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Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk

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Author Info

  • Peter C. Fishburn

    (The Pennsylvania State University)

  • R. Burr Porter

    (Southern Methodist University)

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    Abstract

    This paper examines changes in the optimal proportions of investment capital placed in a safe asset and in a risky asset by an expected utility maximizing risk averse investor. If the return for the safe asset increases and the risky asset distribution remains fixed, the optimal proportion invested in the safe asset will increase provided that the investor's absolute risk aversion is nondecreasing or his proportional risk aversion never exceeds unity. Otherwise, it can be optimal to decrease holdings in the safe asset when its return increases. If the return for the safe asset remains fixed and the risky distribution improves by a first degree stochastic dominance change, the optimal proportion invested in the risky asset will increase (or not decrease) provided that proportional risk aversion never exceeds one plus the product of the gross return for the safe asset times absolute risk aversion. Otherwise, it may be optimal to decrease holdings in the risky asset when its distribution improves in the indicated manner.

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    File URL: http://dx.doi.org/10.1287/mnsc.22.10.1064
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 22 (1976)
    Issue (Month): 10 (June)
    Pages: 1064-1073

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    Handle: RePEc:inm:ormnsc:v:22:y:1976:i:10:p:1064-1073

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    Cited by:
    1. Christian Gollier & Edward E. Schlee, 2006. "Increased Risk-Bearing with Background Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 0(1), pages 3.
    2. Gollier, Christian, 2004. "Optimal Positive Thinking and Decisions under Risk," IDEI Working Papers 268, Institut d'Économie Industrielle (IDEI), Toulouse.
    3. Gollier, Christian, 2009. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," TSE Working Papers 09-068, Toulouse School of Economics (TSE).
    4. Hennessy, David A., 1999. "Capacity choice in a two-stage problem under uncertainty," Economics Letters, Elsevier, vol. 65(2), pages 177-182, November.
    5. Jouini, Elyès & Napp, Clotilde, 2008. "On Abel's Concepts of Doubt and Pessimism," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/198, Université Paris-Dauphine.
    6. Gollier, Christian, 2005. "Optimal Illusions and Decisions under Risk," IDEI Working Papers 340, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. Edward Schlee & Christian Gollier, . "Information and the Equity Premium," Working Papers 2133505, Department of Economics, W. P. Carey School of Business, Arizona State University.
    8. Eichner, Thomas & Wagener, Andreas, 2011. "Increases in skewness and three-moment preferences," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 109-113, March.
    9. Thomas Eichner & Andreas Wagener, 2011. "Portfolio allocation and asset demand with mean-variance preferences," Theory and Decision, Springer, vol. 70(2), pages 179-193, February.
    10. Jean Fernand Nguema, 2005. "Stochastic dominance on optimal portfolio with one risk-less and two risky assets," Economics Bulletin, AccessEcon, vol. 7(7), pages 1-7.
    11. Masamitsu Ohnishi & Yusuke Osaki, 2005. "The Monotonicity of Asset Prices with Changes in Risk," Discussion Papers in Economics and Business 05-14, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
    12. Ormiston, Michael B. & E. Schlee, Edward, 1999. "Comparative statics tests between decision models under risk," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 145-166, October.
    13. Thomas Eichner, 2010. "Slutzky equations and substitution effects of risks in terms of mean-variance preferences," Theory and Decision, Springer, vol. 69(1), pages 17-26, July.

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