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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%

Respuesta :

Answer:

Option (D) 16.57%

Explanation:

Data provided in the question:

Realized gain

r₁ = 20%

r₂ = 20%

r₃ = 10%

Now,

Geometric average = [tex][(1+r_1)\times(1+r_2)\times...\times(1+r_n)]^{\frac{1}{n}}[/tex] - 1

here,

n = 3

therefore,

Geometric average = [tex][(1+0.20)\times(1+0.20)\times(1+0.10)]^{\frac{1}{3}}[/tex] - 1

or

Geometric average = [tex][1.584]^{\frac{1}{3}}[/tex] - 1

or

Geometric average = 1.1657 - 1

or

Geometric average = 0.1657

= 0.1657 × 100%

= 16.57%