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Aged and Recent Market Betas in Securities Prices_ Gerard Hoberg University of Maryland firstname.lastname@example.org Ivo Welch Brown University and NBER email@example.com September 9, 2007 ABSTRACT Instead of computing only one five-year market-beta, we compute one ―recent‖ beta from 1 month to 2 years ago, and one ―aged‖ market beta from 2 to 10 years ago, both using daily stock returns. We find that the aged beta has a positive influence on stock returns, consistent with standard hedging concerns. The recent beta has a negative influence on stock returns, whose cause is less clear. The evidence suggests that it is due to a novel factor, possibly behavioral or attention related. Previous research had failed to find that market-beta matters, primarily because ordinary market-betas combine these two opposing forces and because betas based on monthly stock returns are too weak. The importance of the two separate betas increases if we control for the 1 Fama-French factors. The seminal paper by Fama and French (1992b) documented that market-betas of U.S. stocks seem to have no influence on future stock returns in cross-sectional Fama and MacBeth (1973) regressions when book-market and firm-size are controlled for. One does not have to believe in the CAPM to be astonished by this fact. The rate of return on the overall stock market seems to be the first principal component in the equity markets, so stocks that move less with the market should be useful hedges. They should therefore require lower expected rates of returns. This can be viewed as an unconditional statement (that betas should be important by themselves) and as a conditional statement (that betas should be important for investors that have hedged other factors). Not surprisingly, there have been a number of attempts to resurrect market-beta as an important component of the pricing of stocks. Many of these attempts derive some power from the correlation of market-betas with the two Fama-French factors. A loose interpretation is that these papers suggest good reasons why one should apportion to market-beta at least some of the explanatory power that is joint. Prominent examples are Ang and Chen (2005), Avramov and Chordia (2006), and Campbell and Vuolteenaho (2004). The latter decompose beta into a cash flow related beta that has a positive influence, and a discount factor related market beta, that has a negative influence. Their betas, too, have power that is overlapping considerably with that of the other Fama-French factors. Thus, Fama and French (2006) would probably still argue that the ―CAPM’s general problem is that variation in beta unrelated to size and value-growth goes unrewarded throughout 1926–2004,‖ and especially after 1962. Another attempt to ―rescue‖ market beta was proposed by Jagannathan and Wang (1996). They work with conditional market-betas and control for labor income, and find that there are specifications in which market-beta remains 1 _We thank Eric Jacquier and Sophocles Mavroeidis for help with the error-in-variables issues. Jonathan Lewellen, our NBER discussant, also helped us improve our paper considerably. We thank seminar participants at Purdue, Boston College, the University of Toronto, and York University. Ken French graciously made some of the data used in our paper available on his website. Our beta factor portfolios are posted at http://www.rhsmith.umd.edu/faculty/ghoberg/ and http://welch.econ.brown.edu/academics/hoberg-welchbetas. csv. significant. This is critiqued by Lewellen and Nagel (2006), who argue that the potential magnitude of their effect is small. Our own paper adds to this literature, though with little overlap. We hypothesize that a beta computed from recent stock returns could play a different role than a beta computed from earlier stock returns. Our original motivation was behavioral: If investors are slow to recognize and adjust to changes in beta, a reduction in beta could be associated with a short-lived increase in the stock price, and therefore a positive average rate of return. A simple perpetuity model suggests that even a small delay in the full adjustment could have a large opposing impact—holding future cash flows constant, a change from, say, a 5% to a 5.1% expected rate of return can induce a one-time price adjustment of about 2%—twenty 2 times as high as the 0.1% change in the expected return itself. To uncover such an opposing effect, this hypothesis suggests that one should find that the recent change in beta would matter. Upon reflect, such a ―slow adjustment‖ effect is not the only hypothesis that could overwhelm the standard hedging motive effect—a negative effect of recent betas on stock prices that is different from the positive asset-pricing effect that theory would suggest for (older) betas. For example, investors could pay more attention to stocks that have recently moved against the stock market, and this could increase their returns temporarily. Alternatively, stocks that have recently underperformed relative to the market could become more attractive, while stocks that have recently outperformed even the market in a bull market could become less desirable. Thus after the market has just gone up, investors might pour money into those firms that have not yet similarly appreciated. Or, less specifically, recent betas could simply pick up exposure to some novel factor that investors care about, for whatever reason. Again, these hypotheses for a different role for short-term market betas are not based on standard market-hedging motives, and they are of course just conjectures.1 It is the empirical evidence that matters. Our paper finds that this evidence suggests that if we include both recent beta and aged betas, then • Aged betas (computed from daily stock returns at least two years old) have a solid positive influence on future stock returns. • Recent betas (computed from daily stock returns no more than two years old) have