strong-form efficiency on the toronto stock exchange: an examination of analyst price forecasts

f^,^.^. , ,1.... r..ui\.in,i may ur; i l

Coovriphi law Hitle 1? M S Cod?'

Strong-form efficiency on the TorontoStock Exchange: An examination of

analyst price forecasts*

LAWRENCE D. BROWN Sra!e University of New York at Buffalo

GORDON D. RICHARDSON University of Waterloo

CHARLES A. TRZCINKA State University of New York at Buffalo

Absiracr. Strong-form efficiency on the Toronto Stock Exchange is examined by focusingon the stock price forecasts of brokerage-firm analysts who follow TSE firms. Twoprincipal analyses are undertaken. First, there is considerable evidence in both the U.S.and U.K. that analysts possess valuable private information at the firm-specific level. Thispaper provides evidence that this finding is generalizable to Canadian analysts. Second.VS. and U.K. studies generally have been based on a single-factor tnodel (e.g.. theCAPM). The choice of benchmarks (CAPM versus APT) has been shown to be importantin a variety of contexts. We provide evidence that the choice of benchmark does not alterthe fundamental conclusion that Canadian analysts possess valuable private informationat the finn-specific level. Our findings have implications for accounting researchers,namely, the appropriateness of researchers to use CAPM in lieu cf the computationally,more burdensome APT and the appropriateness of researchers to use Canadian analystforecasts uhen a proxy is required for the (unobservable) market expectation.

Resumi. Les auteurs examinen! I'efficiejice « fone » de la Bourse de Toronto, ens interessant aux previsions relatives au prix des actions formulees par les analystesdes socieses de courtage qui suivent les entreprises de la Bourse de Toronto. Deux analy-ses principales les menent aux conclusions suivantes. PretniJrement. les faits demontrentpresque indubitablement que sur le marche des Etats-Unis aussi bien que sur celui duRoyaume-Uni, les analystes possedem de i'information a caractere prive' citiie, specifiquei l'entreprise. Les resultats de I'etude demontrent que cette constatation peut etreJifneralisec aux analystes canadiens. Deuxiemement, les etudes des Elats-Unis et duRoyaume-Uni sont generalement fondees sur un modele a un seu! facteur (le modeleJ'equilibre des marches financiers, par exemple). 11 a ete etabli que le choix des criteres'le modele d'equilibre des marches financiers ou !a theorie de l'etablissement des prix pararbitrage) est important dans des circonstances tres diverses. Les auteurs demontrent quele choix des criteres n'a aucune incidence sur la conclusion fondamentale selon laquel-le les analystes canadiens possedem de l'information a caractere prive utile. specifiquea l'entreprise. Les resultats de leur etude entrainem certaines consequences pour ies

Funding for Ihis research was provided by the Canadian Studies Faculty Research GrantProgram, ihe Social Sciences and Humanities Research Council of Canada, the Deloitte &Touche/Canadian .Academic Accounting Association Research Fund, and the AccountingResearch and Education Cemre of McMaster University. We appnxiare Che ficlpful assistanceof the Financiai Post Informanon Services for d a a provision and Calvin Lai. Kwon-JungKira. ard David Lesmond for programming assistance. We also appreciate tht comments of P.Grier and S.P. Kothari.

Coniemporary Accounting Reseajth Vol. 7 No. 2 pp. 323-346

324 L.D. Brown G.D. Richardson C.A. Trzcinka

chercheurs du domaine de la compiabiliie : ils ont avamage a uiiiiser le modeie d'equi!ibredes marches financiers de preference a la theorie de I'etablissement des pri.i par ajy.trage. qui exige davantage de calcuis, e[ a recourir aux previsions des analysics canadicntlorsqu'il ietir foul un substilut aux anticipations du marche (qui ne peuvent etre obscr\eei).

IntroductionWe examine strong-form information efficiency on ihe Toronto Stock Exchange(TSE) by focusing on the ssock price forecasts of brokerage-firm analysts whofollow TSE firms. In its null form, strong-form efficiency predicts zero corre-lation between analyst price forecasts and subsequent realizations of abnormalstock retums. Because any test of the efficient markets hypothesis is joint innature, it is possible that use of an incorrect asset-pricing model will lead to_the erroneous conclusion that analysts possess valuable infotmation when in"fact they do not. If the correct asset-pricing model is used, rejection of the nullhypothesis permits the researcher to unambiguously conclude that analysts haveregular access to valuable private, firm-specific infonnation that enables them 'to forecast idiosyncratic price movements. This suggests that the strong-form ofthe efficient markets (nul!) hypothesis can be rejected, and. consistent with the ;Grossman and Stiglitz (1980) model, that valuable information can be purchased.

Accounting researchers have long been interested in the relationship betweenanalyst forecasts and firm valuation. Most of this research has involved U.S. idata, and it generally has related analyst eamings forecasts (and revisions there- ;of) to abnormal stock price movements. For example. Fried and Givoly (1982) ;and Brown, Gdffin, Hagerman, and Ztnijewski (19S7) used U.S. data to show ;thai eamings "surprise" conditional upon analysts* expectations is more closelyrelated to abnormal stock price movements than is eamings "surprise" condition-al upon forecasts of time-series models. Givoly and Lakonishok (1979), Elton, ;Gruber, and Gultekin (1981), Ajinkya and Gift (1984), and Brown, Foster, andNoreen (1985) used U.S. data to show that analyst eamings forecast revisionsare associated with abnormal share price movements.

A recent study by Suret and L'Her (1991), using Intemational Brokers Es-timate System (IBES) data, shows that Catiadian analyst forecast revisions areassociated with abnormal retums. They demonstrate profitable trading strategiesbased on such revisions, provided the investor has access to these revisions priorto publication. Our study, using Research Evaluation Service data (RES), showsthat Canadian analyst forecasted abnomial retums are associated with actualabnormal retums. We demonstrate profitable trading strategies based on suchforecasts, provided the investor has access to the forecasts prior to publication.Because the information sets underlyitig analyst eamings forecast revisions .indprice forecasts are likely to be highly overlapping, the results of the two stud-ies complement one another. Moreover, our study and that by Suret and L Her(1991) suggest that Canadian analyst forecasts are reasonable proxies for the(unobservable) market expectation of price and eamings.

As reviewed in ihe next section, there is considerable evidence in both the

Strong-Form Efficiency on the Toronto Stock Exchange 325

United States and the United Kingdom that analysts possess valuable privateinformation at the firm-specific level. Little evidence on strong-form efficiencyby analysts exists in Canada. Unlike analysts associated with other markets,analysts following TSE firms make their point forecasts of stock prices publiclyavailable. A study of Canadian analysts will allow us to test the conclusions ofprevious studies by using actual price forecasts. Our first hypothesis is that theconclusions of the U.S. and U.K. literature apply to Canadian analysts of theTSE.

The U.S. and U.K. studies have been based on a single-factor model (e.g.,the Capital Asset Pricing Model (CAPM)). The choice of benchmarks (CAP-M versus Arbitrage Pricing Theory (APT)) has been shown to be important inthe ranking of mutual funds (Lehman and Modest, 1987), suggesting that ex-cess returns eamed by following analyst recommendations may disappear if amultifactor asset-pricing model is used. No study has used the APT to evaluateanalysts' forecasts. The use of an APT model is especially important with Cana-dian data because Hughes (1984) has shown that at least three to four systematicrisk factors are priced in Canadian capital markets. Our second hypothesis is thatthe choice of benchmark (CAPM or APT) affects the conclusion that analystspossess useful information.

We show that the gains to following Canadian analyst recommendations aresubstantial (i.e.. up to 3 percent after transactions costs), suggesting that theconclusions of the U.S. and U.K. literature do apply to Canadian analysts ofthe TSE. We show that strong-fonm efficiency in Canada is rejected with eitherthe CAPM or the APT model, suggesting that the choice of benchmark doesnot alter the fundamental conclusion that analysts possess valuable information.Although this conclusion is predicated on our having the "correct" asset-pricingmodel to estimate abnormal retums. the robustness of our results to both theCAPM and APT increases our confidence in this conclusion. Our results implythat researchers who seek to test the usefulness of Canadian analysts' recom-mendations can use the CAPM in lieu of the computationally, more burdensomeAPT model, with no loss of generality.

