Expected Option Returns

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 BlackScholes 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

The pricing kernel puzzle: survey and outlook

“…A stronger result is presented in Coval and Shumway (2001): the expected return on a call should be greater than the expected return on the underlying, which broadly holds in the data. 11 The authors then investigate returns on option straddles and find evidence of priced volatility risk, which they cannot reconcile with power utility for the representative investor.…”

“…Chaudhury and Schroder (2015) extend the results of Coval and Shumway (2001) by showing that the pricing kernel is only monotonically decreasing if (conditional) expected returns on certain option positions (called "log-concave" and encompassing long calls, puts, butterfly spreads, and others) increase in the strike price. They confirm the pricing kernel puzzle based on data for the S&P 500 index but fail for individual stock options.…”

“…12 Ni (2009) investigates a test similar to Coval and Shumway (2001) for individual stock options instead of index options. Her surprising results could be due to methodological problems, see the critical discussion in Chaudhury and Schroder (2015).…”

“…Another extension in Bali, Cakici, Chabi-Yo, and Murray (2014) looks at the higher risk-neutral moments of option returns. Song (2012) applies the ideas of Coval and Shumway (2001) to returns on options on volatility in the case of u-shaped pricing kernels.…”

Variance Risk Premia in Energy Commodities

“…3 The source of the data is NYMEX (the New York Mercantile Exchange), which is the largest marketplace for these options. 4 The risk and return characteristics of equity index volatility has been studied in a number of papers -see, e.g., Coval and Shumway (2001), Pan (2002), Bakshi and Kapadia (2003a), Bondarenko (2004), Bollerslev, Gibson, and Zhou (2004), and Carr and Wu (2009). It is interesting to compare the results for energy commodities with the results reported in these papers.…”