BibTeX
@MISC{Cover96universalportfolios,
author = {Thomas M. Cover},
title = {Universal Portfolios},
year = {1996}
}
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Abstract
We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i1 ; x i2 ; : : : ; x im ) t denote the performance of the stock market on day i ; where x ij is the factor by which the j-th stock increases on day i : Let b i = (b i1 ; b i2 ; : : : ; b im ) t ; b ij 0; P j b ij = 1 ; denote the proportion b ij of wealth invested in the j-th stock on day i : Then S n = Q n i=1 b t i x i is the factor by which wealth is increased in n trading days. Consider as a goal the wealth S n = max b Q n i=1 b t x i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that S n exceeds the best stock, the Dow Jones average, and the value line index at time n: In fact, S n usually exceeds these quantities by an exponential factor. Let x 1 ; x 2 ; : : : ; be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence ...
