Question

A stock has had the following year-end prices and dividends: Year Price Dividend1 $43.55 - 2 48.53 $.87 3 57.45 .90 4 45.53 .95 5 52.45 1.00 6 61.53 1.08 What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

10.27% and 9.11%

Explanation:

The computation is shown below:

Given that

Year                            Price                  Dividend            Return

1                                $43.55                                      

2                               $48.53                 $.87                   13.43%

3                               $57.45                 $.90                   20.23%  

4                               $45.53                 $.95                   -19.90%

5                               $52.45                 $1.00                  17.39%

6                               $61.53                  $1.08                  19.37%

Total                                                                                  51.34%

Now the arithmetic average return is

= 51.34% ÷ 5

= 10.27%

And, the geometric average return is

= ((1 + 13.4328%) × ( 1+ 20.2349%) × (1 - 19.9049%) × (1 + 17.3951%) × (1 + 19.3708%))^(1 ÷ 5) - 1

= 9.11%

Working Note:

Rate of Return from year 1-2 = (Ending Price - Beginning Price+Dividend) ÷ Beginning Price

= ($48.53-  $43.55 + 0.87) ÷ $43.55

= 13.4328%

Rate of Return from 2-3 = ($57.45 - $48.53 + $0.90) ÷ $48.53

= 20.2349%

Rate of Return from 3-4 = ($45.53 - $57.45 + $0.95) ÷ $57.45

= -19.9049%

Rate of Return from 4-5 = ($52.45 - $45.53 + 1) ÷ $45.53

= 17.3951%

Rate of Return from 5-6 = ($61.53 - $52.45 + $1.08) ÷ $52.45

= 19.3708%