Smart Stochastic Discount Factors

We provide a no-arbitrage framework for stochastic discount factors (SDFs) that satisfy convex pricing constraints in markets characterized by a wide range of trading frictions. We demonstrate a duality relationship connecting minimum dispersion SDFs to portfolio optimization problems with penalty functions directly capturing the underlying frictions. Empirically, we examine how mispricing impacts the SDF’s effectiveness in explaining both cross-sectional and time series variation in asset returns. We find that a minimum-variance SDF, constructed by combining the capital asset pricing model SDF with a portfolio that constrains the mispricing of nonmarket risks, achieves a favorable tradeoff between time series and cross-sectional fit. This paper was accepted by Kay Giesecke, finance. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.05750 .