Money weighted rate of return

This question is directly taken from schweser: The owen account is valued at $900,000 at the start of the month. On dat 15 a contribution of $50,000 is made. At the end of the month, the account is worth $1,466,553. Calculate MWRR (assuming 30 days a month)

Keystrokes on BAII plus



900,000 ENTER

50,000 ENTER

-1,466,553 ENTER

IRR CPT -> 24.904

So essentiall 24.904 is the answer that the calculator throws out. Schweser says that this is 15-day return and hence calculates the monthly return as (1+0.24904)^2 -1.

Hows is 24.904% 15-day return? I know this might be pretty basic but it beats the hell out of me. Rescuers please help!

On day 15 a contribution of $50,000 is made

But where do we specify the period (15th day) while entering the contribution cash flows in the calculator? Are we assuming that the return 24.904 is 15 day return since it is given in the question?

Mathematically: (900,000 * 1.24904 ^2) + (50,000 *1.24904 ^ 1) = $1,466,542 ( I probably didn’t use enough decimals in the interest rate)

You can’t enter a time period in the CF worksheet: all it assumes is that you are using time periods that are of equal length. In your case, you have 1 interval between each cash flow, where the interval is 15 days.

To calculate the monthly return, you have to compound over 2 intervals of 15 days, which is where the 1.24904^2 -1 comes from.

IRR works out the return per cashflow period. Eg if you had five years of annual cash flows and put them into your calculator it would give you an annual IRR.

in this case your period between cash flows is 15days so you have to compound it to get a 30 day rate of return (ie, a month.)

Based on the formula:

900,000 (1+R)^2 + 50,000(1+R)

aren’t you already Squaring the return in the formula [(1+R)^2)] ? So why square the answer?

If 24.09% is the R that makes the formula equal $1,466,553 than why is that not your answer?

BMiller , the R in the formula you wrote is a 15 day return. BAII plus and any excel sheet that does a cash flow based IRR will give you an equivalent 1-period return only .

If your periods are not equal length , then you have to use a modified Dietz method to simplify .

If you want a horizon total return , from the 1-period return R , you have to compound it yourself as in (1+R)^T where T is total number of 1-period periods . i.e. 2 in this case

But since you are squaring the R in the equation isn’t the result in monthly terms (that is: (1+R)^2)? And the second part of the equation [CF1 (1+R)] is raised to the 1, is that because it’s only around for 1-period?

The blue box example on the following page has the Time period in Days, is that because we are dealing with uneven periods that don’t simply as nicely as 30-days and 15-days ?

And why again if 24.09% is the R that makes the formula equal $1,466,553, than why is that not your answer - seems like squaring the answering would make them not equal?

It seems like it would be difficult to give a MWRR problem with uneven time periods, no? Not sure what modified Dietz is.

Thanks for the help!

actually you do not just square it.

it is 30 over 15 30/15 so with other periods you get other number.

it’s just like annualizing a 6 months return.

While trying to calculate, I’m getting error 5 on the calculator. Please help with the exact keys to punch for this cal.


you sure you entered the minus sign on the last cash flow?

yes. When I press irr and then CPT it gives me an error 5.

on BAII plus when you press enter on CFo, and then down-arrow ,it will take you to C01 . When you enter a value and press enter and then down-arrow , it will take you to F01 and pre-fill it with 1.0 . You should leave it alone and press down-arrow again. It will then show the C02 . Enter the last cash flow ( -1466553 ) and then press enter and down-arrow again. Then press down-arrow two more times until it comes back to CFo. At this point , press IRR , then CPT. It will take a few seconds ( unless you have a quad-core BAII plus ) and then show the IRR .

I think you have forgotten L2 stuff for cash flows with the BAII plus

CF, 2nd Clr Work

900000, Enter, down arrow, 50000, Enter, down arrow, down arrow, -1466553 Enter, 2nd quit, IRR, CPT

CF0 = 900,000 C01= 50,000, F01=1, C02 = -1,466,553, F02 = 1 and IRR=24.90444

CF, 2nd Clr Work

900000, Enter, down arrow, 50000, Enter, down arrow, down arrow, -1466553 Enter, 2nd quit, IRR then when I press CPT it gives me an error message- error 5

Have you double-checked the inputs in the CF worksheet to see if they match up? For the -1466553, are you using the +/- key or the - key??? I get Error 5 if CF02 is +1,466,553.

Thanks breadmaker. I was using +/- key at the bottom. I now used - on the top and I got the answer. Thanks a lot for clarifying that. I was going crazy.

Maybe you have a different version of the BAII Plus, but mine has the +/- key to change the sign of a number. At any rate, make sure you know which button on your calculator does the sign change vs. subtraction.

Thanks for the tip. I will be aware of that.