Geometric Mean Maximization : Expected, Observed, and Simulated Performance

Portfolios can be optimized in a wide variety of ways, depending on the definition of risk and the goal stated. Although the traditional criterion of maximizing a portfolio's Sharpe ratio remains the standard, many other alternatives exist and are currently used by practitioners. One of those alternatives is to maximize a portfolio's geometric mean return, which amounts to maximizing the expected growth of the capital invested, or, similarly, the capital expected at the end of a holding period. In this article we assess the expected, observed, and simulated performance of this criterion and we compare it to those of the traditional criterion. We find that geometric mean maximization outperforms Sharpe ratio maximization in more than one dimension, ultimately providing investors with higher growth, much higher upside potential, and rather limited downside potential