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Unformatted text preview: SUMMER 1993 Are the Reports of Beta’s Death Premature? Let’s think twice before rushing to discard beta. Louis K.C. Chan andjosef Lakonishok LOUIS K.C. CHAN is assistant professor of finance. andJOSEF LAKONISHOK is the Karnes professor of finance, at the Univer— sity of Illinois at Urbana-Cham— paig'n (IL 61820). any would name the concept of beta risk as the single most important contri— bution of academic researchers to the financial community. At first slow to accept beta, practitioners have come to use it widely as a risk measure and for computing expected returns In European capital markets, the concept of beta is n0w beginning to gain popularity. Yet, just as beta seems to be on the verge of widespread use, an article by Fama and French [1992a] has caused both academics and practitioners to re—catanuuc the empirical support for beta’s importance In retrospect. some earlier studies of beta (Fama and MacBeth [1973]; Black, jeuserr, and Scholes [1972]) do not provide conclusive evidence in suppor: of beta. Later studies dating from the 19803 (such as Reinganum [1982]; Lakonishok and Shapiro [1986]; and Ritter and Chopra [1989]) are not able to detect any significant relation between beta and average returns The negative findings of these later studies. however, have been largely ignored. The recent study of Fama and French [1992a], which echoes the results of some of these papers from the 19803, has been interpreted as the final nail in the coffin. Do we really have sufficient evidence to bury beta? The question assumes added urgency when we consider how dramatically the practice of portfolio management has changed in the last five years. 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[LL61] H0“ 'S'BJDq 03 133115191 Sq IOU 11131111 311111191 Aqm moses: sn0:sumu ‘ssmos 10 ‘s112 szsql 'po11sd 91111110 ss10qs sq: 0: 31111591 sq: 30 2111111115113 3T1] IDPTSUOD 091'? 311A ‘suxnm: JO AJOJSFLI 9111113 91.13 31111111111119 Ag ’ss1p111s $1101As1d 111 pssn ss1qe111zA Isq10 111113 sum:s1 ussm19q 1101113191 sq: SB 11sm se ~511111191 DUB SPRQq IIDQMJQq [101219131 Oql 11’1qu 5938919}U1 111113 111211) 0: 11113111111 :1 9111111 1311311 s1qe111A1 sq: 10 $1101: —e:111111 sq: moq 110 ssuspms :ss11p sp1A01d 9/10. ‘sum1s: 113015 ssA11p :Eqm sms 1011 s11 sm :Bq: 11111118 01 mm A1d11115 A1111 sm pm: ‘ps:esqd1u00 s10111 qsnu: sq A2111 pes1su1 $3u1q J; '11qu )0 ssmauoduq 91.1] 111qu 5111311101113 3110119 $111.1.usd su:n:sz 510015 8u11'e1sus8 111s11111011A11s 3111811qu 11111115151103 put 1151011 A1sA sq: 1sq:sqm su11111axs sm 0131111: s1q1 111 'AIOAFJFUIJQP 59110911: 1110 15s: 01 111111111 1110 spnop qs1qm “1151011,, 10 ssusngu1 sA1seAlsd sq: 0: 1115 511 ps11s1'e SEq [9861] )1381g 19113515 111111131 310mg 110 1131129831 1120111d1us 11101} 51101511131103 sA111ugsp A111 mexp 0: s1 11 11113q11p A1sA Axoq 11111111 111 Icsq ‘pes15111 ‘p1110qs 9/10. 0111912911: 51511 11111101311111 111: SE 9819119 11181111 1a:sq 11qu p113 ‘pssds 311111123 51 1101:12211u11d0 011031.10d 13111110: sA0111 sq: 11qu 15111 B:sq 131133511: 01 s1sm s11 ‘110ddns 153111de 111105 111011111111 5.113911 $111111“: ICU 210:1 :dssse 0: 81111111111103 1s1}12 ‘31 3111011 111113111 sq 131110111 :1 'e:sq puB 511111391 U99Ml9q 110118191 1911.131] E 01 K113113111 3111131231 ‘11511 3111:1us1sAs szqums 0: sum: 111m 51015911111 s101u naq: sq A8111 smosmo suO "5011031101: 11110} 01 513551: 10 spuesnoq: I9AO sz11111:d0 01 1191210191911 3111901 51 1130 -10uqss: sq: pm: ‘3111111013 1111s 31 pus11 s1q_L 30110311011 :us1s111s pug 0: ssnb1uq39: 1.1011821111111210 ssn 0: Sum for returns. Rather, our point is that. given the limita- tions of the data. it is still an open question whether beta is dead or alive as a determinant of expected returns. NOISY STOCK RETURNS Twenty years is a long time in financial markets. Needless to say, the horizon of the money manage— ment business is very much shorter than twenty years. There are only a handful of countries where it is possi— ble to obtain comprehensive data