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suppose that an investor opens and aacount by investing $1,000. At the beginning

ID: 2637751 • Letter: S

Question

suppose that an investor opens and aacount by investing $1,000. At the beginning of each of the next four years, he deposits aditional $1,000 ach year, and he liquidates the account at the end of the total five-year period. Suppose the 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 geometic average returns for this investments, and determine what the investor;s actual dollar-weighted average return was for his five-year period. Why is the dollar-weighted average return higher or lower than the geometric average return?

Explanation / Answer

Suppose that an investor opens and aacount by investing $1,000. At the beginning of each of the next four years, he deposits aditional $1,000 ach year, and he liquidates the account at the end of the total five-year period. Suppose the the yearly returns in this account, beginning in year 1, are as follows: -9 percent, 17 percent, 9 percent, 14 percent, and 4 percent.

determine what the investor;s actual dollar-weighted average return was for his five-year period. Why is the dollar-weighted average return higher or lower than the geometric average return?

Geometric average Return = ( .91*1.17*1.09*1.14*1.04)^5 - 1 = .0659 = 6.59%

Arithmetic return = (-9% + 17% + 9% + 14% + 4%) / 5 = 7%

difference between arithmentic return and Geometric return comes because

arithmentic return is affected by extreme value and gives equal weight to all values.

Geometric return gives more weight to smaller values and less weight to bigger values

total value after five year =1000*.91*1.17*1.09*1.14*1.04 + 1000*1.17*1.09*1.14*1.04 + 1000*1.09*1.14*1.04 + 1000*1.14*1.04 + 1000*1.04

= 1375.91 + 1512 + 1292.3 + 1185.6 + 1040 = 6405.8