Communications—A Comment on Geometric Mean Portfolios

In a recent paper in this journal [Vander Weide, J. H., D. W. Peterson, S. F. Maier. 1977. A strategy which maximizes the geometric mean return on portfolio investments. Management Sci.23(June) 1117–1123.], Vander Weide, Peterson, and Maìer (WPM) incorrectly point out several of the properties of the portfolio strategy which maximizes the geometric mean return (GMR), in which the GMR strategy is equivalent to maximizing the expected logarithm of the total return (including principal). Specifically, they state that GMR portfolios “maximize the probability of exceeding a given wealth level in a fixed amount of time”. This is clearly not true.