Sometimes, the labels don’t matter

We just finished our European conference PMAR, an event that we felt was a huge success. And, as I often do, I made an attempt to interject a bit of humor.

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!