Question

A stock had returns of 5.10%, 31.60%, and -21.20% in each of the past three years. Over the past four years, the arithmetic average annual return for the stock was 6.75%. What was the geometric annual return for the stock over the past four years

Answer 1

geometric annual return = 5.23%

Step-by-step explanation:

first we must determine the return for year 4 (I will call it X)

5.1% + 31.6% - 21.2% + X = 6.75% x 4

14.5 + X = 27

X = 12.5%

geometric annual return = ⁴√(1.051 · 1.316 · 1.125 · 0.788) - 1 = ⁴√1.226132334 - 1 = 1.055287 - 1 = 0.055287 = 5.23%