On-line portfolio selection using multiplicative updates

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

Research output: Contribution to journalReview articlepeer-review

221 Scopus citations


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.".

Original languageEnglish (US)
Pages (from-to)325-347
Number of pages23
JournalMathematical Finance
Issue number4
StatePublished - Oct 1998

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Economics and Econometrics
  • Accounting
  • Finance
  • Social Sciences (miscellaneous)


  • Machine learning algorithms
  • Portfolio selection
  • Rebalancing


Dive into the research topics of 'On-line portfolio selection using multiplicative updates'. Together they form a unique fingerprint.

Cite this