Question

Ten annual returns are listed in the following​ table: negative 19.5−19.5​% 16.916.9​% 18.318.3​% negative 49.8−49.8​% 43.843.8​% 1.51.5​% negative 16.9−16.9​% 45.545.5​% 44.844.8​% negative 3.7−3.7​% 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? round to five decimal places

Answer 1

Arithmetic average = sum of return / no of years

Years	Returns
1	-19.5
2	16.9
3	18.3
4	-49.8
5	43.8
6	1.5
7	-16.9
8	45.5
9	44.8
10	-3.7
Total	80.9

Arithmetic average return = 80.90 / 10 = 8.09%

Geometric average return = (1- 0.195) * ( 1 + 0.169) * ( 1 + 0.183) * ( 1 -0.498) * ( 1 + 0.438) * ( 1 +0.015) * ( 1-0.169) * ( 1 +.0455) * ( 1 +0.448 ) * ( 1 -0.037) - 1

= 0.805 * 1.169 * 1.183 * 0.502 * 1.438 * 1.015 * 0.831 * 1.455 * 1.448 * 0.963 - 1

= 1.3752531 - 1

= 37.52531%

Value of investment = 100 * 1.3752531 = $137.52531