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Explaining Stock Returns: A Literature Survey

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Daniel and Titman (1997) doubt the risk-based explanation. They contend that it is "characteristics, not covariances," that produce return dispersion. For example, the risk-based story says that high BtM stocks have high average returns because they are sensitive to common variation in stock returns. In other words, the high returns are due to a high sensitivity to HML. In contrast, Daniel and Titman argue that high BtM stocks have high returns due to some other reason (possibly overreaction), so that the high returns have nothing to do with systematic risk. In their opinion, it is the characteristic (high BtM) rather than the covariance (high sensitivity to HML) that is associated with high returns.

The cross-sectional correlation between BtM and HML sensitivity is quite high, so it is difficult to see which of these variables has more explanatory power for returns. Nevertheless, Daniel and Titman provide results suggesting that the characteristics-based story is more plausible for the 1973-1993 period. However, Davis, Fama and French (2000) show that the Daniel and Titman results are confined to their relatively short sample period. When the longer 1929-1997 period is examined, covariances show more explanatory power than characteristics. It is not clear why the shorter period produces different results, but the longer period should produce more reliable results, and these results favor the risk-based story.

VIII. Recent Developments

The research into stock price behavior and asset pricing continues, and a number of interesting results have surfaced recently. Perez-Quiros and Timmermann (2000) provide evidence that small firms have high average returns because they are more affected by tight credit market conditions. Small firms do not have the same access to domestic and international bond markets that are enjoyed by large firms. Since the availability of credit is tied to economic conditions, so that a credit contraction typically occurs near a recession, small firms would be very sensitive to systematic variation in credit market conditions. Thus, the high returns to small firms might be compensation for the high sensitivity to a credit-related risk factor.

A study by Elton, Gruber, Agrawal and Mann (2001) reports a potentially important link between the equity and fixed income markets. If certain risk factors are pervasive enough to explain common variation in stock returns, it is reasonable to expect that these same risk factors would be at work in the bond market as well. Elton, et al. provide evidence that SMB and HML do just that. Their research isolates the portion of a bond's return that is due to changing risk premiums, and they show that this part of the bond's return is strongly related to SMB and HML. Not only does this result support the risk-based story, but it also suggests some interesting avenues for future research in fixed income portfolio management.

In an interesting recent study, Lettau and Ludvigson (2001) show that a consumption-oriented capital asset pricing model (CCAPM) that allows expected returns to vary over time provides a nice cross-sectional explanation of equity returns. They use the ratio of aggregate consumption to wealth as a "conditioning variable" to model the evolution of expected returns over time. The relation between the consumption/wealth ratio and expected returns is straightforward. If investors expect returns to be high in the future, they would be more likely to raise their consumption level (relative to their level of wealth). So, an increase in the consumption/wealth ratio would signal high expected returns. Lettau and Ludvigson also find that the variation in returns that is picked up by the Fama/French three-factor model appears to be related to the changing risk premium from the CCAPM.

Lettau and Ludvigson's results bolster the risk-based explanation of the size and value effects. SMB and HML capture common variation in returns because they seem to be related to variation in a consumption-based risk premium that changes over time.8 Financial theory (the CCAPM) and empirical observation (the size and value effects) are linked in an intuitively appealing way. It would be ironic if the asset pricing model that received the least empirical support in the early years turned out to be the best description of expected returns.

Pastor and Stambaugh (2001) provide evidence that sensitivity to market-wide shifts in liquidity might be a priced risk factor. Stocks that are highly sensitive to shifts in market liquidity (they have a high "liquidity beta") have high average returns. This liquidity factor appears to be distinct from SMB and HML, suggesting an independent source of risk. However, it appears that liquidity betas are highly unstable, and there is substantial variation in the corresponding premium. While it is too early to conclude that there is a systematic liquidity factor in stock returns, more research is sure to be forthcoming in this area.

