Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allow for flexibility in the dynamics of assets' covariances with risk factors and market prices of risk (MPR). First, conditional covariances are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and covariances using the entire sample. We prove the consistency and asymptotic normality of the estimators. Results from a Monte Carlo simulation for the three-factor model of Fama and French (1993) suggest that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that MPR associated with the three Fama-French factors exhibit substantial variation through time. Finally, the flexible version of the three-factor model beats alternative parametric specifications in terms of forecasting future returns.