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Energy, entropy, and arbitrage


  • Soumik Pal
  • Ting-Kam Leonard Wong


We introduce a pathwise approach to analyze the relative performance of an equity portfolio with respect to a benchmark market portfolio. In this energy-entropy framework, the relative performance is decomposed into three components: a volatility term, a relative entropy term measuring the distance between the portfolio weights and the market capital distribution, and another entropy term that can be controlled by the investor by adopting a suitable rebalancing strategy. This framework leads to a class of portfolio strategies that allows one to outperform, in the long run, a market that is diverse and sufficiently volatile in the sense of stochastic portfolio theory. The framework is illustrated with several empirical examples.

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  • Soumik Pal & Ting-Kam Leonard Wong, 2013. "Energy, entropy, and arbitrage," Papers 1308.5376,, revised Jan 2016.
  • Handle: RePEc:arx:papers:1308.5376

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    References listed on IDEAS

    1. Daniel Kuhn & David Luenberger, 2010. "Analysis of the rebalancing frequency in log-optimal portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 221-234.
    2. Michael A. H. Dempster & Igor V. Evstigneev & Klaus R. Schenk-hoppe, 2007. "Volatility-induced financial growth," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 151-160.
    3. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
    4. Eckhard Platen & Renata Rendek, 2010. "Approximating the Numeraire Portfolio by Naive Diversification," Research Paper Series 281, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
    6. Fernholz, Robert & Shay, Brian, 1982. " Stochastic Portfolio Theory and Stock Market Equilibrium," Journal of Finance, American Finance Association, vol. 37(2), pages 615-624, May.
    7. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
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