Ten annual returns are listed in the following table 195 169

Ten annual returns are listed in the following? table:

?19.5?%

16.9?%

18.1?%

?49.3?%

43.3?%

1.8?%

?16.6?%

46.4?%

44.6?%

?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?

Solution

Average return = Sum of all returns / Number of period

Average return = -0.195+0.169+0.181-0.493+0.433+0.018-0.166+0.464+0.446-0.039)/10

Average return = 8.18%

.

Geometric average = [Product of (1+per period return)]^(1/Number of period)-1

Geometric average = ((1-0.195)*(1+0.169)*(1+0.181)*(1-0.493)*(1+0.433)*(1+0.018)*(1-0.166)*(1+0.464)*(1+0.446)*(1-0.039))^(1/10)-1

Geometric return = 3.38228%

.

Total value today = Investment*(1+Geometric return)^Years

Total value today = 100*(1+3.38228%)^10

Total value today = 139.463660

Total Value = ~ $139.46