Good beta, bad beta

American Economic Association Bad Beta, Good Beta Author(s): John Y. Campbell and Tuomo Vuolteenaho Reviewed work(s): Source: The American Economic Review, Vol. 94, No. 5 (Dec., 2004), pp. 1249-1275 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/3592822 . Accessed: 04/12/2011 09:41 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org Bad Beta, Good Beta By JOHN Y. CAMPBELL AND TUOMO VUOLTEENAHO* This paper explains the size and value "anomalies" in stock returns using an economically motivated two-beta model. We break the beta of a stock with the market portfolio into two components, one reflecting news about the market's future cash flows and one reflecting news about the market's discount rates. Intertemporal asset pricing theory suggests that the former should have a higher price of risk; thus beta, like cholesterol, comes in "bad" and "good" varieties. Empirically, we find that value stocks and small stocks have considerably higher cash-flow betas than growth stocks and large stocks, and this can explain their higher average returns. The poor performance of the capital asset pricing model (CAPM) since 1963 is explained by the fact that growth stocks and high-past-beta stocks have predomi- nantly good betas with low risk prices. (JEL G12, G14, N22) How should a rational investor measure the risks of stock market investments? What deter- mines the risk premium that will induce a ra- tional investor to hold an individual stock at its market weight, rather than overweighting or underweighting it? According to the CAPM of William Sharpe (1964) and John Lintner (1965), a stock's risk is summarized by its beta with the market portfolio of all invested wealth. Controlling for beta, no other characteristics of a stock should influence the return required by a rational investor. It is well known that the CAPM fails to describe average realized stock returns since the early 1960s, if a value-weighted equity index is used as a proxy for the market portfolio. In * Campbell: Department of Economics, Littauer Center, Harvard University, Cambridge, MA 02138, and National Bureau of Economic Research (e-mail: john_campbell@ harvard.edu); Vuolteenaho: Department of Economics, Lit- tauer Center, Harvard University, Cambridge, MA 02138, and NBER (e-mail: t_vuolteenaho@harvard.edu). We would like to thank Ben Bernanke, Michael Brennan, Jo- seph Chen, Randy Cohen, Robert Hodrick, Matti Keloharju, Owen Lamont, Greg Mankiw, Lubos Pastor, Antti Petajisto, Christopher Polk, Jay Shanken, Andrei Shleifer, Jeremy Stein, Sam Thompson, Luis Viceira, two anonymous refer- ees, and seminar participants at various venues for helpful comments. We are grateful to Ken French for providing us with some of the data used in this study. All errors and omissions remain our responsibility. This material is based upon work supported by the National Science Foundation under Grant No. 0214061 to Campbell. particular, small stocks and value stocks have delivered higher average returns than their betas can justify. Adding insult to injury, stocks with high past betas have had average returns no higher than stocks of the same size with low past betas. These findings tempt investors to tilt their stock portfolios systematically toward small stocks, value stocks, and stocks with low past betas.1 We argue that returns on the market portfolio have two components, and that recognizing the difference between these two components can eliminate the incentive to overweight value, small, and low-beta stocks. The value of the market portfolio may fall because investors re- ceive bad news about future cash flows; but it may also fall because investors increase the discount rate or cost of capital that they apply to these cash flows. In the first case, wealth de- creases and investment opportunities are un- changed, while in the second case, wealth decreases but future investment opportunities improve. 1 Seminal early references include Rolf Banz (1981) and Marc Reinganum (1981) for the size effect, and Benjamin Graham and David Dodd (1934), Sanjoy Basu (1977, 1983), Ray Ball (1978), and Barr Rosenberg et al. (1985) for the value effect. Eugene Fama and Kenneth French (1992) give an influential treatment of both effects within an integrated framework and show that sorting stocks on past market betas generates little variation in average returns. 