Question of the Week

The ABC Global mutual fund exhibited the following rates of return over the last five years, starting with the most recent year: 15%, -7%, 6.5%, -11.3% and 32.7%. How much would the difference between the arithmetic mean and the geometric mean of this historical performance be?

a) Arithmetic mean is higher by 1.14%.
b) Both means would be the same, so the difference is zero.
c) Arithmetic mean is 1.14 times greater than geometric mean.
d) Arithmetic mean is lower by 1.14%.

Answer:

The correct answer is: a)

Arithmetic Mean = (15 + -7 + 6.5 + -11.3 + 32.7)/5 = 7.18%

Geometric Mean =[(1.15 x 0.93 x 1.065 x 0.887 x 1.327)^(1/5)] - 1 = 6.04

Therefore, the arithmetic mean is higher than the geometric mean by 1.14% (7.18 - 6.04)