Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

The Cost of Achieving the Best Portfolio in Hindsight

Erik Ordentlich and Thomas M. Cover
Mathematics of Operations Research
Vol. 23, No. 4 (Nov., 1998), pp. 960-982
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690641
Page Count: 23
  • Download ($30.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Cost of Achieving the Best Portfolio in Hindsight
Preview not available

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 $V_{n}=[\Sigma \ 2^{-nH(n_{1}/n,\ldots ,n_{m}/n)}(n!/(n_{1}!\cdots n_{m}!))]^{-1}$, 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.

Page Thumbnails

  • Thumbnail: Page 
960
    960
  • Thumbnail: Page 
961
    961
  • Thumbnail: Page 
962
    962
  • Thumbnail: Page 
963
    963
  • Thumbnail: Page 
964
    964
  • Thumbnail: Page 
965
    965
  • Thumbnail: Page 
966
    966
  • Thumbnail: Page 
967
    967
  • Thumbnail: Page 
968
    968
  • Thumbnail: Page 
969
    969
  • Thumbnail: Page 
970
    970
  • Thumbnail: Page 
971
    971
  • Thumbnail: Page 
972
    972
  • Thumbnail: Page 
973
    973
  • Thumbnail: Page 
974
    974
  • Thumbnail: Page 
975
    975
  • Thumbnail: Page 
976
    976
  • Thumbnail: Page 
977
    977
  • Thumbnail: Page 
978
    978
  • Thumbnail: Page 
979
    979
  • Thumbnail: Page 
980
    980
  • Thumbnail: Page 
981
    981
  • Thumbnail: Page 
982
    982