**Sometimes, the labels don’t matter**

We just finished **PMAR Europe 2017**, an event that we felt was a huge success. And, as I often do, I made an attempt to interject a bit of humor from time-to-time.

In one case, the “spark” behind it was one of the tea selections that was available: it was labeled “Pure Green Tea.” This made me think that with such a name, surely there also must be “Impure Green Tea” available.

A favorite label of mine to pick on is “regular coffee,” as the opposite would, of course, have to be “irregular coffee.” But, as you no doubt know, it is not.

The timing for me to mention these odd labels was my colleague **John Simpson’s** talk on attribution linking methods. He referenced David Cariño’s **Logarithmic method**, which uses “natural logs.” When I teach our attribution class, which includes a long session on this topic, I mention that the opposite of “natural” logs must surely be “unnatural” logs.

Sadly, few in attendance found my attempt to garner some laughter by making reference to these rather oddly labeled terms funny, though I did manage a chuckle out of my friend, Carl Bacon (although it may have been a sympathy vote).

**A label that we think matters, but doesn’t: time-weighting**

Our rates of return are either time or money weighted. But what do we mean when we speak of time-weighting?

I challenge you to ask your head of performance, or the performance analyst who just passed the CFA Institute’s CIPM program. I suspect they’ll offer some answer, though I can almost guarantee that it will be incorrect. Unless, of course, they’ve recently attended my **Fundamentals of Performance** course (as I’ve only addressed the derivation and meaning of this term in the past year or two), or, perhaps, heard me speak on this before, or read an earlier explanation on this subject (e.g., in a **blog post** from last year).

Chances are any explanation to the meaning of “time-weighting” will be based on the timing of cash flows, but that would be incorrect.

**But does the timing of cash flows matter?**

Well, yes, they do!

Dr. Stefan Illmer delivered a great talk at this week’s PMAR Europe on investment reporting best practices. And, because he appreciates the role of money-weighting, he spent time contrasting the two approaches to rates of return. He did a superior job justifying why it’s incredibly important to see returns that are derived from the internal rate of return (IRR).

He advocated asset owners seeing both time- and money-weighted returns, with the difference between them to be labeled the “timing effect.” I think this is a clever statistic, as it will clearly identify the result of cash flows.

Recall that time-weighting eliminates (or at least reduces, in the case of approximation methods (e.g., Modified Dietz, Modified BAI)) the impact of cash flows, while money-weighting takes the flows into consideration. Therefore, the difference has to be the effect of the flows. Brilliant!

But, the timing of cash flows has nothing to do with “time-weighting.”

**Who came up with the term “time-weighting”?**

A brief background: the source for the term “time-weighting.”

Was it Peter Dietz?

One might think so, since he is credited with bringing to light the idea of measuring returns free from the impact of cash flows. But no, he didn’t label his results or method as being time-weighted.

It was the U.S. Bank Administration Institute (BAI), in their 1968 paper, who gave us the term “time-weighted.”

The BAI formed a “blue ribbon committee” to draft the first performance standards. One has to conclude that the impetus behind it was Peter Dietz’s 1966 dissertation, which they make reference to early in the report. Since banks had historically had something to do with money management, getting the returns right was an important objective.

The BAI identified three ways to derive returns:

**Exact Method: we revalue the portfolio for each cash flow, and calculate returns between these flows periods, thus totally eliminating their effect on the resulting return. These sub-period returns would be linked to derive the return for the loner period.****Linked IRR Method: here, we break the period (e.g., a year) into sub-periods (e.g., months or quarters (today, of course, we’d insist on at least monthly)), where we revalue the portfolio. And, for each period we derive a return using the IRR. As with the Exact Method, we link the sub-period returns. Oh, and today we refer to this approach as “Modified BAI.”****Regression Method: we employ a regression technique across the period to derive the returns. No one does this; even the BAI seemed to think that such a method was overly complex.**

**Okay, so where’d the “time-weighting” come in?**

Well, as noted above, we want to “link” the sub-period returns. But how?

Today, of course, we “geometrically link” the returns, in order to compound them. Most performance measurement professionals are familiar with both the concept and the technique. But, back then, this approach hadn’t yet been developed.

