A Critique of Stochastic Discount Factor Methodology

The stochastic discount factor (SDF) methodology is becoming quite popular in recent empirical asset pricing studies. It appears that this new methodology, as claimed, is going to replace traditional methodologies. In this paper, we point out that, because the current practice of the stochastic discount factor methodology ignores a fully specified model for asset returns, it suffers from two potential problems, especially when asset returns follow a linear factor model. The first problem is that risk premium estimate from the SDF methodology is unreliable. For reasonable value of parameters, the standard error of the estimated risk premium is more than forty times greater than those of the traditional methodologies. The second problem is the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology. Asset pricing theories, such as those of Sharpe (1964), Lintner (1965), Black (1972), Merton (1973), Ross (1976) and Breeden (1979), show that the expected return on a financial asset is a linear function of its covariances (or betas) with some systematic risk factors. This implication has been tested extensively in the finance literature by the socalled “traditional methodologies.” In the traditional methodologies, a data generating process is first proposed for the returns, and then the restrictions imposed by an asset pricing model are tested as parametric constraints on the return generating process. The approach taken by the traditional methodologies has a potential problem. It is that when the proposed return generating process is misspecified, the test results could be misleading. Therefore, in applying the traditional methodologies, researchers typically have to justify that the proposed data generating process provides a good description of the returns. For example, when the proposed return generating process is a factor model, one would like the model to have high R in explaining the returns on the test assets, especially when the test assets are well diversified portfolios. As many of the earlier theories are special cases of the stochastic discount factor (SDF) model, recent empirical asset pricing studies have been focused on testing the pricing restrictions in terms of the SDF model, rather than on the traditional risk measures such as the beta and the Sharpe ratio. One of the most prominent papers in this line of research is Cochrane (1996), where the SDF methodology is fully explained. The formulation typically estimates the parameters and tests the pricing implications without a fully specified model of how the asset returns are generated in the economy. On the one hand, this appears very general and requires fewer assumptions and parameters than the traditional methodologies. On the other hand, it seems counter intuitive that one can be sure that the pricing restrictions are true if one knows little about the dynamics of the returns, i.e., without a fully specified model (either parametric or nonparametric) of the returns. This paper shows that if asset returns are generated by a linear factor model, then by