The caPm is Wanted. Dead or Alive TORIo Eugene F Fama: Kenneth R. French The Journal of finance, Vol. 51, No. 5.(Dec, 1996), pp. 1947-1958 Stable url: http://links.jstor.org/sici?sici=0022-1082%028199612%2951903a5%03c1947%03atciwdo%3e2.0.c0%03b2-6 The Journal of finance is currently published by American Finance Association Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://wwwjstor.org/journals/afina.html Each copy of any part of a JSTOR transmission must contain the same copy tice that appears on the screen or printed page of such transmission jStOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor. org http://www」]stor.org Thu mar3005:36:512006
E JJOURNAL OF FINANCE. VOL. LI. NO 5. DECEMBER 1996 The caPm is Wanted Dead or Alive EUGENE F FAMA and Kenneth R. French shanken, and Sloan(1995)claim that &s from annual returns produce positive relation between B and average return than Bs from monthl They also contend that the relation between average return and book-to- market equity(BE/ME)is seriously exaggerated by survivor bias. We argue that urvivor bias does not explain the relation between BE/mE and average return. We also show that annual and monthly Bs produce the same inferences about the B premium. Our main point on the B premium is, however, more basic. It cannot the Capital asset pricing model(CAPM), given the evidence that B alone cannot FAMA AND FRENCH(FF 1992)PRODUCE two negative conclusions about the em- pirical adequacy of the capital asset pricing model(CAPM)of Sharpe(1964) and Lintner(1965): (i)when one allows for variation in CAPM market Bs that is unrelated to size. the ur te relation between B and turn fo 1941-1990 is weak; (ii)B does not suffice to explain average return. Size (market capitalization)captures differences in average stock returns for 1941- 1990 that are missed by B For the post-1962 period where we have book equity data, Be/mE (the ratio of book to market equity) and other variables also help explain average return Kothari, Shanken, and Sloan(KSS 1995) have two main quarrels with these conclusions. First, they claim that using Bs estimated from annual rather than monthly returns produces a stronger positive relation between average return and B. Second, KSS contend that the relation between average return and BE/ME observed by Ff and others is seriously exaggerated by survivor bias in the COMPUStat sample We argue( Section Ii) that survivor bias does not explain the relation be tween BE/mE and average return. We also show(Section III)that annual and monthly Bs produce the same inferences about the presence of a B premium in expected returns. But our main point on the B premium( Section I)is more basic: It cannot save the CaPm, given the evidence that B alone cannot explain expected return I. The Logic of Tests of the CAPM As emphasized by Fama(1976), Roll (1977), and others, the main implication of the CaPM is that in a market equilibrium, the value- weight market port- s Graduate School of Business, University of Chicago(Fama), and Yale School of Management (French). We acknowledge the helpful comments of Josef Lakonishok, Rene Stulz, and a referee 1947
1948 The Journal of finance folio, M, is mean-variance-efficient. The mean-variance-efficiency of M in turn says that: (i) B, the slope in the regression of a securitys return on the market return, is the only risk needed to explain expected return ii) There is positive expected premium for B risk Our main point is that evidence of (ii), a positive relation between B and expected return, is support for the CAPM only if (i)also holds, that is, only if suffices to explain expected return. Confirming Banz(1981), however, and like FF(1992), KSS find that size adds to the explanation of average return provided by B. Moreover, size is no longer the prime embarrassment of the CAPM. Variables that (unlike size)do not seem to be correlated with B(such as earnings/price, cashflow/price, BE/ME, and past sales growth) add even more significantly to the explanation of average return provided by B(Basu (1983), Chan, Hamao, and Lakonishok (1991), FF(1992, 1993, 1996), and Lakonishok, Shleifer, and Vishny(1994)). A The average-return anomalies of the CAPM suggest that, if asset pricing is tional, a multifactor version of Mertons(1973) intertemporal CAPm (ICAPM)or Ross'(1976)arbitrage pricing theory(APT) can provide a better description of average returns. The excess market return of the CAPM is a relevant risk in many multifactor alternatives, like the ICAPM and Connor's (1984)equilibrium version of the APT. Thus, evidence of a positive relation between B and expected return does not favor the CAPm over these alterna The three-factor model in Fama and French(1993, 1994, 1995, 1996)illus- trates our point. The model provides a better description of average returns than the CaPM, and it captures most of the average-return anomalies missed by the CAPM. Because of its strong theoretical standing, the excess market return is one of the