.0014 2.2370 1.364 0.3107 2.5510 0.2632 0.2685 0.2612 0.0390 0.94591995,00 0.0368 0.0005 2.4730 1.540 0.2483 2.7660 0.1544 0.1551 0.1688 0.0738 0.47972000,05 0.0327 0.0015 2.5550 2.094 0.6270 2.3010 0.1855 0.1898 0.0282 0.0229 0.97282005,10 0.0272 0.0016 1.1120 0.8607 0.6140 1.1990 0.2890 0.2927 0.2791 0.1310 0.9795
1935,2010 0.0411 0.0026 6.5970 4.941 1.7420 6.8720 0.0905 0.0962 0.0815 0.0395 0.9763
TABLE!4f:!Equal,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Value,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
58
[hp]
! ! ! ! ! ! ! ! ! ! ! !! ! !
Period
1935,6/68 0.0109 0.0096 0.0071 0.0053 0.0013 0.2138 0.1583 0.0449 0.0450 ! !
1935,45 0.0115 0.0114 0.0123 0.0029 0.0001 0.1899 0.2052 0.0600 0.0600 ! !1946,55 0.0123 0.0114 0.0028 0.0080 0.0009 0.3078 0.0770 0.0370 0.0370 ! !1956,6/68 0.0092 0.0066 0.0060 0.0053 0.0026 0.1925 0.1742 0.0344 0.0345 ! !
1935,40 0.0092 0.0092 0.0085 0.0017 0.0001 0.1238 0.1150 0.0739 0.0739 ! !1941,45 0.0143 0.0141 0.0168 0.0042 0.0002 0.3709 0.4442 0.0379 0.0378 ! !1946,50 0.0082 0.0075 0.0027 0.0046 0.0007 0.1819 0.0646 0.0414 0.0413 ! !1951,55 0.0165 0.0152 0.0030 0.0114 0.0012 0.4794 0.0949 0.0318 0.0319 ! !1956,60 0.0085 0.0064 ,0.0061 0.0146 0.0021 0.1905 ,0.1800 0.0337 0.0339 ! !1961,6/68 0.0097 0.0068 0.0140 ,0.0009 0.0029 0.1928 0.4003 0.0350 0.0351 ! !
7/1968,2010 0.0088 0.0043 0.0034 0.0077 0.0045 0.0959 0.0771 0.0444 0.0444 ! !
1970,80 0.0078 0.0023 0.0100 0.0005 0.0055 0.0478 0.2055 0.0488 0.0490 ! !1980,90 0.0130 0.0060 ,0.0048 0.0183 0.0071 0.126 ,0.1016 0.0476 0.0480 ! !1990,00 0.0123 0.0082 0.0030 0.0084 0.0041 0.2167 0.0780 0.0379 0.0379 ! !2000,10 0.0034 0.0014 0.0027 0.0069 0.0021 0.0308 0.0606 0.0443 0.0444 ! !
1970,75 0.0034 ,0.0014 ,0.0008 0.0065 0.0048 ,0.0271 ,0.0161 0.0524 0.0528 ! !1975,80 0.0157 0.0097 0.0234 ,0.0033 0.0060 0.2122 0.5114 0.0457 0.0458 ! !1980,85 0.0147 0.0064 ,0.0005 0.0179 0.0083 0.149 ,0.0116 0.0430 0.0437 ! !1985,90 0.0132 0.0076 ,0.0089 0.0202 0.0056 0.150 ,0.1767 0.0505 0.0506 ! !1990,95 0.0106 0.0067 0.0027 0.0084 0.0040 0.1986 0.0801 0.0336 0.0336 ! !1995,00 0.0163 0.0120 0.0026 0.0108 0.0043 0.302 0.0656 0.0397 0.0397 ! !2000,05 0.0032 0.0010 0.0018 0.0094 0.0023 0.0254 0.0467 0.0384 0.0385 ! !2005,10 0.0041 0.0021 0.0039 0.0036 0.0019 0.0451 0.0820 0.0471 0.0471 ! !
1935,2010 0.0097 0.0066 0.0050 0.0066 0.0031 0.1482 0.1131 0.0446 0.0447 ! !
Period
1935,6/68 0.0371 0.0012 4.8620 4.276 2.6130 2.8610 ,0.0194 ,0.0164 0.0385 0.1187 0.9661
1935,45 0.0482 0.0002 2.2010 2.1750 1.9300 0.6796 ,0.0815 ,0.0814 ,0.0447 0.0382 0.63721946,55 0.0260 0.0004 3.6520 3.374 0.8473 3.3650 0.0116 0.0101 0.0727 0.0774 0.89231956,6/68 0.0334 0.0009 3.2860 2.351 1.5620 1.9360 0.1149 0.1207 0.1807 0.2817 0.8512
1935,40 0.0571 0.0002 1.0520 1.0440 0.8214 0.2566 ,0.1453 ,0.1445 ,0.1096 ,0.0111 0.43611941,45 0.0353 0.0001 2.9180 2.8770 2.5150 0.9199 0.1957 0.1941 0.1567 0.1897 0.72331946,50 0.0312 0.0003 1.5340 1.4120 0.4984 1.1400 0.0581 0.0551 0.0352 0.1512 0.91021951,55 0.0191 0.0004 4.0120 3.699 0.7384 4.6160 ,0.1387 ,0.1314 0.0893 ,0.0670 0.75561956,60 0.0190 0.0007 1.9610 1.467 ,1.2630 5.9630 0.1006 0.1152 0.1473 0.3042 0.65991961,6/68 0.0392 0.0008 2.6250 1.827 2.6030 ,0.2290 0.1061 0.1064 0.1437 0.2186 0.8900
7/1968,2010 0.0395 0.0025 4.4750 2.160 1.3050 4.3780 0.0676 0.0695 0.1968 0.1329 0.9605
1970,80 0.0472 0.0020 1.8350 0.547 1.7260 0.1312 0.0239 0.0253 0.2249 0.2053 0.89311980,90 0.0434 0.0023 3.1430 1.431 ,0.8950 4.8320 0.0647 0.0750 0.2373 0.0780 0.89031990,00 0.0386 0.0011 3.7280 2.488 0.5882 2.4910 ,0.0867 ,0.0849 0.1857 0.1143 0.90552000,10 0.0299 0.0016 0.8911 0.354 0.5685 2.6400 0.1825 0.1854 0.1263 0.0712 0.9778
1970,75 0.0490 0.0013 0.5462 ,0.228 ,0.1130 1.1310 0.0966 0.1058 0.2010 0.1290 0.82951975,80 0.0464 0.0023 2.9150 1.797 2.8700 ,0.5987 ,0.0320 ,0.0340 0.2614 0.2718 0.89641980,85 0.0423 0.0022 2.9040 1.240 ,0.0727 3.5900 0.0511 0.0778 0.2079 0.1734 0.83061985,90 0.0434 0.0010 2.2190 1.270 ,1.1950 3.9500 0.0862 0.0844 0.2491 ,0.0047 0.77271990,95 0.0381 0.0014 2.6910 1.684 0.4138 1.8670 ,0.1039 ,0.1042 0.2861 0.1994 0.94591995,00 0.0388 0.0005 3.4740 2.560 0.3781 2.3620 ,0.0801 ,0.0776 0.0906 0.0507 0.47972000,05 0.0299 0.0015 0.7153 0.215 0.2794 2.6650 0.0366 0.0436 ,0.0084 ,0.0592 0.97282005,10 0.0280 0.0016 0.7322 0.3824 0.6466 1.0880 0.2615 0.2618 0.2612 0.2149 0.9795
1935,2010 0.0385 0.0026 6.5800 4.458 2.6640 5.1950 0.0292 0.0346 0.1364 0.1306 0.9763
TABLE!4g:!Value,Weighted!NYSE!Market!Portfolio!!!!!!!!!+!!!!!!!5x5!Double,Sort!Test!Portfolios!Built!Using!Equal,Weighted!SecuritiesTHE!BEHAVIOR!OF!THE!MARKET
Statistics
Statistics
Rm Rm � Rf¯�1
¯�0 RfRm�Rf
s(Rm)
¯�1
s(Rm)s(Rm) s(Rm � Rf )
s(�0) s(Rf ) t(Rm � Rf ) t( ¯�1) t( ¯�0) ⇢M (Rm) ⇢(Rm � Rf ) ⇢M (�1) ⇢M (�0) ⇢M (Rf )t(Rm)
59
!!
!!
!!
!
Perio
dPe
riod
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0013
0.0011
0.0024
2.1600
0.0020
0.0010
0.0030
3.0010
193516/68
0.0014
0.0017
0.0031
1.8390
0.0015
0.0032
0.0048
1.4640
1935145
0.0026
0.0021
0.0047
2.2150
0.0038
0.0019
0.0057
2.9390
1935145
0.0030
0.0028
0.0058
2.0750
0.0021
0.0059
0.0079
1.3510
1946155
0.0006
0.0005
0.0011
2.2090
0.0013
0.0004
0.0017
3.9120
1946155
0.0010
0.0008
0.0018
2.2930
0.0021
0.0018
0.0038
2.1950
195616/68
0.0007
0.0007
0.0013
2.0110
0.0010
0.0006
0.0017
2.6040
195616/68
0.0004
0.0015
0.0019
1.2840
0.0006
0.0021
0.0027
1.2600
1935140
0.0045
0.0030
0.0075
2.5300
0.0049
0.0027
0.0076
2.7700
1935140
0.0046
0.0035
0.0081
2.3340
0.0030
0.0079
0.0109
1.3830
1941145
0.0004
0.0012
0.0015
1.3070
0.0026
0.0010
0.0036
3.5550
1941145
0.0011
0.0020
0.0032
1.5630
0.0008
0.0035
0.0043
1.2380
1946150
0.0010
0.0004
0.0014
3.1630
0.0017
0.0004
0.0021
5.2430
1946150
0.0015
0.0007
0.0022
3.1410
0.0022
0.0021
0.0043
2.0610
1951155
0.0002
0.0006
0.0008
1.4210
0.0009
0.0005
0.0014
2.9010
1951155
0.0005
0.0008
0.0013
1.6000
0.0020
0.0014
0.0034
2.4240
1956160
0.0003
0.0005
0.0008
1.5090
0.0004
0.0004
0.0008
1.8180
1956160
10.000
20.0014
0.0012
0.8514
0.0000
0.0016
0.0016
1.0170
196116/68
0.0009
0.0008
0.0017
2.2330
0.0014
0.0008
0.0022
2.8590
196116/68
0.0009
0.0015
0.0024
1.5730
0.0008
0.0025
0.0033
1.3060
7/196812010
0.0009
0.0009
0.0018
1.9740
0.0023
0.0009
0.0033
3.5070
7/196812010
0.0009
0.0017
0.0026
1.5160
0.0031
0.0040
0.0071
1.7690
1970180
0.0013
0.0010
0.0023
2.3560
0.0027
0.0010
0.0038
3.5930
1970180
0.0014
0.0020
0.0035
1.7090
0.0009
0.0056
0.0065
1.1640
1980190
0.0011
0.0012
0.0023
1.9120
0.0027
0.0013
0.0040
3.1600
1980190
0.0007
0.0019
0.0026
1.3840
0.0061
0.0041
0.0102
2.4690
1990100
0.0004
0.0010
0.0014
1.3980
0.0017
0.0010
0.0028
2.7230
1990100
0.0005
0.0015
0.0020
1.3090
0.0023
0.0027
0.0050
1.8330
2000110
0.0006
0.0005
0.0011
2.0970
0.0025
0.0005
0.0030
5.6550
2000110
0.0007
0.0015
0.0022
1.4890
0.0033
0.0037
0.0070
1.8940
1970175
0.0018
0.0012
0.0029
2.5430
0.0025
0.0012
0.0037
3.1090
1970175
0.0020
0.0022
0.0042
1.9010
0.0019
0.0063
0.0081
1.2950
1975180
0.0009
0.0009
0.0018
1.9780
0.0029
0.0010
0.0039
3.9670
1975180
0.0007
0.0021
0.0027
1.3300
10.000
20.0051
0.0049
0.9657
1980185
0.0017
0.0009
0.0026
2.8820
0.0027
0.0010
0.0037
3.8110
1980185
0.0010
0.0016
0.0026
1.6140
0.0055
0.0035
0.0090
2.5680
1985190
0.0004
0.0014
0.0018
1.2890
0.0025
0.0014
0.0039
2.7440
1985190
0.0004
0.0020
0.0024
1.2030
0.0065
0.0045
0.0110
2.4510
1990195
0.0001
0.0012
0.0013
1.0920
0.0019
0.0013
0.0031
2.4560
1990195
0.0003
0.0016
0.0019
1.1960
0.0017
0.0029
0.0045
1.5820
1995100
0.0008
0.0006
0.0014
2.2380
0.0016
0.0006
0.0023
3.5780
1995100
0.0007
0.0013
0.0021
1.5590
0.0024
0.0024
0.0048
1.9980
2000105
0.0007
0.0006
0.0013
2.3110
0.0020
0.0006
0.0025
4.6180
2000105
0.0010
0.0015
0.0025
1.6920
0.0040
0.0029
0.0069
2.4200
2005110
0.0004
0.0005
0.0009
1.7900
0.0027
0.0005
0.0032
6.8350
2005110
0.0002
0.0013
0.0015
1.1550
0.0021
0.0042
0.0063
1.5030
193512010
0.0010
