We propose a measure for the convexity of an option-implied volatility curve, IV convexity, as a forward-looking measure of excess tail-risk contribution to the perceived variance of underlying equity returns. Using equity options data for individual U.S.-listed stocks during 2000-2013, we find that the average return differential between the lowest and highest IV convexity quintile portfolios exceeds 1% per month, which is both economically and statistically significant on a risk-adjusted basis.