And so, it was left to the members of the BAI committee to derive one. I can imagine what must have been going through some of their heads; what some of the discussion might have been like. Perhaps something like this:

**Member 1: okay, now that we have the returns for each sub-period, how do we link them?****Member 2: good question. In the case of the Linked IRR approach, all the sub-periods will be approximately the same, but with the Exact Method, we could have very short periods, perhaps just a few days, as well as long periods, extending several months.****Member 3: I think I know where you’re going. Should the returns that cover long periods count for more than those that cover short periods?****Member 2: Exactly! Doesn’t that make sense? If there’s a return for, perhaps, just a day or two, versus one that covers six months, shouldn’t the longer period return be weighted more heavily?****Other members, in unison: Yes! Or course!!!**

Think about it: doesn’t that make perfect sense?

Who would argue with such an approach?

In fact, this idea frequently arises in my classes when we talk about geometric linking. If, for example, we are going to link the following returns:

**November 11-30, 2015 (partial month)****December 2015 (full month)****2016 (full year)****1Q 2017 (quarterly return)****April, 2017 (full month)****May 2017 (full month)****June 1-15 2017 (partial month)**

in order to derive, for example, a since-inception return, shouldn’t the return for 2016 count for more than the *quarterly* return, that counts for more than the *monthly*, which counts for more than the partial month results?

**And, the answer is**:

See below.

**But, back to the BAI. **

Given that the group came to this intuitive conclusion about returns for longer periods counting for more, they derived a linking method. And here is the text, taken directly from their document:

**“The recommended rate is called ‘time-weighted’ because it is simply the weighted average of internal rates of return for the subperiods between cash flows with each weight being only the length of its corresponding subperiod.” <emphasis added>**

**BUT, no one, NO ONE, does this! No one!!!**

But this is where the label “time-weighted” (and of course its associated “time-weighting”) comes from! And despite that fact that no one uses this linking approach, the meaningless label remains. The term, however, has nothing to do with how we calculate our time-weighted returns.

What does it mean? That the method is eliminating or reducing the effect of cash flows. That is it! Nothing to do with “time” or “time-weighting.”

Oh, and as for the question above, about with geometric linking counting periods that are longer more heavily than those shorter, the answer is **absolutely not!** No, we don’t give greater weight to long periods than short: they all count the same! And while this may not make intuitive sense, I’ll let you reflect on it a bit. I’ll take it up in our newsletter!

Hi David nice to discuss on IRR. I have few comments to share.

Few vital elements necessary to be fair with the performance measurement are

-Consistency of methodology, time period and weight. I have no doubt every one knows the importance of it. However there is a peculiarity about IRR calculation methodology -which is that it fails to give the reliable RoR sometime or even fail to calculate return. I have seen the method failing to give correct return specially for since inception return. The return calculated using N/Raphson or XIRR fails to give rate within the limits of their iteration. This happens if the size of the flows are huge and asymmetrical with a very small starting value. Since the inception point is fixed and the portfolio keeps on accumulating flows which are not only erratic in terms of time period but also asymmetrical. There comes a time IRR calculation becomes counter-intuitive if it fails to calculate return at one point. Surprisingly IRR are back to give return when another flow happens and reference point of measurement changes. At this point it looks like there is something wrong with the system. But it is not the case. It is hard to capture such instance and explain to the client, the actual reason for incalculable since they might have limited experience on return calculation oddities.

In these circumstances it is easier to link IRR to keep the calculation engine running or simply day fraction weight the flows to arrive at a sensible return. I do remember from the curriculum that modified BAI is same as IRR. It is very imperative that the calculation should not only be accurate but also intuitive. If the investors can’t understand the methodology and remains sceptical about the return that they receive it is no point labelling very complex return calculation as the only best method.

One of the central reasons to do an IRR is that rate of return should be internal and there should not be any influence of external flows or inflation. It has its roots in NPV calculation where the main target is to find a discount rate for series of cash flows so that the NPV is 0. That discount rate is IRR. This also serves the way to check accuracy of IRR ie-the NPV should be zero. One can also use Goal seek function in excel.

When we talk in terms of weighting many sub periods IRR return of different length then IRR should not be very different return from the usual TWR. For the same portfolio linking IRR gives very close return to TWR. However if there is a composite return say portfolio A, B, and C with different market values or starting capital then weighting becomes necessary as same return earned by three portfolio will contribute differently. This is to keep the proportion right for each participating portfolio to the total. This is not the case when it is the case to link IRR for sub periods of different length within single portfolio. The longer period will anyway have bigger return than the smaller periods and it tracks market value movements. The capital gains will be captured and effect of flows neutralized.

