**Why are time-weighted returns called time-weighted?**

Before I answer this question, it might help to explain where the terms “time-weighting” and “time-weighted” come from.

It’s not what you may think. No, Peter Dietz, who gave us the “Original Dietz” as well as the “asset-weighted Dietz” (aka, “Modified Dietz”) formulas was not the one who coined this term. It actually comes from the Bank Administration Institute’s 1968 publication, *Measuring the Investment Performance of Pension Funds*, the first “standard” for performance measurement.

At one time it was common for firms to indicate that they were “BAI compliant,” or “complied with the BAI standards.” Not the case any longer. However, these standards were quite important in establishing time-weighting as the preferred approach to evaluate the performance of asset managers. AND, two of their return formulas as well as the term “time-weighted” remain with us.

**What did the BAI standards give us?**

In addition to the term “time-weighted,” which I’ll address shortly, they provided us with three approaches to deriving rates of return:

**the Linked IRR, which is an approximation to the true, exact, time-weighted rate of return; today we know it better as “Modified BAI”****the Exact method, which we know of today as, well, the “exact method,” or simply “time-weighted,” as it is the true, exact, TWRR. It involves revaluing the portfolio whenever a cash flow occurs****the Regression method, which, to my knowledge, no one uses; it’s quite complex, and not worth the effort.**

One other thing they gave us: a way to link returns across time. They didn’t use geometric linking; rather, their method involved taking an average of the subperiod returns, thus …

**Finally: the meaning of the term “time-weighted”**

Within the BAI Standards we find the following:

“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>

This method involves annualizing the subperiod returns, and taking a weighted average, based on the length of the subperiod.

But, NO ONE does this.

**NO ONE! NOBODY! **

We all use geometric linking. This idea probably sounded like a reasonable approach, but it has since been deemed inappropriate. At least if we judge by the consensus of the investment community.

BUT, the term “time-weighting” has stuck, even though WE DO NOT WEIGHT TIME!

Imagine that! Kind of funny, right?

No wonder many find what we do confusing.

David…Thank You!

I have been trying to figure out where in the formula the time-weighting was done – and never found it. Now I know why 🙂

Thomas, you’re welcome. I had known this for some time, but hadn’t gone in to the book until a few days ago to pull the quote. I typically make reference to this in our Fundamentals class, but I think this quote “says it all.” And, I suspect very few folks knew this, especially since the BAI standards are not readily available. Thanks for your note!

Dave

Thanks David – Wondering if (although not “coined” by Dietz, per se) folks refer to both “Modified Dietz”, as well as the “exact method” as “time-weighted” methods because they both apply a weight to capital flows in the denominator of the formula based on an assumption of when (i.e., at what point in “time”) those capital flows were invested in/divested from the portfolio? In the case of MD, the “when” would be the day of the month, while in the case of Exact, would be beginning-of-day vs. end-of-day? Thanks for your always thought-provoking posts!

John, thanks, as always, for your note. I suspect that many folks assumed that the term “time-weighting” had to do with the timing of cash flows. However, that wasn’t the meaning, obviously from the source, when it began. And today, the with the exact method, there is no timing of anything, right? With BAI, they encouraged revaluing when any flows occurred, which could occur at varying time periods. Thus, the application of “time-weighting” as a linking method fit. If you were to ask a dozen CIPMs what it means, I’m sure most would suggest it has something to do with the timing of flows, but that’s limited to Modified BAI and Modified Dietz; nowhere else do we use this weighting. Further, the purists say that only the exact method is “time-weighted,” though there is ZERO weighting of anything!

I think that few folks ever got copies of the BAI, and fewer still read it, at least to much degree. I did, 30+ years ago, and it’s been on my bookshelf since, with only an occasional glance. When I designed my first performance system (in 1986), it wasn’t based on the BAI, but actually a paper Dietz had written, as it was much easier to follow.

