Question

A stock was trading at $22.90 at the end of year 1. It was trading at the end of year 2 at $23.23 immediately after giving a dividend of $0.37. At the end of year 3. it was trading at $22.59 immediately after giving a dividend of $0.39. Finally, it was trading at $24.41 at the end of year 4 without giving out any dividend. What was the geometric average annual return of this stock for the three years between years 1 and 4?

3.03%

3.11%

3.20%

3.28%

3.36%

Answer 1

Annual rate of return[ARR]

The risk and return are two basic determinants of investments in shares. Risk can be referred to as the chance of loss. Return is a measure resulting from the total gain or loss experienced by the owner with respect to a share over a given period of time.

Formula for ARR = D + [P₁ - P₀] ÷ P₀

D - Dividend

P₁ - End of stock price

P₀ - Beginning of stock price

Year 1

0.37 + (23.23 – 22.90) ÷ 22.90

0.03

3%

Year – 2

0.39 + (22.59 – 23.23) ÷ 23.23

-0.25

-25%

Year 3

(24.41 – 22.59) ÷ 22.59

0.0805

8.06%

Geometric Average Return

The geometric average return formula (also known as geometric mean return) is a way to calculate the average rate of return on an investment that is compounded over multiple periods.

Formula for GAR = [(1+R₁) × (1+R₂) × (1+R_n)]^T – 1

R₁ – Return for each period

T – Number of periods

= [(1+0.03) × (1+-0.25) × (1+0.0806)]⁴– 1

=3.1803