Question

12. You are tracking fund XYZ, which has earned returns of 2%, 8%, -7%, and 13% over the last four years, respectively. Which of the following is closest to the geometric return of XYZ over this time period? (a) 3.00% (b) 3.25% (c) 3.50% (d) 3.75% (e) 4.00% 13. Suppose you invested $100 per year in fund XYZ at the beginning of each of those four years. Which measure of return over the four years would you use to forecast next year's expected return? (a) Geometric average (b) Not enough information (c) Dollar-weighted (d) Arithmetic average (e) None of the above 14. If you had invested $1000 at the beginning of each year in fund XYZ from problem 12, which of the following would be closest to your dollar-weighted return? (a) 5.5% (b) 4.5% (c) 4.0% (d) 5.0% (e) 6.0%

Answer 1

Compute the geometric return using the equation as shown below:

Geometric return = {( 1 + return 1) * ( 1 + return 2) * ( 1 + return 3) * ( 1 + return 4) }^{1/ Period} – 1

                            = {( 1 + 2%) * ( 1 + 8%) * ( 1 + (-7%)) * ( 1 + 13%)} ^¼ - 1

                            = {( 1.02) * (1.08) * (0.93) * 1.14}^1/4 – 1

                            = 3.72807775826%

Hence, geometric return is 3.72807775826%

It is closest to 3.75%. So, the correct answer is (d).