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Stocks for the log-run and constant relative risk aversion preferences

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  • Levy, Moshe

Abstract

Almost Stochastic Dominance implies that stocks are preferred over bonds in the long-run by all preferences with bounded marginal utility. Unfortunately, this analysis excludes the very central Constant Relative Risk Aversion (CRRA) preferences, which have unbounded marginal utility. We derive a simple closed-form solution for the portfolio-choice problem of CRRA investors which, with the empirical parameters, implies that stocks are preferred over bonds for all CRRA investors with relative risk aversion smaller than 3.9. As a by-product, the analysis offers an alternative derivation of the continuous-time CAPM, that does not rely on dynamic programming, and allows for ambiguous investment horizons.

Suggested Citation

  • Levy, Moshe, 2019. "Stocks for the log-run and constant relative risk aversion preferences," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1163-1168.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:3:p:1163-1168
    DOI: 10.1016/j.ejor.2019.03.033
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    Cited by:

    1. Haim Levy, 2020. "Aging Population, Retirement, and Risk Taking: Reply," Management Science, INFORMS, vol. 66(6), pages 2796-2799, June.
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    3. M. Mercè Claramunt & Maite Mármol & Xavier Varea, 2023. "Facing a Risk: To Insure or Not to Insure—An Analysis with the Constant Relative Risk Aversion Utility Function," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    4. Liesiö, Juuso & Xu, Peng & Kuosmanen, Timo, 2020. "Portfolio diversification based on stochastic dominance under incomplete probability information," European Journal of Operational Research, Elsevier, vol. 286(2), pages 755-768.

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