0.0010
0.0020
2.0630
0.0022
0.0010
0.0032
3.2740
193512010
0.0011
0.0017
0.0028
1.6560
0.0024
0.0037
0.0061
1.6490
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0009
0.0046
0.0055
1.1890
0.0023
0.0205
0.0228
1.1130
193516/68
0.0015
0.0071
0.0085
1.2080
0.0024
0.0218
0.0242
1.1120
1935145
0.0017
0.0061
0.0079
1.2840
0.0000
0.0296
0.0296
1.0010
1935145
0.0043
0.0094
0.0137
1.4560
0.0036
0.0317
0.0353
1.1140
1946155
0.0003
0.0029
0.0032
1.1020
0.0051
0.0113
0.0164
1.4510
1946155
10.000
70.0043
0.0036
0.8340
0.0037
0.0114
0.0152
1.3280
195616/68
0.0006
0.0046
0.0053
1.1380
0.0024
0.0200
0.0224
1.1200
195616/68
0.0008
0.0072
0.0081
1.1180
0.0007
0.0214
0.0221
1.0310
1935140
0.0043
0.0078
0.0121
1.5520
0.0058
0.0344
0.0402
1.1700
1935140
0.0097
0.0112
0.0209
1.8690
0.0143
0.0372
0.0515
1.3840
1941145
10.001
20.0041
0.0029
0.7112
10.006
60.0239
0.0173
0.7231
1941145
10.002
10.0072
0.0052
0.7131
10.008
60.0251
0.0165
0.6582
1946150
0.0006
0.0019
0.0026
1.3190
0.0073
0.0073
0.0146
2.0010
1946150
0.0000
0.0036
0.0036
0.9976
0.0064
0.0074
0.0138
1.8550
1951155
0.0000
0.0038
0.0039
1.0040
0.0032
0.0153
0.0185
1.2070
1951155
10.001
40.0050
0.0036
0.7264
0.0014
0.0154
0.0168
1.0900
1956160
0.0000
0.0021
0.0022
1.0200
0.0026
0.0089
0.0115
1.2890
1956160
0.0001
0.0035
0.0036
1.0290
0.0016
0.0100
0.0116
1.1620
196116/68
0.0011
0.0063
0.0074
1.1710
0.0024
0.0273
0.0297
1.0890
196116/68
0.0014
0.0097
0.0111
1.1410
0.0002
0.0291
0.0293
1.0080
7/196812010
0.0011
0.0053
0.0064
1.1980
0.0088
0.0278
0.0366
1.3180
7/196812010
0.0015
0.0069
0.0083
1.2140
0.0070
0.0311
0.0381
1.2250
1970180
0.0012
0.0090
0.0103
1.1340
0.0051
0.0433
0.0485
1.1180
1970180
0.0026
0.0112
0.0138
1.2360
10.002
20.0501
0.0478
0.9552
1980190
0.0034
0.0067
0.0100
1.5040
0.0285
0.0319
0.0604
1.8940
1980190
0.0040
0.0083
0.0124
1.4840
0.0298
0.0341
0.0639
1.8720
1990100
10.000
90.0040
0.0032
0.7832
10.004
00.0288
0.0247
0.8595
1990100
10.000
80.0051
0.0044
0.8513
10.004
20.0307
0.0265
0.8641
2000110
0.0000
0.0014
0.0015
1.0200
0.0055
0.0082
0.0136
1.6710
2000110
10.000
30.0030
0.0026
0.8837
0.0067
0.0105
0.0172
1.6430
1970175
0.0014
0.0098
0.0112
1.1390
10.004
00.0478
0.0437
0.9154
1970175
0.0032
0.0130
0.0162
1.2500
10.005
70.0507
0.0450
0.8868
1975180
0.0019
0.0083
0.0102
1.2280
0.0144
0.0394
0.0537
1.3650
1975180
0.0024
0.0093
0.0116
1.2540
0.0015
0.0507
0.0522
1.0290
1980185
0.0031
0.0068
0.0100
1.4590
0.0232
0.0301
0.0533
1.7700
1980185
0.0037
0.0086
0.0123
1.4330
0.0223
0.0310
0.0533
1.7190
1985190
0.0041
0.0060
0.0101
1.6910
0.0355
0.0309
0.0664
2.1480
1985190
0.0053
0.0075
0.0128
1.7100
0.0393
0.0340
0.0734
2.1560
1990195
10.002
00.0061
0.0040
0.6630
10.010
10.0435
0.0334
0.7687
1990195
10.001
30.0072
0.0058
0.8158
10.011
70.0451
0.0333
0.7394
1995100
0.0007
0.0015
0.0022
1.4330
0.0037
0.0106
0.0144
1.3520
1995100
0.0004
0.0026
0.0030
1.1400
0.0049
0.0126
0.0175
1.3900
2000105
10.000
20.0015
0.0012
0.8499
10.001
10.0092
0.0081
0.8852
2000105
10.000
30.0029
0.0027
0.9119
0.0029
0.0108
0.0137
1.2660
2005110
0.0003
0.0013
0.0016
1.2470
0.0113
0.0063
0.0176
2.7900
2005110
10.000
50.0027
0.0022
0.8251
0.0097
0.0090
0.0187
2.0870
193512010
0.0010
0.0050
0.0060
1.1930
0.0059
0.0246
0.0305
1.2420
193512010
0.0015
0.0069
0.0084
1.2110
0.0050
0.0270
0.0319
1.1840
TABLE!5b
:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
COMPO
NEN
TS!OF!TH
E!VA
RIAN
CES!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
60
Perio
d! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.1083
0.7801
0.8884
1.1390
1935145
11
11
11
11
1935145
11
11
0.2241
0.5135
0.7376
1.4360
1946155
11
11
11
11
1946155
11
11
0.2575
0.5563
0.8138
1.4630
195616/68
11
11
11
11
195616/68
11
11
10.106
01.1920
1.0860
0.9110
1935140
11
11
11
11
1935140
11
11
0.0546
0.4053
0.4599
1.1350
1941145
11
11
11
11
1941145
11
11
0.4243
0.6415
1.0660
1.6610
1946150
11
11
11
11
1946150
11
11
0.1558
0.5227
0.6785
1.2980
1951155
11
11
11
11
1951155
11
11
0.3692
0.5900
0.9592
1.6260
1956160
11
11
11
11
1956160
11
11
10.042
21.2300
1.1880
0.9657
196116/68
11
11
11
11
196116/68
11
11
10.162
71.1660
1.0030
0.8605
7/196812010
11
11
11
11
7/196812010
11
11
0.2134
1.0800
1.2940
1.1980
1970180
11
11
11
11
1970180
11
11
0.0525
1.5110
1.5640
1.0350
1980190
11
11
11
11
1980190
11
11
0.4749
0.9183
1.3930
1.5170
1990100
11
11
11
11
1990100
11
11
0.2312
0.5972
0.8284
1.3870
2000110
11
11
11
11
2000110
11
11
0.1349
1.2010
1.3360
1.1120
1970175
11
11
11
11
1970175
11
11
0.0708
1.8280
1.8980
1.0390
1975180
11
11
11
11
1975180
11
11
10.218
31.2770
1.0590
0.8291
1980185
11
11
11
11
1980185
11
11
0.2333
0.7890
1.0220
1.2960
1985190
11
11
11
11
1985190
11
11
0.7624
1.0030
1.7650
1.7600
1990195
11
11
11
11
1990195
11
11
0.2451
0.5037
0.7488
1.4870
1995100
11
11
11
11
1995100
11
11
0.1108
0.6836
0.7944
1.1620
2000105
11
11
11
11
2000105
11
11
0.5375
0.9037
1.4410
1.5950
2005110
11
11
11
11
2005110
11
11
10.307
41.3750
1.0680
0.7764
193512010
11
11
11
11
193512010
11
11
0.1661
0.9481
1.1140
1.1750
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
10.000
50.0047
0.0042
0.8929
11
11
193516/68
10.000
70.0058
0.0052
0.8873
0.0826
0.9386
1.0210
1.0880
1935145
10.001
90.0074
0.0055
0.7425
11
11
1935145
10.001
50.0096
0.0081
0.8469
0.3045
0.6806
0.9851
1.4470
1946155
0.0006
0.0023
0.0028
1.2540
11
11
1946155
10.000
20.0026
0.0024
0.9277
0.0321
0.7005
0.7326
1.0460
195616/68
10.000
10.0044
0.0043
0.9769
11
11
195616/68
10.000
30.0051
0.0049
0.9465
10.065
81.3550
1.2890
0.9514
1935140
10.002
30.0083
0.0060
0.7227
11
11
1935140
10.000
20.0112
0.0110
0.9828
0.3079
0.6029
0.9108
1.5110
1941145
10.001
40.0063
0.0049
0.7854
11
11
1941145
10.002
90.0078
0.0049
0.6289
0.2962
0.7724
1.0690
1.3830
1946150
0.0009
0.0013
0.0022
1.6580
11
11
1946150
0.0004
0.0017
0.0021
1.2200
10.188
30.7424
0.5541
0.7464
1951155
0.0003
0.0032
0.0035
1.0970
11
11
1951155
10.000
70.0035
0.0028
0.7930
0.2624
0.6587
0.9210
1.3980
1956160
0.0003
0.0019
0.0022
1.1510
11
11
1956160
0.0004
0.0021
0.0025
1.2050
0.0470
1.2950
1.3420
1.0360
196116/68
10.000
40.0061
0.0057
0.9381
11
11
196116/68
10.000
80.0072
0.0064
0.8933
10.157
91.3940
1.2360
0.8867
7/196812010
0.0013
0.0073
0.0086
1.1830
11
11
7/196812010
0.0014
0.0079
0.0093
1.1730
0.1814
1.1700
1.3510
1.1550
1970180
10.000
10.0104
0.0103
0.9905
11
11
1970180
10.000
30.0112
0.0109
0.9724
0.0476
1.6590
1.7070
1.0290
1980190
0.0076
0.0080
0.0156
1.9460
11
11
1980190
0.0085
0.0089
0.0174
1.9540
0.4857
0.9530
1.4390
1.5100
1990100
10.002
20.0095
0.0073
0.7666
11
11
1990100
10.002
10.0103
0.0082
0.7964
0.2405
0.6648
0.9052
1.3620
2000110
0.0004
0.0021
0.0025
1.1940
11
11
2000110
0.0003
0.0023
0.0026
1.1500
0.0468
1.3190
1.3650
1.0350
1970175
10.001
40.0115
0.0101
0.8809
11
11
1970175
10.001
30.0126
0.0113
0.9000
0.1185
2.0250
2.1430
1.0580
1975180
0.0018
0.0094
0.0112
1.1860
11
11
1975180
0.0010
0.0101
0.0111
1.1040
10.273
31.3550
1.0820
0.7983
1980185
0.0058
0.0068
0.0126
1.8450
11
11
1980185
0.0063
0.0073
0.0136
1.8590
0.3224
0.8253
1.1480
1.3910
1985190
0.0097
0.0084
0.0181
2.1460
11
11
1985190
0.0112
0.0096
0.0208
2.1720
0.7493
1.0240
1.7740
1.7310
1990195
10.004
50.0146
0.0102
0.6952
11
11
1990195
10.003
90.0157
0.0118
0.7506
0.3753
0.5633
0.9386
1.6660
1995100
0.0006
0.0032
0.0039
1.1900
11
11
1995100
0.0004
0.0035
0.0040
1.1240
0.0397
0.7500
0.7897
1.0530
2000105
10.000
20.0026
0.0024
0.9255
11
11
2000105
10.000
10.0027
0.0026
0.9536
0.5223
1.0160
1.5380
1.5140
2005110
0.0009
0.0014
0.0023
1.6590
11
11
2005110
0.0007
0.0016
0.0023
1.4530
10.445
51.4890
1.0430
0.7008
193512010
0.0005
0.0062
0.0067
1.0840
11
11
193512010
0.0005
0.0070
0.0075
1.0670
0.1382
1.0680
1.2060
1.1290
FF
FF
TABLE!5b
:!Equ
al1W
eighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Va
lue1Weighted!Securities
COMPO
NEN
TS!OF!TH
E!VA
RIAN
CES!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
61
!!
!!
!!
!
