Equity Risk Premium and Volatility: A Correlation Structure

Abstract:     
This paper investigates the relation between stock market returns and volatility using a bivariate factor model governing the evolution of a volatility indicator and the market price of risk. The model-implied volatility measured by the conditional standard deviation of equity returns is compared with the predictable volatility measured by the expected value of the selected volatility indicator. Using the Standard and Poor's Composite Return Index and three volatility indicators (the VIX, the standard deviation of historical returns, and a GARCH(1,1)-fitted indicator), we study a predictive model with a set of the selected market state variables, such as past excess stock returns, current indicated volatility level, aggregate dividend yield, changes in the aggregate consumption, changes in the production output, and stock earnings. The daily risk premiums follow similar patterns for the three volatility indicators with the GARCH(1,1) indicator providing the most consistent predictability. While a positive relation between the intertemporal risk premium and volatility is plausible, the correlations between unexpected returns and volatility indicators are mixed with different volatility indicators. For the selected sample data, we find both strong leverage and volatility feedback effects. Finally, we discuss a portfolio strategy to show the predictive power of the model.

Number of Pages in PDF File: 52

Keywords: Risk Premium, Volatility Risk Premium, Volatility Indicator, Market Price of Risk, Volatility Feedback Effect, Leverage Effect

JEL Classification: C5, C22, C51, G12

working papers series