Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

Kassimatis, Konstantinos

doi:10.1016/j.irfa.2021.101932

Cited by 4 publications

(1 citation statement)

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“…Based on state-dependent risk aversion and efficient dynamic programming, Rainer (2022, see [15]) presented a heuristic mean-variance optimization in Markov decision processes to achieve a balance between maximizing expected rewards and minimizing risks. By using a CRRA utility function, Kassimatis (2021, see [7]) examined whether mean-variance is a good proxy for portfolios, and found that MV portfolios are a poor proxy for investors with CRRA preferences. Marianil et al (2022, see [12]) proposed a measure for portfolio risk management by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns.…”

Section: Introductionmentioning

confidence: 99%

Utility basis of consumption and investment decisions in a risk environment

Kang-ping

2022

Acta Math Sci

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Using expectations regarding utilities to make decisions in a risk environment hides a paradox, which is called the expected utility enigma. Moreover, the mystery has not been solved yet; an imagined utility function on the risk-return plane has been applied to establish the mean-variance model, but this hypothetical utility function not only lacks foundation, it also holds an internal contradiction. This paper studies these basic problems. Through risk preference VNM condition is proposed to solve the expected utility enigma. How can a utility function satisfy the VNM condition? This is a basic problem that is hard to deal with. Fortunately, it is found in this paper that the VNM utility function can have some concrete forms when individuals have constant relative risk aversion. Furthermore, in order to explore the basis of mean-variance utility, an MV function is founded that is based on the VNM utility function and rooted in underlying investment activities. It is shown that the MV function is just the investor’s utility function on the risk-return plane and that it has normal properties. Finally, the MV function is used to analyze the laws of investment activities in a systematic risk environment. In doing so, a tool, TRR, is used to measure risk aversion tendencies and to weigh risk and return.

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Section: Introductionmentioning

confidence: 99%