A Nonparametric Approach to Multifactor Modeling

Recent literature has started to explore the use of nonparametric methods to estimate alphas and betas in the conditional CAPM and conditional multifactor models. This paper explores two of the most recent contributions and proposes a third method. Nonparametric estimation of factor modeling involves choosing techniques which are different both technically and in application, but common in the nonparametric literature. The methodology does not impose any functional form on how alphas (pricing errors) or betas (factor loadings) evolve over time. Local data is used in estimations, but of crucial significance is the bandwidth selection or optimal window size. Clearly, observations further away from time t are less relevant in estimating time t alphas and betas, so if we are too far away from time t we potentially have a very large bias. However, if too small a bandwidth is selected, the estimate could be quite noisy, leading to a large variance. A popular technique in the literature is the leave-one-out-cross-validation method which is completely data driven. The researcher may use simulations to illustrate how the optimal window size varies with changes in the underlying unobservable state variables. Another bandwidth selection procedure often used in the literature is the plug-in method. The plug-in method however, relies on choosing an unknown parameter in estimating the optimal window size, while the leave-one-out method is completely data driven. This paper explores the effectiveness of these two methods and proposes a nonparametric estimation of multifactor models using a cross validated local polynomial regression method. Local polynomial regression has emerged as a leading approach to nonparametric estimations of regression functions. Using a completely data driven approach to the joint determination of polynomial order and bandwidth eliminates the ad-hoc approach to determining polynomial order which may not be optimal.