On Stable Factor Structures in the Pricing of Risk

Much of the research describing the cross-sectional and time series behavior of asset returns can be characterized as a search for the relevant state variables and also a search for the relevant model specification. Ultimately the scope of such efforts is to find a satisfactory and stable asset pricing structure. In this paper we discuss various methods to accomplish this and appraise the success of two recently proposed classes of asset pricing models in tracking predictable patterns in risk and return trade-offs. The two classes are the conditional CAPM and the nonlinear APT. The parameters of both models are estimated via a set of moment conditions using the GMM estimator and the model fit is judged on the basis of the overidentifying restrictions. The fundamental problem is that overidentifying restrictions tests are not designed to diagnose whether a model provides a stable relationship between the return series and the risk factors. We use a set of recently developed tests for structural stability of parameter estimates for the GMM estimator to diagnose which factor structures appear stable through time in the context of the two aforementioned classes of models. In the course of trying to sort out whether there is systematic mispricing we also try to determine what type of model looks most promising for further development. In that regard we find the nonlinear APT more satisfactory than the conditional CAPM and APT. The paper covers several empirical examples ranging from international asset pricing to the pricing of size-sorted and industry classified portfolios of stocks listed on the NYSE