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Non-convex optimal portfolio sets and constant relative risk aversion

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  • Zhang, Duo
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    Abstract

    This paper shows by example that, under constant relative risk aversion (CRRA), the set of optimal portfolios can be non-convex even in the presence of a complete set of Arrow-Debreu securities. This implies that, with exclusively CRRA investors, market models without a strong distributional assumption such as that of the capital asset pricing model cannot be tested by testing the optimality of the market portfolio, or by assuming a representative investor. This demonstration extends the key result of Dybvig and Ross [Dybvig, P. H., & Ross S. A. (1982). Portfolio efficient sets. Econometrica, 50, 1525-1546], who showed an example of non-convexity with less restrictive utility assumptions but which could not apply to the case of a complete set of Arrow-Debreu securities.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economics and Business.

    Volume (Year): 60 (2008)
    Issue (Month): 6 ()
    Pages: 551-555

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    Handle: RePEc:eee:jebusi:v:60:y:2008:i:6:p:551-555

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    Web page: http://www.elsevier.com/locate/jeconbus

    Related research

    Keywords: Optimal portfolio sets Constant relative risk aversion Convexity;

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    1. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
    2. 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.
    3. Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-46, November.
    4. Gelles, Gregory M. & Mitchell, Douglas W., 2002. "Increasingly mean-seeking utility functions and n-asset portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(5), pages 911-919.
    5. Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
    6. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
    7. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
    8. Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, vol. 48(10), pages 1334-1349, October.
    9. Blume, Marshall E & Friend, Irwin, 1975. "The Asset Structure of Individual Portfolios and Some Implications for Utility Functions," Journal of Finance, American Finance Association, vol. 30(2), pages 585-603, May.
    10. Russell, Thomas, 1986. "On the convexity of the portfolio choice set," Economics Letters, Elsevier, vol. 21(4), pages 371-373.
    11. Shefrin, Hersh & Statman, Meir, 1985. " The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence," Journal of Finance, American Finance Association, vol. 40(3), pages 777-90, July.
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