going back twenty years. Most of the international data bases available to money managers extend back no farther than ten years. Widely used commercial data bases. for example, carry accounting information on SWiss companies from 1986 onward only. Even the data that are avail— able are plagued with problems. as they focus only on surviving companies. It is thus fair to say that many would feel that having a complete monthly history of twenty years of data on thousands of stocks should be more than adequate to answer the simple question whether there is a significant relation between beta and returns. Yet is twenty years really enough? One popular procedure to test for the existence of a relation between betas and returns comes from Fama and MacBeth [1973]. Monthly cross—sectional regressions are run relating stock returns to betas. The slope coefficient from each regression is our estimate of the compensation per unit of beta in that particular month. The average of the monthly slopes is thus the estimate of the compensation per unit of beta risk received by investors on average. We can then use the standard deviation of the monthly series on the slope coefficients to examine whether the average slope is statistically significantly different fiom zero. Suppose that each month for the last twenty years in the US. we follow the standard methodology and run monthly cross—sectional regressions relating returns to betas. Suppose. moreover, that every month we obtain a slope coefficient exactly equal to rm — If, the return on the market minus the risk—free rate. This accords perfectly with the Sharpe—Lintner CAPM. Indeed. we cannot obtain a more favorable result than this for the model. Yet would our regressions reveal that beta plays a Significant role in explaining stock returns? From our regressions, we would obtain an annualized average SUMMER 1993 slope coefficient of 5.05%, and an annualized standard deviation ofthe slope coeffiCient of 16.58%. The stan~ dard procedure is to test whether the average slope COCETCICI’IE is significantly different from zero. The t— statistic for tesring for the significance of the premium for beta risk is 1.36. significant at a level of about 9%. This significance level is not enough to reject the null hypothesis that the premium is zero, given our typical insistence on a 5% significance level. Given the level of noise in the lasr twenty years of stock returns, we would need a risk premium of about 7.4% per year before we could reliably reject the null hypothesis. What if the compensation per unit of risk were lower, 4% per year, consistent with the Black [1972] model but still a non negligible number? How many years then would we need before we could declare the premium statistically significant? We would have to report back to you in sixtyinine years. Because we assume in this exercise that the premium for beta risk is indeed equal to rm — rf, what we are doing is the same as testing for the existence of an equity risk premium (i.e.. whether stocks do better than T—bills). We thus infer that the annual difference of5.05% per year does not suffice to reject reliably the null that stocks do not outperform T—bills. A dollar invested in T—bills at the beginning of the twenty—year period in question would have grown to $4.41, while an equivalent investment in stocks would have yielded $9.211 Yet this huge difference is still not statistically significant at the §% level. Noise poses a problem in cases beyond testing whether high—beta stocks outperform low—beta stocks. Strategies based on B/M (the book—EO—market ratio) have recently gained popularity (Chan, Hamao. and Lakonishok [1991], Fama and French [1992a]). Following this rack. for each year fiom 1968 to 1990. we form ten portfolios from the universe of NYSE and AMEX stocks. ranked by B/M. we compare the returns of the two extreme portfolios: the portfolio comprising those stocks with the highest B/M ratio, and the portfolio made up of those stocks with the lowest B/M portfolio, The standard error of the difference is 3.6%. implying