| The appeal and allure of Cover's universal portfolio is that it presents an implementable investment strategy that in many ways eliminates the regret that one would experience from viewing their investment decisions with the benefit of hind sight. In this thesis, 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 statistical estimation---we are able to resolve a long standing and false perception of a disconnect between information theory and empirical finance. We show that by allowing short sales and leverage the universal portfolio algorithm is approximately equivalent to a sequential Markowitz mean-variance portfolio optimization. If short sales and leverage are not allowed or restricted, then the universal portfolio is approximately equivalent to a constrained sequential optimization. In light of this equivalence, we conclude that universal portfolio construction, while presented as a distributional free procedure, embeds a well known statistical problem---estimation of a multivariate mean and covariance matrix. |