The paper proceeds as follows. The next section reviews the literature anddevelops hypotheses. The data are discussed in the third section. The fourthsection presents results using the CAPM. and the fifth section presents retumsusing two APT models. The final section presents a summary and conclusions.

Literature review and hypothesis development

Literature reviewBlack (1973), Holloway (1981), Copeland and Mayers (1982). Stickel (1985).and Huberman and Kandei (1987) have examined the forecasting ability of ValueLine's ranking system and have shown that Value Line rankings earn abnormalprofits. Other researchers have examined a broader group of analysts. Dimsonand Marsh (1984) studied more than 4,000 forecasts of excess retums made by 35


U.K. stockbrokers and "'internal" analysts of a large U.K. inve.stment institutionfor 1980-81. They asked each analyst for his forecast abnormal retum (FAR);namely, his prediction of retum in excess of the market.' They then estimateda regression equation with FAR as the independent variable and CAPM-basedactual abnormal return (AAR) as the dependent variable. Elton, Gruber. andGrossman (1986), acquiring data from 720 analysts at 33 brokerage finn.s for33 months from March 1981 to November 1983, examined the informationcontained in analysts' buy. hold, and sell recommendations made on a five-point scale. Both studies found that analysts exhibited a small, but significant,degree of forecasting ability.

Numerous researchers have rejected the CAPM as an adequate model of .se-curity pricing. Roll and Ross (1980), Brown and Weinstein (1983), and Lehmanand Modest (1987) demonstrated that more than one factor is necessary to mea-.sure systematic risk. Except for Huberman and Kandel (1987), the performancemeasures used in this literature are almost exclusively based on the C.-XPNI.Several studies using U.S. data have demonstrated that efficient-market conclu-sions based on CAPM residuals are changed when more powerful asset pricingmodels are used.- Moreover, Hughes (1984), using 120 monthly retums on 220Canadian firms listed on the Toronto stock exchange, finds that at least three tofour factors have statistically significant risk premia in two subgroups of 110firms each. Furthermore, Hughes found that the factor risk premia are consistentacross the two subgroups. The findings of previous studies that abnormal retumscan be eamed by following analysts' recommendations may be attributable tothe CAPM being a misspecified asset-pricing model. Consider, for example, ananalyst with no firm-specific information who correctly believes that the normalretum is composed of two systematic risk factors, and who has correct forecastsof the equilibrium risk premia. If the researcher erroneously uses CAPM to e.sti-mate AAR and FAR, the second systematic, market-wide factor will be in bothAAR and FAR and the statistical relationship between AAR and FAR will besignificant regardless of whether the analyst has access to useful information.Thus, it is important to examine whether multibeta benchmarks give different

Dimson and Mar.sh (1984, p. 1266. fn. 4) recognize that measurement error may exist in thesrFARs because brokers could have trtismterpreted their instructions.Chen. CopeJajid, and Mayers (1987) find that the CAPM and multifactor models produceconsiderably different average residuals when portfolios are based on known anomalies,such a.s size, even when a "future benchmark methodology" is employed. Rozeff and Zaman(1988) show that trading by corporate insiders, whicb have high abnormal retums when theCAPM is used, is only marginally profitable after the CAPM is adjusted for E/P ratios andfirm size. Lehmann and Modest {1987} find that using CAPM residuals to rank mutual fundsproduces very different rankings than using residuals from time-sehes regressions of a fund'sretum on the retums of "basis portfolios,'' constructed to mimtc factors in the APT, Grinblattand Tittnan (1989a, 1989b) demonstrate that the CAPM leads to senous errors in judgingthe performance of mutual funds. TTiey use the Lehman-Modest ba.sis portfDlio.s to mitigateproblems with CAPM betas. Moreover. Lehman and Modest (1988) show that ba.sis portfolioscapture mucb of the dividend yield and size effects, neither of which is measured by CAPMbetas.


results than CAPM benchmarks in the evaluation of forecasting abilities.

Hypotheses and methodologyWe test the first hypothesis that analysts have valuable information that is notpossessed by the market in two ways: (1) we determine whether forecasted ab-normal retums have any ability to predict actual abnormal retums and (2) we usean actual trading rule. We test the second hypothesis that the choice of bench-mark can affect this conclusion by examining the sensitivity of the CAPM-basedresults to employing two versions of the Arbitrage Pricing Theor>' (APT) modelsdeveloped in Lehman and Modest il987). To conduct these tests, we observer, the analyst's forecast of retum. which is composed of a forecasted "normal"or "systematic " retum. r,,. and a forecasted firm-specific (i.e.. nonsystematic)retum. T. or':

r = ('•„ + T (1)

We cannot observe either (•„ or x. and we must estimate r,, by regressing r onvarious measures of systematic nsk, genericaily denoted b. Let r,,(b) be theestimated i,, implied by the measure of systematic risk b:

r,,{b) = 8i, + g,h (2)

where (^n.^'i) are the regression coefficients from the regression of r on b. Ourestnnate of the analyst's forecasted abnormal return (FAR) is T given by:

i = r - rjb) (3)

We test whether FAR is related to actual abnormal returns (AAR) where AAR ismeasured using the same asset pricing model as FAR. We conclude that analystshave forecasting ability if the relationship is significant and positive.

Our measure of the analysts" firm-specitic forecast (x) can be wrong in atleast two ways. First, we may be using the wrong model for r,,(b) because theanalyst uses no model at all or else she uses a model that differs from tbe onewe specify. Second, our constramt that analysts agree on the riskless retum andthe factor risk premia may be inappropriate. Nevertheless, although there arerea.sons to suspect that t is misspecified, the measurement errors in x bias theregression coefficient fi towards zero."" Thus, conditional on a correct AAR.

?> We toiiow Ihe standard practice of referring to "nonsystematic ' factors as "tinn-specific"'factors eveti though we recognize that industry factors that are not pervasive and distinct mayalso he "nonsystematic" factors.

4 To show this, define T = 1 + (X ~ Tt and suhstilute from (i) artd (3) to obtain;

T = -[ + ,--„-f,(b) (41

Define the errctrs in r,,(b) a.s:

328 L.D. Brown G.D. Richardson CA. Trzcinka

any significant, positive c\ is due to the analyst's ability to forecast firm-specificinfonnation.

DataThe price forecasts are supplied by the Research Evaluation Service (RES) of theFinancial Past Informanon Sen'ice, a division of the Financial Post Corporation.RES consists of analysts' forecasts of earnings, dividends, and stock prices forover 300 Canadian stocks covering more than 90 percent of the Toronto StockExchange 300 (TSE 300) index. RES has been available on a quarterly basissince March 31. 1983, and we obtained it through December 31, 1985 (12quarters).

Forecasts by individual analysts are as of the end of the calendar quarterand are on a company-by-company basis. RES instructs analysts to providetheir current forecasts. However, because the forecasts are likely to be "stale."having been disclosed earlier to the analysts' preferred clientele, our tests arebiased toward finding no valuable forecasting ability. The names of the analystsand their brokerage houses are provided, along with their most recent eamings.dividends, and price forecasts. The eamings and dividend forecasts are for thecurrent and following fiscal years. The share price forecasts are for 12 monthsahead. Consider the RES data collected on March 31. 1983, for a firm with afiscal year ending December 31, 1983. Analysts were asked lo provide expectedeamings per share for the 1983 and 1984 hscal years, expected dividends pershare for the 1983 and 1984 fiscal years, and expected share price on March 31,1984. The RES analysts' forecasted retum as of March 31, 1983 is the forecastedshare price for March 31, 1984, less the actual March 31. 1983, share price plusforecasted dividends for the 12-nionth holding period, all divided by the actualMarch 31, 1983. share price.'

where 6 is> the correlation between r̂ Cb) and r,,. and e is a random variable with mean \i^ andvariance O". If 6 = } and o^ — 0, r^fbl i.s a perfect proxy for }•„ and t = l. The more genera!result is obtained by substituting (5) into (4j:

t = T + (1 - 6)rn-t (6)

Where AAR, defined a.s r — r^, is regres.sed on T, the regression equation is:

