The Puzzle of Index Option Returns

We document that leverage-adjusted returns on S&P 500 index call and put portfolios are decreasing in their strike-to-price ratio over 1986-2010, contrary to the prediction of the Black-Scholes-Merton model. We test a large number of plausible unconditional factor models and find that only factors which capture jumps in the market index and jumps in the market volatility and, to a lesser extent, volatility and liquidity reasonably explain the cross-section of index options. The principal finding is that these factors require economically and statistically different factor premia on subsamples split across type (calls and puts), maturity, and moneyness, pointing towards market segmentation