Academic journal article Academy of Accounting and Financial Studies Journal

Why the Fama-French Factors Work and Serial Correlation Too

Academic journal article Academy of Accounting and Financial Studies Journal

Why the Fama-French Factors Work and Serial Correlation Too

Article excerpt

INTRODUCTION

Firms with high book to market ratios tend to have higher stock returns (e.g. Fama and French, 1992) as do firms with smaller market capitalizations, or "size" (e.g. Banz, 1981). Fama and French (1993) augment the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965) by adding two additional factors, HML and SMB, which mimic the effects of book to market and size, respectively. The Fama and French factors are extremely useful for modeling return, but the theoretical justification for including these additional variables in the model for returns has lagged behind the empirical justification that "they work". Fama and French (1993, p.7) argue that "although size and book to market equity seem like ad hoc variables for explaining average stock returns, we have reason to expect that they proxy for common risk factors in returns". Fama and French (1993) essentially argue that a firm's size and book to market are proxies for the firm's coefficients (loadings) on risk factors that are priced by the market and that the HML and SMB factors they create serve as proxies for these risk factors. Fama and French (1995) attempt unsuccessfully to explain the linkage of the mimicking factors to returns by searching for such common factors in earnings. Daniel and Titman (1997) find that firm specific measures of size and book to market ratio model returns better than the Fama and French factors.

Fama and French (2008b, p.2973) explain the motivation for using the book to market ratio as a proxy for a factor which affects expected returns by noting that the dividend per share is earnings per share less the change in book value per share. They point out that the dividend discount model would therefore indicate that both the dividend stream and its present value are dependent on book value. In this paper, we build on this observation, but take a slightly different approach to explain the linkage between return and the book to market ratio and market value. We analyze the definition of expected next period total return and highlight the presence of current period book to market and size as components therein. We find that the reason initial book to market and initial market value "work" is not so much because they proxy for expectations of other common risk factors. Rather, it is because these variables are themselves implicitly contained in the definition of expected return and the Fama and French factors, along with the firm-specific loadings, mimic them. In the appendix, we show why individual firm book to market and market value should be expected to be proportional to the Fama and French HML and SMB mimicking factors in accordance with the Fama and French (1993) intuition.

In addition, we find that the fact that the definition of return contains the book to market ratio and market size (and thus the Fama and French (1993) mimicking factors) from two successive time periods offers a partial explanation for the well known serial correlation of returns (e.g. Fama, 1965) which allows prediction of future returns (e.g. Jagadeesh, 1990). Fama and French (1986) find that negative serial correlation of stock portfolio returns is due to common factors and that, when the common factor that generates negative serial correlation is removed, another factor or factors tend(s) to generate positive serial correlation. Fama and French (1988) point out that negative serial correlation for long horizons indicates a tendency toward reversal. Jegadeesh (1990, p.897) finds strong negative first order serial correlation and significant positive higher order serial correlation of returns. Jegadeesh and Titman (1993) find that the serial correlation can be exploited for individual stocks by developing trading strategies based on previous return: i.e. buying past winners and selling past losers can earn "momentum" returns above those predicted by the Fama and French (1993) three factor model. Fama and French (2008a) find evidence that momentum trading strategies are possible even after controlling for the possibility of undue influence from volatile micro- and small-cap stocks in portfolios. …

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