Question

A stock was trading at $123.45 at the end of year 1. It was trading at the end of year 2 at $116.75 immediately after giving a dividend of $4.70. At the end of year 3. it was trading at $126.95 immediately after giving a dividend of $4.90. Finally, it was trading at $137.05 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 = ($116.75 - $123.45) + $4.7 / $123.45

Return = (-$6.7 + $4.7) / $123.45

Return = -$2 / $123.45 = -1.62%

For year 3:

Return = ($126.95 - $116.75) + $4.90 / $116.75

Return = ($10.2 + $4.90) / $116.75

Return = $15.1 / $116.75 = 12.93%

For year 4:

Return = ($137.05 - $126.95) + $0 / $126.95

Return = ($10.1 + $0) / $126.95

Return = $10.1 / $126.95 = 7.96%

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 = (-1.62 + 12.93 + 7.96) / 3

Arithmetic average return = 19.27 / 3 = 6.42 %