Question

You are operating a mutual fund which today has $100mil in assets. Your returns and fund flows into/out of the fund are listed below.

Time =	Return	Fund Flow $Mil
1	20.00%	5
2	10.00%	3
3	-30.00%	-10
4	10.00%	4
5	-5.00%	-2

Question 1: What is the arithmetic average (mean) of the returns?

Question 2: What is the geometric average (mean) of the returns?

Question 3: What is the dollar-weighted average (mean) of the returns?

Answer 1

1. Arithmetic Average of returns = (20% + 10% - 30% + 10% - 5%)/5 = 1%

2. Geometric Average of returns = (1.2*1.1*0.7*1.1*0.95)^(1/5) - 1 = -0.698%

3. Dollar weighted return is the rate of return that equates all the present value of future cash flows to present value of investment.

If year 1 return is 5 which is 20% of Initial Investment, then initial investment = 5/0.2 = 25 millions

=> 25millions = (5 mil)/(1+k) + 3/[(1+k)^2] + (-10)/[(1+k)^3] + 4/[(1+k)^4] + (-2)/[(1+k)^5 ]+ 100/[(1+k)^5]

where k = dollar weighted return

So on solving the bove equation, we get

k = 34%