I understand why we are subtracting the cash flow in the numerator, but why are we adding it in the denominator?
Seems like we are removing the effect of cash in/out flows in mgt performance in the numerator but being dinged for the cash flows in the asset base (denominator) - thereby lowering return.
When we calculate the TWRR and the cash flow occurs at the beginning of the period we add the entire cash flow back onto the denominator. It therefore seems reasonable that in using the modified dietz method if the cash flow occurs at time t then we shoul add back the prorated amount of the cash flow based on the number of days remaining in the month to the denominator.
Bmiller12 , try it out for yourself with an excel sheet .
case 1 : cash flow happens at the beginning of the month .
Return in dollars is (value at month end) - ( ( value at month beg) + (cash flow) )
case 2 : cash flow happens at end of month.
Return in dollars is (value at month end) -(cash flow) -( value at month beg).
So in both cases cash flow is subtracted in the numerator .
In fact theses are two extreme cases of the general case which is cash flow is always subtracted from the numerator.
The simple reason is that it is cash flow contribution , not returns from the asset . So it is not return created by the manager , but net contribution a la macro attribution analysis
I appreciate the help.
I understand why you subtract CF from the numerator, I just didn’t understand why it’s still included in the denominator though. Seems like you would also subtract it from the denominator as well to remove all effects of the CF, instead it seems like the manager is getting dinged for it still being in the denominator.
I guess I understand though, let me know if this makes sense. The ending market value in the numerator captures all return, and since this is what we want, you subtract the CF (and BGN mkt value ) bc it does not represent a real return on investment. Nevertheless, any return generated by having the CF in the account is captured in the numerator. This is why you still include the CF in the asset base (denominator) for the amount of time it was invested. Sound ok?
Thanks again.
Original Deitz assumes midpoint assumption.
ROrigDeitz = [MV1 - (MV0+CF)] / (MV0 + 0.5CF)
Modified deitz is similar - except the CF is weighted by the period for which it was invested in.
RModDeitz = [MV1 - (MV0+CF)] / (MV0 + w * CF)
w = # of days for which the cash flow was available / total # of days
e.g if cashflow was on the 10th of the month w = 20 / 30.
BMiller , you are correct. The purpose of investing cash is to generate return .
presumably ending values in the account have some returns in them due to the returns generated by the extra cash coming in , so the effect of the cash is already captured in the numerator, even after subtracting the principle amount of cash invested.
The denominator simply captures the amount invested , paying due attention to the weights each cash flow should have depending on when in the month it happened
I think I understood…
Imagine you have a portfolio of value $100 at time t0, and then, 200 days from now (t1), this portfolio would be valued at $120, giving us a return of 20%.
Now let’s imagine the same portfolio but that on the 180th day would have an external cash flow coming in of $10, and in these 20 days this small value would turn into $11, bringing us a return of 10% in those 20 days (for this small part of the portfolio in this small amount of time)…
In a first look we could wrongly consider the return to be:
[($120 - $100) + ($11 - $10)] / ($100 + $10)
But wait, these $100 initial dollars are not comparable to the $10 cash flow that came in later, because this last amount got invested for less time… Then we would need to do a proper comparison using the Modified Dietz Method, which would be:
[($120 - $100) + ($11 - $10)] / [(200 days / 200 days) * $100 + (20 days / 200 days) * $10]