Question

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)

Answer 1

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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