Ii CT̂ is large. C] will not be significant because the measurement error in the regressor wiiioverwhelm the explanatory' power of t. If 6 = 0 (no correlation between r^ib) and r^,] and theanalyst's forecast of the normal retum is perfect so that r̂ = rn, then T = T + r̂ — t. In thiscase, any increases (decreases) in r̂ will exactly offset changes in the dependent variable.ir — rn), causing C] to be insignificant, [f the analyst's forecast of normal retum is not realizedexactly, i.e.. r™ ^ ?„, then ?„ will not be perfectly related to rn and the noise in t will be in-creased again, re.suhing in ci being insignificant.The forecasted dividend i.s. for this example, three-quarters of the expected 1983 dividendplus one-quarter of the expected 1984 dividend because buyers on March 31. I9K3, will notreceive the first quarter ciividend of 1983. Each future quarterly dividend is assumed to equalone-quarter of the expected future annual dividend-


TABLE 1Description of RES forecast and actual retums*

A. Distribution of RES forecast retums

Years

1983-85198319841985

1

Observations

11,0544,0333,3753,646

B, Comparison of RES forecast

Forecast date

Yr

1983198319831983198419841984i9841985198519851985

Q

123412341234

Number ofTSE 300Index firms

1761861871871861921951941931922(M205

Mean

0.2170.2410.231O.!77

Summary statistics for 11

standard deviationmedian forecastmaximum forecastminimum forecast

retums with actual retums

Percentage

TSE Index

91.692.091.792.692.392.092.492.091 089.890.990.4

Equal weighted retums

Forecast

0.2470.2070.2580.2380.2660.2600.2030.2220.1600.1940.2170,139

Actual

0.187-0.065-0,037- 0 072

0.0870.2180.1170.2490.1830. !440.1300.053

,054 observations

0.2000.1993.122

-0.913

Value weighted retums

Forecast Actual

0.2270,2140.2580.2270.2270 2350.2000.1720.1630.1760 2!30 142

0.139- 0 059-0.004-0.024

0.1360,2670.1350.2370,1850.1420.1380.056

The total number of firms in the RES data base is 318. but only a subset is in the TSE 300. Theequal-weighted RES forecasted reEum is the mean forecasted retum for the nexf 12 months, using themedian forecasted retum for each RES stock included in the TSE 300 index. The value-weightedRES forecasted retum is the value-weighted average forecasted retum for the next 12 months, usingmedian forecast retums and the TSE index weights. Actual retums are calculated in a manner similarto the forecasted retums A simple holding penod retum formula, including dividends, is used forboth forecasted and corresponding actual retums.

Table 1 provides a description of the forecasted and actual returns.^ Panel Acontains summary statistics of the distribution of the forecasted retums; panelB compares forecasted retums with actual retums. The 11.054 observations inpanel A are forecasts of 318 firms over the 12 quarters. IQ. 1983, to 4Q, 1985with approximately 3 analysts per firm quarter. Consistent with Dimson andMarsh (1984) with respect to U,K, data, panel B shows that the RES analysts"forecasts are overly optimistic. For example. 11 quarters of the equal-weightedforecasted returns in panel B are higher than their corresponding equal-weightedactual retums. An examination of the individual observations shows the opti-mism more clearly, 75,2 percent of forecasts in 1983 are larger than the actual

6 The descriptive properties of retums calculated using a log-relative formula were qualitativelyidentical to those calculated using a simple holding-period retum formula. All retums in thispaper are calculated using a simple holding-period retum formula.


retums; 55.3 percent and 54.3 percent of forecasts in 1984 and 1985, respec-tively, are larger than the actual retums. A comparison of actual retums for theTSE 3(X) firms shows that our sample includes the largest firms traded on theTSE and that the number of TSE 3{X) firms covered by RES has grown sincethe beginning of the service.

Forecasted price and abnormal profits using the CAPM

Actual abnormal retums and forecast abnormal returnsTo test the hypothesis that RES-analyst price forecasts possess firm-specificinformation, we assume that equation (2) represents analysts" forecasts of retumsthey believe the market will require in the absence of firm-specific information.Thus, EAR is as defined in equation (3). If this forecast abnormal retum containsuseful information, it should be related to AAR.

Our approach is similar to that in the recommendations literature, in whichFAR is indirectly provided by the analyst to the researcher. A recommendationto buy (sell) occurs when the analysts" r exceeds her fn(f < ?„). and thusthe analyst signals her EAR. At minimum, a recommendation to buy signals aFAR in excess of transactions costs, conveying the sign and some informationabout the magnitude of EAR. A ranking scheme such as Value Line's conveysthe relative magnitude of FAR. Because we have access to the analyst's stockretum forecasts, rather than to her recommendations, we must estimate EAR.TTius, our estimate of FAR is more likely to be subject to measurement eiTorthan is the recommendations literature's EAR. and we are less likely to observean association between EAR and AAR. Nevertheless, as argued in the secondsection, provided that we use the correct model to estimate AAR, a findingthat AAR is significantly and positively related to EAR implies that analysts dopossess valuable information (i.e., the measurement errors bias our tests to thenull of insignificance). To ameliorate the problem of using the wrong model, weuse three altemative asset-pricing models.

Our data have one principal advantage versus the recommendations literaturewhen making AAR and FAR comparisons. It is not possible with recommen-dations data to determine which model the analyst is using because r is notidentified. Thus, it is not known which asset-pricing model should be used toput AAR and EAR on a "common footing." We put AAR and EAR on a commonfooting by using altemative asset-pricing models (CAPM and two APT mod-els) to estimate both AAR and EAR. Beginning with the CAPM, EAR withoutcorrecting for heteroscedasticity is:

fari^jU) = ptjit) - go(0 - 1̂ U)bj(t} (8)

where

= analyst k's prediction of the retum on stock j from r to r + 12.bj(t) — Ordinary least squares (OLS) beta computed using the retums in ex-

cess of the risk-free rate (govemment of Canada treasury bills) and the


market proxy (the equal-weighted portfolio of all stocks on the Lavaltape) more than 60 months prior to and including f: r — 59 t.^

Heteroscedasticity in the regression equation of forecast retums on systematicrisk wili cause the OLS estimator of the disturbance term to be inefficient andalter the distribution of the f-ratios (Johnston, 1984, p, 302).** Because firmsare likely to differ considerably in their predictability, the fars are likely tobe heteroscedastic. Our correction for heteroscedasticity is to divide far by anestimate of residual risk. sjil). which is the standard error of the regression usedto estimate beta.

The remaining heteroscedasticity-adjusted variables are:

R,(t. f + i) = rjit. t + i)jsji!].= heteroscedasticity-adjusted retums. where r,(/./ + ;) is the actual

retum on stock j from date ; to date ; + ;.

= heteroscedasticity-adjusted predictions.= b,U)js,U).= heteroscedasticity-adjusted betas.

After adjusting for heteroscedasticity. we operationally estimate equation (2)

as":

Pkjit) = A'()+SiP;(') + % i r ) f o r i . = 1 n a n d j = 1 318, (9)

The actual retums for holding periods of interval (r, t -k- i) are defined as:

r,{i.! + i) = [1 + i-jit.t + l ) ! | l + r , ( r + l . r + 2 ) ] ••• [1 +rj(r-H f - l , r + OJ - 1

(10)

The normal retums are defined by the asset pricing model. For the CAPM, thenormal retum is:

N,(K ! + i) = RfU. r + 0 + hjittlRJr. t + i) - Rf{t. / + /)] d 1)

where Rm is the equal weighted retum of all stocks on the Lava! tape and theabnormal retum is:

We used a Canadian market index rather than a U.S./Canadian nrtarket index because the twomarkets appear to be segmented (Jorion and Schwartz, 198f>l.If forecasts are drawn from distributions with different variances, the OLS estimators will bemore influenced hy high variance forecasts than the low variance ones because the errors aresquared. Thus, forecasts with high variances will influence the estimates more, and we aremore likely to reject the hypothesis that analyst foreca.sts have firm-specific information.We tested the tran.sformed model for any remaining heteroscedasticity using a variety- ofdiagnostic tests. Dividing by residual risk reduces, but does not eliminate, heteroscedasticity-.Thus, we report all r-statistics using the White (1^80) estimator on the transformed model.


