Explaining the size and value premia as a tradeoff between risk and return is an important challenge for asset pricing theory. The failure of the CAPM to explain the high average returns of small stocks relative to large stocks and value stocks relative to growth stocks has been well documented (cf. Fama and French (1992)). Mankiw and Shapiro (1986) and Breeden, Gibbons, and Litzenberger (1989) find that the Consumption CAPM (CCAPM) does no better in explaining the cross section of average stock returns.
As a response to these failures, Fama and French (1993) proposed an influential three factor model. In addition to the market return, they introduce two factors based on portfolios sorted by size and book-to-market equity. Although the model is an empirical success, it falls short of a satisfactory understanding of the underlying risk reflected in stock returns. “Without a theory that specifies the exact form of the state variables or common factors in returns, the choice of any particular version of the factors is somewhat arbitrary.” (Fama and French 1993, p. 53) As emphasized by Cochrane (2001, Chapter 9), a satisfactory factor model must ultimately connect the factors to the marginal utility of consumption.
This paper tests a consumption-based linear factor model, where the two factors are non durable and durable consumption growth. The model is derived from the canonical consumption and portfolio choice problem of a household, where the intraperiod utility takes the CES form. It nests the CCAPM as a special case when utility is separable in nondurable and durable consumption. Previous papers have tested the conditional moment restrictions implied by the model with non-separable preferences, using T-bill returns as test assets (cf. Dunn and Singleton (1986), Eichenbaum and Hansen (1990), and Ogaki and Reinhart (1998)). This paper tests the model’s unconditional moment restrictions using the 25 Fama-French (1993) portfolios sorted by size and book-to-market equity.
Figure 1(d) illustrates the empirical success of the durable consumption model. On the vertical axis is the realized average excess return, and on the horizontal axis is the return predicted by the model. The points represent the 25 Fama-French portfolios, and the corresponding vertical distance to the diagonal line represents the pricing error. The points line up close to the diagonal, especially compared to the CCAPM in Figure 1(c).