Portfolio choice algorithms, including exact stochastic dominance

Abstract

Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions f(xj) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved f(xj) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe f(xj). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.