Forward-Looking Market Risk Premium

Abstract

A method for computing forward-looking market risk premium is developed in this paper. We first derive a theoretical expression that links forward-looking risk premium to investors’ risk aversion and forward looking volatility, skewness, and kurtosis of cumulative return. In addition, investors’ risk aversion is theoretically linked to volatility spread, defined as the gap between the risk-neutral volatility deduced from option data and the physical return volatility exhibited by return data. The volatility spread formula serves as the basis for using the generalized method of moments to estimate investors’ risk aversion. We adopt the generalized autoregressive conditional heteroskedasticity model for the physical return process and estimate the model using the S&P 500 daily index returns and then deduce the forward-looking variance, skewness, and kurtosis of the corresponding cumulative return. The forward-looking risk premiums are estimated monthly over the sample period of 2001–2010, and all are found to be positive. Furthermore, two asset pricing tests are conducted. First, change in forward-looking risk premiums is negatively related to the S&P 500 holding period return, reflecting that an increase in discount rate reduces current stock prices. Second, market illiquidity positively affects forward-looking risk premium, indicating that forward-looking risk premium contains an illiquidity risk premium component.