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Relative arbitrage in volatility-stabilized markets

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  • Robert Fernholz
  • Ioannis Karatzas

Abstract

We provide simple, easy-to-test criteria for the existence of relative arbitrage in equity markets. These criteria postulate essentially that the excess growth rate of the market portfolio, a positive quantity that can be estimated or even computed from a given market structure, be ‘‘sufficiently large’’. We show that conditions which satisfy these criteria are manifestly present in the U.S. equity market. We then construct examples of abstract markets in which the criteria hold. These abstract markets allow us to isolate conditions similar to those prevalent in actual markets, and to construct explicit portfolios under these conditions. We study in some detail a specific example of an abstract market which is volatility-stabilized, in that the return from the market portfolio has constant drift and variance rates while the smallest stocks are assigned the largest volatilities. A rather interesting probabilistic structure emerges, in which time changes and the asymptotic theory for planar Brownian motion play crucial roles. The largest stock and the overall market grow at the same, constant rate, though individual stocks fluctuate widely. Copyright Springer-Verlag Berlin Heidelberg 2005

Suggested Citation

  • Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
    • Handle: RePEc:kap:annfin:v:1:y:2005:i:2:p:149-177
    DOI: 10.1007/s10436-004-0011-6
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    References listed on IDEAS

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    1. 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.
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    More about this item

    Keywords

    Portfolios; Relative arbitrage; Diversity; Volatility-stabilized markets; Stochastic differential equations; Strict local martingales; Time-change; Bessel processes; G10;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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