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Competitive Nash Equilibria and Two Period Fund Separation

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  • Thorsten Hens
  • Stefan Reimann
  • Bodo Vogt
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    Abstract

    We suggest a simple asset market model in which we analyze competitive and strategic behavior simultaneously. If for competitive behavior two-fund separation holds across periods then it also holds for strategic behavior. In this case the relative prices of the assets do not depend on whether agents behave strategically or competitively. Those agents acting strategically will however invest less in the common mutual fund. Constant relative risk aversion and absence of aggregate risk are shown to be two alternative sufficient conditions for two-period fund separation. With derivatives further strategic aspects arise and strategic behavior is distinct from competitive behavior even for those utility functions leading to two-fund separation.

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    Bibliographic Info

    Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 172.

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    Handle: RePEc:zur:iewwpx:172

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    Keywords: strategic behavior; competitive behavior; two-fund-separation; CAPM.;

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    1. Pagano, Marco, 1986. "Trading Volume and Asset Liquidity," CEPR Discussion Papers 142, C.E.P.R. Discussion Papers.
    2. Kraus, Alan & Litzenberger, Robert H, 1975. "Market Equilibrium in a Multiperiod State Preference Model with Logarithmic Utility," Journal of Finance, American Finance Association, vol. 30(5), pages 1213-27, December.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
    5. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    6. Luenberger, David G., 1997. "Investment Science," OUP Catalogue, Oxford University Press, number 9780195108095, July.
    7. Carlos Alós-Ferrer & Ana B. Ania, 2003. "The Asset Market Game," Vienna Economics Papers 0320, University of Vienna, Department of Economics.
    8. Brunnermeier, Markus K., 2001. "Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis, and Herding," OUP Catalogue, Oxford University Press, number 9780198296980, July.
    9. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
    10. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
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