Monotonicity of the Stochastic Discount Factor and Expected Option Returns

Empirical evidence shows that the pricing kernel, or stochastic discount factor (SDF), is not always downward sloping when estimated using Samp;P 500 data. On the other hand, we show that individual stock SDFs are in general downward sloping. We show that a simple jump diffusion returns model can reconcile these empirical findings. The same model also implies a steeper implied volatility curve for the index compared to the typical stock, a well-known empirical fact from the options literature. Both the SDF results and the implied-smile results can be explained by a common source of jump risk among stocks together with diversification of Brownian risk in the index. SDF violations arise when the per-unit-return compensation for Brownian risk exceeds that for jump risk. Diversification increases the former compensation more than the latter, making SDF violations more likely in the index than the typical stock. We also devise novel empirical tests of overall SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the density functions of returns