Expected Option Returns

TLDR: The authors examines expected option returns in the context of mainstream asset pricing theory and shows that option risk can be thought of as consisting of two separable components, i.e., leverage effect and systematic stochastic volatility.

Abstract: This paper examines expected option returns in the context of mainstream assetpricing theory. Under mild assumptions, expected call returns exceed those of the underlying security and increase with the strike price. Likewise, expected put returns are below the risk-free rate and increase with the strike price. S&P index option returns consistently exhibit these characteristics. Under stronger assumptions, expected option returns vary linearly with option betas. However, zero-beta, at-the-money straddle positions produce average losses of approximately three percent per week. This suggests that some additional factor, such as systematic stochastic volatility, is priced in option returns. ASSET-PRICING THEORY CLAIMS that options, like all other risky securities in an economy, compensate their holders with expected returns that are in accordance with the systematic risks they require their holders to bear. Options which deliver payoffs in bad states of the world will earn lower returns than those that deliver their payoffs in good states. The enormous popularity of option contracts has arisen, in part, because options allow investors to precisely tailor their risks to their preferences. With this in mind, a study of option returns would appear to offer a unique opportunity in which to investigate what kinds of risks are priced in an economy. However, although researchers have paid substantial attention to the pricing of options conditional on the prices of their underlying securities, relatively little work has focused on understanding the nature of option returns. Understanding option returns is important because options have remarkable risk-return characteristics. Option risk can be thought of as consisting of two separable components. The first component is a leverage effect. Because an option allows investors to assume much of the risk of the option’s underlying asset with a relatively small investment, options have characteristics similar to levered positions in the underlying asset. The Black‐ Scholes model implies that this implicit leverage, which is ref lected in option betas, should be priced. We show that this leverage should be priced under