One of those confusing things in the world of performance measurement: Modified Dietz
Modified Dietz is one of the most commonly used return measures. Granted, Peter Dietz probably never referred to it as “Modified” (he called it “Day-Weighted,” as opposed to “Mid-Point Weighted”), but that’s the term we all know. Most investment firms used it at least one time, if not still today. And what’s it used for? Primarily as an approximation to the true, exact, time-weighted return (TWR).
It also serves as an approximation to the true, exact, money-weighted return (MWR): the internal rate of return (IRR).
Doing double-duty: Modified Dietz as an approximation for both MWR & TWR
Let’s say you’re calculating returns for 2018 using Modified Dietz. How do you do it for both TWR and MWR?
- For TWR, we value the portfolio monthly, and calculate returns for each of the 12 months. AND, we will value for large cash flows, and calculate two or more returns for months that experience them. We geometrically link (“chain link”) the individual returns to derive the annual return.
- For MWR, we value the portfolio at the start and end of year (i.e., just two valuations), and day-weight any flows that occurred throughout the year
If you’ve been introduced to the IRR, you know it cannot usually be solved directly (rather, it’s solved through trial-and-error). Ideally, we start with a “guess,” which is generally recommended to be the result obtained from using Modified Dietz (the “first order approximation”).
2020 GIPS Standards open to Modified Dietz for money-weighting, but wait …
The 2020 GIPS® standards allows firms to use any money-weighted method; this is a change from prior versions, where only the IRR can be used.
It so happens that Modified Dietz is often an excellent estimate for the IRR. However, there are times when it isn’t. I have not done any research to try to ascertain when it is or when it isn’t; I just know that it can be WAY OFF!
I discuss this topic in this video. And, I recommend that you avoid using it for money-weighting, but instead use the IRR.
Hi David,
I generally agree with you, although I would add some food for thought: Firstly, Modified Dietz will always produce only one (easy-to-audit) solution; whereas IRR may produce no solution or multiple (not-so-easy to audit) solutions, not to mention the occasional really-difficult-to-determine IRR solution. And secondly, at least with most software implementations, such as with EXCEL, in many cases, you will only see one of the solutions and therefore will blindly use that IRR solution and never know that there might have been other IRR solutions. As regards your comment about MD and IRR sometimes being so different, I would argue that, when IRR and MD differ dramatically, probably neither is a good answer and one should use some of the other new and advanced money-weighted rate of return metrics instead, such as by Magni or Jiang or others. I have no idea but am hoping that GIPS chose to use the MWR language because they realized that IRR is not the only MWR game in town for everyone. Lastly, I note that, just as you have argued that there is no time-weighting in True TWR, there is no money-weighting in IRR; rather IRR is a constant (for every cash flow period) rate of return solution, one which contradicts any known (e.g., for a portfolio of publicly traded stocks) or estimated interim valuations. Should our preferred rate of return metric care? That is an important question, IMHO.
Best regards,
Dean Altshuler
Dean, so sorry for the long delay in responding. Our system is to report when comments come in, but apparently didn’t in this case. I agree with you that there is much more to this topic, and appreciate you sending the articles to me. I intend to write an article in the near future to address this further.
Stay safe! And thanks for your comment.