Geometric Mean(GM)

Unlike arithmetic mean, geometric mean uses multiplication rather than addition to summarize data values. It is useful for actual compound growth rate of investment which is linked over time. However, it is affected by extremes.

GM=(X₁ x X₂ …X_n)1/n

GM return: (1+R_g={(1+R₁ x (1+R₂ x …(1+R_n}1/n

Notes:

• Do NOT use a geometric mean, if you have any negative or zero values in your data.
• GM equals arithmetic mean for constant returns over time.
• Greater variability of returns over time leads to greater difference between AM and GM.
• GM is always less or equal to arithmetic mean, never be greater.
• Use GM to calculate time-weighted return