aarj(l,l + i) = rjit.t + i) - Njil.t + i) (12)

AARjit. t + ;•) = aar^(i. t + i)jsj(t) (13)

where ail variables are as previously defined. Dimson and Marsh (1984) andElton et al. (1986) find that the British and U.S. capital markets, respectively,impound the analyst's informational advantage within three months. Thus, wealso calculated AARj for one, two, and three months. More specifically, weregressed AAR on FAR:

AARjit, t + i) = ao + a-,FARi,j{t) + htj(t) (!4)

where / = I to 3, and a firm's AAR, is included k times in the regressionfor each of the k analysts who follow the firm. Because the dependent variablerepresents nonoverlapping monthly returns that we assume to be independent, weestimate the AAR on FAR regressions using pooled time-sehes cross-sectionalobservations. However, temporal pooling assumes stationarity in the process-generating model disturbances, and cross-sectionai pooling results in potentiallyupward biased r-statistics as a result of cross-sectional correlation of modeldisturbances. Accordingly, we also estimate 11 cross-sectional models, one foreach quarter in which an AAR exists, and perform a cross-temporal f-test (seeFama and MacBeth, 1973) on the vector of i 1 coefficients.'"

The results are in Table 2. Panel A contains the results for the one-, two-, andthree-month cumulative returns subsequent to the forecast; panel B shows themonth one, month two, and month three returns. Both panels reveal a significantslope (i.e., ai) coefficient for the AARs defined over one and two months. Thethird-month cumulative return in panel A has a significant slope coefficient,bat the third-motith (noncumulative) return is not significant in panel B. Thepositive significant slope indicates that when FAR is positive, AAR is generallypositive.''

Panels C and D of Table 2 report results using cross-temporal f-tests. TheAAR on FAR regressions were run for each quarter, the regression coefficientswere averaged, and a r-test was constructed using the time series of coefficients(see Fama and MacBeth, 1973). The f-statistics indicate that the average coeffi-cient of all the cumulative regressions is significant.'^ Thus, it appears that the

10 Because the Laval tape u.sed for this study contained data through December 31, 1985, wewere unabie to obtain AARs for the last set of foreca.sts made on December 31. 1985.

11 The negative intercepts resuh from analyst optimism. The forecast returns are almost alwayspositive, but the actual returns are not, implying that AAR equals FAR less a correction foroptimism.

12 The temporal f-test procedure represents a test of the hypothesis that the average of mode]coefficients across 11 quarters is zero. Another testable hypothesis is whether each quarter'smodel coefficients are drawn from a zero distribution. To test the hypothesis that the vectorof coefficients is a zero vector, we used a Hotelling T^ test described in Morrison (1976,p. 489) assuming the slope coefficients were independent of each other. The T' statisticrejected the hypothesis for ail models and all horizons. The finding that the temporal t isalways insignificant for the third month, while the 7'~ is not, implies that the positive third-month slope coefficients in certain conditioning quarters are offset by the negative third-


TABLE 2Regression of actual abnormal retums on forecast abnormal retums using the CAFMEquation:* AARfi, t + i) = a^ + a,fARtj(t) + ki/t)

Horizon

Results using pooled time-series cross-sectional regressions

A. Cumulative retumstOne monthTwo monthsThree months

-0.002-0.006-0.004

B. One-month retumsiFirst motithSecond monthThird month

-0.002-0.003-0.003

-2.01|j-5.89§-2.84§

-2.0111-3.97S

4.45S

0.0250.0430.038

0.0250.017

-0.003

5.04§5.99S4.40§

5.04§3.02S

- 0 66

Adjusted

0.0040.0050.003

0.0040.0010.000

ModelF

36.81§49.22§26.9OS

36.81S13.25§0.67§

Number ofobservations

100661005710043

100661006710058

Results using cross-temporai T-tests

C Cumulative returns'*'One month -0.001 -0.23Two months -0.006 -0.51Three months -0.003 -0.20

D. One-month returns?First month -0.001 -0 .23Second month -0.003 -0.26Third month 0.003 0.71

0.0280.0410.036

4.59!;6.20§4 S6§

0.028 4.59§0.013 !.88

-0.004 -0.78

11IIII

IIII

The cross-sectional equation appears in the text as equation (!4).The cumulative retums are for the first month (month : + I!. the first two months (months f ^ Iand / ^ 2), and the first three months (months ; + 1. r — 2. and / ^ 3) after the month of theforecast (month ;). respectively.The single-month retums are for the first tnonth (month r ^ I ]. the second month (month r -^ 2],and the third month (month r + 3} after the month of the forecast (month r), respectively.

[ Significant at the 0-0! (0-05i level or better (T-statistic: two-tailed tesr. f-statistic. one-taitedtest). The T-statistics in panels A and B are computed using White's (1980} covariance matrixestimator.

RES analysts possess firm-specific information.'

A trading ruleTo determine the profits from use of the forecasts, we constmct a trading mle

month slope coefficients in other conditioning quarters. This means that using the analyst'sforecast two months after she publishes it and holding the position for one month thereafterproduces significant positive retums in certain condifioning quarters, but that these are offsetby positions that produce significant negative retums in other condifioning quarters. Thus, itappears that the analyst information is valuable for at most two months.

13 In the presence of beta shifts known to the analyst, the use of historical betas may result ina spurious AAR-FAR correlation because the measurement error in beta will show up in theresearcher's AAR and FAR. However, if the positive AAR-FAR correlation is caused by betashifts, one should not observe a decay in the AAR-F.\R correlation over the three monthsfollowing the forecast. Because we observe such a decay, we conclude that beta shifts do notsignificantly bias our results.

334 L.D. Brown G.D, Richardson CA, Trzcinka

based on the fars. Commencing on the first day of the month subsequent to thecalendar quarter end, we buy those securities that the analysts predict will be thetop 10 percent performers and short-sell those securities that analysts predict tobe the bottom 10 percent performers. This position is held for three months andthe procedure is repeated each quarter as new forecasts arrive. To implementthis trading rule, equation (8) is estimated, the resulting forecasted abnormalreturns are placed into deciles, the securities in the top and bottom deciles areidentified, and each security' is associated with its actual abnormal retum overthe forecast quarter. The procedure is repeated each quarter,

RES subscribers receive the forecasts approximately seven days after the endof the calendar quarter. Hence, by implementing a trading mle on the first dayafter the end of the calendar quarter, we assume that inve,stors have access tothe price forecasts prior to publication in RES, It is reasonable to assume thatfavored clientele would possess the analysts" price predictions by the first of themonth, and thus could profit from this trading rule, Suret and L"Her (1990) alsoadopt a prior private-access assumption. They form trading strategy portfolioson the first day of the month of publication of IBES (with publication in IBESon the third Thursday of that month).

The results of this trading rule are reported in Table 3. The mean quarterlyactual abnormal retums—computed using equation 112) over the 12 quarters are3,06 percent. As a measure of the analysts' promised retum. we computed theaverage far for these firms. The mean far of 0,6753 differs dramatically frotn theactual abnormal retums. Nevertheless, it appears that the trading mle is prof-itable before transaction costs. There are two transactions (buy/sell) for eachlong position and two transactions (sell/buy) for each short position. With eachtransaction costing approximately 1 percent (one-way commission plus one-halfof the average bid-asked spread), the abnormal retums will be wiped out if theportfolio turns over ) 00 percent in each quarter. However, the average tumoverof the top and bottom deciles between consecutive quarters was approximately55 percent for the sample period, suggesting that the average portfolio transac-tions costs each quarter were approximately 2,2 percent rather than 4 percent.Subtracting 2.2 percent from each quarter's aar and compounding quarterly, theannualized after-transactions cost abnormal retums equal 3.38 percent. Inter-estingly, the results are similar to those of Suret and L'Her (1990), Using 2,0percent transactions costs, and forming portfolios on the first day of the monthof IBES publication, their annualized after-transactions cost abnormal retumsequal 3,6 percent. Of course, the trading profits would increase for those traders(brokerage firms, etc) who pay low commissions.

