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, the stock's risk-neutral variance, and average stock-level risk-neutral variance. These components can be computed from the prices of index and stock options. We test the formula by running predictive panel regressions at the individual stock level. We conduct joint hypothesis tests and find, in most of our specifications, that the estimated coefficients are significantly different from zero and insignificantly different from the values predicted by our theory; moreover, our predictor variables drive out CAPM beta, size, book-to-market, and momentum in predictive regressions. When coefficients are fixed at the levels implied by our theory, the formula -- which has no free parameters -- outperforms a range of competitors in predicting individual stock returns.