A nonparametric approach to multifactor modeling
Recent literature has started to explore the use of nonparametric methods to estimate alphas (pricing errors) and betas (factor loadings) in the conditional Capital Asset Pricing Model and conditional multifactor models. Nonparametric estimation of factor modeling involves choosing techniques which are different both technically and in application, but common in the nonparametric literature. Nonparametric methodology does not impose any functional form on how alphas or betas 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. This paper discusses three topics in the realm of nonparametric multifactor modeling. First, I explore two of the most recent contributions to the literature, a leave-one-out-cross-validation technique and a plug-in technique, and compare their effectiveness. The cross-validation method is completely data driven, while the plug-in method relies on choosing an unknown parameter in estimating the optimal window size. Cross validation emerges as the more robust methodology. Next I challenge the linear parametric specification of the Fama French Model. The model fails the conditional model specification test. Alternative models, including nonparametric specifications, are tested and the nonparametric emerges as a better fitting model, however the improvement is not significant. Lastly, nonparametric approaches have been criticized for the extreme computational demands. I create a high performance web based virtual computing environment and provide succinct details to access and utilize the vast computational resources available in the cloud. ^
Gallagher, Michael J, "A nonparametric approach to multifactor modeling" (2015). ETD Collection for Fordham University. AAI3715927.