By using the geometric mean annual return for a particular financial asset, the cumulative wealth index can be found by converting the return on a geometric mean basis into a return relative and raising this return relative to the power representing the number of years involved. Consider the geometric mean of 12.47 percent for small common stocks for the period 1926–2007. The cumulative wealth index, using a starting index value of $1, is (note the 82 periods)

$1(1.1247)⁸² = $15,311.19

Conversely, if we know the cumulative wealth index value, we can solve for the geometric mean by taking the nth root and subtracting 1.0:

($15,311.19)^1/82 - 1.0 = 1.1247 - 1.0 = 0.1247 or 12.47%

number of years to use = [ending year - beginning year] + 1.