On Exact and Approximate Stochastic Dominance Strategies for Portfolio Selection

Enhanced Indexation is the selection of a portfolio that should produce a return in excess to that of a given benchmark index. One recent and promising strategy for this task is the selection of portfolios that stochastically dominate the benchmark. Several types of stochastic dominance relations are known, but their practical application can be troublesome. We propose here a new type of approximate stochastic dominance relation that is more suitable for portfolio selection problems. We show that this relation is stronger than other existing approximate stochastic dominance relations, and we use it to nd the portfolio that approximately stochastically dominates a given benchmark with the best possible approximation. Our model is formulated as an LP with exponentially many constraints. Nonetheless, we show that it has a theoretical polynomial time complexity through the equivalence of optimization and separation, and we propose an efficient constraint generation algorithm for its solution. We present some further improvements of stochastic dominance approaches. We evaluate the practical behavior of the selected portfolios with extensive empirical analyses on real and publicly available datasets, obtaining very good out­of­sample performances.