To ascertain whether these results are significant, we estimated the followingbootstrap distribution. For iQ, 1983, we obtained a random buy sample ofN = 102 with replacement from the original sample of 1,020 observations, andcomputed the mean (X^), We repeated this procedure to get X*, the randomsell sample, and defined DIFF* = X* - Xj, We repeated these steps 1,000times to get 1,000 observations of DIFF*. For the first conditioning quarter, we

Strong-Eorm Efficiency on the Toronto Stock Exchange 335

TABLE 3Trading rule profils as measured by CAPM

Trading rule: Buy largest far decile and sell lowest far decile*

0.00070.04850.04S00.03240.03240.03230.07220.04630.01030.01340.0028

0 0.^060 6753

(0 4S9|(OXmi(O.OfJll(0 0281(0 0211(0 Ct43)(0 0{)!)i0.026)10 3.50)(0.193)iO.438)

(0.001 1

Year-0 aiu-r l-Prob(X* £ Xli

1983-1

34

1984-1T

34

1985-123

Arithmcric mean aarCorresponding mean far

Annual cumulative profit after 2.2 percent transaction costs: 0.0338

* Forecasted abnormal returns (farl are ranked from highest to lowest in each conditioning quarterusing CAPM. Observ-ations are placed into l(> deciles from highest to lowest far The tradingstrategy consists of buying Ihe securities m the highest far decile, selling short secunties in thelowest far decile, and holding for three months The actual abnormal retums from this strategyare reported in the table. Forecasted abnormal retums are for a 12.month bonzon and are estimatedas the fitted residual from the ex ante regressions defined in equation t8) of the text. The annualcumulative profit after 2.2 percent transaction costs is:

r = 1(1 ^ r, - O.O22)it T r, - 0 022) ... (1 + r,, - O.O221]-' ' ' - I

where r̂ is the aar in conditioning quarter i. if — 1 1 M^ .Actual abnormal retums (aar) are defined in equation (12) of the text and represent three-month

cumulative abnormal retumsi l-Prob(A** ^ A) IS the empirical probability that tbe aar equals zero. For example, the number

in parentheses for the penod 1983- I indicates that 48.9 percent of the distnbution of DIFF* lay tothe right of 0 0007. DIFF* is defined using the bootstrap procedure discussed in section five.

determined where 0.0007 (see Table 3) was on the distribution of DIFF*. Thenumber in parentheses in Table 3 indicates that 48.9 percent of the distribution ofDIFF* he to the right of 0.0007. This indicates that the 0.0007 ts not significant.The aar of 0.0007 was obtained by subtracting the mean of the bottom decileobservations from that of the top decile observations (each with N = 102). Werepeated this procedure for each of the other 10 conditioning quarters, usingthe appropriate sample sizes. The number in parentheses following each aarindicates where it lies on the bootstrap distribution. The aar is significantlydifferent from zero in 7 of 11 conditioning quarters {\Q. 1983 to \Q, 1984,inclusive) at the 0.05 significance level or better. The simulation procedure gaverise to 11.000 observations (i.e.. 1.000 simulations per conditioning quarter times11 conditioning quarters). An average DIFF* was calculated by taking the meanof each of the 1.000 simulations (averaged over the 11 quarters). We comparedthe mean aar of 0.0306 with this distribution and found that it lay to the right

336 L.D, Brown G,D. Richardson C.A. Trzcinka

of all 1 ,(XX) simulations. Thus, we reject the null hypothesis that the average aarof 0,0306 occurred by chance at the 0.001 level of significance.

We also explored trading strategy performance by implementing tbe abovetrading rule .starting on the first day of the second month subsequent to calendarquarter end and holding for two months. Once RES is public (approximatelyseven days after the end of the calendar quarter), it should not be possible,given semistrong efficiency, to earn abnormal retums. In fact, the annualizedpretransaction cost abnonnaJ retum for such a strategy is 1,44 percent (notreported in Table 3). which is unprofitable after transaction costs,''* This resultis consistent with Elton et al. (1981). who demonstrate that abnormal retumsdisappear after the date of publication of eamings forecast revisions. The findingis also consistent with Suret and L'Her (1991), who show that abnormal retumsafter transactions costs disappear when trading strategy portfolios are formedon the first day of the month subsequent to the month of IBES publication.

Three features of our trading strategy deserve mention. First, we portray theprofits available to clientele who have a relationship with RES analysts allowingaccess to forecasts as of the end of the calendar quarter, rather than (on average)seven days later when RES is published. Second, this economically viable excessretum can be eamed by a very simple trading rule, so it is likely that a higherretum can be eamed by a more careful examination of each analyst's forecastingperformance. For example, if the RES forecasts are at ail "stale" because ofleakages to favored clientele prior to the end of the calendar quarter, we areunderestimating the u.sefulness of these forecasts to favored clientele. Third, thedollar profits can be substantial. If we assume that all 318 firms have the medianequity capitalization of Si50 million and that no more than 5 percent of eachfirm can be purchased before information is revealed, an investor could havemade $80.6! 3 million per year following this trading rule (i,e,, 0.05 x $150million x 318 x 0.0338).

Forecasted price and abnormal profits using APT modelsThe conclusions of the previous section are derived using CAPM beta as ameasure of risk. The CAPM has led to erroneous conclusions in mutual fundstudies (Gdnblatt and Titman, 1989b; Lehman and Modest, 1987) and studiesof corporate insider trading (Rozeff and Zaman, 1988), Any omitted factorswill be in both AAR and FAR, and the significant coefficients in Table 2 maybe spurious. Similarly, the trading rule in Table 3 may reflect a ranking onan omitted factor. Prior to determining whether these findings are sensitive toaltemative benchmarks, we examine which, if any, asset-pricing model RESanalysts appear to be using to make their forecasts. This will be importantin determining the errors in rn(b) and the dimension of b, as well as which

14 Similar results and conclusions are obtained for APT trading strategies discussed in the fifthsection.


TABLE 4Comparison of asset pricing models

Equation I: Individual forecasts regressed on systematic riskEquation 2; Consensus forecasts regressed on systematic risk

A. Comparison of intercepts and adjusted R

Intercepts

CAPM

Equation 1 0.132(0.043)

Equation 2 0.130(0.042)

LM

0.152(0.043)

0.142(0.059)

FM

0.145(0.043)

0.130(0.056)

Adjusted /f-s

CAPM

0.046(0.039)

0.077(0.0661

LM

0.091(0.046)

0.151(0.082)

FM

0.090(0.047)

0.14510.092)

B. Postenor odds tes[+

Numberofquarters that one measure of systematic risk is favored over another by 19lo I odds or better.

Equation 1Equation 2

CAPM favored over

FM

11

LM

14

LM favored over

CAPM FM

11 011 0

FM favored

CAPM

l j

8

over

LM

8

* Mean over I ] quarters wiih standard deviation in parentheses,•?• The postenor odds are computed assuming diffuse priors with equally probable models, Zellner

(1971, p, 312) gives the posterior probability of model 3 relative to model 2 as

\SSEyl

where

benchmark appears to be best for putting the AARs and FARs on a "commonfooting.""

Our tests using the CAPM beta as a measure of systematic risk generally showthat the forecasted return is significantly related to beta. However, the very low/?'s (.see Table 4) indicate that there may be more asset-pricing factors than wehave tested. In this section, we determine whether a general methodology thatcaptures omitted factors in the asset-pricing equation matters in the estimationof either the AAR on FAR regression or in the construction of the trading rule.

Basis portfoliosAPT predicts that expected returns are a linear function of the sensitivities,

15 Kryzanowski and To (1983) show that although the factor structure of the Toronto StockExchange is similar to the U.S. stock exchanges, more factors are necessary to representCanadian security returns than U.S. returns.

338 L.D. Brown G.D. Richardson CA. Trzcinka

bij. of a .stock's retum to k factors. Following Lehmann and Modest (1988), weassutne that there are n reference or "basis" portfolios whose retums are perfectlycorrelated with the k factors. To constmct these portfolios, we estimate a samplecovariance matrix using the retums of 145 firms on the Laval tape, which hadcomplete data for 276 months."'Unlike Lehmann and Modest (1987. 1988). whouse the suboptima! EM algorithm because of computational problems, we usethe Joreskog algorithm (see Morrison, 1976) to obtain 10 maximum likelihoodfactors.'-' As in Lehmann and Modest. (LM), two sets of 10 basis portfoliosare constructed from the factor loadings.'* The other set of 10 basis portfoliosreplicates the Fama-MacBeth (FM) procedure in which betas sum to unity acrossall firms. An important feature of FM is that there are no constraints on theportfolio weights, and the solution to the minimization problem with typicalstock retum data produces widely varying weights. Our weights ranged as highas I4(X); percent, implying ver\' large long and short positions."

