Problem 4: Arithmetic vs geometric means (5 points) (a) Compute the geometric and arithmetic (normal) mean of the following ve years of returns:

Year Net return

1 7%

2 25%

3 -12%

4 -21%

5 18.74%

Geometric mean:?

Arithmetic mean:?

(b) What would be the the total net return over all ve years for an investor who bought at the beginning of year 1 and held to the end of year 5?

Total ve-year return:

(c) What constant annual return would you have to get for each of the ve years in order to match the total ve-year return you found in part (b)? (Hint: Annualized EAR)

Constant annual return:

(d) Which of the following would you prefer for a ve-year investment? Why? (i) An investment that, after ve years, will have a geometric mean return of 8% and an arithmetic mean return of 10%. (ii) An investment that, after ve years, will have a geometric mean return of 7% and an arithmetic mean return of 11%.