The Case For A Geometric Mean For Quoting Returns

[Bryan Hancock]

Return citations were getting thrown around on another thread a few weeks ago so I took the liberty of dusting off some old finance texts where people try to get quite specific about citing returns. The case is made frequently for using a geometric mean instead of an arithmetic mean. There are also frequently negative returns with large enough samples so people like to add one to each of the observations and subtract one from the output of the geometric mean using these observations to arrive at a return metric.

So in other words you would use:

=GEOMEAN(Range_of_Percentages + 1) - 1

This mean is always equal to or smaller than the arithmetic mean that most people use to cite returns over a period of years. Presumably this is why it is not used even though it is more accurate.

Does anyone use this when they analyze their portfolio's returns? If so, do you use the percentages annually or make it more granular? Are there any problems you see with using geometric mean instead of arithmetic mean other than the greater difficultly in arriving at the figure?