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Relative arbitrage in volatility-stabilized markets


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  • Robert Fernholz


  • Ioannis Karatzas


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    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

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    Bibliographic Info

    Article provided by Springer in its journal Annals of Finance.

    Volume (Year): 1 (2005)
    Issue (Month): 2 (November)
    Pages: 149-177

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    Handle: RePEc:kap:annfin:v:1:y:2005:i:2:p:149-177

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    Keywords: Portfolios; Relative arbitrage; Diversity; Volatility-stabilized markets; Stochastic differential equations; Strict local martingales; Time-change; Bessel processes; G10;

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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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    Cited by:
    1. Adrian Banner & Daniel Fernholz, 2008. "Short-term relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 4(4), pages 445-454, October.
    2. Aleksandar Mijatovi\'c & Mikhail Urusov, 2010. "Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models," Papers 1005.1861,
    3. Abdelkoddousse Ahdida & Aur\'elien Alfonsi, 2011. "A Mean-Reverting SDE on Correlation matrices," Papers 1108.5264,, revised Feb 2012.
    4. Irene Klein & Thorsten Schmidt & Josef Teichmann, 2013. "When roll-overs do not qualify as num\'eraire: bond markets beyond short rate paradigms," Papers 1310.0032,
    5. Abdelkoddousse Ahdida & Aurélien Alfonsi, 2013. "A Mean-Reverting SDE on Correlation matrices," Post-Print hal-00617111, HAL.
    6. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
    7. Soumik Pal & Ting-Kam Leonard Wong, 2014. "The geometry of relative arbitrage," Papers 1402.3720,, revised Mar 2014.
    8. Winslow Strong, 2012. "Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage," Papers 1212.1877,, revised Oct 2013.
    9. Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Shkolnikov, Mykhaylo, 2013. "Large volatility-stabilized markets," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 212-228.
    11. Robert Fernholz & Ioannis Karatzas, 2006. "The implied liquidity premium for equities," Annals of Finance, Springer, vol. 2(1), pages 87-99, January.
    12. Soumik Pal & Ting-Kam Leonard Wong, 2013. "Energy, entropy, and arbitrage," Papers 1308.5376,
    13. Eckhard Platen, 2008. "The Law of Minimum Price," Research Paper Series 215, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Ashkan Nikeghbali & Eckhard Platen, 2008. "On Honest Times in Financial Modeling," Research Paper Series 229, Quantitative Finance Research Centre, University of Technology, Sydney.
    15. Aleksandar Mijatović & Mikhail Urusov, 2012. "Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models," Finance and Stochastics, Springer, vol. 16(2), pages 225-247, April.
    16. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1472-1520.
    17. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    18. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999,
    19. repec:hal:wpaper:hal-00617111 is not listed on IDEAS
    20. Ioannis Karatzas & Constantinos Kardaras, 2008. "The numeraire portfolio in semimartingale financial models," Papers 0803.1877,
    21. Radka Picková, 2014. "Generalized volatility-stabilized processes," Annals of Finance, Springer, vol. 10(1), pages 101-125, February.
    22. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399,


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