A statistical view of universal stock market portfolios

Abstract

Cover's universal portfolio has deep connections to universal data compression. In this paper, we provide a statistical view of universal portfolios in order to develop a clearer understanding of their performance on actual financial data sequences. By recasting the analysis of a universal portfolio in statistical terms - with a special emphasis on means and covariances - we are able to resolve a long standing and false perception of a disconnect between information theory and empirical finance. We first show that the universal portfolio can be characterized as a conditional expectation of a multivariate normal random variable. We then show that this implies that the universal portfolio algorithm is asymptotically approximately equal to a constrained sequential Markowitz mean-variance portfolio optimization based on estimates of the mean of a multivariate normal distribution. In light of this equivalence, we propose alternative estimation methods and conclude with some practical investment advice