| A stock has had the following year-end prices and dividends: |
| Year | Price | Dividend | |||||
| 1 | $ | 43.25 | – | ||||
| 2 | 48.23 | $ | .42 | ||||
| 3 | 57.15 | .45 | |||||
| 4 | 45.23 | .55 | |||||
| 5 | 52.15 | .60 | |||||
| 6 | 61.23 | .68 | |||||
| What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) |
| Arithmetic return | % |
| Geometric return | % |
Answer :
Arithmetic return
9.48 %
Geometric return
9.47 %
Working notes for the above answer is as under
To calculate the arithmetic and geometric average returns, we must first calculate the return for eachyear. The return for each year is:
R1= ($48.23 – 43.25 + 0.42) / $43.25 = 0.1249, or 12.49%
R2= ($57.15 – 48.23 + 0.45) / $48.23 = 0.1943, or 19.43%
R3= ($45.23 – 57.15 + 0.55) / $57.15 = –0.1990, or –19.90%
R4= ($52.15 – 45.23 + 0.60 / $45.23 = 0.1663, or 16.63%
R5= ($61.23 – 52.15 + 0.68) / $52.15 = 0.1872, or 18.72%
The arithmetic average return was:
RA= (0.1249+0.1943+-0.1990+0.1663+0.1872)/5 = 0.09474, or 9.48%
And the geometric average return was:RG= [(1 + 0.1249)(1 + 0.1943)(1 – 0.1990)(1 + 0.1663)(1 + 0.1872)]1/5– 1 = 0.094719, or 9.47%
