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Universal Portfolios

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  • Thomas M. Cover

Abstract

We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i , x i2 ,…, x im )-super-t denote the performance of the stock market on day i, where x ii is the factor by which the jth stock increases on day i. Let b i = ( bi1 b i2 , b im )-super-t, b; ij > 0, b ij = 1, denote the proportion b ij of wealth invested in the "j" th stock on day i. Then S n = II i -super-n= bi-super-tx i is the factor by which wealth is increased in "n" trading days. Consider as a goal the wealth S n *= max b II i -super-n= 1 b-super-tx i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * 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 of portfolios db yields wealth such that , for every bounded sequence x 1 , x 2 …, and, under mild conditions, achieve Copyright 1991 Blackwell Publishers.

Suggested Citation

  • Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
  • Handle: RePEc:bla:mathfi:v:1:y:1991:i:1:p:1-29
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