expected returns on stock and bonds

8/12/2019 Expected Returns on Stock and Bonds

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Journal of Financial Economics 25 (1989) 23-49. North-Holland

BUSINESS CONDITIONS AND EXPECTED RETURNS ONSTOCKS AND BONDS

Eugene F. FAMALr~rrwsi~rfChicugo, Chicugo. IL 60637. ti.54

Kenneth R. FRENCH:vhtcR uml tirlirersip of Chicago. Chicago, IL 606_?i, tiSA

Rcccived January 1989. final version received August 1989

Expected returns on common stocks and long-term bonds contain a term or maturity premiumthat has a clear business-cycle pattern (low near peaks. high near troughs). Expected returns alsocontain a risk premium that is related to longer-term aspects of business conditions. The variationthrough time in this premium is stronger for low-grade bonds than for high-grade bonds andstronger for stocks than for bonds. The general message is that expected returns are lower wheneconomic conditions are strong and higher when conditions are weak.

1. IntroductionThere is mounting evidence that stock and bond returns are predictable.

Some argue that predictability implies market inefficiency. Others contend thatit is a result of rational variation in expected returns. We offer evidence on thisissue. The evidence centers on whether there is a coherent story that relates thevariation through time of expected returns on bonds and stocks to businessconditions. The specific questions we address include:1)2)

Do the expected returns on bonds and stocks move together? In particular.do the same variables forecast bond and stock returns?Is the variation in expected bond and stock returns related to businessconditions? Are the relations consistent with intuition, theory, and existingevidence on the exposure of different assets to changes in business condi-tions?

*The comments of John Cochrane. Bradford Cornell, Kevin Murphy. Richard Roll. G. WilliamSchwert (the editor). and John Campbell (the referee) are gratefully acknowledged. This researchis supported by the National Science Foundation (Fama) and the Center for Research in SecurityPrices (French).

0304-405X/X9/%3.50 c 1989. Eisevier Science Publishers B.V. (xorth-Holland)


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2-I E. F. Fumu und K. R. French. Bustness conditions und e.xpected returm

Our tests indicate that expected excess returns (returns net of the one-monthTreasury bill rate) on corporate bonds and stocks move together. Dividendyields, commonly used to forecast stock returns, also forecast bond returns.Predictable variation in stock returns is, in turn, tracked by variables com-monly used to measure default and term (or maturity) premiums in bondreturns. The default-premium variable (the default spread) is the differencebetween the yield on a market portfolio of corporate bonds and the yield onAaa bonds. The term- or maturity-premium variable (the term spread) is thedifference between the Aaa yield and the one-month bill rate.

The dividend yield and the default spread capture similar variation inexpected bond and stock returns. The major movements in these variables,and in the expected return components they track, seem to be related tolong-term business episodes that span several measured business cycles. Thedividend yield and the default spread forecast high returns when businessconditions are persistently weak and low returns when conditions are strong.

The term spread is more closely related to the shorter-term business cyclesidentified by the National Bureau of Economic Research (NBER). In particu-lar, the term spread - and the component of expected returns it tracks - arelow around measured business-cycle peaks and high near troughs.

There are clear patterns across assets in the slopes from regressions ofreturns on the forecasting variables. The slopes for the term spread arepositive and similar in magnitude for all the stock portfolios and (long-term)bond portfolios we examine. This suggests that the spread tracks a term ormaturity premium in expected returns that is similar for all long-term assets. Areasonable and old hypothesis is that the premium compensates for exposureto discount-rate shocks that affect all long-term securities (stocks and bonds)in roughly the same way.

In contrast to the slopes for the term spread, the slopes for the defaultspread and the dividend yield increase from high-grade to low-grade bondsand from bonds to stocks. This pattern corresponds to intuition about thebusiness risks of the assets. that is, the sensitivity of their returns to unex-pected changes in business conditions. The slopes suggest that the defaultspread and the dividend yield track components of expected returns that varywith the level or price of some business-conditions risk.

