On the competitive theory and practice of portfolio selection

Abstract

Given a set of say m stocks (one of which may be "cash"), the online portfolio selection problem is to determine a portfolio for the i th trading period based on the sequence of prices for the preceding i - 1 trading periods. Competitive analysis is based on a worst case perspective and such a perspective is inconsistent with the more widely accepted analyses and theories based on distributional assumptions. The competitive framework does (perhaps surprisingly) permit non trivial upper bounds on relative performance against CBAL-OPT, an optimal offline constant rebalancing portfolio. Perhaps more impressive are some preliminary experimental results showing that certain algorithms that enjoy "respectable" competitive (i.e. worst case) performance also seem to perform quite well on historical sequences of data. These algorithms and the emerging competitive theory are directly related to studies in information theory and computational learning theory and indeed some of these algorithms have been pioneered within the information theory and computational learning communities. We present a mixture of both theoretical and experimental results, including a more detalied study of the performance of existing and new algorithms with respect to a standard sequence of historical data cited in many studies. We also present experiments from two other historical data sequences. © Springer-Verlag Berlin Heidelberg 2000.