Non-convex optimal portfolio sets and constant relative risk aversion
AbstractThis 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 InfoArticle provided by Elsevier in its journal Journal of Economics and Business.
Volume (Year): 60 (2008)
Issue (Month): 6 ()
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Web page: http://www.elsevier.com/locate/jeconbus
Optimal portfolio sets Constant relative risk aversion Convexity;
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