Question

A stock was trading at $125.10 at the end of year one. It was trading at the end of year two at $118.40 immediately after giving a dividend of $5.00. At the end of year three. it was trading at $128.60 immediately after giving a dividend of $5.20. Finally, it was trading at $138.70 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 = ($118.4 - $125.10) + $5 / $125.10

Return = (-$6.7 + $5) / $125.10

Return = -$1.7 / $125.10 = -1.36%

For year 3:

Return = ($128.6 - $118.4) + $5.2 / $118.4

Return = ($10.2 + $5.2) / $118.4

Return = $15.4 / $118.4 = 13%

For year 4:

Return = ($138.7 - $128.6) + $0 / $128.6

Return = ($10.1 + $0) / $128.6

Return = $10.1 / $128.6 = 7.85%

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 = (-1.36 + 13 + 7.85) / 3

Arithmetic average return = 19.49 / 3 = 6.50 %