Question
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
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%.
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