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 rebalanc...

A positive real interval, [a, b] can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval ”‘average”’ values remains constant. That both Arithmetic Mean and Geometric Mean ”‘average”’ values produce constant ratios for the same log scale is the stated invariance proved in this short note. The continuous analog is briefly considered and shown to have similar pr...