Risk Preferences Implied by Synthetic Options

The historical returns on equity index options are well known to be strikingly negative. That is typically explained either by investors having convex marginal utility over stock returns (e.g. crash/variance aversion) or by intermediaries demanding a premium for hedging risk. This paper examines the consistency of those explanations with returns on dynamically replicated, or synthetic, options. Theoretically, it derives conditions under which convex marginal utility leads synthetic options to also have negative excess returns. Empirically, synthetic options have CAPM alphas near zero over the period 1926--2022, in stark contrast to exchange-traded options. Over the last 15 years, returns on traded options have converged to those on synthetic options -- with the variance risk premium shrinking towards zero -- while various drivers of the cost and risk of hedging options exposures have declined, consistent with a model in which intermediaries drive option prices.