A name can take you places. Often it leads you to a novel idea, sometimes it pushes you off-road.
In spite of the name, the Modified Dietz Time-Weighted Rate of Return (TWRR) is a money-weighted metric.
In this case, the name pushes investors off road.
The Modified Dietz Methodology (MDM) was originally developed to provide an estimate of the Internal Rate of Return (IRR) of a transaction involving multiple cash flows. The IRR requires iterative calculations, which, in the case of long series of cash flows, can be highly complex and deliver multiple solutions.
The MDM is an elegant solution, which weighs the cash flows with the time elapsed since inception to determine the implicit average capital that prodeced the (positive or negative) change in value.
Formulas of the MDM are available in many places, although not often associated with the parallel IRR calculation. I will do this exercise in the table below.
MD TWRR and XIRR (the IRR formula which considers actual dates) are indeed very close.
But the MD TWRR is considered time-weighted, annualised and compounded. The use of geometrically linked TWRR based of the MDM is widespread.
Nevertheless, TWRR hide the same reinvestment assumption that biases the IRR.
As it is well known in fixed income, cash distributions “shorten the time” of financial transaction. This is why duration equals maturity only in zero coupon bonds, otherwise is shorter.
IRR have an implicit duration that is shorter than the contractual times. An approximation of the IRR duration (in days) is calculated using the well known formula ln(TVPI) / ln (1+IRR) x 365 sourced from “Inside Private Equity”, Kocis et al.
In the example of the table, the IRR duration is 248 days (and not the 361 days of the full transaction). Re-engineering the duration of the MDM as I have done in the right upper part of the table, I derive an implicit net duration of 247 days – pretty close, and interestingly forward 83 days.
The implications are not irrelevant.
Assuming the MD TWRR as an annualised rate, implicitly assumes the growth rate of the capital for a full one year at that rate.
But in this example, we can see that the average capital grows at 11.50% only for 247 days out of 365. The reinvestment assumption is powerful for one third of the year.
In the negative scenario of zero-interest-rate-reinvestment possibilities, the annualised return may “only” be 7.83% (using a super-simplified estimation).
Now you know why duration is our guiding principle. It’s when real money happens (and how risk can be managed).