Perio
dPe
riod
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0012
0.0003
0.0016
4.6250
11
11
193516/68
0.0016
0.0009
0.0025
2.9090
0.0020
0.0007
0.0027
3.6870
1935145
0.0022
0.0007
0.0030
4.0150
11
11
1935145
0.0033
0.0017
0.0050
2.8770
0.0029
0.0010
0.0039
3.9210
1946155
0.0006
0.0001
0.0007
6.4080
11
11
1946155
0.0008
0.0001
0.0009
6.5630
0.0015
0.0004
0.0019
4.8850
195616/68
0.0009
0.0002
0.0010
6.1890
11
11
195616/68
0.0009
0.0007
0.0016
2.3900
0.0015
0.0008
0.0023
2.9820
1935140
0.0036
0.0011
0.0047
4.2570
11
11
1935140
0.0048
0.0027
0.0074
2.7870
0.0044
0.0011
0.0055
4.9550
1941145
0.0007
0.0003
0.0010
3.1690
11
11
1941145
0.0016
0.0007
0.0023
3.4080
0.0011
0.0008
0.0020
2.3700
1946150
0.0009
0.0001
0.0010
8.6930
11
11
1946150
0.0011
0.0001
0.0012
8.8920
0.0019
0.0005
0.0024
5.1940
1951155
0.0003
0.0001
0.0004
3.6400
11
11
1951155
0.0005
0.0002
0.0007
4.3910
0.0012
0.0003
0.0015
4.5610
1956160
0.0003
0.0001
0.0004
3.6440
11
11
1956160
0.0006
0.0004
0.0010
2.4940
0.0008
0.0009
0.0017
1.8870
196116/68
0.0012
0.0002
0.0014
6.8490
11
11
196116/68
0.0010
0.0008
0.0019
2.2550
0.0020
0.0007
0.0027
3.8870
7/196812010
0.0012
0.0002
0.0015
6.2740
11
11
7/196812010
0.0016
0.0006
0.0021
3.7690
0.0038
0.0013
0.0051
3.9110
1970180
0.0015
0.0003
0.0018
5.5880
11
11
1970180
0.0020
0.0005
0.0025
5.0050
0.0039
0.0014
0.0053
3.8160
1980190
0.0015
0.0003
0.0018
6.5230
11
11
1980190
0.0017
0.0005
0.0022
4.8200
0.0055
0.0017
0.0073
4.1870
1990100
0.0013
0.0003
0.0015
5.5980
11
11
1990100
0.0014
0.0005
0.0019
3.8290
0.0023
0.0014
0.0037
2.6900
2000110
0.0008
0.0001
0.0010
6.8390
11
11
2000110
0.0011
0.0009
0.0020
2.2300
0.0046
0.0012
0.0058
4.8080
1970175
0.0014
0.0004
0.0017
4.8900
11
11
1970175
0.0021
0.0007
0.0028
4.1670
0.0030
0.0011
0.0041
3.6640
1975180
0.0016
0.0003
0.0019
5.9210
11
11
1975180
0.0018
0.0003
0.0022
6.3850
0.0050
0.0018
0.0068
3.6930
1980185
0.0016
0.0002
0.0018
8.0790
11
11
1980185
0.0018
0.0005
0.0022
4.8700
0.0050
0.0019
0.0069
3.7110
1985190
0.0013
0.0003
0.0017
5.4060
11
11
1985190
0.0015
0.0005
0.0020
4.1780
0.0057
0.0016
0.0072
4.6310
1990195
0.0012
0.0003
0.0016
4.6380
11
11
1990195
0.0013
0.0004
0.0017
4.7410
0.0017
0.0012
0.0029
2.4460
1995100
0.0013
0.0002
0.0015
7.9450
11
11
1995100
0.0014
0.0006
0.0020
3.4410
0.0028
0.0014
0.0042
3.0200
2000105
0.0008
0.0002
0.0009
6.2400
11
11
2000105
0.0006
0.0009
0.0014
1.6660
0.0040
0.0014
0.0054
3.8750
2005110
0.0007
0.0001
0.0009
7.5620
11
11
2005110
0.0015
0.0009
0.0024
2.6880
0.0046
0.0009
0.0055
5.9920
193512010
0.0012
0.0003
0.0015
5.3970
11
11
193512010
0.0016
0.0007
0.0023
3.2970
0.0030
0.0010
0.0040
3.8530
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0015
0.0019
0.0034
1.8190
0.0056
0.0066
0.0121
1.8500
193516/68
0.0018
0.0040
0.0058
1.4630
0.0055
0.0069
0.0123
1.7960
1935145
0.0017
0.0025
0.0043
1.6740
0.0051
0.0069
0.0119
1.7400
1935145
0.0025
0.0071
0.0096
1.3600
0.0051
0.0076
0.0127
1.6680
1946155
0.0006
0.0010
0.0016
1.5740
0.0041
0.0029
0.0070
2.4290
1946155
0.0005
0.0018
0.0023
1.2550
0.0037
0.0030
0.0067
2.2040
195616/68
0.0021
0.0020
0.0041
2.0760
0.0072
0.0092
0.0164
1.7800
195616/68
0.0024
0.0031
0.0055
1.7890
0.0073
0.0093
0.0166
1.7890
1935140
0.0018
0.0034
0.0051
1.5180
0.0079
0.0090
0.0169
1.8790
1935140
0.0019
0.0102
0.0121
1.1920
0.0086
0.0106
0.0191
1.8100
1941145
0.0017
0.0016
0.0033
2.1210
0.0019
0.0044
0.0063
1.4410
1941145
0.0033
0.0034
0.0067
1.9780
0.0011
0.0041
0.0052
1.2610
1946150
0.0009
0.0012
0.0021
1.7090
0.0049
0.0030
0.0079
2.6090
1946150
0.0012
0.0021
0.0033
1.5980
0.0050
0.0032
0.0082
2.5850
1951155
0.0003
0.0008
0.0011
1.3860
0.0035
0.0028
0.0063
2.2700
1951155
10.000
30.0015
0.0012
0.8133
0.0024
0.0029
0.0053
1.8260
1956160
0.0003
0.0007
0.0010
1.4560
0.0023
0.0038
0.0061
1.6050
1956160
0.0000
0.0019
0.0020
1.0140
0.0024
0.0042
0.0067
1.5760
196116/68
0.0033
0.0028
0.0062
2.1690
0.0106
0.0129
0.0234
1.8240
196116/68
0.0040
0.0038
0.0079
2.0480
0.0107
0.0126
0.0233
1.8470
7/196812010
0.0035
0.0016
0.0051
3.2120
0.0137
0.0070
0.0207
2.9710
7/196812010
0.0048
0.0031
0.0080
2.5300
0.0153
0.0078
0.0231
2.9450
1970180
0.0073
0.0031
0.0105
3.3360
0.0226
0.0109
0.0335
3.0720
1970180
0.0107
0.0063
0.0170
2.7100
0.0250
0.0120
0.0370
3.0800
1980190
0.0051
0.0017
0.0068
4.0490
0.0200
0.0074
0.0274
3.7270
1980190
0.0058
0.0032
0.0090
2.7930
0.0222
0.0088
0.0310
3.5350
1990100
0.0019
0.0014
0.0033
2.3770
0.0103
0.0089
0.0192
2.1630
1990100
0.0025
0.0026
0.0051
1.9540
0.0118
0.0104
0.0221
2.1350
2000110
0.0009
0.0003
0.0012
3.6320
0.0066
0.0022
0.0087
4.0140
2000110
0.0011
0.0012
0.0023
1.9600
0.0081
0.0027
0.0108
4.0210
1970175
0.0076
0.0035
0.0110
3.1740
0.0227
0.0123
0.0350
2.8440
1970175
0.0104
0.0074
0.0179
2.3970
0.0230
0.0141
0.0371
2.6250
1975180
0.0082
0.0029
0.0111
3.8740
0.0255
0.0099
0.0355
3.5730
1975180
0.0115
0.0055
0.0170
3.1020
0.0285
0.0107
0.0392
3.6760
1980185
0.0059
0.0017
0.0076
4.4210
0.0187
0.0061
0.0248
4.0520
1980185
0.0053
0.0026
0.0079
3.0210
0.0189
0.0061
0.0251
4.0810
1985190
0.0041
0.0015
0.0055
3.7670
0.0201
0.0078
0.0279
3.5710
1985190
0.0058
0.0035
0.0093
2.6350
0.0238
0.0104
0.0342
3.2920
1990195
0.0021
0.0019
0.0039
2.0990
0.0083
0.0118
0.0200
1.7030
1990195
0.0031
0.0035
0.0066
1.8970
0.0109
0.0142
0.0251
1.7680
1995100
0.0018
0.0007
0.0025
3.3900
0.0122
0.0049
0.0171
3.4910
1995100
0.0018
0.0014
0.0032
2.3270
0.0123
0.0052
0.0176
3.3640
2000105
0.0008
0.0004
0.0011
2.9260
0.0057
0.0030
0.0087
2.8800
2000105
0.0004
0.0012
0.0015
1.3340
0.0068
0.0036
0.0105
2.8810
2005110
0.0010
0.0003
0.0013
4.8240
0.0066
0.0011
0.0077
7.1170
2005110
0.0018
0.0011
0.0029
2.6110
0.0083
0.0015
0.0098
6.7380
193512010
0.0026
0.0017
0.0044
2.5410
0.0101
0.0068
0.0169
2.4930
193512010
0.0035
0.0035
0.0070
1.9980
0.0109
0.0074
0.0184
2.4740
TABLE!5c:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
COMPO
NEN
TS!OF!TH
E!VA
RIAN
CES!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
62
Perio
d! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.2183
0.3448
0.5631
1.6330
1935145
11
11
11
11
1935145
11
11
0.2104
0.2867
0.4972
1.7340
1946155
11
11
11
11
1946155
11
11
0.1916
0.1699
0.3614
2.1280
195616/68
11
11
11
11
195616/68
11
11
0.2450
0.5354
0.7804
1.4580
1935140
11
11
11
11
1935140
11
11
0.0533
0.2877
0.3409
1.1850
1941145
11
11
11
11
1941145
11
11
0.3956
0.2856
0.6812
2.3850
1946150
11
11
11
11
1946150
11
11
0.1598
0.1556
0.3154
2.0270
1951155
11
11
11
11
1951155
11
11
0.2295
0.1841
0.4136
2.2460
1956160
11
11
11
11
1956160
11
11
0.3437
0.4751
0.8188
1.7230
196116/68
11
11
11
11
196116/68
11
11
0.1800
0.5756
0.7556
1.3130
7/196812010
11
11
11
11
7/196812010
11
11
0.3908
0.4057
0.7965
1.9630
1970180
11
11
11
11
1970180
11
11
0.6683
0.4016
1.0700
2.6640
1980190
11
11
11
11
1980190
11
11
0.1888
0.4214
0.6102
1.4480
1990100
11
11
11
11
1990100
11
11
0.1206
0.3253
0.4459
1.3710
2000110
11
11
11
11
2000110
11
11
0.4434
0.5336
0.9770
1.8310
1970175
11
11
11
11
1970175
11
11
0.8098
0.4781
1.2880
2.6940
1975180
11
11
11
11
1975180
11
11
0.6576
0.3522
1.0100
2.8670
1980185
11
11
11
11
1980185
11
11
0.2309
0.4884
0.7194
1.4730
1985190
11
11
11
11
1985190
11
11
0.0959
0.3728
0.4688
1.2570
1990195
11
11
11
11
1990195
11
11
0.1444
0.1966
0.3411
1.7350
1995100
11
11
11
11
1995100
11
11
0.0805
0.4177
0.4982
1.1930
2000105
11
11
11
11
2000105
11
11
0.2154
0.4985
0.7139
1.4320
2005110
11
11
11
11
2005110
11
11
0.6159
0.5350
1.1510
2.1510
193512010
11
11
11
11
193512010
11
11
0.3171
0.3789
0.6960
1.8370
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0007
0.0012
0.0019
1.5830
11
11
193516/68
0.0005
0.0015
0.0021
1.3400
0.1331
0.4686
0.6017
1.2840
1935145
0.0006
0.0009
0.0015
1.6030
11
11
1935145
0.0003
0.0014
0.0017
1.2540
0.1106
0.4487
0.5593
1.2470
1946155
0.0004
0.0004
0.0008
1.9400
11
11
1946155
0.0002
0.0006
0.0009
1.3580
0.1220
0.2570
0.3790
1.4750
195616/68
0.0011
0.0021
0.0032
1.5100
11
11
195616/68
0.0009
0.0024
0.0034
1.3810
0.1619
0.6553
0.8172
1.2470
1935140
0.0002
0.0012
0.0014
1.1610
11
11
1935140
0.0000
0.0019
0.0019
1.0070
10.088
50.5017
0.4133
0.8237
1941145
0.0010
0.0006
0.0016
2.7860
11
11
1941145
0.0007
0.0008
0.0015
1.9980
0.3397
0.3860
0.7257
1.8800
1946150
0.0002
0.0004
0.0006
1.6650
11
11
1946150
0.0002
0.0006
0.0007
1.3420
0.1133
0.2372
0.3505
1.4780
1951155
0.0006
0.0005
0.0011
2.1750
11
11
1951155
0.0003
0.0007
0.0010
1.3840
0.1365
0.2767
0.4132
1.4930
1956160
0.0006
0.0010
0.0016
1.5730
11
11
1956160
10.000
10.0018
0.0016
0.9260
0.0935
0.7810
0.8744
1.1200
196116/68
0.0014
0.0029
0.0043
1.5020
11
11
196116/68
0.0017
0.0029
0.0045
1.5750
0.2158
0.5716
0.7874
1.3780
7/196812010
0.0023
0.0016
0.0039
2.4170
11
11
7/196812010
0.0025
0.0024
0.0049
2.0280
0.3834
0.5015
0.8849
1.7650
1970180
0.0036
0.0019
0.0056
2.8660
11
11
1970180
0.0044
0.0031
0.0075
2.3900
0.7271
0.6402
1.3670
2.1360
1980190
0.0021
0.0017
0.0038
2.2220
11
11
1980190
0.0027
0.0031
0.0058
1.8740