three risk-factors in the model, and our tests confirm that it is important. It captures strong common times-series variation in returns, and the market premium is needed to explain the large differences between the average returns on stocks and bills. Moreover, as in the CaPm, the market premium in our multifactor model is just the average return on M in excess of the risk-free rate. Tests on long sample periods say that this premium reliably positive In short, our tests of the CAPm against a multifactor alter native illustrate that a positive p premium does not in itself resuscitate the CAPM, or justify using it in applications KSS are not misled on this basic point. But their focus on the univariate p premium may confuse some of their readers. Indeed, because the CAPM is such a simple and attractive tool, we think that many of our colleagues want to be confused on this point. Otherwise, we cant explain the strong interest in the KSS p tests, given that, like many others(including Amihud, Christensen, and Mendelson(1992)and Jagannathan and Wang( 1996), KSS consistently find that B does not suffice to explain expected return
The capm is Wanted, Dead or Alive 1949 I. Survivor bias and bEme KSS argue that survivor bias in COMPUSTAT data is important in the strong positive relation between average return and book-to-market-equity(BE/me) observed by FF(1992)and others. COMPuStat is more likely to add dis tressed (high-BE/ME) firms that ultimately survive and to miss distressed firms that die. The survivors are likely to have unexpectedly high returns in the turnaround years immediately preceding their inclusion on COMPUStat. Since comPustat typically includes some historical data when it adds firms there can be positive survivor bias in the returns of high-BE/ME firms or COMPUSTAT There are counter arguments. In the most detailed study of the issue, Chan, Jegadeesh, and Lakonishok(1995)conclude that survivor bias cannot explain the strong relations between average return and be/me observed by lakon- ishok, Shleifer, and Vishny(1994)and FF(1992)in tests on the post-1968 and post-1976 periods After 1968, and certainly after 1976, almost all the traded securities on Center for Research in Security Prices(CRSP) that are not on COMPUSTAT are missing for reasons that have nothing to do with survivor bias. Many of the missing firms are closed-end investment companies, REIts ADRs, primes, and scores that produce no accounting information or produce information that is not comparable to that of other firms. Many financial companies are also missing because, judging that their accounting data are different from that of other firms, COMPUSTAT limited its coverage of finan ials for many years. These omissions, which are the result of COMPUSTAT's ex ante policy decisions, are not a source of survivor bias. Finally, some of the securities that seem to be on CrsP but not COMPUSTat in fact appear on both. but with different identifiers There is other evidence that survivor bias cannot explain the relation be tween average return and BE/ME. Lakonishok, Shleifer, and Vishny(1994) find a strong positive relation between average return and BE/ME for the largest 20 percent of NYSE-AMEX stocks on COMPUSTAT, where survivor bias is not an issue. FF(1993) find that the relation between BE/ME and average return is strong for value-weight portfolios of COMPUSTAT stocks formed on BE/E. Since value-weight portfolios give most weight to larger stocks, any survivor bias in these portfolios is probably trivial. In three differ- ent sets of comparisons Table Vil), kss themselves find that the relation between average return and be/me is strong and strikingly similar for value- weight and equal-weight portfolios of COMPUSTAT stocks formed on BE/ME. KSS concede that survivor bias cannot explain the results for value-weight portfolios To support their survivor-bias story, KSS make much of the fact that stocks on CrsP but not COMPUSTAT have lower average returns than stocks on COMPUSTAT. When they risk-adjust returns using a three-factor model like that in FF(1993), however, only the smallest two size deciles of the NYSE AMEX stocks missing from CoMPUSTaT have strong negative abnormal
1950 The ournal of finance returns(Table IV). This suggests that survivor bias is limited to tiny stocks the average market cap of the stocks in the second decile is $13 million, while the average for the first decile is between $3 million and $7 million. The remaining 80 percent of the stocks missing on COMPUSTAT, which account for almost all the combined value of the missing stocks, have three-factor abnormal returns that are close to zero and random in sign. In other words these missing stocks behave like stocks that are on COMPUSTAT. Similarly, Chan, Jegadeesh, and Lakonishok(1995)fill in missing COMPUSTAT book equity(be)data for the largest 20 percent of the NYSE-AMEX firms on CRSP. The survivor-bias story says that the relation between BE/ME and average return