Question

# Ten annual returns are listed in the following​ table: -19.5​% 16.3% 17.9​% -49.3% 43.5​% 1.6​% -16.7​%...

Ten annual returns are listed in the following​ table: -19.5​% 16.3% 17.9​% -49.3% 43.5​% 1.6​% -16.7​% 46.2​% 44.8​% -3.4​%
a. What is the arithmetic average return over the​ 10-year period?
b. What is the geometric average return over the​ 10-year period? The geometric average return over the​ 10-year period is (round to 4 decimal places)
c. If you invested​ \$100 at the​ beginning, how much would you have at the​ end? (round to four decimal places)

a

 Return -19.50% 16.30% 17.90% -49.30% 43.50% 1.60% -16.70% 46.20% 44.80% -3.40% Sum 81.40%

Arithmetic return = 81.4%/10 = 8.14%

b

 Return (r) (1+r) -19.50% 80.50% 16.30% 116.30% 17.90% 117.90% -49.30% 50.70% 43.50% 143.50% 1.60% 101.60% -16.70% 83.30% 46.20% 146.20% 44.80% 144.80% -3.40% 96.60%

Product of all values of (1+r) = 1.3899

Geometric mean = 1.3899 - 1 = 38.99%

c

Value at end = 100 * (1+38.99%) = 138.99

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