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Market Influence of Portfolio Optimizers

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  • Suhas Nayak
  • George Papanicolaou
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    Abstract

    The paper reports on a study of the feedback effects induced by portfolio optimizers on the underlying asset prices. Through their interaction with reference traders, who trade based on some aggregate incomes process, they are assumed to move asset prices away from the standard log-normal model. With market clearing as the main constraint, the approximate dynamics of the asset price are solved analytically assuming that the wealth of the portfolio optimizers is small relative to the total market capitalization of the stock. The influence of portfolio optimizers when their wealth is not so small is also calculated numerically. There is good agreement between the numerical and analytical results when the wealth of the optimizers is small. It is found that portfolio optimizers influence the price of the risky asset so as to decrease its volatility. The optimal allocation to the risky asset also changes as a result of the portfolio optimizers' actions. In general, it is advantageous to hold more of the risky asset, relative to the log normal Merton model.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701269285
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 15 (2008)
    Issue (Month): 1 ()
    Pages: 21-40

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    Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:21-40

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: Hamilton-Jacobi-Bellman equation; feedback; portfolio optimization;

    References

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    1. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23.
    3. Mattias Jonsson & Jussi Keppo, 2002. "Option pricing for large agents," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(4), pages 261-272.
    4. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84.
    5. Brennan, Michael J & Schwartz, Eduardo S, 1989. "Portfolio Insurance and Financial Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 62(4), pages 455-72, October.
    6. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
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