should be weak for the firms missing on COMPUSTAT. They find that it is as strong for the missing firms as for the included firms KSS also speculate that the positive relation between book-to-market-equity and average return is the result of data dredging and so is special to the post-1962 COMPUSTAT period Using a hand-collected sample of large firms that is not subject to survivor bias, however, Davis(1994)finds a strong relation between BE/ME and average return in the 1941-1962 period In the end, the KSS survivor-bias story rests on their evidence that there is little relation between average return and BE/E for the rather limited industry portfolios in the S&P Analyst s Handbook. Their results for the S&P industries are strange since FF(1994)document a strong positive relation between average return and BE/ME for value-weight industry portfolios that include all NYSE, AMEX, and Nasdaq stocks on CRSP. (We use COMPUSTaT firms only to estimate industry BE/ME) ksS do not say that the relation between average return and BE/e is entirely the result of survivor bias. They push so hard on the survivor-bias story, however, that serious readers are led to strong conclusions. For example, in the lead article to volume 38 of the Journal of Financial Economics MacKinlay(1995, p 5)concludes, " Their analysis suggests that deviations from the CAPM such as those documented by Fama and French(1993)can be explained by sample selection biases III. Minor points KSS claim that using Bs estimated from annual rather than monthly returns explains why they measure somewhat stronger relations between B and aver age return than FF(1992). They also claim that although the explanatory power of size is statistically reliable, for practical purposes, size adds little to the explanation of average return provided by B. The tests that follow explore A. Portfolios Formed on B Table I summarizes returns for 1928-1993 on B deciles of NYSE stocks. Like KSS, we weight the stocks equally. We form the portfolios in June of each year
The CAPM is Wanted, Dead or Alive 1951 Table i Summary Statistics and Cross-Section Regressions for Postformation Equal-Weight Returns on NYSE B Deciles: 1928-1998 Starting in 1927, ten portfolios of NYSE stocks on CRSP are formed in June of each year based or VW-SPs, the sum of the slopes from regressions of monthly returns on the current and one lag of the value-weight NYSE market return. The formation period Bs use 24 to 60 months of past return (as available), except for 1927, where 18 months are used. Equal-weight monthly postformation returns on the B deciles are calculated from July to June of the following year, yielding time-series of postformation returns for July 1927 to December 1993. The equal-weight monthly decile returns are compounded to get annual returns. The Bs shown in Panel A are estimated using all postfor mation monthly(VW, vw-S, Ew, Ew-S)or annual (VwA, EWA)returns for 1928-1993 and the value-weight (VW, VW-S, VWA)or equal-weight (EW, EW-s, EWA) NYSE market portfolio. Vw-s and EW-s Bs are the sums of the slopes from the regressions of the monthly postformation decile turns on the current and one lag of the market return. vW, VWA, EW, and EWA Bs use only the ize)is the av the average monthly value of the natural log of size(price times shares)of the stocks in a b decile Panel B shows the ge slopes(Means)and the t-statistics for the average slopes from univariate cross-section regressions of postformation monthly or annual returns on the ten B portfolio on each of the six different estimates of their postformation Bs Panel A: Summary Statistics wβ2 Highβ Monthly Postformation Returns: 792 Months Mean1.101.161.231341.391.321.331.441,451.39 5.125.766.306.997.66 11.10 Mean14911553164317,73179817.0317.1918.4418,4417.40 std2569263928.252985295230.763204359636.0340.55 Postformation B Estima 1.161271.321.351.521 1.141.241361.411.441.631.701.87 1.061.131.231331.331.371.431.5 0.780.820.890.960.95.991.02 1,16 70 12,76127 123612.16120311.73113611,00 Panel B: Cross-Section Regressions, R=a+ bB+e Monthly Dependent Returns, R Annual Dependent Returns, R VW VW-S VWA EW EW-S EWA VW VW-S VWA EW EW-S EWA a0.860.850.630.900.90 1294128910.8513.713.3211.24 b0.360.340.500410.42 t-Statistics for Means tatistics for Means a4.784.531.945.575282.143.813.722274.13404245 b1.311.291.291.291.271.251.031.001.011.010.98098
