Efficient Universal Portfolios for Past‐Dependent Target Classes

Abstract

We present a new universal portfolio algorithm that achieves almost the same level of wealth as could be achieved by knowing stock prices ahead of time. Specifically the algorithm tracks the best in hindsight wealth achievable within target classes of linearly parameterized portfolio sequences. The target classes considered are more general than the standard constant rebalanced portfolio class and permit portfolio sequences to exhibit a continuous form of dependence on past prices or other side information. A primary advantage of the algorithm is that it is easily computable in a polynomial number of steps by way of simple closed-form expressions. This provides an edge over other universal algorithms that require both an exponential number of computations and numerical approximation.

PAMR: Passive aggressive mean reversion strategy for portfolio selection

“…Following their work, Cover and Ordentlich (1996) developed universal procedures when side information 1 is taken into account as a finite number of values. Cross and Barron (2003) proposed a new universal portfolio strategy tracking the best in-hindsight wealth achievable within target classes of linearly parameterized portfolio sequences, which are more general than the standard CRP class and permit the portfolio to display a continuous form of dependence on past prices or other side information. Belentepe (2005) presented a statistical view of Cover's UP, showing that it is approximately equivalent to a constrained sequential portfolio optimization, which connects Cover's UP with traditional mean-variance portfolio theory.…”

Stochastic interpretation of universal portfolio and generalized target classes

“…In other words, a CMP can use past observations as side information, i.e. this can be thought of as a special type of portfolio with side information, which is studied by [4], [6] etc.…”

Nonparametric Kernel‐based Sequential Investment Strategies

“…For example, CRPs are known to be asymptotically optimal if the market vectors x 1 , …, x n are realizations of an independent, identically distributed sequence of random vectors (see below) but are insufficient if the market vectors of different trading periods have a statistical dependence, which seems to be the case in real‐world markets. For this reason, larger reference classes have also been considered (see, e.g., the side‐information model of Cover and Ordentlich [1996], the switching portfolios of Singer [1997], and also Cross and Barron [2003]) but similar limitations still hold.…”