Does the expected-return variation we document reflect rational pricing inan efficient market? On the plus side, it is comforting that three forecastingvariables. all related to business conditions. track common variation in theexpected returns on bonds and stocks. It is appealing that the term spread,known to track a maturity premium in bond returns, identifies a similarpremium in stock returns. It is also appealing that a measure of businessconditions like the default spread captures expected-return variation thatincreases from high-grade bonds to stocks in a way that corresponds tointuition about the business-conditions risks of assets. Finally, it is comforting


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E. F. Famu and K. R. French. Business condirrons and esprcred returns 25

that variation in the dividend yield, which might otherwise be interpreted asthe result of bubbles in stock prices, forecasts bond returns as well as stockreturns, and captures much the same variation in expected bond and stockreturns as the default spread.

What one takes as comforting evidence for market rationality is, however,somewhat a matter of predilection. As always, the ultimate judgment must beleft to the reader.

2. Data2.1. Common stocks

We use the value- and equal-weighted portfolios of New York StockExchange (NYSE) stocks. from the Center for Research in Security Prices(CRSP). to represent the behavior of stock returns. The value-weighted portfo-lio is weighted toward large stocks; equal-weighted returns are affected moreby small stocks. The two portfolios thus provide a convenient way to examinethe behavior of stock returns as a function of firm size, a dimension known tobe important in describing the cross-section of expected stock returns [Banz(1981)] and the variation through time of expected returns [Keim andStambaugh (1986). Fama and French (1988a)].

2.2. Corporute bondsTo study corporate bond returns, we use a sample maintained by Ibbotson

Associates (obtained for us by Dimensional Fund Advisors). This database hasmonthly returns and yields for 19261987. The sample includes 100 bonds,chosen to approximate a value-weighted market portfolio of corporate bondswith maturities longer than one year. The sample starts in 1926 with 100randomly chosen bonds, with probability of selection proportional to facevalue outstanding. Random selection based.on face value is used at the start ofeach following year to add and delete bonds to maintain a loo-bond samplethat approximates a value-weighted market portfolio. We use the portfolio ofall 100 bonds (called All), and portfolios of bonds rated Aaa, Aa, A, Baa, andbelow Baa (LG. low-grade). Portfolio returns and yields are price-weightedaverages of individual bond returns and yields. The average maturity of bondsin these portfolios is almost always more than ten years.

2.3. Exptanatoty cariables for excess returnsThe tests attempt to measure and interpret variation in expected excess

returns for return horizons T of one month, one quarter. and one to four years.A one-month excess return is the difference between the continuously com-


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26 E. f. Fume und K. R. French. Business condirions und expected rewns

pounded one-month return on a bond or stock portfolio and the continuouslycompounded one-month Treasury bill return (from Ibbotson Associates).Excess returns for quarterly and one- to four-year holding periods are ob-tained by cumulating monthly excess returns. The monthly, quarterly, andannual excess returns are nonoverlappin,. 0 The two- to four-year returns areoverlapping annual (end-of-year) observations. Henceforth, the word return,used alone, implies excess return.

The tests center on regressions of future stock and bond returns, r(t, t + T).on a common set of variables, X(t), known at r,

One of the explanatory variables is the dividend yield, D(r)/P(t), on thevalue-weighted NYSE portfolio, computed by summing monthly dividends onthe portfolio for the year preceding time r and dividing by the value of theportfolio at f. [See Fama and French (1988b).] We use yields based on annualdividends to avoid seasonals in dividends. These annual yields are used toforecast the returns. r(f, t + T), for all horizons.

The hypothesis that dividend yields forecast stock returns is old [see, forexample, Dow (1920) and Ball (1978)]. The intuition of the efficient-marketsversion of the hypothesis is that stock prices are low in relation to dividendswhen discount rates and expected returns are high (and vice versa), so D/Pvaries with expected returns. There is a similar prediction, however, if varia-tion in dividend yields is due to irrational bubbles in stock prices. In this case,dividend yields and expected returns are high when prices are temporarilyirrationally low (and vice versa). Evidence that dividend yields forecast stockreturns is in Rozeff (1984) Shiller (1984) Flood, Hodrick. and Kaplan (1986)Campbell and Shiller (1988), and Fama and French (1988b). The novel resulthere is that D/P also forecasts bond returns.