We used the weights that resulted from the FM and LM procedures to con-struct monthly retums (/?i,... Rioi) on both sets of basis portfolios, and we usedthese weights in the same manner as the market retum in the CAPM. Let bj bethe 10x1 vector of coefficients obtained from the regression:

rj{t.t+ \) = be, +bijR], + --- +bu)]Rio, + •v ' ; ( ' ) (15)

We use Pijit) as a measure of expected retums. Our test of whether analystpredictions at time t are represented by the sensitivity of retums to the 10 basis

16 Using a shorter time period would reduce the problem of assuming a stationary covariancematrix but the degrees of freedom would be smaller.

17 We obtained only 10 factors because Lehtnan and Modest (1988) found little difference inpricing results using more than 10 factors, and the findings of Hughes (1984! suggest that tenfactors are adequate for representing Canadian security returns.

18 h&i A be the 145 x 10 matrix of maximum likelihood factor loadings and D he the145 X 145 matrix of estimated idiosyncratic nsks. Then if I is the covariance matrix ofretums. the assumptions of the APT model allow the decomposifion below:

1 = AA' + D

where 1 denotes a transpose. The k''' basis portfolio is constructed by solving for the weightsaj Ck),.... a]45(k) in the quadratic programming problem:

Min a(kyDa(k) subject to a(ki 'C = e'

where C and e define the set of basis portfolios. For basis portfolios thut reprodtice the pro-cedures of Fama and MacBeth (1973), let C = A the 145 x 10 matrix of factor loadings, andlet 1? be a 10 X I vector with zeros everywhere but in the k̂** row. The correlation betweenthe k* basis portfolio and the k"" factor will be 1.0. (i.e., a(k)'a(kj = 1. where a(ki is the k"'column of A. and the correiafion of the k'̂ basis portfolio with the other factors will be zero.

19 Lehmann and Modest observe that if there are no measurement errors in factor loadings, theFama-MacBeth procedure will produce weights that are sensitive to true differences acrossfactors. If, however, loadings contain measurement errors, the Fama-MacBeth weights maynot perform as well as a diversified portfolio since a well-diversified portfolio will be lessre-sponsive to both measurement errors and factor differences. Lehmann and Modest suggestforcing the weights to sum to one hut not ''normalizing" the betas as in the Fama-MacBethprocedure. The solution to the minimization problem with the Lehmann-Modest constraintsproduces weights that are roughly on order of l/n or 1/145.


portfolios is to regress P^jit) on all 10 regression coefficients where capital lettersdenote variables deflated by Sj(t), the standard error from estimating equation(15), Formally, our test is:

for k = 1 n analysts;

J = 1 , . , , , 318 firms. (]6j

where Sy(/} is the OLS estimate of by in equation (15), deflated by Sj(t) usingmonthly data from r-59 to /, Although the weights used to constmct the monthlyretums on each set of 10 basis portfolio do not change, the sensitivities of eachfirm to these portfolios are updated for each quarter.

The results of estimating equation (16) for the LM and EM basis portfoliossupport the hypothesis that analysts' forecast retums are linearly related to theAPT measures of systematic risk,-*̂ The F-statistics of the regression significantlyreject the hypothesis that the vector of coefficients is zero in every quarter forboth sets of basis portfolios. The adjusted R's in these regressions are muchhigher (see Table 4) than those in the CAPM regressions, suggesting that theCAPM omits factors used by RES analysts in formulating their retum forecasts.As with the CAPM measure of risk, the use of consensus (defined as median),rather than individual, forecasts as the dependent variable in the regressions doesnot appear to affect the results. This implies that correlation across analysts ofthe same firm does not contaminate the regression statistics.

Table 4 compares the results of the cross-sectional regressions of CAPMand the two APT models. Panel A shows the mean intercept and its time-seriesstandard deviation. In spite of their greater explanatory' power, the basis portfolioregressions have larger intercepts than the CAPM regressions, perhaps due togreater measurement error that is impounded in the intercept. Because there are10 "betas" in each APT regression rather than one in the CAPM regression, moreopportunities for measurement errors arise. Panel B of Table 4 uses a posteriorodds test described in Zellner (1971) and Judge, Griffiths, Hill. Lutkepohl andLee (1985), The number in the table is the number of quarters that a model isfavored by at least 19 to 1 odds,-' Both the LM and FM basis portfolios arefavored over the CAPM in almost every quarter, not shown in the table is thefact that the odds favoring the APT models are very large," Comparing the

20 For purposes of brevity, some of the results discussed in this paragraph are not presented in atable. They are available on request,

21 As pointed out by Zellner (1971), there is an unavoidable degree of arbitrariness in such odds.If 19 to 1. which corresponds to a conhdence interval of 0.05, is judged as acceptable or"significant," then why not 15 to H However, the same degree of arbitrariness occurs when a0.05 confidence level is judged to be an acceptable probability for a Type 1 error.

22 Comparing the two sets of basis portfolios, the FM portfolios perform somewhat better thanthe LM portfolios. The FM portfolios are favored in a majonty of quaners and the LM port-folios are never favored over the FM portfolios. Furthermore, the FM regressions have lowerintercepts, suggesting that there is less measurement error in the proxies for the FM factorsthan for the LM factors


two sets of basis portfolios, the FM portfolios perform somewhat better thanthe LM portfolios. The EM portfolios are favored in a majority of quarters, andthe LM portfolios are never favored over the FM portfolios. Furthermore, theEM regressions have lower intercepts, suggesting that there is less measurementerror in the proxies for the FM factors than for the LM factors.

We conclude that RES analysts act as if they use an asset-pricing model inforecasting retums. Moreover, consistent with Huberman and Kandei (1986),analysts' expectations appear to better conform with a "multibeta" asset-pricingmodel than with a single measure of systematic risk. We tum next to testsof whether the increased dimension of risk matters in the evaluation of theusefulness of forecasts.

Benchmark sensitivityWe argued in the second section that a single measure of systematic risk mayomit systematic factors that lead researchers who use the CAPM as a benchmarkto erroneously conclude that analysts possess valuable firm-specific information.Moreover, we showed in this section that RES analysts' forecasts are morestrongly correlated with multibeta measures of systematic risk than single betameasures. If the APT measures show no excess retums, whereas the CAPMmeasures show significant excess retums, the APT measures may justify theiradditional complexity vis a vis the CAPM. Altematively, if the APT and CAPMmeasures provide similar results, future researchers who test the usefulness ofanalysts' recommendations can use the CAPM in lieu of APT with no loss ofgenerality.

Tables 5A and 5B demonstrate that the findings using the APT benchmark aresimilar to those using the CAPM benchmark. This strengthens our conclusionthat analysts have access to firm-specific information. The estimates of ao andfli in equation (14) are not sensitive to the choice of benchmark, and the cross-temporal r-statistics do not differ in the first month between the three choicesof benchmark.-'

Table 6 replicates the trading mle of Table 3 with the LM and EM models.Abnormal profits are reduced but remain significant. In comparison with themean aar in Table 3 of 0.0306. the mean aars in Table 6 are 0.0248 and 0.0290for the LM and EM models, respectively. In an effort to ascertain whetherthe results are significant, we conducted bootstrap simulations similar to thosereported in Table 3. The difference between Table 3 and Table 6 simulations isthat Table 3 uses CAPM aars, whereas Table 6 uses (Lehman-Modest and Eama-MacBeth) APT aars. Similar to Table 3 results. Table 6 results indicate that theaars for most conditioning quarters and the period as a whole are significantly

23 Panel B of Table 2 (CAPM) and panels B and D of Tables 5A and 5B f APT) show a sig-nificant AAR-FAR association for month-two AARs. implying ihat the market may take twomontbs to determine the value of the information provided by the RES analysts. However,as explained in the fourth section, investors cannot profit from trading strategies based onmontb-two retums.