1249 THE AMERICAN ECONOMIC REVIEW These two components should have different significance for a risk-averse, long-term inves- tor who holds the market portfolio. Such an investor may demand a higher premium to hold assets that covary with the market's cash-flow news than to hold assets that covary with news about the market's discount rates, for poor re- turns driven by increases in discount rates are partially compensated by improved prospects for future returns. To measure risk for this in- vestor properly, the single beta of the Sharpe- Lintner CAPM should be broken into two different betas: a cash-flow beta and a discount- rate beta. We expect a rational investor who is holding the market portfolio to demand a greater reward for bearing the former type of risk than the latter. In fact, an intertemporal capital asset pricing model (ICAPM) of the sort proposed by Robert Merton (1973) suggests that the price of risk for the discount-rate beta should equal the variance of the market return, while the price of risk for the cash-flow beta should be y times greater, where y is the inves- tor's coefficient of relative risk aversion. Thus, if the investor is conservative in the sense that y > 1, the cash-flow beta has a higher price of risk. An intuitive way to summarize our story is to say that beta, like cholesterol, has a "bad" va- riety and a "good" variety. Just as a person's heart-attack risk is determined not by his overall cholesterol level but primarily by his bad cho- lesterol level with a secondary influence from good cholesterol, so the risk of a stock for a long-term investor is determined not by the stock's overall beta with the market but by its bad cash-flow beta with a secondary influence from its good discount-rate beta. Of course, the good beta is good not in absolute terms but in relation to the other type of beta. We test these ideas by fitting a two-beta ICAPM to historical monthly returns on stock portfolios sorted by size, book-to-market ratios, and market betas. We consider not only a sam- ple period since 1963 that has been the subject of much recent research, but also an earlier sample period 1929-1963 using the data of James Davis et al. (2000). In the moder period, July 1963 to December 2001, we find that the two-beta model greatly improves the poor per- formance of the standard CAPM. The main reason for this is that growth stocks, with low average returns, have high betas with the market portfolio; but their high betas are predominantly good betas, with low risk prices. Value stocks, with high average returns, have higher bad betas than growth stocks do. The two-beta model also explains why stocks with high past CAPM betas have offered relatively little extra return: these stocks have higher good betas but almost the same bad betas as other stocks. Since the good beta carries only a low premium, the almost flat relation between average returns and the CAPM beta is no puzzle to the two-beta model. In the early period, January 1929 to June 1963, we find that the ratio of good to bad beta is rela- tively constant across the assets we consider, so the single-beta CAPM adequately explains the data. Our model explains why stocks with high cash-flow betas may offer high average returns, given that long-term investors are fully invested in equities at all times, or, in a slight generali- zation of the model, maintain a constant alloca- tion to equities. Our model does not explain why long-term investors would wish to keep their equity allocations constant. If the equity premium is time-varying, it is optimal for a long-term investor with a fixed coefficient of relative risk aversion to invest more in equities at times when the equity premium is high (Campbell and Luis Viceira, 1999; Tong Suk Kim and Edward Omberg, 1996). We could generalize the model to allow a time-varying equity weight in the investor's portfolio, but this would not be consistent with general equilib- rium if all investors have the same preferences. Thus our model cannot be interpreted as a representative-agent general-equilibrium model of the economy. Our achievement is merely to show that the risks of value, small, and low- past-beta stocks are sufficient to deter invest- ment in these stocks by conservative long-term investors who eschew market timing.2 2 There are numerous competing explanations for the size and value effects. The Arbitrage Pricing Theory (APT) of Stephen Ross (1976) allows any pervasive source of common variation to be a priced risk factor. Fama and French (1993) introduce an influential three-factor model to describe the size and value effects in average returns. Ravi Jagannathan and Zhenyu Wang (1996), Martin Lettau and 1250 DECEMBER 2004 CAMPBELL AND VUOLTEENAHO: BAD BETA, GOOD BETA In developing and testing the two-beta ICAPM, we draw on a great deal of related literature. The idea that the market's return can be attributed to cash-flow and discount-rate news is not novel. Campbell and Robert Shiller (1988a) develop a loglinear approximate frame- work in which to