Empirical pricing kernels

Abstract

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which is referred to as the empirical pricing kernel (EPK). The empirical pricing kernel is the preference function that rationalizes a contemporaneous cross-section of asset prices, given a forecast payoff probability density. We estimate the EPK on a monthly basis from 1991 to 1995 using S&P500 index option data and a stochastic volatility model for the S&P500 return process. We find substantial evidence of time-varying risk aversion over S&P500 return states. In addition, we find that empirical risk aversion over S&P500 return states is linked to business conditions; the level of risk aversion is positively correlated with indicators of recession and negatively correlated with indicators of expansion. An option hedging methodology is developed to test the predictive information in the empirical pricing kernel and its associated state probability model. Hedging performance is significantly improved using hedge ratios based on a time-varying pricing kernel rather than a time-invariant pricing kernel.