Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios

Taras Bodnar, Dmytro Ivasiuk, Nestor Parolya and Wofgang 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, 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.

Date: 2018-06, Revised 2019-05
New Economics Papers: this item is included in nep-rmg and nep-upt
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Citations: View citations in EconPapers (1)

Published in Mathematics and Financial Economics 14, 675-698, 2020

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