study the effects of changing cash-flow and discount-rate forecasts on stock prices. Campbell (1991) uses this framework and a vector autoregressive (VAR) model to decompose market returns into cash-flow news and discount-rate news. Empirically, he finds that discount-rate news is far from negligible; in postwar U.S. data, for example, his VAR sys- tem explains most stock-return volatility as the result of discount-rate news. The insight that long-term investors care about shocks to investment opportunities is due to Merton (1973). Campbell (1993) solves a discrete-time empirical version of Merton's ICAPM, assuming that asset returns are ho- moskedastic and that a representative investor has the recursive preferences proposed by Law- rence Epstein and Stanley Zin (1989, 1991). The solution is exact in the limit of continuous time, if the representative investor has elasticity of intertemporal substitution equal to one, and is otherwise a loglinear approximation. Campbell writes the solution in the form of a K-factor model, where the first factor is the market return Sydney Ludvigson (2001), and Lu Zhang and Ralitsa Pet- kova (2002) argue that the CAPM might hold conditionally, but fail unconditionally, although Jonathan Lewellen and Stefan Nagel (2003) show that the magnitude of the value effect is too large to be explained by the conditional CAPM. Tobias Adrian and Francesco Franzoni (2004) and Lewellen and Jay Shanken (2002) explore learning as a possible explanation of these anomalies. Richard Roll (1977) em- phasizes that tests of the CAPM are misspecified if one cannot measure the market portfolio correctly. While Rob- ert Stambaugh (1982) and Shanken (1987) find that the tests of the CAPM are insensitive to the inclusion of other financial assets, Campbell (1996), Jagannathan and Wang (1996), and Lettau and Ludvigson (2001) find that human- capital wealth may be important. Josef Lakonishok et al. (1994), Rafael La Porta (1996), and La Porta et al. (1997) argue that investors' irrationality drives the value effect. Alon Brav et al. (2002) show that analysts' price targets imply high subjective expected returns on growth stocks, consistent with the hypothesis that the value effect is due to expectational errors. and the other factors are shocks to variables that predict the market return.3 The two recent empirical papers that are clos- est to ours in their focus are by Michael J. Brennan et al. (2004) and Joseph Chen (2003). Brennan et al. model the riskless interest rate and the Sharpe ratio on the market portfolio as continuous-time AR(1) processes. They esti- mate the parameters of their model using bond market data and explore the model's implica- tions for the value and size effects in U.S. equities since 1953, with some success. Chen (2003) extends the framework of Campbell (1993) to allow for heteroskedastic asset re- turns, but given the state variables he includes in his model, he finds little evidence that growth stocks are valuable hedges against shocks to investment opportunities. A key to our success in explaining a number of asset pricing anomalies is our use of the small-stock value spread to predict aggregate stock returns. Recently, several authors have found that high returns to growth stocks, partic- ularly small growth stocks, seem to forecast low returns on the aggregate stock market. Venkat R. Eleswarapu and Reinganum (2004) use lagged three-year returns on an equal-weighted index of growth stocks, while Brennan et al. (2001) use the difference between the log book- to-market ratios of small growth stocks and small value stocks to predict the aggregate mar- ket. In this paper we use a measure similar to that of Brennan et al. (2001) and find that, indeed, growth stock returns have high covari- ances with declines in market discount rates. It is natural to ask why high returns on small growth stocks should predict low returns on the stock market as a whole. This is a particularly important question since time-series regressions of aggregate stock returns on arbitrary predictor variables can easily produce meaningless data- mined results. The most powerful motivation is provided by the ICAPM itself. We know that value stocks outperform growth stocks, partic- ularly among smaller stocks, and that this can- not be explained by the traditional static CAPM. 3 Campbell (1996), Yuming Li (1997), Robert Hodrick et al. (1999), Anthony Lynch (2001), Brennan et al. (2001, 2004), David Ng (2004), Hui Guo (2003), and Chen (2003) explore the empirical implications of Merton's model. VOL. 94 NO. 5 1251 THE AMERICAN ECONOMIC REVIEW If the ICAPM is to explain this anomaly, then small growth stocks must have intertemporal hedging value that