Let A be the balance in a fund on January 1, 1999, B the balance on June 30, 1999, and Cthe balance on December 31, 1999.

(a) If there are no deposits or withdrawals, show that the dollarweighted and time-weighted rates of return for 1999 are both equal to

(b) If there was a single deposit of W immediately after the June 30 balance was calculated, find expressions for the dollarweighted and time-weighted rates of return for 1999.
(Assume simple interest for periods of less than a year.)

(c) If there was a single deposit of W immediately before the June 30 balance was calculated, find expressions for the dollar-weighted and time-weighted rates of return for 1999.
(Assume simple interest for periods of less than a year.)

(d) Give a verbal explanation for the fact that the dollarweighted rates of return in parts

(b) and

(c) are equal.

(e) Show that the time-weighted rate of return in part

(b) is larger than the time-weighted rate of return in part (c).AppendixLO1

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C-A A