We present a sufficient condition under which the prices of options written on a particular stock can be aggregated 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. We estimate the bound empirically and study its cross-sectional properties. We find that the bound increases with beta and book-to-market ratio and decreases with size and momentum. The bound provides an economically meaningful signal about future stock returns. (JEL G11, G12) Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

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