Mean-variance efficiency of optimal power and logarithmic utility portfolios

Taras Bodnar, Dmytro Ivasiuk, Nestor Parolya, Wolfgang Schmid

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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, we extend the derived theoretical finding to the general class of the log-skew-normal distributions. Finally, an application to the stock market is presented and the behaviour 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.

Original languageEnglish
Pages (from-to)675-698
Number of pages24
JournalMathematics and Financial Economics
Volume14
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Log-normal distribution
  • Logarithmic utility
  • Mean-variance analysis
  • Optimal portfolio selection
  • Power utility

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