Abstract

We present a sufficient condition under which the prices of options with different strike prices written on a particular stock can be used to calculate a lower bound on the expected returns of that stock. The sufficient condition imposes a restriction on a combination of the stock’s systematic and idiosyncratic risk. The lower bound is forward-looking and can be calculated on a high-frequency basis for stocks with liquid option trading. We estimate the lower bound empirically for constituents of the S&P 500 index and study its cross-sectional properties. We find that the bound increases with beta and decreases with size. The bound also provides an economically meaningful signal on future realized stock returns.