Exact and Approximate Stochastic Dominance for Portfolio Selection

One recent and promising strategy for Enhanced Indexation [1,5] is the selection of portfolios that stochastically dominate the benchmark. We propose here a new type of approximate stochastic dominance rule and we show that it implies other existing approximate stochastic dominance rules [3,4]. We then use it to find the portfolio that approximately stochastically dominates a given benchmark with the best possible approximation. Our model is initially formulated as a Linear Program with exponentially many constraints, and then reformulated in a more compact manner so that it can be very efficiently solved in practice. This reformulation also reveals an interesting financial interpretation. We then compare our approach with several exact and approximate stochastic dominance models [2,4,5] for portfolio selection by means of an extensive empirical analysis on real and publicly available datasets, obtaining good out‐ofsample performances.