Linear Approximations and Tests of Conditional Pricing Models

Abstract:     
How important is the potential misspecification introduced into measured pricing errors by a standard linear approximation to a conditional pricing model? The answer to this question depends on the particular model being tested. We construct a simple reduced-form example with modest intrinsic nonlinearity. The theoretical magnitude of the pricing errors (alphas) induced by misspecification can be derived as a direct consequence of an omitted variables bias. When the model is calibrated to either characteristics-sorted or industry sorted portfolios, we find that the asymptotic alphas generated by approximation-induced specification error are economically large in both cases, although the choice of test assets has a significant effect on the magnitude of the alphas. Finally, a Monte Carlo analysis shows that finite-sample alphas are even larger, and the power to detect omitted factors through tests based on estimated risk premiums is low, even when the effect on alphas is large.

Number of Pages in PDF File: 47

JEL Classification: G12, C13, C22

working papers series