Suppose the geometric mean for Japanese Government Bond monthly return in a year is 1.75% and arithmetic mean is 2%. Suppose the Emerging market equity is twice as volatile as the Japanese bond in the same period. If the geometric mean for emerging market equity monthly return is 2% in a year, what's the arithmetic mean of the Emerging market equity monthly return in a year? See Formula in. attached Snipit.

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Arithmetic mean and geometric mean The arithmetic mean over T periods is the average over those T periods. The geometric mean is the single, per period return which would result in the same ending balance at the end of T periods. Period Return Wealth 0 $100 1 100% $200 2 -50% $100 (100%-50%) Arithmetic mean = = 25% 2 Geometric mean = 20.5-1=0% Arithmetic mean = Geometric mean + 0.5* (volatility of return) ^2 Arithmetic mean and geometric mean The arithmetic mean over T periods is the average over those T periods. The geometric mean is the single, per period return which would result in the same ending balance at the end of T periods. Period Return Wealth 0 $100 1 100% $200 2 -50% $100 (100%-50%) Arithmetic mean = = 25% 2 Geometric mean = 20.5-1=0% Arithmetic mean = Geometric mean + 0.5* (volatility of return) ^2