that unless the high B/M portfolio outper— forms the low B/M portfolio by at least 7.2% a year. the difference will not be significant. Luckily for the partisans of B/M, the difference over the sample peri— od is 8.7%, passing the test of significance. Strategies developed in hindsight do not ensure THE _lOURNA_L OF PORTFOLIO MANAGEMENT 53 successful future performance for a money manager, however. How confident can one be that high B/M stocks will continue to outperform low B/M stocks at such a pace? On the one hand, the publicity that we have collecrively given to B/ M may make'high B/M stocks less attractive in the future. On the other hand, if B/M is simply proxying for risk, then we might expect simi- lar returns in the future for high B/M SEOCkS. Many of us, however, have serious doubts whether the extraor— dinary performance of high B/M stocks can be explained by their riskiness (see Lakonishok, Shleifer, and Vishny [1992a]). Another popular trading strategy is based on market capitalization. We compare the returns over the period 1979—1991 on the Russell 2000 index to the returns on the S&P 500. The standard error for the difference in returns is 3.63% per year. Llnless the return on small stocks is at least twice this much (7.26%) over the return on the S&P 500, we cannot judge the difference to be significant. As it turns out, the mean returns over the lasr thirteen years differ by 0.28% per year. This difference does not amount to much — should we conclude that the size effect is dead? In a different context. take a money manager who outperforms a benchmark by 2% a year, repre- senting an extraordinary feat. Assume that tracking error is 5% a year, which is below the median for active money managers (based on the SE1 universe of equity managers). we would still need to accumulate twenty—five years of data on returns earned by this manager before we can reject the null hypothesis that performance of this magnitude is no better than the benchmark. This example highlights how dangerous our assumption of stability can be. Are we getting twenty years later the same money manager as the one responsible for the extraordinary early performance? These examples illustrate how difficult it is to make unambiguous inferences from the very noisy and ever—changing environment generating stock returns. While our research is often posed as clear—cut black— and—white statements, we often do not have the luxury of drawing such unqualified conclusions fiom the data at hand. If a hypothesis is based on a sound theory (some might say “story”) and is relatively free of data— snooping biases, it may not be the most productive way to proceed if we insist unthinkingly on a signifi— 54 ARE THE REPORTS OF BETA'S DEATH PREMATURE cance level of 5% before we can reject the null hypothesis. TESTS OF THE CAPM W'c use all the available data on the monthly Center for Research on Security Prices (CRSP) tape from 1926 to 1991 to examine the relation between beta and returns, following the Fama~MacBeth proce— dure. The first three years of monthly observations are used in a market model regression to estimate each stock’s beta relative to the CRSP value—weighted market index. Our universe is restricted to NYSE and AMEX stocks. The stocks are then ranked on the basis of the estimated betas and assigned to one of ten portfolios. Portfolio 1 contains steels with the lowest betas, while Portfolio 10 contains stocks With the highest betas. The assignment of stocks to portfolios in part refleCts measurement errors in the betas Such errors would result in a “regression to the mean.” To avoid such bias. an intermediate step 18 necessary: the beta of each stock in a portfolio is re— estimated using the next three years of returns; a port~ folio’s beta is then a simple average of the betas of the individual stocks assigned to that portfolio. Thus the first three—year period is used to classify stoela to port— folios. and the next three—year period is used to esti- mate betas for the portfolios. In each month of the subsequent year, we