Portfolio Choice Based on Third-Degree Stochastic Dominance

TLDR

The study develops an optimization method to construct portfolios that achieve third‑degree stochastic dominance over a benchmark. The method uses a semivariance‑based superconvex dominance condition and quadratic constrained programming, applied to historical stock data with an industry momentum strategy. The resulting portfolio outperforms mean‑variance and second‑degree stochastic dominance approaches, raising out‑of‑sample returns by nearly seven percentage points per year versus the CRSP all‑share index while keeping downside risk unchanged. Paper accepted by Lauren Cohen, finance.

Abstract

We develop an optimization method for constructing investment portfolios that dominate a given benchmark portfolio in terms of third-degree stochastic dominance. Our approach relies on the properties of the semivariance function, a refinement of an existing “superconvex” dominance condition, and quadratic constrained programming. We apply our method to historical stock market data using an industry momentum strategy. Our enhanced portfolio generates important performance improvements compared with alternatives based on mean-variance dominance and second-degree stochastic dominance. Relative to the Center for Research in Security Prices all-share index, our portfolio increases average out-of-sample return by almost seven percentage points per annum without incurring more downside risk, using quarterly rebalancing and without short selling. This paper was accepted by Lauren Cohen, finance.