a solid negative influence on future stock returns. As noted, the positive influence of aged betas is easy to explain as the standard hedging motive. Indeed, we see it as the primary contribution of our paper that it is able to uncover such a reliable positive influence of this aged beta in the cross-section of future stock returns. The negative part is more mysterious. Although our paper does offer some explanations (those mentioned above) and some related evidence, these do not have the same theoretical grounding as the hedging motive and are thus more speculative. Moreover, some of our evidence suggests that we document a ―change in beta‖ effect, although other evidence points to two separate and opposite beta effects.2 2 A combination of these hypotheses has also been proposed by Jacquier, Titman, and Yalcin (2001). They omit the most recent 12 months in computing beta, include a contemporaneous beta, and then explore the differences in portfolios across momentum losers and momentum winners. Nor have changes in beta gone unnoticed, either. For example, Cohen, Polk, and Vuolteenaho (2003) noticed that betas of growth firms tended to fall, while betas of value firms tended to rise. Unlike earlier attempts to rescue beta, the role of our two betas does not overlap with those of the two Fama-French factors or momentum. Indeed, the two market betas become stronger if we control for these factors. Moreover, the influence of the two market betas seems economically significant: An extreme corner quintile portfolio of stocks with high aged betas and low recent betas outperforms its mirror image by an annualized 5% to 7% per year. If anything, the effect seems to have become stronger in recent years, unlike that of the other factors (e.g., the book-market effect) that we are controlling for. VI Conclusion Our paper’s most important contribution is a diagnosis of why market-betas have performed so poorly in detecting the positive hedging role of low-beta stocks in cross-sectional predictive return regressions. Stocks that have a high aged beta also tend to have a high subsequent recent beta. (If they did not, historical betas would have no use in designing hedges.) However, aged beta and recent beta have opposite roles in predicting future stock returns. Using only either the aged or the recent beta in a regression without including the other therefore inevitably picks up the opposite effect of the other beta. Thus, it is no wonder that earlier work has not found that market-betas by themselves are not important. Successful prediction in which aged beta can help explain the cross-section of future stock returns requires holding the recent beta constant—or at least including a set of alternative variables that can assume the role of recent beta (as in we did in Table X). To compute good market-betas, we recommend using daily stock returns, about two years of history, and Vasicek shrinkage. We find that the hedging role of recent market betas seems to be overwhelmed by a non-hedging related effect—possibly a delayed response, an attention-related effect, or a novel factor exposure. In contrast, aged market betas do have the theoretically predicted positive hedging correlation with the stock market. These two effects are robust among firms of difference sizes, types, and momentum. The effect is stronger in Januaries, and after 1990. It is also fairly persistent. Aged betas are significantly positively related to stock returns for up to two years, recent market betas for about 6-12 months. Including other variables does not change the importance of aged beta, but can affect the importance of recent betas. Indeed, the influence of aged and recent betas does not arise because these variables ―steal‖ explanatory power from the Fama-French variables or from the momentum variables. On the contrary, the two betas are stronger when the Fama-French factors are controlled for. However, it is not yet fully clear whether we are observing primarily a ―change in beta‖ effect or two separate beta effects. We also proposed a test to determine whether aged and recent betas pick up covariation with the stock market, or covariation with a novel unspecified factor. This test suggests that aged beta matters primarily because it is a covariation with the stock market per sé, not because it is an exposure to a novel factor. In contrast, recent beta primarily picks up a covariation to some novel factor—a contaminant. Although we would prefer knowing why this novel factor is so important to investors, we could only speculate about its ultimate source (slow response, attention changes, etc.). We would argue that this puts our novel factor in the same category as many other familiar non-hedging related pricing factors. In fact, although there are good suggestions after 20 years of empirical research, there is still some disagreement why the Fama-French factors and momentum work so well. Although there may be other more or equally important factors determining stock market pricing, the effect of our betas is not economically small. We find an observed spread of 5% to 7% per annum between a portfolio with high aged market beta and low recent market beta and its reverse. When recent market beta is replaced by our proposed novel factor exposure, this increases to 8% to 10% per annum. Again, in our opinion, it is the relation of this spread to the predictions of hedging theory that renders this cross-sectional return spread more interesting than return spreads that factors without much theoretical background would produce. Finally, as expected, we found that only recent market beta constituted a novel factor detectable by the Fama-French time-series techniques. The hedging motive has of course always been a part of the Fama-French factors (captured by their XMKT factor), and it is thus not a surprise that aged market beta could not pick up a novel factor above and beyond the Fama-French factors.
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