Measuring risk aversion from excess returns on a stock index

Measuring risk aversion from excess returns on a stock index presents two obstacles: 1. the time path of the stock-index variance needs to be modeled and estimated, and 2. other components of wealth must be accounted for. We distinguish two measures that relate the risk premium to variance: 1. the measure of risk aversion which, by the single-factor CAPM, would be the slope coefficient in the linear relation between the mean excess return and the variance of the overall risky portfolio of the representative investor, and 2. the slope coefficient in the linear relationship between the mean excess return on a stock index and its variance. Even when risk aversion is constant, the latter can vary significantly with the relative share of stocks in the risky wealth portfolio, and with the beta of unobserved wealth on stocks. We introduce a statistical model with ARCH disturbances and a time-varying parameter in the mean (TVP ARCH-M). The model decomposes the predictable component in stock returns into two parts: the time-varying price of volatility and the time-varying volatility of returns. The relative share of stocks and the beta of the excluded components of wealth on stocks are instrumented by macroeconomic variables. The ratio of corporate profit over national income and the inflation rate are found to be important forces in the dynamics of stock price volatility.