What is the Expected Return on a Stock?

Abstract

We derive a formula that expresses the expected return on a stock in terms of the risk-neutral variance of the market and the stock's excess risk-neutral variance relative to the average stock. These quantities can be computed from index and stock option prices; the formula has no free parameters. We run panel regressions of realized stock returns onto risk-neutral variances, and find that the theory performs well at 6-month, 1-year, and 2-year forecasting horizons. The formula drives out beta, size, book-to-market and momentum, and outperforms a range of competitors in forecasting stock returns out of sample. Our results suggest that there is considerably more variation in expected returns, both over time and across stocks, than has previously been acknowledged.

Keywords: Equity Returns, Cross-Sectional Asset Pricing, Risk-Neutral Variance, Idiosyncratic Volatility, Equity Options

JEL Classification: G11, G12, G13