0.0612
0.5702
0.6314
1.1070
1990100
0.0025
0.0026
0.0051
1.9610
11
11
1990100
0.0025
0.0040
0.0065
1.6280
0.1303
0.4085
0.5388
1.3190
2000110
0.0014
0.0006
0.0020
3.1640
11
11
2000110
0.0014
0.0006
0.0020
3.1760
0.4582
0.4852
0.9434
1.9440
1970175
0.0044
0.0022
0.0066
2.9860
11
11
1970175
0.0043
0.0035
0.0077
2.2180
0.6724
0.7218
1.3940
1.9320
1975180
0.0041
0.0018
0.0059
3.2210
11
11
1975180
0.0050
0.0033
0.0082
2.5240
0.7562
0.6297
1.3860
2.2010
1980185
0.0019
0.0011
0.0031
2.6800
11
11
1980185
0.0017
0.0014
0.0031
2.2480
0.0092
0.5573
0.5665
1.0170
1985190
0.0020
0.0021
0.0041
1.9680
11
11
1985190
0.0034
0.0044
0.0078
1.7790
0.0551
0.5845
0.6396
1.0940
1990195
0.0023
0.0035
0.0057
1.6570
11
11
1990195
0.0023
0.0059
0.0082
1.3910
0.1718
0.3511
0.5229
1.4890
1995100
0.0026
0.0014
0.0040
2.8320
11
11
1995100
0.0026
0.0015
0.0041
2.7240
0.0745
0.4143
0.4888
1.1800
2000105
0.0022
0.0010
0.0032
3.1910
11
11
2000105
0.0022
0.0010
0.0032
3.1870
0.2205
0.4580
0.6786
1.4810
2005110
0.0004
0.0002
0.0006
2.9840
11
11
2005110
0.0004
0.0002
0.0006
3.0630
0.6393
0.4859
1.1250
2.3160
193512010
0.0016
0.0014
0.0030
2.1010
11
11
193512010
0.0016
0.0020
0.0036
1.7980
0.2775
0.4870
0.7645
1.5700
FF
FF
TABLE!5c:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!B
uilt!Usin
g!Eq
ual1W
eighted!Securities
COMPO
NEN
TS!OF!TH
E!VA
RIAN
CES!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
63
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0016
0.0012
0.0028
2.2660
0.0015
0.0007
0.0022
3.0780
193516/68
0.0018
0.0016
0.0034
2.0880
0.0014
0.0016
0.0030
1.8220
1935145
0.0031
0.0023
0.0053
2.3560
0.0024
0.0010
0.0034
3.3670
1935145
0.0034
0.0027
0.0061
2.2390
0.0018
0.0021
0.0039
1.8250
1946155
0.0008
0.0007
0.0014
2.1280
0.0012
0.0004
0.0016
3.9150
1946155
0.0008
0.0008
0.0016
2.0360
0.0014
0.0012
0.0027
2.1430
195616/68
0.0009
0.0008
0.0017
2.1460
0.0010
0.0007
0.0017
2.3060
195616/68
0.0012
0.0014
0.0026
1.8560
0.0009
0.0015
0.0025
1.6100
1935140
0.0051
0.0030
0.0081
2.6740
0.0032
0.0014
0.0046
3.3220
1935140
0.0055
0.0036
0.0091
2.5200
0.0021
0.0026
0.0048
1.7940
1941145
0.0008
0.0014
0.0021
1.5720
0.0015
0.0006
0.0021
3.5170
1941145
0.0010
0.0017
0.0027
1.5880
0.0014
0.0016
0.0029
1.8960
1946150
0.0013
0.0006
0.0020
3.0830
0.0017
0.0003
0.0021
6.3310
1946150
0.0012
0.0007
0.0019
2.7770
0.0020
0.0012
0.0032
2.7240
1951155
0.0001
0.0007
0.0008
1.1770
0.0006
0.0005
0.0011
2.3050
1951155
0.0003
0.0008
0.0011
1.3600
0.0008
0.0013
0.0021
1.6460
1956160
0.0000
0.0007
0.0007
1.0320
0.0004
0.0007
0.0010
1.5530
1956160
10.000
20.0013
0.0011
0.8708
0.0008
0.0018
0.0026
1.4690
196116/68
0.0015
0.0009
0.0024
2.7310
0.0013
0.0008
0.0021
2.7430
196116/68
0.0021
0.0015
0.0036
2.4310
0.0010
0.0014
0.0024
1.7490
7/196812010
0.0009
0.0011
0.0020
1.7920
0.0020
0.0010
0.0030
3.0270
7/196812010
0.0011
0.0018
0.0029
1.5920
0.0012
0.0028
0.0041
1.4260
1970180
0.0013
0.0015
0.0028
1.8410
0.0019
0.0011
0.0030
2.7680
1970180
0.0021
0.0020
0.0041
2.0650
0.0008
0.0039
0.0047
1.2170
1980190
0.0009
0.0014
0.0023
1.6040
0.0028
0.0013
0.0041
3.2130
1980190
0.0008
0.0018
0.0026
1.4310
0.0020
0.0037
0.0057
1.5470
1990100
0.0003
0.0011
0.0014
1.2840
0.0016
0.0011
0.0028
2.4470
1990100
0.0006
0.0017
0.0023
1.3540
0.0010
0.0021
0.0031
1.4840
2000110
0.0007
0.0006
0.0013
2.2220
0.0018
0.0006
0.0024
4.1700
2000110
0.0003
0.0018
0.0021
1.1750
0.0011
0.0020
0.0031
1.5530
1970175
0.0021
0.0018
0.0039
2.1500
0.0015
0.0012
0.0027
2.1830
1970175
0.0030
0.0025
0.0055
2.2300
0.0013
0.0042
0.0055
1.3140
1975180
0.0009
0.0014
0.0023
1.6560
0.0022
0.0010
0.0032
3.0880
1975180
0.0021
0.0017
0.0039
2.2290
0.0008
0.0040
0.0048
1.1960
1980185
0.0010
0.0013
0.0024
1.7960
0.0024
0.0011
0.0035
3.2000
1980185
0.0009
0.0015
0.0025
1.5830
0.0027
0.0038
0.0065
1.7030
1985190
0.0006
0.0015
0.0021
1.4300
0.0029
0.0013
0.0042
3.1430
1985190
0.0006
0.0019
0.0025
1.3140
0.0013
0.0032
0.0045
1.3900
1990195
0.0000
0.0012
0.0012
0.9897
0.0013
0.0012
0.0024
2.0710
1990195
0.0001
0.0015
0.0016
1.0910
0.0002
0.0021
0.0023
1.0820
1995100
0.0008
0.0009
0.0017
1.9360
0.0020
0.0010
0.0030
3.0890
1995100
0.0013
0.0018
0.0030
1.7070
0.0019
0.0018
0.0037
2.0580
2000105
0.0004
0.0006
0.0010
1.7480
0.0014
0.0007
0.0021
2.9550
2000105
10.000
10.0014
0.0014
0.9591
0.0008
0.0019
0.0027
1.4340
2005110
0.0008
0.0005
0.0013
2.6920
0.0020
0.0004
0.0024
6.4460
2005110
0.0006
0.0020
0.0026
1.2880
0.0010
0.0020
0.0030
1.5150
193512010
0.0012
0.0012
0.0024
2.0080
0.0018
0.0009
0.0026
3.0450
193512010
0.0014
0.0017
0.0031
1.7970
0.0013
0.0023
0.0036
1.5550
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
10.000
10.0066
0.0065
0.9895
0.0025
0.0217
0.0242
1.1170
193516/68
0.0000
0.0092
0.0092
0.9985
0.0024
0.0235
0.0259
1.1010
1935145
0.0003
0.0086
0.0088
1.0290
0.0027
0.0212
0.0239
1.1270
1935145
0.0016
0.0121
0.0138
1.1340
0.0044
0.0231
0.0275
1.1910
1946155
10.000
40.0046
0.0042
0.9159
0.0021
0.0134
0.0156
1.1570
1946155
10.000
60.0054
0.0048
0.8826
0.0016
0.0133
0.0148
1.1180
195616/68
0.0000
0.0064
0.0064
0.9977
0.0030
0.0287
0.0318
1.1060
195616/68
10.000
80.0096
0.0088
0.9137
0.0016
0.0321
0.0336
1.0490
1935140
0.0026
0.0097
0.0123
1.2690
0.0089
0.0225
0.0314
1.3970
1935140
0.0068
0.0129
0.0197
1.5250
0.0142
0.0238
0.0380
1.5960
1941145
10.002
40.0073
0.0049
0.6695
10.004
40.0197
0.0154
0.7793
1941145
10.004
30.0112
0.0069
0.6187
10.006
80.0222
0.0154
0.6958
1946150
10.000
50.0043
0.0037
0.8779
0.0007
0.0096
0.0104
1.0770
1946150
10.000
30.0048
0.0045
0.9466
0.0003
0.0095
0.0098
1.0370
1951155
10.000
20.0049
0.0047
0.9594
0.0037
0.0172
0.0210
1.2160
1951155
10.001
00.0061
0.0051
0.8289
0.0030
0.0170
0.0201
1.1790
1956160
10.000
20.0035
0.0033
0.9399
0.0013
0.0200
0.0213
1.0670
1956160
10.000
60.0043
0.0037
0.8617
0.0008
0.0202
0.0210
1.0400
196116/68
0.0001
0.0084
0.0085
1.0170
0.0042
0.0346
0.0388
1.1210
196116/68
10.000
90.0132
0.0122
0.9294
0.0020
0.0400
0.0420
1.0510
7/196812010
0.0018
0.0074
0.0092
1.2380
0.0062
0.0307
0.0369
1.2030
7/196812010
0.0023
0.0090
0.0113
1.2580
0.0043
0.0333
0.0376
1.1310
1970180
0.0080
0.0147
0.0226
1.5420
0.0248
0.0471
0.0720
1.5270
1970180
0.0109
0.0159
0.0268
1.6850
0.0191
0.0497
0.0688
1.3830
1980190
0.0003
0.0080
0.0083
1.0370
0.0058
0.0330
0.0388
1.1760
1980190
10.000
30.0102
0.0100
0.9731
0.0051
0.0373
0.0424
1.1370
1990100
10.001
70.0051
0.0033
0.6588
10.009
30.0345
0.0251
0.7292
1990100
10.002
00.0072
0.0052
0.7175
10.009
30.0378
0.0285
0.7528
2000110
0.0002
0.0015
0.0017
1.1440
0.0014
0.0093
0.0107
1.1550
2000110
0.0000
0.0025
0.0025
0.9953
0.0007
0.0120
0.0127
1.0610
1970175
0.0102
0.0176
0.0278
1.5800
0.0273
0.0560
0.0833
1.4870
1970175
0.0142
0.0190
0.0332
1.7430
0.0244
0.0593
0.0837
1.4100
1975180
0.0063
0.0121
0.0183
1.5190
0.0220
0.0395
0.0615
1.5580
1975180
0.0083
0.0129
0.0212
1.6440
0.0123
0.0429
0.0551
1.2860
1980185
0.0018
0.0085
0.0103
1.2160
0.0118
0.0300
0.0419
1.3930
1980185
0.0021
0.0101
0.0122
1.2080
0.0100
0.0320
0.0420
1.3130
1985190
10.000
50.0069
0.0064
0.9281
0.0043
0.0334
0.0377
1.1270
1985190
10.001
00.0096
0.0085
0.8926
0.0043
0.0393
0.0436
1.1090
1990195
10.002
30.0062
0.0039
0.6320
10.013
40.0398
0.0264
0.6627
1990195
10.002
80.0088
0.0060
0.6800
10.013
20.0453
0.0321
0.7086
1995100
10.000
60.0034
0.0028
0.8181
10.002
30.0248
0.0225
0.9057
1995100
10.000
40.0047
0.0043
0.9048
10.002
40.0255
0.0231
0.9072
2000105
10.000
10.0017
0.0016
0.9610
10.002
60.0131
0.0105
0.8024
2000105
10.000
50.0024
0.0019
0.7810
10.002
60.0149
0.0122
0.8230
2005110
0.0005
0.0012
0.0017
1.4530
0.0049
0.0044
0.0092
2.1130
2005110
0.0004
0.0024
0.0029
1.1800
0.0037
0.0080
0.0117
1.4670
193512010
0.0010
0.0071
0.0080
1.1350
0.0046
0.0267
0.0313
1.1710
193512010
0.0013
0.0091
0.0103
1.1410
0.0035
0.0290
0.0324
1.1190
TABLE!5d
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!Bu
ilt!Using!Value
1Weighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
64
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.1638
0.4877
0.6515
1.3360
1935145
11
11
11
11
1935145
11
11
10.048
10.2734
0.2252
0.8239
1946155
11
11
11
11
1946155
11
11
0.2441
0.4152
0.6593
1.5880
195616/68
11
11
11
11
195616/68
11
11
0.2895
0.7330
1.0230
1.3950
1935140
11
11
11
11
1935140
11
11
10.011
20.2109
0.1997
0.9470
1941145
11
11
11
11
1941145
11
11
10.088
60.3473
0.2587
0.7450
1946150
11
11
11
11
1946150
11
11
0.2113
0.3070
0.5183
1.6880
1951155
11
11
11
11
1951155
11
11
0.2834
0.5234
0.8069
1.5420
1956160
11
11
11
11
1956160
11
11
0.7421
0.9252
1.6670
1.8020
196116/68
11
11
11
11
196116/68
11
11
0.0005
0.6048
0.6053
1.0010
7/196812010
11
11
11
11
7/196812010
11
11
0.0282
0.7707
0.7989
1.0370
1970180
11
11
11
11
1970180
11
11
0.3510
1.0530
1.4040
1.3330
1980190
11
11
11
11
1980190
11
11
10.134
00.6760
0.5421
0.8018
1990100
11
11
11
11
1990100
11
11
0.0157
0.4121
0.4277
1.0380
2000110
11
11
11
11
2000110
11
11
10.229
30.8347
0.6054
0.7253
1970175
11
11
11
11
1970175
11
