Diversification, Rebalancing, and the Geometric Mean Frontier

The effective (geometric mean) return of a periodically rebalanced portfolio always exceeds the weighted sum of the component geometric means. Some approximate formulae for estimating this effective return are derived and tested. One special case of these formulae is shown to be particularly simple, and is used to provide easily computed estimates of the benefits of diversification and rebalancing. The results are also used to show how classical Mean-Variance Optimization may be modified to generate the Geometric Mean Frontier, the analog of the efficient frontier when the geometric mean is used as the measure of portfolio return.