Neeraj, thanks for your detailed comments. Please send me examples, as it is difficult to grasp in the abstract. You can send to dspaulding@spauldinggrp.com. Thanks!

sure will send. Thanks

Neeraj makes excellent points about other factors potentially causing unintended differences between TWR and IRR. However, his focus on what I will call ‘badly behaving’ cash flows understates the omnipresent problem with IRR. I do not believe I have reviewed Stefan’s latest work, but when David says:

“Therefore, the difference has to be the effect of the flows.”

I must beg to differ that one would get only the impact of cash flows when one compares TWR and IRR. If you use IRR as your MWR metric, and compare it with TWR, then you are not only seeing the impact of cash flows. You are also seeing the impact of IRR assuming different interim valuations than the ‘market values’ used in your TWR. Although it is hidden from the user, because IRR is only interested in a rate of return that is constant, i.e., the same during each cash flow period, IRR internally infers each of the interim periodic valuations – each which is easily computed from the IRR result as the net present value of all subsequent cash flows, discounted at that IRR rate. If you compute those implied valuations, you will inevitably find that they are different from the ‘market valuations’ used in your TWR. Keep in mind that those interim periodic valuations used in a TWR, for example for a stock portfolio, may be more than just your best estimate of market value, but may be perfectly known! Then imagine that IRR has the gall to ignore those real values, and substitute its own artificially-inferred interim values, all so it can fantasize that the only good MWR is one that is constant, i.e., the same for each and every cash flow period. This problem with IRR exists even when the cash flows are perfectly ‘well-behaved’.

.

Fortunately, there are alternatives. One is Magni’s AROI which is an MWR that can be a weighted average of the same periodic returns that are linked to form a TWR and, as such, can use the same interim valuations as the TWR uses. If such is done, then the difference between TWR and your MWR will, indeed, actually be due to the impacts of the cash flows only, all else equal. Bottom line, IRR is a flawed MWR and better ones now exist, MWRs that also would allow one to better gauge only the impact of cash flows when comparing it to a TWR.

Thanks, Dean.

I realize that this view of IRR is alien to virtually all of its users and,at the risk of appearing to be interested in nothing more than shameless self-promotion, if David will permit, I am adding a link to SSRN below that covers this view in the simplest terms I have been able to come up with. I think readers of this blog will find it very readable and I welcome any critical feedback.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2800643

Thanks, Dean!

David,

If the BAI article truly is the inspiration for the term “time-weighting” then I think we must ask ourselves why has this term caught on. I think its most likely because in dollar (money)weighting we are giving each dollar equal weight but in time weighting we are giving each time period equal weight. Certainly students seem to like this explanation and I think it explains very well the difference. The BAI explanation of time-weighting is so bizarre I can only put it down to poor drafting – I can’t really believe they meant what they actually wrote.

By the way I’m fully behind the EC’s consultation on the uses of money weighted and time weighted returns – there are circumstances where money weighted is more appropriate (although I think in fewer cases than you might)

I note you’ve offered a simply rule for using money-weighted – when the asset owner/manager is in control of cash flows. I don’t think it is as simple as that – for example a pension fund does not control its own external cash flow – it receives contributions and pays benefits – it has no control of either – therefore under your simplistic definition it should use time-weighted (actually I agree with you in this instance- but I don’t think it was your intention for pension funds to be required to use time-weighted)

Best regards

Carl

Carl, thanks for your input.

First, it isn’t a “BAI article,” but rather a monograph or book, as it’s fairly long. I am not aware of any work that preceded it that uses the term “time-weighting” (Dietz, as you may know, referred to his method as an “average” return.

It caught on because it was the ONLY standard for some time (granted, the ICAA came up with one three years later, but not all managers were members, and they tended (and often still tend) to be rather small in size). The BAI document was geared towards larger managers. For a time (in the 1980s, for example), it was quite common to hear that firms “complied with the BAI standards” (just as today GIPS is referenced).

Your suggestion for its use is an intriguing one, but clearly was not what occurred here. There was no “poor drafting.” They were trying to come up with a method to link subperiods, and arrived at this one, where the periods between IRRs is “time-weighted.” It’s quite clear. The industry has chosen to shift that term and broadly apply it to the calculations; this wasn’t the BAI’s intent, as is obvious from the document.

