Question

# A stock was trading at \$20.50 at the end of year 1. It was trading at...

A stock was trading at \$20.50 at the end of year 1. It was trading at the end of year 2 at \$20.83 immediately after giving a dividend of \$0.21. At the end of year 3. it was trading at \$20.19 immediately after giving a dividend of \$0.23. Finally, it was trading at \$22.01 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?

Calculation of the geometric average annual return of this stock for the three years:

Formula

Geometric average annual return = [(1+R1)×(1+R2)×(1+R3)….....×(1+Rn)]1/n −1

Where,

R = return

n = time period

Let us calculate returns.

Between years 1 and 4, The dividend paid two times.

R1   = (\$0.21/\$20.83) x 100

= 1.008%

R2 = (\$0.23/\$20.19) x 100

= 1.139%

n = 3

Therefore

Geometric average annual return = [(1+R1)×(1+R2)×(1+R3)….....×(1+Rn)]1/n −1

= [(1+0.01008)×(1+0.01139)]1/3 −1

= [(1.01008)×(1.01139)]1/3 −1

= (1.0214815)1/3 −1

= 1.00715538 −1

= 0.00715538

The geometric average annual return of this stock for the three years is 0.0072 or 0.72%

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