offsets their low returns; that is, their returns must be negatively correlated with innovations to investment opportunities. In order to evaluate this hypothesis it is natural to ask whether a long moving average of small- growth-stock returns predicts investment oppor- tunities. This is exactly what we do when we include the small-stock value spread in our fore- casting model for market returns. In short, the small-stock value spread is not an arbitrary fore- casting variable, but one that is suggested by the asset pricing theory we are trying to test. The organization of the paper is as follows. In Section I, we estimate two components of the return on the aggregate stock market, one caused by cash-flow shocks and the other by discount-rate shocks. In Section II, we use these components to estimate cash-flow and discount- rate betas for portfolios sorted on firm charac- teristics and risk loadings. In Section III, we lay out the intertemporal asset pricing theory that justifies different risk premia for bad cash-flow beta and good discount-rate beta. We also show that the returns to small and value stocks can largely be explained by allowing different risk premia for these two different betas. Section IV concludes. I. How Cash-Flow News and Discount-Rate News Move the Market A simple present-value formula points to two reasons why stock prices may change. Either expected cash flows change, discount rates change, or both. In this section, we empirically estimate these two components of unexpected return for a value-weighted stock market index. Consistent with findings of Campbell (1991), the fitted values suggest that over our sample period (January 1929 to December 2001) discount-rate news causes much more varia- tion in monthly stock returns than cash-flow news. A. Return-Decomposition Framework Following Campbell and Shiller (1988a) and Campbell (1991), we use a loglinear approxi- mate decomposition of returns: (1) rt+I - E,r,t+ = (Et+1 - Et) I fAdt+1+j j=o - (Et+ - Et) E Pirt+ l+j = NCF,t+i j=1 NDR,t + 1 where r + is a log stock return, d+ 1 is the log dividend paid by the stock, A denotes a one- period change, Et denotes a rational expectation at time t, and p is a discount coefficient.4 NCF denotes news about future cash flows (i.e., div- idends or consumption), and NR denotes news about future discount rates (i.e., expected re- turns). This equation, which is an accounting identity rather than a behavioral model, says that unexpected stock returns must be associ- ated with changes in expectations of future cash flows or discount rates. An increase in expected future cash flows is associated with a capital gain today, while an increase in discount rates is associated with a capital loss today. The reason is that with a given dividend stream, higher future returns can be generated only by future price appreciation from a lower current price. These return components can also be inter- preted approximately as permanent and transi- tory shocks to wealth. Returns generated by cash-flow news are never reversed subse- quently, whereas returns generated by discount- rate news are offset by lower returns in the future. From this perspective it should not be surprising that conservative long-term investors 4 While Campbell and Shiller (1988a) constrain the dis- count coefficient p to values determined by the average log dividend yield, p has other possible interpretations as well. Campbell (1993, 1996) links p to the average consumption- wealth ratio. In effect, the latter interpretation can be seen as a slightly modified version of the former. Consider a mutual fund that reinvests the dividends paid by the stocks it holds, and a mutual-fund investor who finances her consumption by redeeming a fraction of her mutual-fund shares every year. Effectively, the investor's consumption is now a div- idend paid by the fund, and the investor's wealth (the value of her remaining mutual fund shares) is now the ex-dividend price of the fund. Thus, we can use the loglinear model to describe a portfolio strategy as well as an underlying asset and let the average consumption-wealth ratio generated by the strategy determine the discount coefficient p, provided that the consumption-wealth ratio implied by the strategy does not behave explosively. 1252 DECEMBER 2004 CAMPBELL AND VUOLTEENAHO: BAD BETA, GOOD BETA are more averse to cash-flow risk than to discount-rate risk. To implement this decomposition, we follow Campbell (1991) and estimate the cash-flow- news and discount-rate-news series using a VAR model. This VAR methodology first estimates the terms Etrt+ and (Et+ - Et) lJ=1 prt++ and then uses r,+l and equation (1) to back out the cash-flow news. This prac- t