11
0.4023
1.3880
1.7900
1.2900
1975180
11
11
11
11
1975180
11
11
0.4290
0.8960
1.3250
1.4790
1980185
11
11
11
11
1980185
11
11
10.030
30.6855
0.6553
0.9559
1985190
11
11
11
11
1985190
11
11
10.204
80.6287
0.4239
0.6743
1990195
11
11
11
11
1990195
11
11
10.033
90.3200
0.2861
0.8939
1995100
11
11
11
11
1995100
11
11
0.0697
0.4624
0.5321
1.1510
2000105
11
11
11
11
2000105
11
11
10.067
40.5495
0.4821
0.8773
2005110
11
11
11
11
2005110
11
11
10.452
71.0950
0.6427
0.5867
193512010
11
11
11
11
193512010
11
11
0.0906
0.6461
0.7367
1.1400
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0003
0.0041
0.0044
1.0750
11
11
193516/68
0.0000
0.0047
0.0048
1.0070
0.1242
0.5770
0.7012
1.2150
1935145
10.000
10.0027
0.0027
0.9790
11
11
1935145
0.0000
0.0034
0.0035
1.0130
10.027
30.3705
0.3431
0.9263
1946155
0.0003
0.0022
0.0025
1.1290
11
11
1946155
0.0000
0.0024
0.0024
1.0110
0.2124
0.4713
0.6837
1.4510
195616/68
0.0007
0.0067
0.0074
1.0990
11
11
195616/68
0.0001
0.0078
0.0078
1.0070
0.1937
0.8421
1.0360
1.2300
1935140
0.0003
0.0028
0.0031
1.0970
11
11
1935140
0.0009
0.0035
0.0043
1.2460
0.0735
0.3031
0.3766
1.2430
1941145
10.000
40.0026
0.0022
0.8417
11
11
1941145
10.000
90.0034
0.0025
0.7442
10.141
80.4502
0.3085
0.6851
1946150
0.0001
0.0011
0.0012
1.0560
11
11
1946150
0.0000
0.0012
0.0013
1.0360
0.2342
0.3440
0.5782
1.6810
1951155
0.0005
0.0032
0.0038
1.1640
11
11
1951155
0.0000
0.0035
0.0036
1.0140
0.1956
0.5985
0.7941
1.3270
1956160
10.000
40.0056
0.0052
0.9254
11
11
1956160
10.000
70.0055
0.0049
0.8822
0.6839
0.9556
1.6390
1.7160
196116/68
0.0013
0.0075
0.0088
1.1740
11
11
196116/68
0.0005
0.0092
0.0097
1.0490
10.121
50.7664
0.6449
0.8415
7/196812010
0.0006
0.0069
0.0076
1.0880
11
11
7/196812010
0.0006
0.0078
0.0084
1.0760
0.0024
0.8456
0.8480
1.0030
1970180
0.0033
0.0080
0.0113
1.4110
11
11
1970180
0.0037
0.0084
0.0121
1.4470
0.3277
1.1210
1.4490
1.2920
1980190
0.0006
0.0074
0.0080
1.0780
11
11
1980190
0.0005
0.0096
0.0101
1.0490
10.152
50.7828
0.6303
0.8052
1990100
10.002
30.0108
0.0085
0.7870
11
11
1990100
10.002
70.0128
0.0100
0.7850
10.021
30.4797
0.4583
0.9555
2000110
10.000
30.0029
0.0027
0.9136
11
11
2000110
10.000
20.0029
0.0027
0.9248
10.240
50.9174
0.6769
0.7378
1970175
0.0048
0.0093
0.0141
1.5180
11
11
1970175
0.0055
0.0096
0.0151
1.5770
0.3866
1.4470
1.8330
1.2670
1975180
0.0020
0.0069
0.0089
1.2910
11
11
1975180
0.0020
0.0074
0.0094
1.2710
0.3683
0.9723
1.3410
1.3790
1980185
0.0019
0.0057
0.0077
1.3410
11
11
1980185
0.0021
0.0066
0.0086
1.3140
10.020
20.7784
0.7581
0.9740
1985190
0.0002
0.0085
0.0088
1.0270
11
11
1985190
0.0002
0.0117
0.0119
1.0180
10.220
40.7245
0.5042
0.6958
1990195
10.003
20.0121
0.0089
0.7330
11
11
1990195
10.003
90.0158
0.0119
0.7546
10.066
40.4250
0.3587
0.8439
1995100
10.000
80.0080
0.0072
0.9032
11
11
1995100
10.000
90.0081
0.0072
0.8918
0.0374
0.4822
0.5197
1.0780
2000105
10.000
80.0046
0.0038
0.8213
11
11
2000105
10.000
70.0046
0.0039
0.8406
10.035
50.5769
0.5415
0.9385
2005110
0.0001
0.0008
0.0009
1.1340
11
11
2005110
0.0001
0.0009
0.0010
1.1220
10.506
71.2390
0.7326
0.5912
193512010
0.0005
0.0057
0.0061
1.0830
11
11
193512010
0.0003
0.0065
0.0068
1.0530
0.0589
0.7274
0.7863
1.0810
FF
FF
TABLE!5d
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!20!Single1Sort!Test!P
ortfolios!Bu
ilt!Using!Value
1Weighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
65
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0012
0.0008
0.0020
2.4090
0.0022
0.0008
0.0030
3.8820
193516/68
0.0012
0.0010
0.0022
2.2610
0.0022
0.0020
0.0042
2.1080
1935145
0.0022
0.0015
0.0037
2.4200
0.0040
0.0014
0.0054
3.9350
1935145
0.0022
0.0017
0.0039
2.2660
0.0032
0.0038
0.0070
1.8290
1946155
0.0007
0.0005
0.0012
2.5880
0.0015
0.0004
0.0019
4.5960
1946155
0.0009
0.0005
0.0014
2.8190
0.0022
0.0010
0.0031
3.2350
195616/68
0.0007
0.0006
0.0013
2.3090
0.0012
0.0005
0.0017
3.3400
195616/68
0.0007
0.0007
0.0014
1.9680
0.0014
0.0012
0.0026
2.1750
1935140
0.0037
0.0019
0.0056
2.9030
0.0059
0.0018
0.0077
4.3060
1935140
0.0037
0.0021
0.0058
2.7750
0.0043
0.0048
0.0091
1.8820
1941145
0.0005
0.0011
0.0015
1.4250
0.0019
0.0009
0.0028
3.0630
1941145
0.0004
0.0013
0.0017
1.3410
0.0019
0.0026
0.0045
1.7400
1946150
0.0011
0.0004
0.0015
3.8380
0.0019
0.0003
0.0023
6.4550
1946150
0.0012
0.0004
0.0016
3.8700
0.0029
0.0010
0.0040
3.8440
1951155
0.0003
0.0005
0.0008
1.6330
0.0010
0.0005
0.0015
3.2540
1951155
0.0006
0.0006
0.0012
2.0690
0.0014
0.0009
0.0023
2.5830
1956160
0.0003
0.0005
0.0008
1.5750
0.0005
0.0005
0.0010
2.1960
1956160
0.0004
0.0008
0.0011
1.4630
0.0006
0.0009
0.0015
1.6240
196116/68
0.0010
0.0006
0.0015
2.6780
0.0016
0.0006
0.0021
3.8120
196116/68
0.0009
0.0007
0.0016
2.3170
0.0019
0.0014
0.0033
2.3400
7/196812010
0.0006
0.0008
0.0014
1.8270
0.0022
0.0008
0.0030
3.6740
7/196812010
0.0009
0.0011
0.0020
1.8680
0.0018
0.0027
0.0045
1.6640
1970180
0.0013
0.0008
0.0020
2.6410
0.0034
0.0008
0.0042
5.1030
1970180
0.0017
0.0012
0.0029
2.3490
0.0007
0.0040
0.0047
1.1780
1980190
0.0006
0.0010
0.0016
1.5530
0.0021
0.0011
0.0032
2.8860
1980190
0.0009
0.0013
0.0021
1.6670
0.0031
0.0033
0.0064
1.9330
1990100
0.0003
0.0009
0.0012
1.3750
0.0013
0.0009
0.0022
2.4770
1990100
0.0007
0.0010
0.0017
1.6900
0.0013
0.0017
0.0031
1.7710
2000110
0.0004
0.0006
0.0010
1.6730
0.0020
0.0006
0.0026
4.6260
2000110
0.0007
0.0009
0.0016
1.8330
0.0024
0.0019
0.0042
2.2690
1970175
0.0018
0.0008
0.0026
3.1770
0.0034
0.0008
0.0043
5.1210
1970175
0.0023
0.0014
0.0038
2.6120
0.0002
0.0051
0.0053
1.0490
1975180
0.0007
0.0008
0.0016
1.9270
0.0038
0.0009
0.0047
5.3240
1975180
0.0012
0.0013
0.0024
1.9380
0.0011
0.0033
0.0045
1.3410
1980185
0.0009
0.0007
0.0016
2.2720
0.0020
0.0008
0.0028
3.6540
1980185
0.0010
0.0009
0.0019
2.0790
0.0023
0.0026
0.0049
1.8920
1985190
0.0002
0.0013
0.0015
1.1930
0.0020
0.0013
0.0033
2.5210
1985190
0.0006
0.0015
0.0022
1.4000
0.0034
0.0039
0.0073
1.8880
1990195
0.0000
0.0011
0.0010
0.9634
0.0011
0.0011
0.0022
2.0120
1990195
0.0002
0.0012
0.0014
1.1830
0.0011
0.0018
0.0029
1.6430
1995100
0.0008
0.0006
0.0014
2.2690
0.0015
0.0006
0.0021
3.5730
1995100
0.0012
0.0007
0.0020
2.7170
0.0014
0.0015
0.0029
1.9250
2000105
0.0004
0.0006
0.0011
1.7200
0.0014
0.0006
0.0020
3.2690
2000105
0.0009
0.0009
0.0018
1.9700
0.0007
0.0017
0.0024
1.4270
2005110
0.0003
0.0005
0.0007
1.5510
0.0025
0.0005
0.0029
6.3980
2005110
0.0005
0.0008
0.0013
1.6440
0.0036
0.0019
0.0055
2.9270
193512010
0.0009
0.0008
0.0017
2.0920
0.0022
0.0008
0.0030
3.7610
193512010
0.0011
0.0010
0.0021
2.0310
0.0020
0.0024
0.0044
1.8250
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0004
0.0041
0.0045
1.0990
0.0070
0.0181
0.0251
1.3890
193516/68
0.0005
0.0051
0.0056
1.1000
0.0057
0.0183
0.0240
1.3100
1935145
10.000
80.0054
0.0047
0.8619
0.0081
0.0258
0.0339
1.3140
1935145
0.0005
0.0070
0.0075
1.0660
0.0081
0.0263
0.0344
1.3080
1946155
0.0018
0.0028
0.0046
1.6340
0.0114
0.0112
0.0226
2.0150
1946155
0.0007
0.0036
0.0042
1.1830
0.0078
0.0114
0.0192
1.6870
195616/68
0.0004
0.0039
0.0043
1.0920
0.0029
0.0168
0.0197
1.1730
195616/68
0.0005
0.0045
0.0050
1.1020
0.0020
0.0169
0.0190
1.1210
1935140
10.001
20.0068
0.0056
0.8225
0.0139
0.0323
0.0463
1.4300
1935140
10.000
50.0084
0.0079
0.9350
0.0124
0.0330
0.0454
1.3750
1941145
10.000
30.0038
0.0035
0.9309
0.0014
0.0181
0.0195
1.0780
1941145
0.0017
0.0053
0.0070
1.3100
0.0033
0.0183
0.0216
1.1790
1946150
0.0009
0.0018
0.0027
1.4990
0.0069
0.0068
0.0137
2.0110
1946150
0.0003
0.0024
0.0027
1.1250
0.0062
0.0068
0.0130
1.9060
1951155
0.0028
0.0039
0.0066
1.7160
0.0160
0.0156
0.0316
2.0260
1951155
0.0011
0.0048
0.0059
1.2260
0.0096
0.0159
0.0255
1.6020
1956160
10.000
20.0024
0.0022
0.9071
0.0013
0.0107
0.0120
1.1190
1956160
10.000
30.0029
0.0026
0.8831
10.000
30.0111
0.0108
0.9720
196116/68
0.0008
0.0050
0.0057
1.1540
0.0042
0.0208
0.0250
1.2000
196116/68
0.0010
0.0056
0.0066
1.1830
0.0037
0.0208
0.0246
1.1800
7/196812010
0.0012
0.0039
0.0051
1.2990
0.0105
0.0203
0.0307
1.5160
7/196812010
0.0019
0.0048
0.0067
1.4040
0.0109
0.0213
0.0322
1.5100
1970180
0.0036
0.0064
0.0100
1.5630
0.0215
0.0299
0.0514
1.7190
1970180
0.0048
0.0078
0.0126
1.6220
0.0215
0.0321
0.0536
1.6680
1980190
0.0021
0.0050
0.0071
1.4150
0.0153
0.0254
0.0406
1.6020
1980190
0.0037
0.0063
0.0100
1.5900
0.0150
0.0263
0.0413
1.5720
1990100
10.000
20.0030
0.0027
0.9214
0.0033
0.0193
0.0226
1.1710
1990100
0.0005
0.0035
0.0040
1.1320
0.0053
0.0187
0.0240
1.2850
2000110
10.000
20.0015
0.0013
0.8830
0.0075
0.0085
0.0160
1.8850
2000110
10.000
10.0018
0.0016
0.9282
0.0091
0.0095
0.0185
1.9570
1970175
0.0020
0.0062
0.0082
1.3150
0.0081
0.0288
0.0369
1.2820
1970175
0.0026
0.0082
0.0108
1.3210
0.0167
0.0314
0.0481
1.5310
1975180
0.0072
0.0068
0.0139
2.0610
0.0387
0.0322
0.0708
2.2020
1975180
0.0086
0.0074
0.0160
2.1500
0.0361
0.0348
0.0709
2.0350
1980185
0.0027
0.0049
0.0076
1.5460
0.0165
0.0227
0.0392
1.7270
1980185
0.0032
0.0060
0.0093
1.5370
0.0171
0.0232
0.0403
