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Super-Replication of the Best Pairs Trade in Hindsight

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  • Alex Garivaltis

Abstract

This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing rule will sell a precise amount of the outperforming stock and put the proceeds into the underperforming stock. Under typical conditions, in hindsight one can find pairs rebalancing rules that would have spectacularly beaten the market. Our trading strategy, which extends Ordentlich and Cover's (1998) "max-min universal portfolio," guarantees to achieve an acceptable percentage of the hindsight-optimized wealth, a percentage which tends to zero at a slow (polynomial) rate. This means that on a long enough investment horizon, the trader can enforce a compound-annual growth rate that is arbitrarily close to that of the best pairs rebalancing rule in hindsight. The strategy will "beat the market asymptotically" if there turns out to exist a pairs rebalancing rule that grows capital at a higher asymptotic rate than the market index. The advantages of our algorithm over the Ordentlich and Cover (1998) strategy are twofold. First, their strategy is impossible to compute in practice. Second, in considering the more modest benchmark (instead of the best all-stock rebalancing rule in hindsight), we reduce the "cost of universality" and achieve a higher learning rate.

Suggested Citation

  • Alex Garivaltis, 2018. "Super-Replication of the Best Pairs Trade in Hindsight," Papers 1810.02444, arXiv.org, revised Oct 2022.
  • Handle: RePEc:arx:papers:1810.02444
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    References listed on IDEAS

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    1. Alex Garivaltis, 2018. "Exact Replication of the Best Rebalancing Rule in Hindsight," Papers 1810.02485, arXiv.org, revised Mar 2019.
    2. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Farshid Jamshidian, 1992. "Asymptotically Optimal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 131-150, April.
    5. Erik Ordentlich & Thomas M. Cover, 1998. "The Cost of Achieving the Best Portfolio in Hindsight," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 960-982, November.
    6. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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