Hi all,
My question is regarding the way to calculate the MWR in the case of inputs in cash flows AND in return percentages.
I would appreciate if you could help as I’m a bit confused.
Here is a 1st example:
At the beginning of Year 1, a fund has $10 million under management; it earns a return of 14% for the year. The fund attracts another $100 million at the start of Year 2 and earns a return of 8% for that year.
I saw 2 ways of calculating this, but with different results.
Way1:
t=0 : -10
t=1 : -100
t=2 : 10*1.14*1.08 + 100*1.08
MWR = 8.53%
Way2:
t=0 : -10
t=1 : -100 + 10*1.14
t=2 : 100*1.08
MWR = 8.58%
Way 1 was used to solve this example.
However, here a second example where Way 2 was used instead :
Year Assets Under Management at the Beginning of Year (€) Net Return (%) 1 30 million 15 2 45 million –5 3 20 million 10 4 25 million 15 5 35 million 3
In this example, we used Way 2 to calculate, meaning :
Way2:
t=0 : -30
t=1 : -45 + 30*1.15 = -10.5
t=2 : -20 + 45*0.95 = 22.75
t=3 : -25 + 20*1.1 = -3
t=4 : -35 + 25*1.15 = -6.25
t=5 : 35*1.03 = 36.05
MWR = 5.86%
With Way 1, I got MWR = 6.73% for this 2nd example.
Could you please help ?
Thank you!
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Money-weighted return is a fancy name for IRR.
In your first example, the value at the end of year 2 is $10,000,000(1.14) + $100,000,000 = $120,312,000
From the viewpoint of the fund, the cash flows are:
- CF0 = $10,000,000
- CF1 = $100,000,000
- CF2 = ($120,312,000)
The IRR is 8.5327%.
Your way 1 is correct.
Your way 2 presumes that at time 1 you withdraw the $10,000,000 plus its return and replace it with the $100,000,000. Clearly, that’s not what you’re doing.
In your second example, you don’t describe the cash inflows and outflows at the end of each year; you describe the assets under management. In that case, you can think of the cash flow at each time as a withdrawal of the previous AUM plus its return and a deposit of the current AUM; that’s what your way 2 does.
Thanks S2000magician,
Your explanation is clear. Indeed, the 1st example refers to “the fund attracting another 100M”, so no withdrawals are made. In this case, we should retain the funds and their returns to the end.
I also understand that a list of AUM assumes withdrawals and deposits. Quite logic.
Again, thank you!
You’re quite welcome.
There are many ways that CFA Institute can describe the cash flows in an account. It’s a good idea to familiarize yourself with those various ways, so that you’re ready for whatever they throw your way on the exam.
I’ve only seen these 2 ways of presenting the cash flows so far. What other ways of presenting accounts CF can we imagine ?
“Many” was hyperbole. The two ways you’ve discovered are likely it.
The point was that, no matter how they present it, you need to be able to get to the cash flows. These two examples give you chances to practice that.
A little confused,
In your first example, the value at the end of year 2 is $10,000,000(1.14) + $100,000,000 =
Isn’t this
= 11,400,000 + 108,000,000
= 119,400,000
From the viewpoint of the fund, the cash flows are:
- CF0 = ($10,000,000)
- CF1 = ($100,000,000)
- CF2 = $119,400,000
IRR = 7.7829
MWR = 7.8%
The time-weighted return of the fund is = [√{(1.14)(1.08) } 1/2]−1
TWR = 10.96
Pay attention to the brackets.
in S2000magicians example is:
[$10,000,000 (1.14) + $100,000,000] then multiply by 1.08 because you also got to take in once you brought the first-year value to the second year, you also got to compound that value on the return % generated in the second year
in your case, you did it by
[$10,000,000(1.14)] + [$100,000,000(1.08)] Which is why you got a different answer