TY - JOUR

T1 - Mean-variance efficiency of optimal power and logarithmic utility portfolios

AU - Bodnar, Taras

AU - Ivasiuk, Dmytro

AU - Parolya, Nestor

AU - Schmid, Wolfgang

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Log-normal distribution

KW - Logarithmic utility

KW - Mean-variance analysis

KW - Optimal portfolio selection

KW - Power utility

UR - http://www.scopus.com/inward/record.url?scp=85085878188&partnerID=8YFLogxK

U2 - 10.1007/s11579-020-00270-1

DO - 10.1007/s11579-020-00270-1

M3 - Article

AN - SCOPUS:85085878188

VL - 14

SP - 675

EP - 698

JO - Mathematics and Financial Economics

JF - Mathematics and Financial Economics

SN - 1862-9679

IS - 4

ER -