Finally, an indication of the acceptance of the three-factor model is the frequency with which it is now used as a benchmark for performance measurement. For example, Quigley and Sinquefield (2000) use a three-factor benchmark to analyze the performance of UK unit trusts, and Carhart (1997) and Davis (2001) use the Fama/French model in studies of US mutual fund performance (although Carhart adds a fourth factor to reflect momentum).

IX. Conclusions

The issue of whether the value and size premiums are caused by risk or inefficiency may never be resolved to everyone's satisfaction. Feelings run strong on both sides of the argument. For investors, there are two crucial points to remember. First, factors based on value and size have explained much of the common variation in US stock returns for the past three-quarters of a century. Second, value and size premiums have been observed in several other countries, with the value premium being observed in nearly every country that has been studied. While these observations are consistent with a risk-based story, they do not prove anything. Nevertheless, something very fundamental would have to change in the financial markets in order for these premiums to disappear. Furthermore, the returns observed in the US market during 1999 show that "value-minus-growth" is not a low-risk strategy.

The inability of the Fama/French three-factor model to explain stock price momentum is a problem for the model's proponents. However, the problem may not be all that serious. Consider the following facts:

  1. Pure momentum strategies involve very high turnover. Consequently, transaction costs and taxes can significantly erode momentum profits.
  2. Most of the return to the "winner-minus-loser" momentum portfolio is due to the poor performance of the losers. So, in order to capture the bulk of the momentum effect, short positions are necessary. This is not feasible for some investors.
  3. The momentum effect is stronger among small cap stocks, which tend to be less liquid. Trying to implement a high-turnover strategy with small cap stocks is unrealistic.

These facts suggest that momentum strategies probably do not represent a real opportunity for investors to earn abnormal returns, at least not to the extent implied by recent studies.

The helpful comments of Robert Dintzner, Ken French, Kate Hudson, Graham Lennon, and Weston Wellington are gratefully acknowledged.

1 Readers who are already familiar with the theory of asset pricing may skip Section II. However, the remaining sections assume that the reader is familiar with the main implications of the various asset pricing models.

2 For example, all investors are assumed to have the same information, and this information is costless to gather and process. In addition, there are no taxes, transactions costs, or other "frictions". It is also assumed that investors can readily borrow funds at the risk free rate of interest.

3 An arbitrage opportunity is an investment strategy that has the following properties: 1) the strategy's cost is zero; 2) the probability of a negative payoff is equal to zero; and 3) the probability of a positive payoff is greater than zero. In other words, the costless strategy can't lose, and it might win.

4 The beta coefficient in the CCAPM equation is actually the ratio of the consumption betas for asset j and the market portfolio. The main point is that high positive covariance with aggregate consumption requires a higher expected return.

5 CRSP is the Center for Research in Security Prices at the University of Chicago. The CRSP database contains stock market data (prices, returns, shares outstanding, etc.) for NYSE, AMEX, and NASDAQ common stocks. The Compustat database is produced by Standard & Poor's Corporation and contains accounting data for US (and some foreign) companies.

6 Some people have the mistaken belief that the CRSP database suffers from a survivorship bias. CRSP is free of survivorship bias; Compustat is not.

7 Davis, Fama and French (2000) would later provide additional evidence using a much larger database over a longer sample period.

8 It is also important to note that SMB and HML seem to be slightly more precise than the consumption-wealth ratio in describing the time-varying risk premium. So, empirical estimation of expected returns can still be done more precisely with the Fama-French model. The CCAPM does not replace the 3-factor model; it simply provides a theoretical justification for its use.

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This article contains the opinions of the author and those interviewed by the author but not necessarily Dimensional Fund Advisors Inc. or DFA Securities Inc., and does not represent a recommendation of any particular security, strategy or investment product. The author's opinions are subject to change without notice. Information contained herein has been obtained from sources believed to be reliable, but is not guaranteed. This article is distributed for educational purposes and should not be considered investment advice or an offer of any security for sale. Past performance is not indicative of future results and no representation is made that the stated results will be replicated.


December 2001