Question

Ten annual returns are listed in the following​ table: negative 19.6​% 16.8​% 18.4​% negative 49.2​% 43.3​% 1.9​% negative 16.2​% 46.2​% 45.4​% negative 3.9​%

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 1

arithmetic average return = sum of annual returns/no. of years

geometric average return = (ending return/beginning return)^{1/no. of years} - 1

a. & b.

Years	Annual returns
1	-19.60%
2	16.80%
3	18.40%
4	-49.20%
5	43.30%
6	1.90%
7	-16.20%
8	46.20%
9	45.40%
10	-3.90%
arithmetic average return	8.31%
geometric average return	1.80%

year 10 and year 1 returns are negative. so, we need to add 1 to those returns to calculate geometric average return.

Calculation

c. If you invested​ $100 at the​ beginning, you would have at the​ end $141.19.

Years	Annual returns	Amount at the end of year
0	0	$100
1	-19.60%	$80.40
2	16.80%	$93.91
3	18.40%	$111.19
4	-49.20%	$56.48
5	43.30%	$80.94
6	1.90%	$82.48
7	-16.20%	$69.12
8	46.20%	$101.05
9	45.40%	$146.92
10	-3.90%	$141.19

Calculations