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Changes in multiplicative risks and optimal portfolio choice: new interpretations and results

Author

Listed:
  • Marzia Donno

    (Università degli Studi di Parma)

  • Marco Magnani

    (Università degli Studi di Parma)

  • Mario Menegatti

    (Università degli Studi di Parma)

Abstract

This paper reconsiders the conditions determining the optimal response of a decision maker in case of stochastic changes in multiplicative risks. In particular, we focus on an optimal portfolio choice where the return of the risky asset exhibits an Nth-degree risk increase. We provide two interpretations of the conditions analyzed. The first interpretation involves a comparison between the elasticities with respect to the investment in the risky asset of the Nth derivative of the utility function and of the distance between the Nth moments of the two risks. The second interpretation refers to the direction of the change in the utility premium when the investment in the risky asset changes. We then study the linkages between the conditions determining optimal responses of risky investment in the case of risk increases of different degrees. We show that, under some assumptions, the optimal behavior of an agent in the case of Nth degree risk increase makes it possible to infer agent’s behavior in case of risk increases of lower degrees.

Suggested Citation

  • Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:1:d:10.1007_s10203-019-00250-1
    DOI: 10.1007/s10203-019-00250-1
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    More about this item

    Keywords

    Multiplicative risk; Nth-degree risk change; Portfolio choice;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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