A Comparison of Two Types of Universal Portfolios Based on Some Stock-price Data

Abstract

In this paper, we shall compare the performances of the Cover-Ordentlich and Helmbold-Schapire-Singer-Warmuth (abbreviated as HSSW) universal portfolios. We investigate whether the class of HSSW universal portfolios outperforms the general parametric class of the Dirichlet-weighted universal portfolios studied by [3, 5] in all situations. Based on some stock-price data from the Kuala Lumpur Stock Exchange, we show that the performance of the HSSW universal portfolio is sensitive to the initial starting portfolio. The HSSW universal portfolio has the approximate behaviour of a constant rebalanced portfolio. With a proper choice of the initial starting portfolio, the HSSW universal portfolio can achieve a higher wealth than that of any Dirichlet-weighted Cover-Ordentlich universal portfolio. On the contrary, we can also find a HSSW universal portfolio that will achieve a lower wealth than that of any Dirichlet-weighted Cover-Ordentlich universal portfolio. Without the advantage of hindsight, we conclude that it is not practical to use the HSSW universal portfolio unless the problem of choosing the proper initial starting portfolio is resolved.