Expected returns on long-term corporate bonds can vary through time for atleast two reasons: (a) variation in default premiums (differences between theexpected returns on low- and high-grade bonds with similar maturities) and(b) variation in term or maturity premiums (differences between the expectedreturns on long- and short-term bonds).

To identify variation in term or maturity premiums. we use the term spread,TERM(t). the difference between the time t yield on the Aaa bond portfolioand the one-month bill rate. This choice is consistent with evidence thatspreads of long- over short-term interest rates forecast differences betweenlong- and short-term bond returns [see, for example, Fama (1976, 1984, 1986,1988) Shiller. Campbell, and Schoenholtz (1983). Keim and Stambaugh (1986)and Fama and Bliss (1987)]. Our novel result is that TERM tracks a time-varying term premium in stock returns similar to that in long-term bondreturns.


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To track default premiums, we use the default spread, DEF(t). the differ-ence between the time r yield on the portfolio of (All) 100 corporate bondsand the Aaa yield. This choice is in line with evidence in Fama (1986) andKeim and Stambaugh (1986) that spreads of low- over high-grade interestrates forecast spreads of low- over high-grade bond returns.

The regression results are robust to changes in the definitions of thevariables used to forecast returns. The dividend yield on the equal-weightedNYSE portfolio forecasts returns about as well as the yield on the value-weighted portfolio. Substituting a low-grade (Baa or below) bond yield for themarket-portfolio bond yield in the default spread has little effect on theresults. We use a market-portfolio bond yield because it is less subject tochanges through time in the meaning of bond ratings. Substituting a long-termTreasury bond yield for the Aaa yield in the default and term spreads also haslittle effect on the results. We choose the Aaa yield to avoid potential problemscaused by the change in the tax status of Treasury bonds (from nontaxable totaxable) in the early 1940s.

3. Business conditions and the behavior of the forecasting variables3. I. Autocorrelations

The autocorrelations of the variables used to forecast returns are informa-tion about the behavior of expected returns. For the 1927-1987 and 1941-1987periods used in the regressions, the autocorrelations of the dividend yield, thedefault spread, and the term spread (table 1) are large at the first-order(annual) lag, but tend to decay for longer lags. This suggests that D/P, DEF.and TERM track components of expected returns that are autocorrelated butshow some tendency toward mean reversion.

The autocorrelations of TERM for 1941-1987 are smaller than those ofD/P and DEF. Beyond the first (one-year) lag. the autocorrelations of TERMfor 1941-1987 are close to 0. Thus for the last 47 years of the sample, thecomponent of expected returns tracked by TERM is much less persistent thanthose tracked by D/P and DEF. This result is in line with our story thatTERM tracks variation in expected returns in response to short-term variationin business conditions, whereas DEF and D/P track expected-return varia-tion that relates to more persistent aspects of business conditions. The busi-ness-conditions part of this story comes next.

3.2. Plots of the forecasting oariablesSince we measure the variation of expected returns with linear regressions of

returns on the forecasting variables, plots of the forecasting variables picturethe components of expected returns they capture.


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28 E. F. Fumu and K. R. French. Bustness cordttrons uud expecred returns

TableSummary statistics for annual observations on one-year excess returns on the bond and stock

portfolios. and the dividend yield D/P). default spread DEF). and term spread TERM).Autocorrelations

