Question

You make a 5 year investment. The investment returns in each of the 5 years are: 3%, 10%, -15%, 0%, and 25% What is the holding period return of your stock investment? What is the arithmetic mean annual return of the investment? What is geometric mean annual return of the investment?

If the order of the returns were reversed (so 25%, 0%, -15%, 10%, 3%), would the ending value of your investment be different?

Answer 1

Here investment returns of each of the 5 years are : 3%, 10%, -15%, 0% and 25%

so here let assume them r1,r2,r3,r4 and r5 respectively.

So here if Holding period return = r,

then

(1 + r) = (1 + r1)(1 + r2)(1+r3)(1 + r4) (1 + r5)

(1 + r) = (1 + 0.25) * (1 + 0) * (1 - 0.15) * (1 + 0.10) * (1 + 0.03)

1 + r = 1.203825

r = 0.203825

so holding period return = 20.3825%

AIrthmative mean annual return of the investment = (r₁ + r₂ + r₃ + r₄ + r₅)/5 = (25 + 0 - 15 + 10 + 3)/5 = 4.6%

geometric mean annual return (let say R)

R = [(1 + r₁)(1 + r2)(1+r3)(1 + r4) (1 + r5) ]^1/5 -1

R = [(1 + 0.25) * (1 + 0) * (1 - 0.15) * (1 + 0.1) * (1 + 0.03)]^1/5 -1

R = 0.0378

R = 3.78%

so here geometric mean annual return of the investment = 3.78%

Here if the order of the returns were reversed (so 25%, 0%, -15%, 10%, 3%), would the ending value of your investment would not be different as we are multiplying the numbers here so that will not chaged the final value of investment.