Ten annual returns are listed in the following table:
−19.3% |
16.1% |
18.1% |
−49.4% |
43.3% |
1.4% |
−16.1% |
45.7% |
45.2% |
−3.8% |
a. What is the arithmetic average return over the 10-year period?
b. What is the geometric average return over the 10-year period?
c. If you invested $100 at the beginning, how much would you have at the end?
Answer a.
Arithmetic Average Return = [(-0.1930) + 0.1610 + 0.1810 +
(-0.4940) + 0.4330 + 0.0140 + (-0.1610) + 0.4570 + 0.4520 +
(-0.0380)] / 10
Arithmetic Average Return = 0.8120 / 10
Arithmetic Average Return = 0.0812 or 8.12%
Answer b.
Geometric Average Return = [(1-0.1930) * (1+0.1610) * (1+0.1810)
* (1-0.4940) * (1+0.4330) * (1+0.0140) * (1-0.1610) * (1+0.4570) *
(1+0.4520) * (1-0.0380)]^(1/10) - 1
Geometric Average Return = 1.389164^(1/10) - 1
Geometric Average Return = 1.0334 - 1
Geometric Average Return = 0.0334 or 3.34%
Answer c.
Amount Invested = $100
Period = 10 years
Future Value = Amount Invested * (1 + Geometric Average
Return)^10
Future Value = $100 * 1.0334^10
Future Value = $100 * 1.3889
Future Value = $138.89
Ten annual returns are listed in the following table: −19.3% 16.1% 18.1% −49.4% 43.3% 1.4% −16.1%...
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