Q. suppose that an investor opens an account by investing $1000. At the beginnin

Question

Q. suppose that an investor opens an account by investing $1000. At the beginning of each of the next four years, he doposits an additional $ 1000 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%, 17%, 9%, 14% and -4%. Calculate the arithmetic and geometric average returns for this investment, and determine what the investor's actual dollar- weighted average return was for this five year period. Why is the dollar- weighted average return higher or lower than the geometric average return?

Explanation / Answer

Calculation of Arithmetic Average return Returns Year 1 -9.00% Year 2 17.00% Year 3 9.00% Year 4 14.00% Year 5 -4.00% Total 27.00% Average = 27%/5 5.40% Calculation of Geometric Average return Returns Decimal (r) 1+r Year 1 -9.00%             (0.09)           0.91 (1+r1) Year 2 17.00%                0.17           1.17 (1+r2) Year 3 9.00%                0.09           1.09 (1+r3) Year 4 14.00%                0.14           1.14 (1+r4) Year 5 -4.00%             (0.04)           0.96 (1+r5) Geometric Average return = [(1+r1)*(1+r2)*(1+r3)*(1+r4)((1+r5)]^(1/5) -1 =(0.91*1.17*1.09*1.14*0.96)^(1/5) - 1 = 4.90%

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