Question

Suppose that an investor opens an account by investing $1,000. At the beginning of each of the next four years, he deposits an additional $1,000 each year, and he then liquidates the account at the end of the total five-year period. Suppose that the yearly returns in this account, beginning in year 1, are as follows: −9 percent, 17 percent, 9 percent, 14 percent, and −4 percent. Calculate the arithmetic and geometric average returns for this investment.

Answer 1

Answer:

The arithmetic average returns for this investment= 5.4%

The geometric average returns for this investment= 4.89%

Explanation:

Arithmetic average return is simple the addition of all the returns by divided the years which is 5

=(-9)+17+9+14+(-4)/5 =5.4%.

while the geometric mean will require you to first add 1 to each return(this will help you deal with the negative numbers.

{(0.91)*1.17*1.09*1.14*(0.96)^(1/5)}-1=0.0489, to change it to percentage simply multiply it by 100 and the final answer will be 4.89%