PT - JOURNAL ARTICLE
AU - Johnston, Ken
AU - Hatem, John
TI - Geometric Mean Maximization: A Note on Expected, Observed, and Simulated Performance
AID - 10.3905/joi.2021.1.175
DP - 2021 Mar 31
TA - The Journal of Investing
PG - joi.2021.1.175
4099 - http://joi.pm-research.com/content/early/2021/03/31/joi.2021.1.175.short
4100 - http://joi.pm-research.com/content/early/2021/03/31/joi.2021.1.175.full
AB - This note discusses why the maximization of any portfolio optimization model cannot be isolated from the investor’s risk perception. To allow for differing risk preferences among investors, the efficient frontiers of Sharpe ratio maximization (SRM) and geometric mean maximization (GMM) are the appropriate metrics for making a comparison. The authors demonstrate that for a given level of risk the two optimization techniques will choose the same portfolio asset weights. Although GMM provides investors with a different way to approach portfolio optimization (maximizing terminal wealth), it is not a competing portfolio optimization technique to mean–variance maximization but rather a complementary one.TOPICS: Portfolio construction, quantitative methods, statistical methods, performance measurementKey Findings▪ Comparison of portfolio optimization techniques require a predetermined risk level.▪ Geometric mean and Sharpe ratio maximization lead to the same portfolio weights for a given level of risk.▪ Geometric mean maximization expands the opportunity set of the mean–variance space.