Evidence shows that the stochastic discount factor (SDF) is not always a downward-sloping function of S&P 500 returns when estimated using options data. In contrast, our results suggest that SDFs as functions of individual stock returns are generally downward sloping. A simple jump-diffusion model can reconcile these empirical findings. The same model also implies a steeper implied-volatility curve for the index than for the typical stock, a well-known empirical fact from the options literature. Both the SDF and volatility-curve results can be explained by a common source of jump risk among stocks, together with diversification of Brownian risk in the index. We also devise novel empirical tests of SDF monotonicity based on average returns of option trading strategies, thus avoiding the estimation of the return density functions.

We study cross-subsidization among U.S. equity products managed by institutional asset management firms. We find returns-based evidence consistent with both cross-subsidization receipt by strong recent performers that are relatively small in their firms and provision by products that are relatively large in their firms. Tax-exempt investors and taxable investors do not have a clear ranking by expertise, but tax-exempt investors’ agency issues are more complex. Accordingly, taxable clients have more flow-performance nonlinearity and receive more (and provide less) cross-subsidization. Taxable investor flows appear more discerning, but only under the circumstances conducive to cross-subsidization, suggesting that “more discerning” likely means “more cross-subsidized.”Received May 11, 2015; editorial decision April 22, 2017 by Editor Andrew Karolyi.