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Exponential growth of fixed-mix strategies in stationary asset markets

Author

Listed:
  • Igor V. Evstigneev

    (School of Economic Studies, University of Manchester, Oxford Road, Manchester, M13 9PL, UK)

  • Michal A. H. Dempster

    (Centre for Financial Research, Judge Institute of Management, University of Cambridge, Trumpington Street, Cambridge, CB2 1AG, UK)

  • Klaus R. Schenk-Hoppé

    (Institute for Empirical Research in Economics, University of Zurich, Blümlisalpstrasse 10, 8006 Zürich, Switzerland Manuscript)

Abstract

The paper analyzes the long-run performance of dynamic investment strategies based on fixed-mix portfolio rules. Such rules prescribe rebalancing the portfolio by transferring funds between its positions according to fixed (time-independent) proportions. The focus is on asset markets where prices fluctuate as stationary stochastic processes. Under very general assumptions, it is shown that any fixed-mix strategy in a stationary market yields exponential growth of the portfolio with probability one.

Suggested Citation

  • Igor V. Evstigneev & Michal A. H. Dempster & Klaus R. Schenk-Hoppé, 2003. "Exponential growth of fixed-mix strategies in stationary asset markets," Finance and Stochastics, Springer, vol. 7(2), pages 263-276.
    • Handle: RePEc:spr:finsto:v:7:y:2003:i:2:p:263-276
    Note: received: February 2002; final version received: May 2002
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    Citations

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    Cited by:

    1. Cees Diks & Florian Wagener, 2006. "A Weak Bifurcation Theory for Discrete Time Stochastic Dynamical Systems," Tinbergen Institute Discussion Papers 06-043/1, Tinbergen Institute.
    2. Cees Diks & Florian Wagener, 2005. "Equivalence and Bifurcations of Finite Order Stochastic Processes," Tinbergen Institute Discussion Papers 05-043/1, Tinbergen Institute.
    3. Evstigneev, Igor V. & Schenk-Hoppe, Klaus Reiner, 2007. "Pure and randomized equilibria in the stochastic von Neumann-Gale model," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 871-887, September.
    4. Igor Evstigneev & Dhruv Kapoor, 2009. "Arbitrage in stationary markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 5-12, May.
    5. Sjur Flåm, 2010. "Portfolio management without probabilities or statistics," Annals of Finance, Springer, vol. 6(3), pages 357-368, July.
    6. Wael Bahsoun & Igor Evstigneev & Michael Taksar, 2007. "Capital growth theory and von Neumann-Gale dynamics," Economics Discussion Paper Series 0720, Economics, The University of Manchester.

    More about this item

    Keywords

    Asset allocation; fixed-mix strategies; stationary markets; exponential growth; products of random matrices; stochastic version of the Perron-Frobenius theorem;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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