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 autocorrela...