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On‐Line Portfolio Selection Using Multiplicative Updates


  • David P. Helmbold
  • Robert E. Schapire
  • Yoram Singer
  • Manfred K. Warmuth


We present an on‐line investment algorithm that achieves almost the same wealth as the best constant‐rebalanced portfolio determined in hindsight from the actual market outcomes. The algorithm employs a multiplicative update rule derived using a framework introduced by Kivinen and Warmuth. Our algorithm is very simple to implement and requires only constant storage and computing time per stock in each trading period. We tested the performance of our algorithm on real stock data from the New York Stock Exchange accumulated during a 22‐year period. On these data, our algorithm clearly outperforms the best single stock as well as Cover's universal portfolio selection algorithm. We also present results for the situation in which the investor has access to additional “side information.”

Suggested Citation

  • David P. Helmbold & Robert E. Schapire & Yoram Singer & Manfred K. Warmuth, 1998. "On‐Line Portfolio Selection Using Multiplicative Updates," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 325-347, October.
  • Handle: RePEc:bla:mathfi:v:8:y:1998:i:4:p:325-347
    DOI: 10.1111/1467-9965.00058

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