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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- 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.
- Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-46, November.
- 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.
- 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.
- Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-30, June.
- 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.
- Jens Carsten Jackwerth, 1998.
"Recovering Risk Aversion from Option Prices and Realized Returns,"
- 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 433-51.
- 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.
- 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.
- 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.
- 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.
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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.