1952 The Journal of finance using Bs on the NYse value-weight market portfolio estimated with two to five years of past monthly returns(as available). Panel a of the table shows that average monthly and annual postformation returns initially increase with post-formation Bs, but the relation between average return and B is rather flat from the fourth to the tenth B decile. This pattern in average returns on B portfolios is similar to KSS Table I. The spread in average returns for their B portfolios is larger than ours, but including AMEX stocks also makes their B sort more like a sort on size than ours Panel A of Table I confirms KSS' evidence that Bs estimated from monthly and annual returns are different. For the purposes of inferences about the average slopes from cross-section Fama-MacBeth(FM 1973) regressions of return on B, however, the important fact is that postformation Bs estimated on annual or monthly returns, and using either an equal-weight or value-weight NYSE market, are near perfect linear transforms of one another. rounded to two decimals, the correlations between the different Bs range from 0.98 to 1.00 different Bs produce different average slopes. In particular, the average slon e, Panel B of Table I shows that in univariate FM regressions of return on for the regressions that use annual Bs to explain returns are about 50 percent larger than the averages for the regressions that use monthly Bs. Why? The spread in the monthly Bs is about 50 percent larger than the spread in the annual Bs. Since the regressions are asked to explain the same dependent returns, and since the different Bs are almost perfectly correlated, the smaller spreads in the annual Bs lead to larger average slopes. However, although the average slopes in the annual-B regressions are larger, the near-perfect corre- lation among the Bs leads to t-statistics for the average slopes that are nearly identical(Jegadeesh(1992)reports similar results. See also Chopra, Lako- nishok, and Ritter(1992), and Chan and Lakonishok(1993)) In their cross. SS explain h Bs fro regressions of annual returns on an equal-weight market return. One can argue that this combination is far from the spirit of the CAPM. In light of the recent articles of Roll and Ross(1994)and Kandel and Stambaugh(1995) however, we doubt that there is much future in debates about which approach produces bigger B premiums in cross-section regressions Kandel and Stam baugh(1995)show that if the market proxy is not exactly mean-variance- efficient with respect to parameters computed from the sample data, it is possible to form portfolios that produce essentially any univariate B premium in ordinary-least-squares cross-section regressions. This conclusion about B premiums also applies to cross-section regressions that use B and other vari- ables to explain average return. Moreover, generalized-least-squares(GLS) regressions, like those in Amihud, Christensen, and Mendelson(1992), are no cure. Roll and Ross(1994)note that a positive B premium in univariate GLS cross-section regressions simply says that the market proxy has a higher expected return than the global-minimum-variance portfolio
The CAPM is Wanted. Dead or Alive 1953 B. Portfolios Formed on Size and B Kandel and Stambaugh(1995) and roll and ross (1994)teach us to be wary of inferences about B premiums from FM cross-section regressions Cross-section regressions can, however, be useful in judging whether B suffices to explain expected return. Like KSS, we address this issue by testing whether size adds to the explanation of average return provided by B Summary statistics and FM cross-section regressions for 100 portfolios formed yearly first on size (deciles)and then on B are in Tables II and Ill The KSS cross-section regressions(their Table II)consistently show that, on a statistical basis, size improves on Bs explanation of average return. This evidence is inconsistent with the CaPm, but kss argue that the errors of Bs predictions of average return are not large. The message from our Tables Il and Ill, however, is that size does make a large incremental contribution to the explanation of average return Table II shows that the size sort produces a strong spread in both post formation B and average return. The average return for 1928-1993 on the smallest decile of NYSE stocks exceeds that for the largest decile by 1.31 percent per month; the spread in Bs is a healthy 0.93. Table II also shows that the second pass sort on preformation Bs produces large spreads in postformal- tion Bs that are independent of size. As in FF(1992), however, the B sorts do not produce much spread in average return It seems safe to predict that a single average premium for B cannot capture both the strong positive relation between B and average return produced by the size sort in Table ii and the weak relation between B and average return in the B sorts. Table Iii confirms this prediction. Like KSS, our univariate regres- sions of return on B produce positive average premiums that are more than 2.0 standard errors from 0.0. But the univariate B regressions leave an unex plained size effect. The spread in the average residuals from the smallest to the largest size decile is 0. 66 percent in the regressions for monthly returns and 7.02 percent in annual returns. There is an even more systematic pattern in the average residuals for the B sorts, which are large and positive for low-B portfolios and strongly negative for high-B portfolios. The spread in the aver- age residuals from the lowest to the highest B deciles of NYSE stocks is 0.56 percent in the regressions for monthly returns and 7. 25 percent in annual returns In short, for portfolios formed on size and B, the average B premiums from univariate regressions of return on B underestimate the positive relation between B and average return produced by the size sort and overestimate the relation between B and average return produced by the B sort. For the extreme size and B deciles, these CAPM pricing errors are large. These results suggest that B alone cannot explain average return. As in KSS, the bivariate regres- sions of return on B and size in Table III confirm that size always adds substantially to B,s description of average stock returns
