Empirical Pricing Kernels

Abstract

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a daily semi-parametric pricing kernel. The two key features of this estimator are: (1) the functional form of the pricing kernel is estimated semi-parametrically, instead of being prespecified and (2) the pricing kernel is re-estimated on a daily basis, allowing measurement of time-variation in risk-aversion over equity return states.

Important empirical findings of the paper are as follows. Constant relative risk aversion over S&P500 return states is rejected in favor of a model in which relative risk aversion is stochastic. Empirical relative risk aversion over equity return states is found to be positively autocorrelated and positively correlated with the spread between implied and objective volatilities. In addition, the constant relative risk aversion (power utility) pricing kernel is found to underestimate the value of payoffs in large negative return states.

An option hedging methodology is developed as a test of the predictive information in the empirical pricing kernel and its associated state probability model. The results of hedging performance tests for out-of-the-money S&P500 index put options indicate that time-varying risk aversion over equity return states is an important factor affecting option prices.