Measuring Risk Aversion from Excess Returns on a Stock Index

Abstract

We distinguish the measure of risk aversion from 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-N). 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 ore found to be important forces in the dynamics of stock price volatility.