Forward-Looking Market Risk Premium

TLDR: A theoretical expression is derived that links forward-looking risk premium to investors' risk aversion and forward- looking volatility, skewness, and kurtosis of the corresponding cumulative return, and the model adopted is the generalized autoregressive conditional heteroskedasticity model for the physical return process.

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 cumulative return's forward-looking volatility, skewness and kurtosis. In addition, investor's 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 GMM method to estimate investor's risk aversion. We adopt the GARCH model for the physical return process, and estimate the model using the S&P500 daily index returns and then deduce the corresponding cumulative return's forward-looking variance, skewness and kurtosis. The forward-looking risk premiums are estimated monthly over the sample period of 2001-2010 and found to be all positive. The forward-looking risk premium was higher during volatile market periods (such as September 2001 and October 2008) and lower when the market was calm. Furthermore, two asset pricing tests are conducted. First, change in forward-looking risk premiums is negatively related to the S&P500 holding period return, reflecting that an increase in discount rate reduces current stock price. Second, market illiquidity positively affects forward-looking risk premium, indicating that forward-looking risk premium contains an illiquidity risk premium component.