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Non-convex optimal portfolio sets and constant relative risk aversion

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  • Zhang, Duo

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.

Suggested Citation

  • Zhang, Duo, 2008. "Non-convex optimal portfolio sets and constant relative risk aversion," Journal of Economics and Business, Elsevier, vol. 60(6), pages 551-555.
    • Handle: RePEc:eee:jebusi:v:60:y:2008:i:6:p:551-555
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    Cited by:

    1. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.

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