Portfolio Choice Implications of Parameter and Model Uncertainty in Factor Models

Abstract

This paper examines the portfolio choice implications of incorporating parameter and model uncertainty in (conditionally) linear factor models using industry portfolios. I examine a CAPM, a linear factor model with different predictor variables (dividend yield, price to book ratio, price to earnings ratio, and price to sales ratio), and a time-varying CAPM. All approaches incorporate parameter uncertainty in a mean-variance framework. I consider a time-varying CAPM with changing conditional variance. It is shown that taking into account the time variation in market betas improves the portfolio performance as measured by the ex-post Sharpe ratio compared to both an unconditional CAPM and a linear factor model with predictor variables. I also show the implications of using a Black-Litterman framework versus using a standard mean-variance approach in the asset allocation step. Black-Litterman framework can be thought as a model averaging approach and thus helps deal with both the parameter and model uncertainty problems. I show that Black-Litterman approach results in portfolios with a higher Sharpe ratio than those obtained by a standard mean-variance framework using a single model or historical averages.