Expected Stock Returns and Volatility

Abstract

Abstract This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market-risk premium (the expected return on a stock portfolio minus the Treasury-bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility. Many studies document cross-sectional relations between risk and expected returns on common stocks. These studies generally measure a stock’s risk as the covariance between its return and one or more variables. For example, the expected return on a stock is found to be related to covariances between its return and (i) the return on a market portfolio (Black, Jensen, and Scholes (1972), Fama and MacBeth (1973)), (ii) factors extracted from a multivariate time-series of returns (Roll and Ross (1980)), (iii) macro economic variables, such as industrial production and changes in interest rates (Chen, Roll, and Ross (1986)), and (iv) aggregate consumption (Breeden, Gibbons, and Litzenberger (1986)).