1954 The Journal of finance Summary Statistics for 100 Equal-Weight NYSE Portfolios Formed on Size and Then B: 1928-1993, N= 792 Starting in 1927, ten portfolios of the NYSe stocks on CRSP are formed in June of each year based on ze(market capitalization, price times shares outstanding). Each size decile is then subdivided into B deciles using Bs for individual stocks that are the sum of the slopes from regressions of monthly returns n the current and one lag of the value-weight NYSE market return. The formation period Bs use 24 to 60 months of past returns(as available), except for 1927, where 18 months of returns are used Equal-weight monthly returns on the 100 portfolios are calculated from July to June of the following year, yielding time-series of returns for July 1927 to December 1993. The VW-SBs are the sums of the slopes from regressions of monthly postformation returns for the February 1928 to December 1993 period on the current and one lag of the weight NYSE market return. Average Ln(Size) is the in each portfolio. The Ave column of each block is the average across B deciles of the parameter values for a size decile. The Ave row of each block is the average across size deciles of the parameter values for a B decile gh B Ay Panel A: Average Monthly Postformation Returns 15230 211111 1481.53 1 1391.1 061.1 1111121.081151111.211.210.79125 1071.121.17122 0.87 1401.381.331,291331,22 Panel B: Postformation VW-S Bs 1111000 451431.711.5 1,52 1.68 1291331.21 0.81 11111.1 Panel C: Average Ln(Size) 82 8.54855842 1033103410.3410.3410.34103510 10.31103210.34 107410.75107410.7310.72107310.74 812.0812.0812 9127112.7312731271127412. 2.7 4141431142714.24141014.0713.7614.14 Ave11.07110811.0711.0711.0811.08110711.04110410.99
The CAPM is wanted Dead or Alive V. Conclusions Confirming Banz(1981), sorts on size and B like those in KSS or our Tables Il and III consistently reject the central CAPM hyg,the pothesis that B suffices to plain expected return. Moreover, in recent year size effect has been displaced as the prime embarrassment of the CAPM. There is much evidence Cross-Section Regressions for 100 Equal-Weight Size-B Portfolios 1928-1993, R=a+ bB+sLn(Size)+e In June of each year beginning in 1927, NYSE stocks on CRSP are sorted into size deciles, which are then subdivided into B deciles(see Table II). Equal-weight monthly returns on the 100 ortfolios are calculated from July to June of the following year. Annual returns are obtained by mounding the equal-weight monthly returns. Panel a shows the average slopes(Means)and heir t-statistics from univariate cross-section regressions of monthly and annual postformal mple returns on the 100 size-B portfolios on six estimates of their 1928-1993 postformation Bs nd biva ate regressions of the 100 portfolio returns on their of the average size of the stocks in each of the 100 portfolios at the end of the previ ous month or year. The Bs are estimated using all postformation monthly (vw, vw-s, EW, Ew-S)or annual WA, EWA)returns for 1928-1993 and the value-weight(vw, vw-s, vWA)or equal-weight (Ew EW-S, EWA) NYSE market portfolio. VW-S and EW-s Bs are the sums of the slopes from the regressions of the monthly postformation size- B portfolio returns on the current and one lag of the market return. VW, VWA, EW, and EWa Bs use only the contemporaneous market returns. The verage slopes in the cross-section regressions of returns on Ln(Size)alone(not shown)are-0 19 (t=-3.60) for monthly returns and-2.67(t =-323)for annual returns. Panel B shows the average residuals from the univariate regressions of monthly (annual)returns on the vw-s(vwa Bs. The Ave column of each block in part B is the average across B deciles of the average residuals for a size decile. The Ave row of each block is the average across size deciles of the average residuals for a B decile Panel A: Regression Coefficients Annual Dependent Returns: 66 Years VW VW-S VWA EW EW-S VWA VW VW-S VWA EW EW-S EWA 0.500.360.17 7.26 5.615.333.47 b0.650.700.84 083 11.56118413.73 6215122682238342315216226238 43.46372743.41409729.30 292.710.371.486.29 0.18 01 0.16-0.17-0.15-0.13 2.75-2.65-2.28-2.64-248-1.69 Statistics for Means t-Statistics for means 5.665.404.98 4.584.824.504,434,3 b0.400.62 831.46 0.110.790.110.431,43 -4.16-4.1 4.02-3.78-3.47 -3.67-3.88-3.61-3.56-363
