Relative Contributions of Price and Volatility Risk Premiums to S&P 500 Index Returns

As evinced of empirical characteristics of leptokurtosis, skewness, volatility clustering and asymmetric volatility shocks in SP 500 index returns, this study proposes a stochastic volatility process allowing for time-varying correlation with underlying returns, in which the market price of volatility risk is incorporated. A quasi-maximum likelihood function accompanied with Kalman filter is used ot estimate estimates model parameters and the market price of volatility risk. The volatility risk premium is found to be positive and increases with investment horizons. Compared to the price risk premium, however, the relative contribution of the volatility risk premium is most pronounced for long-term SP 500 returns. The premiums for price and volatility risks provided by the stochastic-volatility model are found informative for out-of-sample realized mean returns, indicating the importance of stochastic volatility. Key Words: volatility risk premium, stochastic volatility, Kalman filter, quasi-maximum likelihood estimation