1.7370
1985190
0.0018
0.0046
0.0063
1.3870
0.0145
0.0250
0.0395
1.5780
1985190
0.0046
0.0059
0.0105
1.7890
0.0138
0.0264
0.0402
1.5210
1990195
10.000
90.0043
0.0034
0.7988
0.0011
0.0291
0.0303
1.0380
1990195
10.000
30.0048
0.0045
0.9352
0.0022
0.0283
0.0305
1.0790
1995100
0.0006
0.0013
0.0018
1.4330
0.0053
0.0069
0.0123
1.7700
1995100
0.0015
0.0019
0.0034
1.7670
0.0081
0.0068
0.0149
2.1980
2000105
10.000
30.0016
0.0013
0.8201
0.0035
0.0093
0.0128
1.3800
2000105
10.000
10.0019
0.0018
0.9470
0.0043
0.0097
0.0140
1.4410
2005110
10.000
10.0012
0.0012
0.9541
0.0103
0.0071
0.0174
2.4390
2005110
10.000
10.0015
0.0014
0.9496
0.0116
0.0087
0.0203
2.3420
193512010
0.0008
0.0040
0.0048
1.2110
0.0090
0.0193
0.0283
1.4660
193512010
0.0013
0.0049
0.0062
1.2670
0.0086
0.0200
0.0286
1.4300
TABLE!5f:!Equ
al1W
eighted!NYSE!Market!Po
rtfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!Po
rtfolios!Bu
ilt!Using!Value
1Weighted!Securities
COMPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
66
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.1763
0.2919
0.4682
1.6040
1935145
11
11
11
11
1935145
11
11
0.0485
0.2344
0.2829
1.2070
1946155
11
11
11
11
1946155
11
11
0.2446
0.2233
0.4679
2.0960
195616/68
11
11
11
11
195616/68
11
11
0.2302
0.3971
0.6273
1.5800
1935140
11
11
11
11
1935140
11
11
0.0921
0.1785
0.2706
1.5160
1941145
11
11
11
11
1941145
11
11
0.0015
0.3006
0.3021
1.0050
1946150
11
11
11
11
1946150
11
11
0.2626
0.1734
0.4360
2.5150
1951155
11
11
11
11
1951155
11
11
0.2325
0.2732
0.5057
1.8510
1956160
11
11
11
11
1956160
11
11
0.1277
0.4014
0.5290
1.3180
196116/68
11
11
11
11
196116/68
11
11
0.3024
0.3942
0.6966
1.7670
7/196812010
11
11
11
11
7/196812010
11
11
0.2370
0.5695
0.8065
1.4160
1970180
11
11
11
11
1970180
11
11
0.2008
0.9615
1.1620
1.2090
1980190
11
11
11
11
1980190
11
11
0.3509
0.5776
0.9285
1.6080
1990100
11
11
11
11
1990100
11
11
0.2565
0.2631
0.5195
1.9750
2000110
11
11
11
11
2000110
11
11
0.3076
0.4434
0.7510
1.6940
1970175
11
11
11
11
1970175
11
11
0.1047
1.3510
1.4560
1.0770
1975180
11
11
11
11
1975180
11
11
0.1168
0.7044
0.8212
1.1660
1980185
11
11
11
11
1980185
11
11
0.1212
0.4626
0.5838
1.2620
1985190
11
11
11
11
1985190
11
11
0.4937
0.6875
1.1810
1.7180
1990195
11
11
11
11
1990195
11
11
0.2240
0.2397
0.4637
1.9340
1995100
11
11
11
11
1995100
11
11
0.2701
0.2640
0.5341
2.0230
2000105
11
11
11
11
2000105
11
11
0.3632
0.3586
0.7217
2.0130
2005110
11
11
11
11
2005110
11
11
0.2401
0.4928
0.7328
1.4870
193512010
11
11
11
11
193512010
11
11
0.2097
0.4473
0.6570
1.4690
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0009
0.0040
0.0049
1.2160
11
11
193516/68
0.0008
0.0047
0.0054
1.1710
0.1660
0.3376
0.5035
1.4920
1935145
0.0008
0.0061
0.0069
1.1300
11
11
1935145
0.0018
0.0075
0.0093
1.2460
0.1008
0.2957
0.3965
1.3410
1946155
0.0021
0.0023
0.0043
1.9280
11
11
1946155
0.0010
0.0025
0.0035
1.4000
0.1644
0.2668
0.4313
1.6160
195616/68
0.0000
0.0036
0.0037
1.0050
11
11
195616/68
10.000
30.0039
0.0036
0.9350
0.2195
0.4307
0.6502
1.5100
1935140
0.0014
0.0077
0.0091
1.1810
11
11
1935140
0.0016
0.0096
0.0112
1.1670
0.0927
0.2408
0.3335
1.3850
1941145
0.0000
0.0042
0.0041
0.9940
11
11
1941145
0.0021
0.0050
0.0071
1.4200
0.1172
0.3607
0.4778
1.3250
1946150
0.0008
0.0013
0.0021
1.6710
11
11
1946150
0.0005
0.0014
0.0020
1.3520
0.1729
0.2308
0.4037
1.7490
1951155
0.0034
0.0032
0.0066
2.0350
11
11
1951155
0.0015
0.0036
0.0052
1.4270
0.1631
0.3029
0.4660
1.5390
1956160
0.0004
0.0024
0.0028
1.1690
11
11
1956160
0.0001
0.0025
0.0026
1.0370
0.0660
0.4300
0.4959
1.1530
196116/68
10.000
20.0045
0.0043
0.9530
11
11
196116/68
10.000
50.0047
0.0043
0.9051
0.3248
0.4312
0.7560
1.7530
7/196812010
0.0017
0.0053
0.0070
1.3110
11
11
7/196812010
0.0020
0.0058
0.0078
1.3540
0.2949
0.6178
0.9127
1.4770
1970180
0.0040
0.0070
0.0110
1.5780
11
11
1970180
0.0048
0.0075
0.0123
1.6480
0.3180
1.0360
1.3540
1.3070
1980190
0.0032
0.0068
0.0100
1.4680
11
11
1980190
0.0040
0.0079
0.0119
1.5070
0.4838
0.6432
1.1270
1.7520
1990100
0.0005
0.0061
0.0066
1.0820
11
11
1990100
0.0007
0.0062
0.0069
1.1200
0.3100
0.3040
0.6140
2.0200
2000110
0.0008
0.0023
0.0031
1.3440
11
11
2000110
0.0005
0.0023
0.0028
1.2420
0.2464
0.4451
0.6915
1.5540
1970175
0.0021
0.0067
0.0088
1.3200
11
11
1970175
0.0036
0.0074
0.0110
1.4830
0.3078
1.4780
1.7860
1.2080
1975180
0.0083
0.0077
0.0160
2.0830
11
11
1975180
0.0091
0.0079
0.0170
2.1540
0.2186
0.6982
0.9169
1.3130
1980185
0.0035
0.0055
0.0089
1.6330
11
11
1980185
0.0036
0.0060
0.0096
1.6040
0.1699
0.4869
0.6568
1.3490
1985190
0.0030
0.0073
0.0103
1.4040
11
11
1985190
0.0047
0.0088
0.0136
1.5330
0.7328
0.7799
1.5130
1.9400
1990195
10.000
70.0095
0.0088
0.9267
11
11
1990195
10.000
40.0096
0.0092
0.9611
0.2407
0.2628
0.5035
1.9160
1995100
0.0016
0.0018
0.0035
1.8900
11
11
1995100
0.0018
0.0021
0.0039
1.8310
0.3575
0.3304
0.6879
2.0820
2000105
0.0008
0.0026
0.0034
1.3240
11
11
2000105
0.0004
0.0025
0.0029
1.1610
0.3210
0.3621
0.6831
1.8860
2005110
0.0005
0.0019
0.0024
1.2770
11
11
2005110
0.0005
0.0019
0.0024
1.2560
0.1704
0.4933
0.6638
1.3450
193512010
0.0013
0.0048
0.0061
1.2760
11
11
193512010
0.0015
0.0053
0.0068
1.2830
0.2377
0.4944
0.7322
1.4810
FF
FF
TABLE!5f:!Equ
al1W
eighted!NYSE!Market!Po
rtfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!Po
rtfolios!Bu
ilt!Using!Value
1Weighted!Securities
COMPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
67
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0010
0.0004
0.0014
3.3720
11
11
193516/68
0.0012
0.0003
0.0015
4.4730
0.0022
0.0003
0.0026
7.5410
1935145
0.0014
0.0009
0.0023
2.4920
11
11
1935145
0.0017
0.0007
0.0025
3.3810
0.0037
0.0006
0.0043
6.8840
1946155
0.0006
0.0001
0.0007
5.4590
11
11
1946155
0.0006
0.0001
0.0008
6.6900
0.0016
0.0001
0.0017
12.3400
195616/68
0.0009
0.0002
0.0011
6.2840
11
11
195616/68
0.0011
0.0002
0.0012
7.5590
0.0015
0.0003
0.0018
6.9390
1935140
0.0018
0.0015
0.0033
2.2430
11
11
1935140
0.0023
0.0011
0.0034
3.1030
0.0056
0.0008
0.0064
7.6090
1941145
0.0009
0.0003
0.0012
3.9670
11
11
1941145
0.0011
0.0003
0.0014
4.7990
0.0015
0.0004
0.0018
5.0490
1946150
0.0009
0.0001
0.0010
8.2990
11
11
1946150
0.0008
0.0001
0.0009
8.9280
0.0021
0.0001
0.0022
15.5300
1951155
0.0002
0.0001
0.0004
2.8020
11
11
1951155
0.0004
0.0001
0.0006
4.6060
0.0011
0.0001
0.0013
9.1860
1956160
0.0002
0.0001
0.0004
2.4770
11
11
1956160
0.0004
0.0002
0.0006
3.7670
0.0011
0.0002
0.0013
7.2190
196116/68
0.0013
0.0002
0.0015
7.6980
11
11
196116/68
0.0014
0.0002
0.0015
9.2900
0.0017
0.0003
0.0021
6.6520
7/196812010
0.0013
0.0003
0.0016
5.9720
11
11
7/196812010
0.0016
0.0002
0.0018
7.5020
0.0030
0.0006
0.0036
5.8420
1970180
0.0019
0.0003
0.0022
7.3280
11
11
1970180
0.0020
0.0003
0.0023
8.5300
0.0037
0.0010
0.0047
4.5590
1980190
0.0016
0.0003
0.0019
6.3970
11
11
1980190
0.0018
0.0003
0.0020
7.4470
0.0039
0.0008
0.0047
5.7230
1990100
0.0011
0.0004
0.0015
4.2240
11
11
1990100
0.0017
0.0003
0.0020
7.0360
0.0026
0.0004
0.0031
6.8950
2000110
0.0007
0.0002
0.0009
4.7320
11
11
2000110
0.0011
0.0002
0.0013
6.0550
0.0029
0.0004
0.0032
9.2140
1970175
0.0021
0.0003
0.0024
7.8660
11
11
1970175
0.0023
0.0003
0.0026
9.7050
0.0037
0.0010
0.0047
4.7410
1975180
0.0018
0.0003
0.0022
6.4350
11
11
1975180
0.0018
0.0003
0.0021
6.9130
0.0043
0.0012
0.0055
4.5180
1980185
0.0015
0.0002
0.0018
7.3640
11
11
1980185
0.0016
0.0002
0.0018
7.7830
0.0034
0.0009
0.0043
4.8200
1985190
0.0016
0.0003
0.0019
5.9930
11
11
1985190
0.0019
0.0003
0.0022
7.4640
0.0041
0.0007
0.0048
6.9150
1990195
0.0010
0.0004
0.0015
3.4800
11
11
1990195
0.0015
0.0003
0.0018
5.4960
0.0019
0.0005
0.0024
4.5450
1995100
0.0012
0.0003
0.0015
5.9000
11
11
1995100
0.0019
0.0002
0.0021
9.9920
0.0031
0.0003
0.0034
11.2200
2000105
0.0007
0.0002
0.0009
4.4120
11
11
2000105
0.0013
0.0002
0.0015
7.0050
0.0024
0.0003
0.0028
7.9820
2005110
0.0006
0.0002
0.0008
4.9680
11
11
2005110
0.0008
0.0002
0.0010
4.9120
0.0029
0.0003
0.0033
10.1600
193512010
0.0012
0.0003
0.0015
4.5390
11
11
193512010
0.0014
0.0003
0.0017
5.9260
0.0027
0.0005
0.0032
6.3490
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0020
0.0023
0.0043
1.8490
0.0074
0.0074
0.0147
1.9990
193516/68
0.0016
0.0026
0.0041
1.6110
0.0053
0.0070
0.0123
1.7630
1935145
0.0025
0.0042
0.0067
1.5990
0.0083
0.0111
0.0194
1.7510
1935145
0.0009
0.0045
0.0054
1.2060
0.0036
0.0105
0.0141
1.3420
1946155
0.0014
0.0011
0.0025
2.3540
0.0078
0.0031
0.0109
3.5030
1946155
0.0006
0.0014
0.0020
1.4690
0.0052
0.0033
0.0085
2.5520
195616/68
0.0019
0.0017
0.0037
2.1260
0.0062
0.0075
0.0137
1.8210
195616/68
0.0029
0.0019
0.0048
2.5370
0.0071
0.0068
0.0140
2.0420
1935140
0.0035
0.0063
0.0098
1.5640
0.0132
0.0165
0.0297
1.7980
1935140
0.0013
0.0065
0.0078
1.1920
0.0060
0.0156
0.0216
1.3870
1941145
0.0014
0.0017
0.0031
1.8120
0.0027
0.0046
0.0073
1.5870
1941145
0.0006
0.0020
0.0026
1.2900
0.0008
0.0045
0.0053
1.1730
1946150
0.0018
0.0010
0.0028
2.8760
0.0079
0.0023
0.0102
4.4770
1946150
