Question

Suppose that a stock gave a realized return of 20% over a two-year time period and a 10%

return over the third year. The geometric average annual return is ________.

A) 8.28%

B) 12.43%

C) 14.08%

D) 16.57%

Answer 1

Option (D) 16.57%

Step-by-step explanation:

Data provided in the question:

Realized gain

r₁ = 20%

r₂ = 20%

r₃ = 10%

Now,

Geometric average =
`[(1+r_1)*(1+r_2)*...*(1+r_n)]^{(1)/(n)}` - 1

here,

n = 3

therefore,

Geometric average =
`[(1+0.20)*(1+0.20)*(1+0.10)]^{(1)/(3)}` - 1

or

Geometric average =
`[1.584]^{(1)/(3)}` - 1

or

Geometric average = 1.1657 - 1

or

Geometric average = 0.1657

= 0.1657 × 100%

= 16.57%