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Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios

Author

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  • Taras Bodnar
  • Dmytro Ivasiuk
  • Nestor Parolya
  • Wofgang Schmid

Abstract

We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal portfolios belong to the set of mean-variance feasible portfolios and establish necessary and sufficient conditions such that they are mean-variance efficient. Furthermore, an application to the stock market is presented and the behavior of the optimal portfolio is discussed for different values of the relative risk aversion coefficient. It turns out that the assumption of log-normality does not seem to be a strong restriction.

Suggested Citation

  • Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wofgang Schmid, 2018. "Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios," Papers 1806.08005, arXiv.org, revised May 2019.
    • Handle: RePEc:arx:papers:1806.08005
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    References listed on IDEAS

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    Cited by:

    1. Dmytro Ivasiuk, 2019. "An approximate solution for the power utility optimization under predictable returns," Papers 1911.06552, arXiv.org, revised Oct 2021.

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