0.0012
0.0014
0.0026
1.8330
0.0058
0.0028
0.0086
3.0830
1951155
0.0011
0.0012
0.0023
1.9480
0.0078
0.0040
0.0118
2.9610
1951155
0.0001
0.0013
0.0015
1.0900
0.0046
0.0039
0.0085
2.1990
1956160
0.0007
0.0009
0.0017
1.8180
0.0046
0.0052
0.0097
1.8850
1956160
0.0006
0.0010
0.0016
1.6150
0.0044
0.0046
0.0090
1.9480
196116/68
0.0028
0.0023
0.0050
2.2140
0.0074
0.0091
0.0165
1.8120
196116/68
0.0043
0.0025
0.0068
2.7320
0.0090
0.0083
0.0173
2.0760
7/196812010
0.0036
0.0017
0.0053
3.1210
0.0151
0.0073
0.0223
3.0670
7/196812010
0.0056
0.0019
0.0075
3.8740
0.0171
0.0067
0.0238
3.5450
1970180
0.0085
0.0033
0.0118
3.5810
0.0272
0.0108
0.0379
3.5250
1970180
0.0131
0.0037
0.0168
4.4960
0.0329
0.0097
0.0426
4.3860
1980190
0.0066
0.0020
0.0086
4.2670
0.0237
0.0084
0.0321
3.8030
1980190
0.0114
0.0022
0.0136
6.2140
0.0335
0.0077
0.0412
5.3410
1990100
0.0015
0.0015
0.0030
2.0340
0.0124
0.0095
0.0219
2.3010
1990100
0.0029
0.0016
0.0045
2.7770
0.0091
0.0086
0.0178
2.0540
2000110
0.0009
0.0004
0.0013
2.9910
0.0094
0.0031
0.0124
4.0240
2000110
0.0007
0.0005
0.0012
2.4970
0.0092
0.0026
0.0118
4.5310
1970175
0.0064
0.0032
0.0096
3.0300
0.0203
0.0103
0.0306
2.9820
1970175
0.0089
0.0039
0.0129
3.2760
0.0192
0.0098
0.0290
2.9680
1975180
0.0111
0.0035
0.0146
4.1240
0.0346
0.0119
0.0465
3.9110
1975180
0.0180
0.0038
0.0218
5.7390
0.0459
0.0104
0.0563
5.3960
1980185
0.0089
0.0022
0.0112
4.9820
0.0285
0.0079
0.0364
4.5990
1980185
0.0129
0.0023
0.0152
6.6310
0.0357
0.0069
0.0427
6.1430
1985190
0.0037
0.0015
0.0052
3.3880
0.0163
0.0079
0.0242
3.0540
1985190
0.0087
0.0018
0.0106
5.7500
0.0271
0.0076
0.0347
4.5860
1990195
0.0016
0.0020
0.0036
1.8190
0.0124
0.0123
0.0247
2.0080
1990195
0.0041
0.0022
0.0063
2.8480
0.0079
0.0118
0.0197
1.6720
1995100
0.0014
0.0008
0.0022
2.6340
0.0106
0.0056
0.0162
2.9110
1995100
0.0015
0.0008
0.0023
2.7870
0.0096
0.0044
0.0140
3.1530
2000105
0.0009
0.0005
0.0014
2.6990
0.0098
0.0044
0.0142
3.2310
2000105
0.0006
0.0005
0.0011
2.1110
0.0090
0.0036
0.0126
3.5100
2005110
0.0008
0.0003
0.0011
3.5200
0.0076
0.0014
0.0091
6.3380
2005110
0.0009
0.0004
0.0012
3.2850
0.0082
0.0013
0.0095
7.1740
193512010
0.0029
0.0020
0.0048
2.4570
0.0117
0.0073
0.0190
2.5920
193512010
0.0038
0.0022
0.0060
2.7160
0.0119
0.0068
0.0187
2.7400
TABLE!5g:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
68
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.2136
0.0452
0.2589
5.7220
1935145
11
11
11
11
1935145
11
11
0.1589
0.0479
0.2068
4.3160
1946155
11
11
11
11
1946155
11
11
0.1225
0.0308
0.1533
4.9760
195616/68
11
11
11
11
195616/68
11
11
0.3221
0.0545
0.3766
6.9150
1935140
11
11
11
11
1935140
11
11
0.1916
0.0418
0.2334
5.5830
1941145
11
11
11
11
1941145
11
11
0.1193
0.0551
0.1745
3.1640
1946150
11
11
11
11
1946150
11
11
0.0829
0.0218
0.1047
4.8040
1951155
11
11
11
11
1951155
11
11
0.1612
0.0398
0.2010
5.0500
1956160
11
11
11
11
1956160
11
11
0.1771
0.0418
0.2190
5.2370
196116/68
11
11
11
11
196116/68
11
11
0.4156
0.0629
0.4785
7.6080
7/196812010
11
11
11
11
7/196812010
11
11
0.3451
0.0984
0.4434
4.5070
1970180
11
11
11
11
1970180
11
11
0.5767
0.1710
0.7477
4.3730
1980190
11
11
11
11
1980190
11
11
0.2798
0.1124
0.3923
3.4890
1990100
11
11
11
11
1990100
11
11
0.3408
0.0456
0.3864
8.4820
2000110
11
11
11
11
2000110
11
11
0.2506
0.0707
0.3213
4.5460
1970175
11
11
11
11
1970175
11
11
0.7823
0.2048
0.9871
4.8200
1975180
11
11
11
11
1975180
11
11
0.3403
0.1547
0.4949
3.2000
1980185
11
11
11
11
1980185
11
11
0.2610
0.1238
0.3849
3.1080
1985190
11
11
11
11
1985190
11
11
0.2637
0.0982
0.3619
3.6840
1990195
11
11
11
11
1990195
11
11
0.3335
0.0531
0.3866
7.2760
1995100
11
11
11
11
1995100
11
11
0.3013
0.0326
0.3339
10.2400
2000105
11
11
11
11
2000105
11
11
0.2991
0.0524
0.3515
6.7050
2005110
11
11
11
11
2005110
11
11
0.1988
0.0836
0.2824
3.3770
193512010
11
11
11
11
193512010
11
11
0.2871
0.0750
0.3621
4.8280
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0012
0.0012
0.0025
2.0020
11
11
193516/68
0.0004
0.0013
0.0018
1.3330
0.2236
0.0569
0.2805
4.9280
1935145
0.0015
0.0014
0.0029
2.0330
11
11
1935145
0.0001
0.0016
0.0017
1.0700
0.1630
0.0591
0.2221
3.7600
1946155
0.0009
0.0005
0.0014
2.8160
11
11
1946155
0.0003
0.0006
0.0009
1.5700
0.0999
0.0418
0.1418
3.3890
195616/68
0.0013
0.0017
0.0030
1.7760
11
11
195616/68
0.0008
0.0017
0.0025
1.4930
0.3621
0.0671
0.4292
6.3950
1935140
0.0019
0.0021
0.0040
1.8790
11
11
1935140
10.000
10.0023
0.0022
0.9551
0.2226
0.0532
0.2758
5.1890
1941145
0.0010
0.0006
0.0016
2.7870
11
11
1941145
0.0004
0.0007
0.0010
1.5710
0.0890
0.0661
0.1550
2.3460
1946150
0.0006
0.0003
0.0009
3.4030
11
11
1946150
0.0003
0.0004
0.0007
1.7700
0.0799
0.0368
0.1167
3.1680
1951155
0.0011
0.0007
0.0019
2.6030
11
11
1951155
0.0004
0.0008
0.0011
1.4770
0.1191
0.0468
0.1659
3.5430
1956160
0.0010
0.0014
0.0023
1.7010
11
11
1956160
0.0005
0.0013
0.0017
1.3560
0.1632
0.0457
0.2089
4.5680
196116/68
0.0015
0.0019
0.0034
1.8140
11
11
196116/68
0.0011
0.0019
0.0030
1.5660
0.4912
0.0814
0.5726
7.0360
7/196812010
0.0030
0.0017
0.0047
2.7650
11
11
7/196812010
0.0028
0.0019
0.0047
2.5100
0.3908
0.1194
0.5103
4.2720
1970180
0.0037
0.0018
0.0055
3.0320
11
11
1970180
0.0052
0.0021
0.0073
3.4340
0.6792
0.2227
0.9020
4.0490
1980190
0.0026
0.0019
0.0045
2.3990
11
11
1980190
0.0057
0.0021
0.0078
3.6450
0.4235
0.1326
0.5561
4.1950
1990100
0.0047
0.0029
0.0076
2.6470
11
11
1990100
0.0019
0.0030
0.0049
1.6230
0.3775
0.0577
0.4352
7.5470
2000110
0.0028
0.0010
0.0038
3.8950
11
11
2000110
0.0018
0.0008
0.0026
3.1090
0.2194
0.0659
0.2853
4.3270
1970175
0.0034
0.0017
0.0051
3.0040
11
11
1970175
0.0024
0.0021
0.0045
2.1140
0.7969
0.2736
1.0710
3.9120
1975180
0.0046
0.0021
0.0067
3.1650
11
11
1975180
0.0082
0.0024
0.0106
4.4070
0.5622
0.1977
0.7599
3.8430
1980185
0.0033
0.0015
0.0047
3.2280
11
11
1980185
0.0056
0.0016
0.0071
4.4790
0.3561
0.1387
0.4949
3.5670
1985190
0.0016
0.0021
0.0036
1.7610
11
11
1985190
0.0049
0.0024
0.0073
3.0130
0.4381
0.1219
0.5599
4.5950
1990195
0.0050
0.0037
0.0087
2.3510
11
11
1990195
0.0018
0.0041
0.0059
1.4250
0.4274
0.0715
0.4989
6.9810
1995100
0.0037
0.0017
0.0054
3.2400
11
11
1995100
0.0017
0.0015
0.0032
2.1840
0.2753
0.0374
0.3126
8.3680
2000105
0.0045
0.0015
0.0060
3.9340
11
11
2000105
0.0026
0.0013
0.0039
3.0090
0.2577
0.0506
0.3083
6.0880
2005110
0.0007
0.0003
0.0010
3.5230
11
11
2005110
0.0007
0.0003
0.0009
3.5950
0.1860
0.0767
0.2627
3.4240
193512010
0.0022
0.0015
0.0037
2.4850
11
11
193512010
0.0018
0.0016
0.0034
2.0870
0.3171
0.0919
0.4090
4.4500
FF
FF
TABLE!5g:!V
alue
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Equ
al1W
eighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
69
!!
!!
!!
!
Period
Period
!!
!!
!!
!!
!Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
0.0013
0.0011
0.0024
2.0960
0.0015
0.0007
0.0022
3.3370
193516/68
0.0013
0.0012
0.0025
2.0860
0.0015
0.0013
0.0027
2.1480
1935145
0.0023
0.0022
0.0044
2.0640
0.0023
0.0010
0.0032
3.3990
1935145
0.0023
0.0022
0.0045
2.0740
0.0024
0.0021
0.0044
2.1320
1946155
0.0007
0.0007
0.0014
2.1080
0.0012
0.0004
0.0016
3.9960
1946155
0.0008
0.0007
0.0015
2.2200
0.0013
0.0007
0.0020
2.8180
195616/68
0.0008
0.0006
0.0014
2.2260
0.0012
0.0006
0.0018
2.9320
195616/68
0.0008
0.0007
0.0015
2.0590
0.0008
0.0010
0.0018
1.8040
1935140
0.0038
0.0029
0.0067
2.2870
0.0030
0.0013
0.0043
3.2400
1935140
0.0039
0.0029
0.0069
2.3390
0.0039
0.0027
0.0066
2.4310
1941145
0.0006
0.0012
0.0018
1.4860
0.0015
0.0005
0.0020
3.9070
1941145
0.0005
0.0013
0.0018
1.4140
0.0006
0.0013
0.0019
1.4480
1946150
0.0012
0.0006
0.0018
2.9110
0.0015
0.0003
0.0018
6.0530
1946150
0.0011
0.0006
0.0017
2.8800
0.0019
0.0007
0.0026
3.7880
1951155
0.0002
0.0007
0.0009
1.3240
0.0008
0.0005
0.0013
2.7140
1951155
0.0005
0.0008
0.0013
1.6540
0.0008
0.0008
0.0015
1.9900
1956160
0.0002
0.0006
0.0007
1.2670
0.0004
0.0006
0.0010
1.6510
1956160
0.0001
0.0007
0.0009
1.1900
0.0005
0.0008
0.0012
1.5810
196116/68
0.0012
0.0007
0.0019
2.7410
0.0017
0.0006
0.0023
3.7000
196116/68
0.0012
0.0007
0.0020
2.6240
0.0010
0.0011
0.0022
1.9170
7/196812010
0.0007
0.0010
0.0017
1.7190
0.0019
0.0009
0.0028
3.2490
7/196812010
0.0010
0.0011
0.0020
1.9130
0.0012
0.0019
0.0031
1.6290
1970180
0.0015
0.0011
0.0026
2.2940
0.0028
0.0008
0.0036
4.4480
1970180
0.0018
0.0011
0.0029
2.6550
0.0011
0.0027
0.0037
1.4070
1980190
0.0007
0.0013
0.0020
1.4920
0.0020
0.0012
0.0032
2.6410
1980190
0.0007
0.0014
0.0022
1.5180
0.0014
0.0027
0.0041
1.5110
1990100
0.0002
0.0011
0.0013
1.2170
0.0014
0.0011
0.0026
2.3040
1990100
0.0007
0.0012
0.0018
1.5550
0.0011
0.0014
0.0025
1.8240
2000110
0.0003
0.0006
0.0009
1.4080
0.0015
0.0006
0.0021
3.5390
2000110
0.0005
0.0008
0.0013
1.6690
0.0013
0.0011
0.0025
2.1710
1970175
0.0020
0.0012
0.0032
2.6950
0.0031
0.0008
0.0039
4.8430
1970175
0.0024
0.0012
0.0036
2.9490
0.0013
0.0028
0.0041
1.4600
1975180
0.0008
0.0011
0.0020
1.7440
0.0025
0.0009
0.0034
3.9000
1975180
0.0013
0.0011
0.0024
2.1950
0.0003
0.0027