As for pension funds, even GIPS (as you fully know) makes the distinction here, pointing out that even though the fund might not control the flows, it is desirable to use the IRR in order to understand how the fund has performed. The question here should be “how are WE doing?,” and the IRR answers that question.

If, as you say, in time-weighting we give each time period equal weight, then where does the “time-weighting” come in? There is no time-weighting, because each period has the same weight! Money-weighting, as I frequently point out, DOES time-weight, as each period between flows is treated differently; but there is no real time-weighting in time-weighted returns. Granted, when we use an approximation method (such as Modified Dietz), then we do time-weight the cash flows, but this is not what the BAI was referring to. The term doesn’t apply; it just somehow caught on and remains with us. Just a bit of trivia, that’s all! Glad you found it of interest.

Best wishes,

Dave

David,

I think the derivation of terms is quite simple – recall that dollar weighted was a more common term than money weighted in the US originally . Basically each dollar is given equal weight in a dollar weighted return – in a time weighted method each time period is given equal weight – so to me it seems obvious that to differentiate between money weighted methods and linked methods you would call the linked methods time-weighted. If it was meaningless it would not have caught on – it obviously has a meaning today (even if that wasn’t the initial meaning)

Your imagination of the members coming up with a method that gives different weights to different length time periods simply doesn’t ring true – it is so stupid – and our predecessors (a Blue Ribbon committee no less) were not that stupid. I can’t imagine such a group coming up with such a bad suggestion untested. I’ve never seen anybody use that method.

By the way the WM company many years ago used a simplified version of the Regression method (WM assumed a beta of 1) and therefore didn’t actually do a regression calculation – I must say I didn’t like it – but it was in common usage. I don’t think its that complicated – but its a lot of work for very little (and that’s debatable ) added value.

I agree with Dean by the way – the difference between time-weighted and money-weighted returns is a methodical difference caused by cash flow – you are correct labels matter.

Best regards

Carl

Carl, “it doesn’t ring true”? Really?

The text I cited was taken DIRECTLY FROM the BAI Standards. I didn’t make it up. If you can find an earlier source for the term, please provide it. This is the earliest I have.

When time periods are of equal length, the idea that time-weighting means they’re being weighted, IMHO, doesn’t ring true. When something is equal-weighted, why qualify it as “time-weighted,” since it isn’t being time-weighted. I think to label something that makes no distinction between time periods as “time-weighted” would be totally and completely misleading, since, well, it’s not! Might as well pick something else that doesn’t factor in to the calculation. The money-weighted method is BOTH time- and money-weighted, in a sense; time-weighted is not, at all. Yes, we do take cash flow timing into consideration, but that wasn’t what the BAI was referring to.

As for dollar-weighting vs. money-weighting: today, we STILL hear people use the term “dollar-weighting.” I, long ago, adjusted, because we know that the world isn’t all about dollars. And so, the more inclusive “money-weighting” is appropriate.

You told me you have a copy of the BAI Standards: and so, you can validate what I wrote yourself. It’s quite simple. The term is used in the context of the linking method they derived. That’s a fact. If you can dispute it, with something concrete and not just an opinion, “I’m all ears.” Would love to see that in fact this term was used earlier and that the apparently stupid members of the BAI just got it wrong! Your statement has to be interpreted to be that if they had, in fact, come up with this term within the context I quoted, they must have been stupid: and since they in fact did, then one has to conclude, based on your logic, that they were, in fact, stupid!

However, I believe, like you, that they were anything but. You apparently didn’t grasp the context: it’s for a linking method. I did a subsequent post solely on that method. I can fully see why they would have they might have chosen the approach they did. Nothing stupid here, at all. Just a bit of trivia that you were apparently unfamiliar with.

As for the regression method, I considered it 30 years ago, but abandoned the idea for, at first, Original Dietz and later Modified Dietz. Why complicate things?

Anyway, it appears that you were unfamilar with this little fact and don’t want to accept it. I don’t know why. But, as always, I do appreciate you chiming in!

BTW, I’ll be addressing this, as part of a longer session, when we’re “down under” together later this year. Perhaps you’ll want to listen in!

As for the term catching on, ask 10 CIPM holders what the term means and see how they respond. If they’re unfamiliar with our discussion, so as to not have the benefit of what we’re each sharing, I’d love to get their answers. Trust me: they’ll be guessing. Oh, well … lots of fun, as always. Again, thanks!