TABLE 5ARegression of actual abnormal retums on forecast abnormal returns using AFT wilh Lehman-Modestbasis portfoliosEquation:* AARp, i + i) = aa + a-,FARt^[l] *- htjit]

Horizon a,, Tia.)Adjusted Model

FNumber ofobservations

Results using pooled time-series cross-sectional regressions

A. Cumulative returns^One month - 0 011 -18.31 S 0.024 5.10§ 0.004Two months - 0 022 -25.018 0.046 7.20§ 0.007Three months -0.033 -31.82§ 0 042 5.44§ 0.004

B. One-month retumstFirst month - 0 011 -18.3!§ 0.024 5.10!) 0.004Second month -0.010 -14.75S 0.021 4.448 0.003Third month -0.011 -17.65S -0.003 - 0 60 0.0(K)

Results using cross-temporal T-tests

C. Cumulative rOne monthTwo monthsThree months

-0.001-0.022-0.0.33

D. One-month retumstFirst monthSecond monthThird month

- 0 . 0 1 !-0.010

0.01!

-8.70S-1I.22S-2I.64S

-8.70S-6.62S-6.78S

0.0270.047O.(M2

0.0270.019

-0.005

462§7 30§3 72§

4.62§4,16§

- 0 75

40.75§ 1006672.92S 1005743.57S 10043

40.758 1006628.74§ 10067

0.58 I005S

11II

II!lil

* The cross-sectional equation appears in the text as equation (141.•f The cumulative retums are for the first month (month t ^ I). the first two months (months r + I and

r -1- 2), and the first three months (months t + 1, / + 2, and ! -̂ 3) after the month of the forecast(month ;), respectively.

+ The single-month remms are for the first month (month : ^ 11, the second month [month f + 2).and the third month (month r + 3) after the month of the forecast {month f), respectively.

§ Significant at the 0.01 (0.05) level or better (J-statistic: two-tailed test; F-statistic: one-tailedtest). The T-statistics in panels A and B are computed using Whites 11980) covariance matrixestimator.

different from zero. With regards to the individual conditioning quarters, theLM and FM models, respectively, indicate 8 and 7 of 11 significant aars (at the0,10 significance level or better). With regard to the entire 11-quarter period, themean aars of the LM and FM models (0,0248 and 0.0290. respectively) are bothsignificant at the 0,00! level of significance. Thus, similar to Table 3 findings,the mean aars lay to right of the entire bootstraped distribution. We concludethat the mean aars are significantly different than zero, regardless of whetherCAPM or APT models are used. In addition, subtracting 2,2 percent transactioncosts, the abnormal profits are 1.02 and 2.78 percent, respectively, for the LMand FM models.

These results reject the strong-form efficient market hypothesis. It appearsthat analysts as a group have an ability to outperform a risk-adjusted retum.This does not, however, imply that a superior analyst exists. Indeed, it is well


TABLE 5BRegression of actual abnormal returns on forecast abnormal return.v using APT with Fama-MatBethbasis portfoliosEquation:* AARj(t. / + i) = ao + a,FARt,U} + htj{t)

Adjusted Model Number ofHorizon ao TdJo) a, Tla,) fl" F observations

Results using fKtoled time-series cross-sectional regressions

One monthTwo monthsThree months

-0.011-0.022-0.034

B. One-month retumstFirst monthSecond monthThird month

-0.011-0.008-0.010

-!7 .SI§-20.22S-23.725

-17.815-13.22S-15.865

0.0260.0450.045

0.0260.019

-0.003

5.7055.7354.335

5.7054.105

-0.66

0.0050.0040.002

0.0050.0020.000

49.55546.08525.195

49.55524.2050.70

100661005710043

100661006710058

Results using cross-temporal T-tests

C. Cumulative retums+One monthTwo monthsThree months

-0.011-0.020-0.033

D. One-month retumsiFirst nnonthSecond monthThird month

-0.011-0.009-0.010

-7.99§-1.61-1.55

-7.995-6.485-8.405

0.0290.0440.039

0.0290.0!7

-0.005

5.35S4.I2S2.98|!

5.35§3.215

-0.83

IIIIII

I ]

• The cross-sectional equation appears in the text as equation (14).t The cumulative returns are for the first month (month r + I ) , the firsttwo months (months r - I

and t -I- 2), and the first Ihree months (months ; -̂ I, ; + 2. and ( -̂ 3) after the month of theforecast (month t), respectively.

t The single-month returns are for the first month (month f + 1), the second month (month / ^ 2),and the third month (month i •+ 3) after the month of the foreca.st (month / ) , respectively.

§,|[ Significant at the 0.01 (0.05) level or better (7"-statistic: two-tailed test; F-statistic: one-tailedtest). The F-statistics in panels A and B are computed using White s (1980) covariance matnxestimator.

documented in the earnings literature that superior earnings forecasting abilitydoes not exist. Brown and Rozeff (1980) and O'Brien (1987, 1990) have shownthat individual analysts fail to exhibit consistent differences in predictive ability.Although our findings are consistent with the hypothesis that analysts randomlydevelop valuable information, it is plausible that no single analyst consistentlyobtains useful information. The employers of analysts undoubtedly know thisand pay a group of analysts for their ability to produce information. This explainswhy analysts do not develop reputations that allow them to be self-employedand why studies have not found a high correlation of superior forecasts betweenperiods,^'' Yet analysts" ability to produce as a group may well justify theirsalaries.

24 We split our sample into iwo six-quarter periods and ranked all analysts" fars relative to thecorresponding aars. Similar to Dimson and Marsh (1984), the rank correlation was insignifi-cant, suggesting the absence of consistency of analyst performance.


TABLE 6Trading rule profits as measured by APT models

Trading rule: Buy largest far decile and sell smallest far decile

Quarter aar-LM l-Proh(X» == X) aar-FM 1 -Prob(A'» £ X)

1983-1234

1984-1234

1985-123

Arithmetic mean aar

Corresponding mean far

Annual cumulative profit after2.2 percent transaction costs

0.03770.05040.02540.03340.02690.04810.0422

-0.0011-0.0004

0.0279-0.0180

0.0248

0.6745

0.0102

(0.063)(0.005)(0.046)(0.018)(0.037)(0.005)(0.028)(0.491)(0.504)fO.055)(0.792)

(o.oon

0.02730.04320.02620.03720.03570.02930.05230.00490.02260.O29S0.0102

0 0290

0.6878

0 0278

(O.il8)(0.023)(0.040)(0.020)(0.007)(0.084)(0.016)(0.4!8((0.198)(0.097)(0.336)

(0.001)

* Forecasted abnonnal retums (far) are ranked from highest to lowest in each conditioning quarterusing APT. Observations are placed into 10 deciles from highest to lowest far. The tradingstrategy consists of buying the securities in the highest far decile, selling short securities in thelowest far decile, and holding for three months. The actual abnormal retums from this strategyare reported in the table. Forecasted abnormal retums are for a 12-month horizon and are estimatedas the fitted residuals from the ex ante regressions defined in equation (16) of the text. The residualsfrom equation [16) are used to estimate far. The annual cumulative profit after 2.2 percenttransaction costs is:

r = [(1 + r, - 0.022)(l + r, - 0.022) ... (I + r,, - 0.022)]-"' - 1

where r, is the aar in conditioning quarter r (;' = 1 I l lt Actual abnormal retums {aar) are defined in equation (12) of the text and represent three-month

cumulafive abnormal retums.t l-Ptx>b(A'* ^ X) is the empirical probability that the aar equals zero. For example, the number

in parentheses in 1983-1 for the LM APT model indicates that 6.3 percent of the distribution ofDIFF* lay to the right of 0.0377. DIFF* is defined using the bootstrap procedure discussed in thefifth section.

Summary and conclusionsThe purpose of this paper is to test two important hypotheses for infonnationeconomics. First, we hypothesize that analysts of the Toronto Stock Exchangehave valuable infonnation that the market does not possess. Second, we hy-pothesize that the choice of benchmark can affect conclusions based on CAPMbenchmarks. We test the first hypothesis in two ways; namely, we determine ifforecasted abnonnal retums have any ability to predict actual abnonnal retums,and we use an actual trading rule. We test the second hypothesis by examiningthe sensitivity of the CAPM-based results to employing two versions of theAPT models developed in Lehman and Modest (1987). To conduct these tests.

