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

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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… Click to show full 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 N th-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 N th derivative of the utility function and of the distance between the N th 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 N th degree risk increase makes it possible to infer agent’s behavior in case of risk increases of lower degrees.

Keywords: portfolio choice; changes multiplicative; case; multiplicative risks; optimal portfolio

Journal Title: Decisions in Economics and Finance
Year Published: 2019

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