Comovement and Volatility Risk Premia

Abstract

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. Using an incomplete information economy, we develop a structural model with multiple assets and explain endogenously the different volatility risk premia of index and single-stock options. We show that higher investors' 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 due to an additional correlation risk premium. In equilibrium, this different exposure to disagreement risk is compensated 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 belief 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 different standard control variables and transaction costs and are not subsumed by other theories explaining the volatility risk premia.