Estimation and Evaluation of Conditional Asset Pricing Models

We find that several recently proposed, consumption-based models of stock returns, when evaluated using an optimal set of managed portfolios and the associated model-implied conditional moment restrictions, fail to capture key features of risk premiums in equity markets. To arrive at these conclusions we address two methodological issues that are central to assessing the goodness-of-fit of asset pricing models in which the stochastic discount factor (SDF ) is a conditionally affine function of a set of priced risk factors. First, we show that there is an optimal GMM estimator for this class of SDF s. That is, there is a choice of instruments that leads to the most efficient estimator within a class that subsumes virtually all of the GMM estimators used to date in assessing the fit of conditionally affine factor models. Second, for the (often relevant) case where a researcher is proposing a generalized SDF relative to some null model, we show that there is an optimal choice of managed portfolios to use in testing the null against the proposed alternative. The form of the optimal choice of test portfolios is derived directly from the (locally) most powerful Wald and Lagrange-multiplier tests of the null against the alternative specification of the SDF . Stanford University, Graduate School of Business, 518 Memorial Way, Stanford, CA 94305, e-mail: Nagel [email protected], http://faculty-gsb.stanford.edu/nagel Stanford University, Graduate School of Business, 518 Memorial Way, Stanford, CA 94305, e-mail: [email protected],http://www.stanford.edu/ kenneths/