Mean SD. 1 2 3 4 5 6 7 81927-1987

Aaa 0.74 6.69 0.21 0.05 - 0.06 -0.10 -0.16 0.05 - 0.03 - 0.04Aa 0.67 6.82 0.20 -0.05 -0.13 -0.15 -0.13 0.03 - 0.02 -0.10A 0.87 8.38 0.25 -0.15 -0.24 -0.13 -0.02 0.12 - 0.05 -0.13Baa 1.45 8.65 0.24 -0.13 - 0.24 -0.14 -0.01 0.15 - 0.01 - 0.07LG 2.25 12.36 0.32 -0.03 -0.21 -0.21 -0.05 0.13 0.05 0.11VW 5.70 2081 0.10 -0.19 -0.06 -0.13 -0.01 -0.02 0.15 0.07EW 8.80 28.26 0.13 -0.18 -0.12 -0.22 -0.10 -0.11 0.11 0.05D/R 4.49 1.36 0.62 0.29 0.20 0.20 0.28 0.32 0.24 0.17DEF 0.96 0.68 0.83 0.70 0.57 0.51 0.49 0.54 0.52 0.51TERM 1.90 1.25 0.54 0.36 0.21 0.22 0.26 0.14 0.18 0.05

1941-1987Aaa -0.01 7.05 0.21 -0.03 -0.13 -0.16 -0.25 -0.03 -0.11 -0.11Aa 0.0x 7.02 0.23 -0.14 -0.12 -0.21 -0.17 -0.06 -0.05 -0.14A 0.55 7.29 0.26 -0.13 -0.19 -0.15 -0.02 -0.02 -0.07 -0.18Baa 1.3x 7.36 0.26 -0.20 -0.17 -0.11 0.01 0.05 -0.01 -0.15LG 2.71 9.8X 0.30 -0.01 -0.13 - 0.03 0.17 0.16 0.06 - 0.02VW 6.97 16.25 -0.03 -0.27 0.08 0.30 0.13 -0.13 0.18 0.05EW 9.84 21.58 0.06 -0.27 -0.03 0.18 - 0.01 -0.22 0.12 - 0.03D/P 4.33 1.20 0.79 0.62 0.52 0.43 0.36 0.35 0.37 0.30DEF 0.74 0.45 0.74 0.61 0.34 0.38 0.42 0.51 0.46 0.43TER,M 1.76 1.23 0.46 0.24 0.04 0.13 0.20 0.01 0.06 -0.13

Onc-year excess returns are sums of one-month excess returns (the difference between thecontinuously compounded one-month return on a portfolio and the one-month bill rate).Aaa. ,LG are bond portfolios formed according to Moodys rating groups. VW and EW are thevalue- and equal-weighted NYSE stock portfolios. D/P LS he ratio of dividends on the VWportfolio for year t to the value of the portfolio at the end of the year. DEF is the differencebetween the end-of-year yield on Ail (the portfolio of the 100 corporate bonds in the sample) andthe Aaa yield. TERM is the difference between the end-of-year Aaa yield and the one-month billrate. The yields and the bill rate in DEF and TER,M are annualized. As in the later regressions.the periods for D/P. DEF. and TERM are one year prior to those for returns. e.g.. 1926-1986rather than 1927-1987.

If bonds are priced rationally, the default spread, a spread of lower- overhigh-grade bond yields, is a measure of business conditions. Fig. 1 shows thatDEF indeed takes its highest values during the depression of the 193Os, andthere are upward blips during the less severe recessions after World WarII - for example, 1957-1958, 1974-1975. and 1980-1982. Although DEFshows some business-cycle variation. its major swings seem to go beyond thebusiness cycles measured by the NBER. DEF is high during the 1930s and theearly years of World War II, a period of getteral economic uncertainty [Officer


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E. F. Fumu and K. R. French. Busi ness condi t i ons und expecred rerurm 29

Lj T

Fig. 1. Beginning-of-month values of the value-weighted dividend yield. D/P. and the defaultspread. DEF. in percent.

