Option Returns and Disagreement Risk

Abstract

We study the relation between beliefs disagreement among investors and the cross-sectional differences in option returns. Writers of index options earn high returns due to a significant and high volatility risk premium but writers of options in single-stock markets earn lower returns. We develop a structural model using an incomplete information economy with multiple assets and explain endogenously the different volatility risk premia of index and single-stock options. We show that higher disagreement increases the volatility of stock returns and the volatility premia of individual options. At the same time, it generates a higher endogenous correlation of stock returns that further increases the volatility premium of index options relative to single-stock options. In equilibrium, this different exposure to disagreement risk is compensated for in the cross-section of options and model-implied trading strategies exploiting differences in disagreement earn substantial excess returns. We test the model predictions in a set of panel regressions, by merging three datasets of firm-specific information on analysts' earning forecasts, options data on S&P 100 index options, options on all constituents, and stock returns. We find that beliefs disagreement is the most powerful determinant of volatility risk premia in individual and index options. Sorting stocks based on differences in beliefs, we find that volatility trading strategies exploiting different exposures to disagreement risk in the cross-section of options earn high Sharpe ratios. The results are robust to stock risk-characteristics and are not subsumed by other theories explaining the volatility risk premia.