Universal Switching and Side Information Portfolios Under Transaction Costs Using Factor Graphs

Abstract

We consider the sequential portfolio investment problem. We combine various insights from universal portfolios research in order to construct more sophisticated algorithms that take into account transaction costs. In particular, we use the insights of Blum and Kalai's transaction costs algorithm to take these costs into account in Cover and Ordentlich's side information portfolio and Kozat and Singer's switching portfolio. This involves carefully designing a set of causal portfolio strategies and computing a convex combination of these according to a carefully designed distribution. Universal (sublinear regret) performance bounds for each of these portfolios show that the algorithms asymptotically achieve the wealth of the best strategy from the corresponding portfolio strategy set, to first order in the exponent. Factor graph representations of the algorithms demonstrate that computationally feasible algorithms may be derived. Finally, we present results of simulations of our algorithms and compare them to other portfolios.