Vertical grid lines are NBER business-cycle peaks (P) and trough (T). The dates are:8/29(P) 3/33(T) 11/48(P)5/37(P) 6/38(T) 7/53(P)2/45(P) 10/45(T) 8/57(P)

(1973) and Schwert (1988)]. It is consistently lower during the 1953-1973period of stronger and more stable economic conditions, which nevertheless

10/49(T) 4/60(P) 2/61(T) l/SO(P) 7/80(T)5/54(T) 12/69(P) 11/70(T) 7/81(P) 11/82(P)4/58(T) 11/73(P) 3/75(T)

includes four measured recessions.Similar comments apply to the dividend yield. Indeed. the correlation

between D/P and DEF 0.61 for 1927-1987 and 0.75 for 1941-1987) isapparent in fig. 1. We interpret the figure as saying that the forecast power ofthe dividend yield and the default spread reflects time variation in expectedbond and stock returns in response to aspects of business conditions that tendto persist beyond measured business cycles. This interpretation is buttressedby the high and persistent autocorrelation of D/P and DEF observed intable 1.

In contrast, fig 2 shows that, except for the 1933-1951 period. the variationof the term spread is more closely related to measured business cycles. TERM


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E. F. Fama und K . R. French Busi ness condi t i ons und expecred retur ns

Fig. 2. Beginning-of-month values of the term spread. TERM . in percent.Vertical grid lines are NBER business-cycle peaks (P) and troughs (T). The dates are:

8/29(P) 3/33(T) 11/48(P) 10/49(T) 4/60(P) 2/61(T) l/SO(P) 7/80(T)5/37(P) 6/38if) 7/53(P) 5/54(T) 12/69(P) 11/70(T) 7/81(P) 11/82(P)2/45(P) 10/45(T) 8/57(P) 4/58(T) 11/73(P) 3/75(T)

tends to be low near business-cycle peaks and high near troughs. The details ofthe story are in fig. 3 which shows the components of TERM, the Aaa yieldand the one-month bill rate.

From 1933 to 1951, the bill rate is stable and close to 0. This period includesmuch of the Great Depression and then the period during and after WorldWar II, when the Federal Reserve fixed bill rates. For the rest of the sample,the bill rate always rises during expansions and falls during contractions.Indeed, fig. 3 suggests that, outside of the 1933-1951 period, the bill ratecomes close to defining the business peaks and troughs identified by theNBER. (The NBER says that interest rates are not used to date businesscycles.)Fama (1988) argues that the business-cycle variation in short-term interestrates is a mean-reverting tendency, which implies that the variation in long-termrates is less extreme. This is confirmed by the behavior of the Aaa yield in


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E. F. Fama and K. R. French. Business conditions and expecred rerurns

27 i: 33 jj 33 92 r5 13 51 5r 57 6 53 63 53 72 75 78 Si SY 37

Fig. 3. Beginning-of-month values of the Aaa bond yield and the (annualized) one-monthTreasury bill rate, in percent.

Vertical grid linea are NBER business-cycle peaks (P) and troughs (T). The dates are:8/29(P) 3/33(T) 11/48(P) 10/49(T) 4/60(P) 2/61(T) 1/80(P) 7/80(T)5/37(P) 6/38(T) 7/53(P) 5/54(T) 12/69(P) 11/70(T) 7/81(P) 11/82(P)2/45(P) 10/45(T) 8/57(P) 4/58(T) 11/73(P) 3/75(T)

fig. 3. The Aaa yield rises less than the bill rate during expansions and fallsless during contractions. As a result, the term spread - the Aaa yield minusthe bill rate - has a clear business-cycle pattern. For all business cycles after1951, T RM is higher at the trough than at the preceding or following peak.*2

Kessel (1965) documents that yields on long-term Treasury bonds rise less during businessexpansions and fall less during contractions than yields on short-term bills. Thus spreads oflong-term over short-term Treasury yields have a clear countercyclical pattern. Figs. 2 and 3 showthat the cyclical behavior of interest rates documented by Kessel extends to the 1963-1987 periodnot included in his sample.

The business-cycle behavior of the one-month bill rate suggests that the anomalous negativerelations between stock returns r( I, t + T) and the time t bill rate [documented by Fama andSchwert (1977) and others] just reflects countercyclical variation in expected returns like thatcaptured by TER,M. Chen (1989) finds that the bill rate and TERM indeed have similar roles instock-return regressions. He also finds that the negative relations between stock returns and thebill rate are typicall>- weaker than the positive relations between stock returns and TERM.


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