Adaptive universal portfolios

Abstract

In this article, we consider Cover's universal portfolio and the problem of multi-period investment in a nonparametric setting. We show that Cover's universal portfolio is equivalent to a Bayes estimator of the optimal growth portfolio. However, as noted by Cover, it can take a long time for the universal portfolio to produce significant growth. Therefore, we propose the adaptive universal portfolio, which retains much of the qualitative nature of Cover's universal portfolio while enhancing early performance. An empirical study is carried out over a range of exchange traded funds over a 5 year period, which exhibits the enhanced early performance generated by the adaptive universal portfolio.