Question

A stock has had the following year-end prices and dividends:

Year Price Dividend
1 $ 64.28 —
2 71.15 $ .59
3 76.95 .64
4 63.22 .70
5 73.01 .79
6 79.25 .86

What are the arithmetic and geometric 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

To calculate the arithmetic and geometric returns for the stock, we need to use the following formulas:

Arithmetic Return = [(Ending Price - Beginning Price) + Dividends] / Beginning Price x 100%

Geometric Return = [(Ending Price / Beginning Price) ^ (1 / n) - 1] x 100%

where n is the number of years.

Using the given data, we can calculate the arithmetic and geometric returns as follows:

Year 1:
Arithmetic Return = [(71.15 - 64.28) + 0] / 64.28 x 100% = 10.64%
Geometric Return = [(71.15 / 64.28) ^ (1/1) - 1] x 100% = 10.64%

Year 2:
Arithmetic Return = [(76.95 - 71.15) + 0.59] / 71.15 x 100% = 9.02%
Geometric Return = [(76.95 / 71.15) ^ (1/2) - 1] x 100% = 8.68%

Year 3:
Arithmetic Return = [(63.22 - 76.95) + 0.64] / 76.95 x 100% = -16.97%
Geometric Return = [(63.22 / 76.95) ^ (1/3) - 1] x 100% = -17.16%

Year 4:
Arithmetic Return = [(73.01 - 63.22) + 0.70] / 63.22 x 100% = 16.06%
Geometric Return = [(73.01 / 63.22) ^ (1/4) - 1] x 100% = 14.63%

Year 5:
Arithmetic Return = [(79.25 - 73.01) + 0.79] / 73.01 x 100% = 11.03%
Geometric Return = [(79.25 / 73.01) ^ (1/5) - 1] x 100% = 10.83%

Year 6:
Arithmetic Return = [(79.25 - 73.01) + 0.86] / 73.01 x 100% = 13.09%
Geometric Return = [(79.25 / 73.01) ^ (1/6) - 1] x 100% = 12.66%

Therefore, the arithmetic and geometric returns for the stock are:

Arithmetic Return = 3.97%
Geometric Return = 3.55%