Question

A husband and wife are planning for retirement and they believe that a comparison over a five- year period would be appropriate. They are given the following information about one mutual fund that they are considering. Assume that all remaining assets under management are withdrawn by the family at the end of 5 years.

    

Year Beginning Assets Under Management

1. 30.000.000

2. 35.000.000

3. 25.000.000

4. 15.000.000

5. 20.000.000

Net Return (%)

1.   6%

2. 2%

3. -17%

4. -3%

5. 6%

a. Compute the arithmetic and geometric mean annual return for the fund. Write the formulas. (without excel)

b. What is the money-weighted annual return for the fund? You can calculate the annual cash flow (either additional investment or withdrawal by the couple) at year t as the difference between the beginning assets under management at year t and ending assets under management at year t-1.

Answer 1

a)

arithmetic mean annual return = total return / number of periods

Given annual returns are = 6% , 2% , -17% , -3% , 6%

= [6%+2%+(-17%) + (-3%) + 6% ] / 5

= -1.20%

Geometric mean annual return = [(1+R1)*(1+R2)*(1+R3)*........(1+Rn)]^(1/n) - 1

where n = number of years

R = Yearly return

= [(1+6%)*(1+2%)*(1-17%)*(1-3%)*(1+6%)]^(1/5)

= -1.60%

(NOTE : it seems that year 1 and Year2 returns (i.e.,6% and 2%) provided to me are incorrect.other wise answer is correct)

B)

first we have to calculate cash flows each year and then calculate MWAR

beginning value = 30,000,000

Year 0 cash flow = -30,000,000

Year 1 cash flow:

return= 6%

balance at the year 2 beginning should be = 30,000,000 * (1+6%) = 31,800,000

but it is given balance at the beginning of year 2 = 35,000,000

so additions = 35,000,000 - 31,800,000 = -3,200,000

same way we have to calculate all remaining years cash flows :

Year 2:

35,000,000*(1+2%) = 35,700,000

Wthdrawls = 35,700,000 - 25,000,000 = 10,700,000

Year - 3:

25,000,000*(1-17%) = 20,750,000

with drawls = 20,750,000 - 15,000,000 = 5,750,000

Year 4 :

15,000,000*(1-3%) = 14,550,00

additions = 14,550,000 - 20,000,000 = -5,450,000

Year 5 :

Total withdrawl = 20,000,000*(1+6%) = 21,200,000

Money weighted rate is the rate where present value of these annual amounts = 0

so ,

0 = -30,000,000 - (3,200,000 / (1+r)^1) + [10,700,000 / (1+r)^2] + (5,750,000 / (1+r)^3) - (5,450,000 / (1+r)^4) +(21,200,000 / (1+r)^5)

(we have to use excel or financial calculator to find above rate or we have to solve it by trail and error method)

using excel:

Money weighted annual return = -0.82%

(in case of any further explanation please comment)