Question

Geometric returns are always greater than arithmetic average returns. Select one: True False

Answer 1

Answer : False

Geometric return can be equal to or less than Arithmetic average.

This is because Arithmetic average is simple average of returns.

for example, if say returns are = 10% and 20% for 2 years

Arithmetic average return = (10% +20%)/2 = 15%

Geometric return = ((1+r1)*(1+r2)......(1+rn)) 1/n - 1

Geometric return = ((1+0.10)*(1+0.20)) 1/2 - 1 = 14.89%

so Geomteric return is mostly less than Arithmetic return and in ver less cases equal to Arithmetic return.