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The Cost of Achieving the Best Portfolio in Hindsight

The Cost of Achieving the Best Portfolio in Hindsight For a market with m assets consider the minimum, over all possible sequences of asset prices through time n, of the ratio of the final wealth of a nonanticipating investment strategy to the wealth obtained by the best constant rebalanced portfolio computed in hindsight for that price sequence. We show that the maximum value of this ratio over all nonanticipating investment strategies is Vn = [∑ 2−nH(n_1/n,…,n_m/n)(n!/(n1! … nm!))]−1, where H(·) is the Shannon entropy, and we specify a strategy achieving it. The optimal ratio Vn is shown to decrease only polynomially in n, indicating that the rate of return of the optimal strategy converges uniformly to that of the best constant rebalanced portfolio determined with full hindsight. We also relate this result to the pricing of a new derivative security which might be called the hindsight allocation option. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics of Operations Research INFORMS

The Cost of Achieving the Best Portfolio in Hindsight

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References (25)

Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0364-765X
eISSN
1526-5471
DOI
10.1287/moor.23.4.960
Publisher site
See Article on Publisher Site

Abstract

For a market with m assets consider the minimum, over all possible sequences of asset prices through time n, of the ratio of the final wealth of a nonanticipating investment strategy to the wealth obtained by the best constant rebalanced portfolio computed in hindsight for that price sequence. We show that the maximum value of this ratio over all nonanticipating investment strategies is Vn = [∑ 2−nH(n_1/n,…,n_m/n)(n!/(n1! … nm!))]−1, where H(·) is the Shannon entropy, and we specify a strategy achieving it. The optimal ratio Vn is shown to decrease only polynomially in n, indicating that the rate of return of the optimal strategy converges uniformly to that of the best constant rebalanced portfolio determined with full hindsight. We also relate this result to the pricing of a new derivative security which might be called the hindsight allocation option.

Journal

Mathematics of Operations Research – INFORMS

Published: Nov 1, 1998

Keywords: Keywords : Portfolio selection ; asset allocation ; derivative security ; optimal investment

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