0.0030
1.0990
1980185
0.0010
0.0010
0.0020
1.9360
0.0021
0.0009
0.0029
3.3980
1980185
0.0011
0.0010
0.0021
2.0790
0.0019
0.0024
0.0043
1.7920
1985190
0.0003
0.0015
0.0018
1.2280
0.0017
0.0014
0.0031
2.2090
1985190
0.0003
0.0017
0.0020
1.2010
0.0009
0.0028
0.0037
1.3270
1990195
0.0001
0.0012
0.0013
1.0780
0.0011
0.0011
0.0023
2.0280
1990195
0.0003
0.0013
0.0016
1.2440
0.0008
0.0014
0.0022
1.5340
1995100
0.0005
0.0009
0.0014
1.5010
0.0017
0.0010
0.0027
2.6800
1995100
0.0011
0.0010
0.0021
2.0840
0.0014
0.0012
0.0026
2.1500
2000105
0.0001
0.0007
0.0007
1.0960
0.0010
0.0008
0.0018
2.3110
2000105
0.0004
0.0008
0.0013
1.5520
0.0006
0.0012
0.0018
1.5440
2005110
0.0004
0.0005
0.0009
1.7820
0.0019
0.0004
0.0023
6.1240
2005110
0.0005
0.0007
0.0012
1.7080
0.0019
0.0010
0.0029
3.0080
193512010
0.0009
0.0011
0.0020
1.8970
0.0018
0.0008
0.0025
3.2800
193512010
0.0011
0.0011
0.0022
1.9920
0.0013
0.0016
0.0029
1.8070
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
10.000
20.0064
0.0061
0.9654
0.0033
0.0191
0.0225
1.1730
193516/68
10.000
70.0072
0.0065
0.8991
0.0022
0.0197
0.0219
1.1110
1935145
10.002
30.0101
0.0078
0.7749
10.001
60.0238
0.0223
0.9344
1935145
10.003
70.0110
0.0073
0.6640
10.002
80.0242
0.0214
0.8828
1946155
0.0002
0.0043
0.0046
1.0550
0.0047
0.0124
0.0171
1.3780
1946155
0.0005
0.0052
0.0058
1.1020
0.0049
0.0129
0.0178
1.3800
195616/68
0.0013
0.0047
0.0060
1.2680
0.0067
0.0205
0.0272
1.3260
195616/68
0.0009
0.0055
0.0064
1.1580
0.0046
0.0211
0.0257
1.2160
1935140
10.002
10.0133
0.0111
0.8408
0.0015
0.0297
0.0312
1.0500
1935140
10.004
70.0142
0.0095
0.6708
10.000
60.0299
0.0293
0.9793
1941145
10.002
40.0064
0.0040
0.6325
10.004
90.0169
0.0120
0.7101
1941145
10.002
40.0071
0.0047
0.6621
10.005
20.0176
0.0124
0.7044
1946150
0.0007
0.0037
0.0044
1.1970
0.0046
0.0083
0.0129
1.5570
1946150
0.0007
0.0044
0.0051
1.1570
0.0049
0.0087
0.0136
1.5610
1951155
10.000
20.0050
0.0048
0.9647
0.0050
0.0164
0.0214
1.3030
1951155
0.0003
0.0061
0.0063
1.0420
0.0052
0.0171
0.0223
1.3020
1956160
0.0003
0.0027
0.0030
1.0950
0.0081
0.0155
0.0236
1.5250
1956160
10.000
20.0031
0.0029
0.9467
0.0066
0.0154
0.0220
1.4250
196116/68
0.0020
0.0060
0.0080
1.3280
0.0060
0.0238
0.0298
1.2530
196116/68
0.0016
0.0071
0.0087
1.2230
0.0035
0.0249
0.0284
1.1400
7/196812010
0.0003
0.0063
0.0066
1.0410
0.0037
0.0263
0.0300
1.1390
7/196812010
0.0009
0.0069
0.0078
1.1240
0.0044
0.0265
0.0309
1.1660
1970180
0.0009
0.0117
0.0125
1.0760
0.0062
0.0368
0.0430
1.1700
1970180
0.0032
0.0126
0.0159
1.2560
0.0060
0.0368
0.0427
1.1620
1980190
0.0004
0.0079
0.0083
1.0560
0.0054
0.0329
0.0384
1.1660
1980190
0.0006
0.0089
0.0095
1.0660
0.0050
0.0339
0.0389
1.1480
1990100
10.000
40.0047
0.0042
0.9060
10.001
30.0315
0.0302
0.9575
1990100
10.000
30.0053
0.0050
0.9405
0.0008
0.0315
0.0323
1.0260
2000110
10.000
30.0015
0.0012
0.8033
0.0007
0.0106
0.0113
1.0700
2000110
10.000
40.0016
0.0012
0.7437
0.0041
0.0099
0.0140
1.4180
1970175
0.0002
0.0119
0.0121
1.0200
0.0008
0.0360
0.0368
1.0230
1970175
0.0002
0.0133
0.0135
1.0140
0.0009
0.0378
0.0387
1.0230
1975180
0.0039
0.0113
0.0152
1.3450
0.0157
0.0377
0.0534
1.4170
1975180
0.0078
0.0118
0.0196
1.6640
0.0162
0.0361
0.0523
1.4470
1980185
0.0012
0.0086
0.0098
1.1440
0.0097
0.0326
0.0423
1.2990
1980185
0.0020
0.0094
0.0115
1.2170
0.0086
0.0327
0.0413
1.2620
1985190
0.0001
0.0063
0.0064
1.0210
0.0018
0.0295
0.0313
1.0620
1985190
10.000
30.0074
0.0071
0.9591
0.0016
0.0311
0.0327
1.0520
1990195
10.000
30.0055
0.0052
0.9462
0.0001
0.0348
0.0350
1.0040
1990195
10.000
70.0062
0.0054
0.8848
10.000
40.0350
0.0346
0.9891
1995100
10.000
60.0033
0.0027
0.8092
10.003
90.0243
0.0204
0.8402
1995100
0.0004
0.0039
0.0043
1.1020
0.0015
0.0239
0.0254
1.0610
2000105
10.000
60.0018
0.0012
0.6792
10.002
50.0159
0.0134
0.8418
2000105
10.000
60.0018
0.0013
0.6962
0.0033
0.0146
0.0179
1.2300
2005110
0.0000
0.0010
0.0010
1.0370
0.0041
0.0038
0.0079
2.0880
2005110
10.000
20.0013
0.0010
0.8169
0.0045
0.0039
0.0084
2.1480
193512010
0.0000
0.0063
0.0064
1.0070
0.0035
0.0232
0.0267
1.1510
193512010
0.0002
0.0071
0.0072
1.0220
0.0034
0.0235
0.0269
1.1450
TABLE!5h
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Value
1Weighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E
FF
FF
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
s2(�
0)
s2(�
0)
s2(�
0)
s2(�
1)
s2(�
1)
s2(�
1)
�j,
t
70
Period
! Pane
l!A!
!!
!!
!!
!Pane
l!C!
!!
!!
!!
!193516/68
11
11
11
11
193516/68
11
11
0.1186
0.1789
0.2975
1.6630
1935145
11
11
11
11
1935145
11
11
0.0070
0.1644
0.1714
1.0430
1946155
11
11
11
11
1946155
11
11
0.1395
0.1474
0.2869
1.9460
195616/68
11
11
11
11
195616/68
11
11
0.1993
0.2167
0.4160
1.9200
1935140
11
11
11
11
1935140
11
11
0.0402
0.1325
0.1727
1.3030
1941145
11
11
11
11
1941145
11
11
10.035
60.2020
0.1665
0.8240
1946150
11
11
11
11
1946150
11
11
0.1659
0.0989
0.2647
2.6770
1951155
11
11
11
11
1951155
11
11
0.1120
0.1959
0.3079
1.5720
1956160
11
11
11
11
1956160
11
11
0.1510
0.2057
0.3567
1.7340
196116/68
11
11
11
11
196116/68
11
11
0.2322
0.2240
0.4562
2.0360
7/196812010
11
11
11
11
7/196812010
11
11
0.2623
0.3056
0.5679
1.8580
1970180
11
11
11
11
1970180
11
11
0.5721
0.5118
1.0840
2.1180
1980190
11
11
11
11
1980190
11
11
0.1535
0.3608
0.5143
1.4250
1990100
11
11
11
11
1990100
11
11
0.2076
0.1313
0.3389
2.5820
2000110
11
11
11
11
2000110
11
11
0.1979
0.2223
0.4202
1.8900
1970175
11
11
11
11
1970175
11
11
0.3630
0.6495
1.0120
1.5590
1975180
11
11
11
11
1975180
11
11
0.6099
0.4492
1.0590
2.3580
1980185
11
11
11
11
1980185
11
11
0.2282
0.2959
0.5241
1.7710
1985190
11
11
11
11
1985190
11
11
0.0681
0.4100
0.4781
1.1660
1990195
11
11
11
11
1990195
11
11
0.1615
0.1360
0.2975
2.1880
1995100
11
11
11
11
1995100
11
11
0.2430
0.1128
0.3558
3.1550
2000105
11
11
11
11
2000105
11
11
0.2928
0.1765
0.4693
2.6600
2005110
11
11
11
11
2005110
11
11
0.0876
0.2515
0.3391
1.3480
193512010
11
11
11
11
193512010
11
11
0.1986
0.2498
0.4485
1.7950
!!
!!
!!
!!
!!
!!
!!
!!
!!
Pane
l!B!
!!
!!
!!
!Pane
l!D!
!!
!!
!!
!193516/68
0.0005
0.0033
0.0038
1.1460
11
11
193516/68
0.0003
0.0036
0.0039
1.0810
0.1202
0.2056
0.3258
1.5850
1935145
10.000
40.0029
0.0025
0.8692
11
11
1935145
10.000
40.0032
0.0028
0.8751
0.0143
0.1898
0.2042
1.0750
1946155
0.0006
0.0019
0.0026
1.3230
11
11
1946155
0.0007
0.0022
0.0029
1.2910
0.1409
0.1814
0.3223
1.7770
195616/68
0.0012
0.0047
0.0059
1.2440
11
11
195616/68
0.0007
0.0052
0.0058
1.1270
0.1963
0.2387
0.4350
1.8220
1935140
10.000
40.0035
0.0030
0.8746
11
11
1935140
10.000
50.0039
0.0034
0.8703
0.0472
0.1629
0.2101
1.2900
1941145
10.000
30.0021
0.0019
0.8774
11
11
1941145
10.000
20.0023
0.0021
0.9006
10.029
30.2217
0.1924
0.8679
1946150
0.0003
0.0010
0.0012
1.2660
11
11
1946150
0.0003
0.0012
0.0015
1.2330
0.1661
0.1364
0.3024
2.2180
1951155
0.0010
0.0029
0.0039
1.3530
11
11
1951155
0.0011
0.0033
0.0043
1.3230
0.1101
0.2265
0.3366
1.4860
1956160
0.0021
0.0043
0.0064
1.5010
11
11
1956160
0.0016
0.0044
0.0059
1.3580
0.1269
0.2112
0.3381
1.6010
196116/68
0.0006
0.0050
0.0056
1.1110
11
11
196116/68
0.0001
0.0057
0.0058
1.0200
0.2436
0.2571
0.5007
1.9480
7/196812010
0.0003
0.0062
0.0065
1.0520
11
11
7/196812010
0.0005
0.0065
0.0070
1.0710
0.2723
0.3360
0.6083
1.8100
1970180
0.0008
0.0061
0.0069
1.1230
11
11
1970180
0.0013
0.0067
0.0080
1.2010
0.6343
0.5713
1.2060
2.1100
1980190
0.0005
0.0075
0.0081
1.0720
11
11
1980190
0.0002
0.0084
0.0086
1.0260
0.1806
0.4002
0.5808
1.4510
1990100
10.000
50.0101
0.0096
0.9513
11
11
1990100
10.000
90.0104
0.0096
0.9174
0.2195
0.1499
0.3694
2.4640
2000110
10.000
60.0037
0.0030
0.8289
11
11
2000110
0.0001
0.0033
0.0034
1.0420
0.1637
0.2331
0.3968
1.7020
1970175
0.0002
0.0057
0.0059
1.0390
11
11
1970175
0.0002
0.0064
0.0066
1.0290
0.3394
0.7240
1.0630
1.4690
1975180
0.0025
0.0067
0.0091
1.3730
11
11
1975180
0.0034
0.0070
0.0104
1.4850
0.6997
0.4801
1.1800
2.4570
1980185
0.0019
0.0066
0.0085
1.2830
11
11
1980185
0.0014
0.0072
0.0086
1.1950
0.2857
0.3240
0.6098
1.8820
1985190
10.000
60.0075
0.0070
0.9249
11
11
1985190
10.000
70.0085
0.0078
0.9174
0.0731
0.4534
0.5265
1.1610
1990195
0.0002
0.0107
0.0109
1.0190
11
11
1990195
10.000
80.0112
0.0104
0.9303
0.1557
0.1485
0.3041
2.0480
1995100
10.001
50.0082
0.0067
0.8151
11
11
1995100
10.001
00.0083
0.0072
0.8766
0.2788
0.1357
0.4145
3.0540
2000105
10.001
40.0061
0.0047
0.7737
11
11
2000105
0.0002
0.0053
0.0055
1.0350
0.3098
0.1799
0.4897
2.7220
2005110
0.0002
0.0007
0.0010
1.3090
11
11
2005110
0.0001
0.0008
0.0009
1.1120
0.0114
0.2689
0.2803
1.0420
193512010
0.0004
0.0049
0.0053
1.0790
11
11
193512010
0.0004
0.0053
0.0056
1.0730
0.2050
0.2786
0.4836
1.7360
FF
FF
TABLE!5h
:!Value
1Weighted!NYSE!Market!P
ortfolio!!!!!!!!!+!!!!!!!5x5!Dou
ble1Sort!Test!P
ortfolios!Bu
ilt!Using!Value
1Weighted!Securitie
sCO
MPO
NEN
TS!OF!TH
E!VARIANCE
S!OF!TH
E!!!!!!!!!!!!!(con
t.)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
s2(�
2)
s2(�
2)
s2(�
2)
s2(�
3)
s2(�
3)
s2(�
3)
�j,
t
71