Question

A stock was trading at $118.50 at the end of year 1. It was trading at the end of year 2 at $111.80 immediately after giving a dividend of $3.80. At the end of year 3. it was trading at $122.00 immediately after giving a dividend of $4.00. Finally, it was trading at $132.10 at the end of year 4 without giving out any dividend. What was the arithmetic average annual return of this stock for the three years between years 1 and 4?

Answer 1

First we will calculate the return for each year by the following formula:

Return = (End of period stock price - Beginning period stock price) + Dividend / Beginning period stock price

For year 2:

Return = ($111.8 - $118.5) + $3.80 / $118.5

Return = (-$6.7 + $3.80) / $118.5

Return = -$2.9 / $118.5 = -2.45%

For year 3:

Return = ($122 - $111.8) + $4 / $111.8

Return = ($10.2 + $4) / $111.8

Return = $14.2 / $111.8 = 12.70%

For year 4:

Return = ($132.1 - $122) + $0 / $122

Return = ($10.1 + $0) / $122

Return = $10.1 / $122 = 8.28%

Now, we will calculate the arithmetic average return as per below:

Arithmetic average return = Sum of returns / Number of returns

Putting the values in the above formula, we get,

Arithmetic average return = (-2.45 + 12.70 + 8.28) / 3

Arithmetic average return = 18.53 / 3 = 6.18 %