Empirical Asset Pricing with Functional Factors

Abstract

We propose a methodology to use functional factors in empirical asset pricing models. The term structure of interest rates and the implied volatility smile are just two common examples. Functional factors usually incorporate investors risk preferences that could be priced in the cross-section of stock returns. We derive a theory for pricing functional factors that encompasses the usual one for scalar valued factors. We then provide estimation algorithms for betas, risk prices and risk premia and show that they are asymptotically Gaussian and suggest the bootstrap as method to carry out inference. We apply our approach to extract additional information embedded in the implied variance curve. We argue that changes in the shape of the implied variance curve provide information about fear and uncertainty and we distinguish between the two. We show that convexity can be seen as a proxy for volatility uncertainty. This uncertainty could explain the premium earned by momentum strategies, which is seen as pricing anomaly in literature. The empirical results show that the S&P500 3-month implied variance curve is a pricing factor for momentum sorted portfolios and a positive risk premium is earned by the convexity of the implied variance curve.