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.

Transaction costs have a first-order effect on the performance of currency portfolios. Proportional costs based on quoted bid–ask spread are relatively small, but when a fund is large, costs due to the trading volume price impact are sizable and quickly erode returns, leaving many popular strategies unprofitable. A mean–variance-transaction-cost optimized approach (MVTC) that accounts for costs in the optimization efficiently tackles the problem with only relatively minor negative implications on before-cost profitability. MVTC is robust even when the price impact of trading is severe. Finally, we introduce an accurate extrapolation approach to expand the sample of the realized Amihud measure of Ranaldo and Santucci de Magistris (2022) from 12 to 26 currencies and from 2012 back in time to 1986.