344 L,D, Brown G,D, Richardson C,A, Trzcinka

we observe analysts' point forecasts of retums as collected by the Financial PostCorporation's RES service. We show that there is a significant and positive rela-tionship between actual abnormal retums (AAR) and forecasted abnormal retums(FAR), and that a simple trading rule can earn economically significant retumsin excess of transaction costs. We find that the AAR-FAR relationship and thetrading m!e results are not sensitive to the choice of benchmark, strengtheningthe conclusions of previous researchers who employed a CAPM benchmark toexamine whether analyst forecasts provide valuable information.

This study increases our understanding of firm information environments andthe role of analysts in preempting the infonnation content of accounting infor-mation. Financial statements are an important source of infonnation to capitalmarkets regarding firm-specific (i,e,, idiosyncratic) events, and they representone medium whereby inside information becomes publicly available. Financialanalysts represent an altemative medium for converting insider infonnation topublicly available information. Their ability to forecast idiosyncratic price move-ments suggests that, through their visits to companies and related infonnationsearch activities, analysts can leam about idiosyncratic events and convey thisinfonnation to the market through their forecasts and recommendations. Thus,analysts are likely to mitigate the information role of financial statements.

The most pressing limitation of our study is whether the trading profits wedocument are in excess of the costs of producing the RES forecasts. Such costsequal at least the compensation paid to analysts as a group plus overhead costsrelated to research activities in the various brokerage firms. In competitive capitalmarkets, these costs should be roughly equal to the profits eamed from usingthe foreca,sts. We have no data on these costs and cannot determine how muchof the trading profits are economic rents. This remains an important area forfuture research.

ReferencesAjitikya B, and M, Gift, "Corporate Managers' Eamings Forecasts and Symtnetrical

Adjustments of Market Expectations," Journal of Accounting Research (Autumn1984) pp. 425^W4,

Black, F,, "Yes, Virginia. There is Hope: Tests of the Value Line Ranking System,"Financial Analysts Journal (September/October 1973) pp, 10. 12, 14,

Brown, L,, P, Griffin, R. Hagerman, and M. Ztnijewski, "Security Analyst SuperiorityRelative to Univariate Time-Series Models in Forecasting Quarterly Eamings,"Journal of Accounting & Economics (April 1987) pp, 61-87,

Brown, L. and M, Rozeff, "Analysts Can Forecast Accurately!" Journal of PortfolioManagement (Spdng 1980) pp, 31-34,

Brown, P.. G, Foster, and E. Noreen, Security Analyst Multi-Year Eamings Forecastsand the Capital Market (Sara,sota, Ba,: American Accounting Association, 1985),

Brown, S, and M. Weinstein. "A New Approach to Testing Asset Pricing Models: TheBilinear Paradigm." Journal of Finance (June 1983) pp, 711-743,

Chen, N,, T, Copeland, and D, Mayers, "A Comparison of Single and MultifactorPortfolio Performance Methodologies," Journal of Financial and QuantitativeAnalysis (December 1987) pp, 401^17,

Copeland, T, and D, Mayers, "The Value Line Enigma (1965-1978): A Case Study of

Strong-Eorm Efficiency on the Toronto Stock Exchange 345

Performance Evaluation Issues." Journal of Financial Economics (November 1982)pp. 289-321.

Dimsoti, E. and P. Marsh, "An Analysis of Brokers' and Analysts' Unpublished Fore-casts tif UK Stock Retums," Joumal of Finance (December 1984) pp. 1257-1292.

Elton, E., M. Gmber, and S. Grossman, "Discrete Expectational Data and PortfolioPerformance," Joumal of Finance (July 1986) pp. 699-714.

Elton, E., M. Gruber, and M. Gultekin, "Expectations and Share Prices." ManagementScience (September 1981) pp. 975-987.

Fama, E. and J. MacBeth, "Risk, Retum, and Equilibrium: Empirical Te.sts," Joumal ofPolitical Economy (May/June 1973) pp. 607-6.36.

Fried. D. and D. Givoly, "Fttiancial Analysts' Forecasts of Earnings: A Better Surro-gate for Market Expectations," Joumal of Accounting & Economics (October 1982)pp. 85-107.

Givoly, D. and J. Lakonishok, "The Information Content of Financial Analysts' Fore-casts of Eamings: Some Evidence on Sen:ii-Strong Inefficiency," Journal of Ac-counting & Economic; (December !979) pp. 165-185.

Grinblatt, M. and S. Titman. "Mutual Fund Performance: An Analysis of QuarterlyPortfolio Holdings," Joumal of Business (July 1985a) pp. 393^11.

Grinblatt, M. and S. Titman, "Portfolio Performance Evaluation: Old Issues and NewInsights," Review of Financial Studies (No. 3, 1989b) pp. 393^21.

Grossman, S. and J. Stigiiu, "On the Impossibility of Informationally Efficient Mar-kets," American Economic Review (June 1980) pp. 393^08.

Holloway. C, "A Note on Testing an Aggressive Investment Strategy U.sing ValueLine Ranks," Joumal of Finance (June 1981) pp. 711-719.

Huberman, G. and S. Kandei, "Auloregressive Slate Variables Explain the Value LineEnigma," Universit>' of Chicago, Working Paper (1986).

Huberman, G. and S. Kandei, "Value Line Rank and Firm Size," Joumal of Business(October 1987) pp. 577-589.

Hughes, P., "A Test of the Arbitrage Pricing Theor)' Using Canadian Security Re-turns," Canadian Joumal of Administrative Science (No. 2, i984) pp. 195-214.

Johnston. J., Econometric Methods. 3rd ed. (New York: McGraw-Hill. 1984).Jodon, P. and E. Schwartz, "Integration vs. Segmentation in the Canadian Stock Mar-

kes," Joumal of Finance (July 1986) pp. 603-614.Judge, G., W. Gnffiths, R. Hill, H. Lutkepohl, and T. Lee, The Theory and Practice of

Econometrics, 2nd ed. (New York: Wiley. 1985).Kryzanowski, L. and M.C. To, "General Factor Models and the Structure of Security

Retums," Joumal of Financial and Quantiiative Analysis (March 1983) pp. 31-52.Lehmann. B. and D. Modesl, "Mutual Fund Performance Evaluation: A Comparison

of Benchmarks and Benchmark Comparisons," Journal of Finance (June 1987) pp.233-265.

, "The Empirical Foundations of the Arbitrage Pricing Theor>," Joumal ofFinancial Economics (September 1988) pp. 213-254.

Morrison, D., Multivariate Statistical Methods, 2nd ed. (New York: McGraw-Hill,1976).

O'Brien, P., "Individual Forecasting Abihty," Managerial Finance (1987) pp. 3-9.. "Forecast Accuracy of Individual Analysts in Nine Industries," Joumal of

Accounting Research (Autumn 1990) pp. 286-304.Roil, R. and S. Ross. "An Empirical Investigation of the .Arbitrage Pricing Theory,"

Journal of Finance (December 1980) pp. 1073-1103.Rozeff, M. and M. Zaman, "Market Efficiency and Insider Trading: New Evidence,"

Joumal of Business (January 1988) pp. 25-44.Stickel, S., "The Effect of Value Line Investment Survey Rank Changes on Common

Stock Prices," Joumal of Financial Economics (March 1985) pp. 121-143.

346 L,D, Brown G.D, Richardson C,A, Trzcinka

Suret, J. atid J.F. L'Her, "The Reactioti of Canadian Securities to Revisiotis of Eam-ings Forecasts" Contemporary Accounting Research (Spring 1991) pp, 378^06.

White. H,, "A Heteroskedasttcity-Consistent Coxariatice Matrix Estimator and a DirectTest for Heteroskedasticity," Econometrica (May 1980) pp. 817-838.

Zellner, A., An Introduction to Bavesian Inference in Econometrics (New York: Wiley,1971).

strong-form efficiency on the toronto stock exchange: an examination of analyst price forecasts

Documents