regress the returns on the ten portfolios on their esti— mated betas. Nore that this is a predictive test in the sense that the explanatory variable (beta) is estimated over a period disjoint from the period over which returns are measured. At the end of the year, we repeat the process of forming portfolios from three years of data, estimating betas over three years, and adding twelve more cross—sectional regressions. Ultimately we obtain 720 cross—sectional regressions. Exhibit 1 provides summary statistics on the betas for the ten portfolios and their average returns. There is a positive relation between betas and average returns: a finding consistent with a recent paper by Black [1992]. Exhibit 2 provides results from the monthly cross—sectional regressions. The mean estimated slope coefficient is 0.47% per month. with a marginally significant t—statistic of 1.84.2 Given our standard errors, it is as likely that the compensation per unit Of SUMMER 1993 l l EXHIBIT 1 Mean. Standard Deviation (in Percent), and Beta ofRetums on Portfolios Formed on Beta january 1932-December 1991 (Low) (High) 1 2 3 4 6 7 8 9 10 Mean 1.30 1.33 1.32 1.46 1.56 1.59 1.52 1.65 1.54 1.60 Standard Deviation 5.51 6.07 6.55 7.36 7.50 7.87 8.58 9.12 9.08 10.37 Beta 0.90 1.03 1.12 1.25 1.26 1.32 1,44 1.49 1.51 1.70 beta is 0% per year as it is 12% per year. The realized market premium (rm — rf) over this period averages 0.76% per month Thus our estimated premium is 62% of the market excess return, in line with the results of earlier work. The Sharpe—Unmet CAPM implies that the risk premium is equal to the mean of (rm — If) — the absolute difference between the average slope and the average market excess return is only 29 basis points, so we cannot reject the null hypothesis that the mean slope coefficient is equal to the average market excess return (the t—statistic is —1.15). In contrast, over the period 1963—1990. Fama and French [1992a] obtain a much lower point esti— mate for the slope coefficient (0.15% per month), with a t—statistic of 0.46. The case against beta is thus much stronger in Fama and French’s sample period. Upon reflection. however. their finding may not be as striking as it first seems. In order for them to undoubtedly on the high side relative to the experi» ence of the last thirty years, or relative to any projec— tion of future returns. 30 the failure to find a statistically significant role for beta should not come as a total surprise. Exhibit 3 plots the average cumulative monthly difference between the estimated premium for beta risk and rm - rf, the value predicted by the Sharpe— Lintner CAPM. We start cumulating the difference from January 1932, although the exhibit focuses on the post—1942 experience. It is clear from the figure that the relation between betas and returns varies considerably over time. If we were to stop our test in 1982, we would conclude that there is a lot (if support For the CAPM. Up until 1982. the estimated compensation for beta EXHIBIT 3 obtain a t—statistic of 2, the compensation per unit of CUMULATIVE AVERAGE DIFFERENCE BETWEEN beta risk would have to be 7.83% per year — EXHIBIT 2 Monthly Fama—MacBeth Cross—Sectional Regressions T‘Test for Slope = Sample Period Intercept Slope R2 rm -— If Jan 1932 — Dec. 1991 0.0059 0.0047 0.48 —1.15 (rm — r5: 0.0076) (3.50) (1.84) Jan. 1932 — Dec. 1961 0.0075 0.0074 0.48 —1.01 (rm — q: 0.0115) (2.80) (1.82) Jan. 1962 - Dec. 1991 0.0042 0.0020 0.47 40.57 (rm — rf = 0.0038) (2.10) (0.64) SUMMER 1993 ESTIMATED SLOPE AND EXCESS MARKET RETURN —JANUARY 1942—DECEMBER 1991 0.0080 0.0060 " 0.0010 — 0 0070 ‘ 0.0000 -.0070 " 'DO‘D ‘ ) . . i . i . . , I i . . . . . . 1512 1947 15S2 I957 1952 1967 1972 1577 1982 “387 THE jOURNAL OF PORTFOLIO MANAGEMENT 55 EXHIBIT 4 FIVE-YEAR MOVING AVERAGES OF ESTLMATED SLOPE AND EXCESS MARKET RETURN jANUARY 1937-DECEMBER 1991 0.030 0.020 0.000 ‘UID' e°’-'C‘ Hint. , "1, trfiyiuwit irm,mimmunrrttumyt' 1337 1942 1947 [552 1557 1552 1557 1572 1977 1532 1937 1I1AIt risk is strik...
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