Testing the boundaries of applicability of standard Stochastic Discount Factor models

We provide a joint non-parametric test to gather insights on the boundaries of applicability of Stochastic Discount Factor (SDF) models. We find that a non-trivial class of models cannot price the U.S. stock market equally weighted portfolio, implying non-monotonic SDFs, especially over the last 50/60 years in (recessionary) periods characterized by higher market volatility. Stocks responsible for this rejection mostly belong to the smallest NYSE market cap decile, are characterized by high idiosyncratic risk, and typically cannot be priced via SDF models where the aggregate level of risk aversion is bigger then 9 or 10. Excluding these stocks increases the ability to explain the cross-section of returns without impairing the ability to span the mean–variance frontier.