Nonparametric Estimation and Instrument Selection in the Conditional Capital Asset Pricing Model∗

This version is incomplete. Please DO NOT circulate. This paper uses a functional coefficient regression to estimate time-varying betas and alphas in the conditional capital asset pricing model. Functional coefficient representation relaxes the strict assumptions on the structure of betas and alphas by combining the predictors into an index that best captures time variations in betas and alphas and estimates them nonparametrically. This index in betas and alphas helps us to determine which economic variables we should track and more importantly, in what combination. We select an appropriate index variable by using smoothly clipped absolute deviation penalty to functional coefficients. In such a way, estimation and variable selection can be done simultaneously. Our model performs better than the alternatives in explaining asset returns. Based on the empirical studies, we find no evidence to reject the conditional CAPM. JEL classification: C13; C52; G1