Beta Smile and Coskewness: Theoretical and Empirical Results in Options Markets

This paper investigates the characteristics of the higher moment risks of option returns, namely beta and coskewness. Under mild assumptions, the investors’ decreasing absolute risk aversion can result in a U-shaped pattern (a beta smile) for put option betas, though call option betas are always nondecreasing in the strike price. The coskewness for call options can be an inverted U-shape when the underlying returns are negatively skewed. We discuss some implications of these results in the context of the investor’s risk preference for skewness. We also provide empirical evidence that supports our theoretical results.