Non-convex optimal portfolio sets and constant relative risk aversion
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jackwerth, Jens Carsten, 2000.
"Recovering Risk Aversion from Option Prices and Realized Returns,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(2), pages 433-451.
- Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers RPF-265, University of California at Berkeley.
- Jens Carsten Jackwerth, 1998. "Recovering Risk Aversion from Option Prices and Realized Returns," Finance 9803002, EconWPA.
- Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-1546, November.
- Russell, Thomas, 1986. "On the convexity of the portfolio choice set," Economics Letters, Elsevier, vol. 21(4), pages 371-373.
- Moshe Levy & Haim Levy, 2002. "Prospect Theory: Much Ado About Nothing?," Management Science, INFORMS, vol. 48(10), pages 1334-1349, October.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
- 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 777-790, July.
- 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.
- 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.
- 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 745-752, June.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:jebusi:v:60:y:2008:i:6:p:551-555. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If references are entirely missing, you can add them using this form.