Adaptive universal portfolios

Abstract

The purpose of this paper is to develop a stock selection algorithm with similar properties as Cover’s Universal Portfolio, but providing superior early growth. Cover’s Universal Portfolio generates a growth rate asymptotically equal to the best achievable growth rate over the set of constant rebalanced portfolios. However, Cover’s Universal Portfolio is empirically seen to generate poor early growth. While much research has been conducted in relation to Cover’s Universal Portfolio, much of this has focused on efficient implementation of the algorithm and considerations of market frictions. As such, there remains a significant research gap in addressing the issue of poor early growth generated by Cover’s strategy. With this in mind we develop the Adaptive Universal Portfolio, a sequential portfolio selection algorithm with similar asymptotic properties as Cover’s Universal Portfolio but providing greater early growth. In this paper we provide an analysis of the growth generated by the two algorithms. Furthermore we present empirical evidence of the superior early growth generated by the Adaptive Universal Portfolio. Finally we discuss possible criticisms of the Adaptive Universal Portfolio, including evidence of momentum following and vulnerability to individual stock risks, and provide an insight into possible future work in this area.