I’m working from home today, and don’t have a copy of the ICAA (1971) standards, but believe they used the term “time-weighting,” too, though I don’t recall that they picked up on BAI’s linking method.

Funny stuff, I think.

Nice post, David! I was very lucky to have been given a copy of that report at the outset of my career – it is a good,albeit technically difficult, read. I think that it is only fitting that we continue to abuse the term TWRR since IRR users continue to refer to it as “money-weighted” (or, to us ugly Americans, dollar-weighted), neither of which is true – it is a constant rate of return, so you can ‘weight’ its underlying periodic rates of return by the size of the planets, if you like, and you will still get the IRR as the answer! So misnomers abound in our industry, it seems.

Although True TWR is a better estimate of the mean rate of return than its approximation brethren, such as Modified Dietz, its one big disadvantage is that, since the component rates of return are not of equal length, you can’t really do risk (volatility versus time) analysis on it.

Dean Altshuler

Thanks, Dean. I’ve had my copy for 30 years and won’t part with it!

Here I’ve been wandering around in this investment performance world for over ten years now confused about this term “time-weighted.” Initially I wrote it off as something I should know but wasn’t smart enough to figure out yet as a newbie. Then I decided it just didn’t make sense but didn’t have the background as to why. Then I became jaded and numb to it and just let it pester me chronically at a subconscious level for years following.

This SHOULD put an end to my mental suffering, but something tells me the effect might linger in my psyche for a while. It also creates a new source of frustration, though, the use of needless misnomers that endlessly confuse many of us, especially the newcomers to the industry. I guess we just keep adding to our mental “mapping tables” that are now becoming larger than our old pieces of notebook paper that store the chicken scratchings of many passwords our modern lives require to authenticate system usages.

Thanks, David!

Brett, thanks for your lovely note. Sadly, this isn’t the only example of confusing terms. In a recent post I identified some of my “wish list” items for GIPS. In our Fundamentals class, I often cite other examples of confusing terms. The reality is that this sort of thing isn’t limited to Performance Measurement. Take the word “peruse,” as in “I perused the newspaper.” I suspect most people would interpret this to mean that I skimmed the paper; but in reality, the word means to read with thoroughness and care! I guess we just need to know that everything isn’t necessarily as it seems. And while we don’t have any lexicographers supporting the investment industry, we can occasionally learn what something really means.

Indeed, they are everywhere, and they remain ugly pet peeves of mine! Sometimes I wish we could all just hit a reset button on the jargon, but I suppose that would create a steep learning curve too. Awareness is of utmost importance!

Thanks David, it is quite interesting to know nuances around different perception of time weighted. Not sure if i have fully understood- time weighted has a reference to fact that one prefer to have earnings/cash flow as quick as possible. It is with this idea that cash flow happening at the end of measurement period is less valued against the cash held at the beginning of period. When NPV are used to make choice between two project, the project with higher NPV(+ve) are preferred. But when they are equally preferable then that project realizing earlier break even on cost is considered good. In long hand formula we use discount factor for future cash flows such that NPV becomes zero. From investment managers perspective the day weighted fraction is like discounting cash flow to rationalize his view point of lost opportunity if cash withdrawn at wrong time or contributing cash when there is little time left to make well planned investment.Like you said “length of time”(fraction) is the key factor in determining cash flow discounting(what worth cash flow carries with the length of time left to invest). The magnitude to cash flow does not get weighted by itself but it uses time fraction(Time remaining to invest/total time in measurement period). With this rationalized time valued flows are then used to calculate return for the sub period. These returns are then linked together to give Return. Hence TWR.

Neeraj, thanks for your note.

Your references are to NPV, which, of course, deals with the IRR. I’ve commented that this is more time-weighted than time-weighted returns.

The key point from the post was to explain the source. It was the Bank Administration Institute (BAI) who coined this neologism (my word of the day), and the use around which it was defined is no longer valid; but, the term remains, even though it has nothing to do with that use, nor are returns time-weighted. I’m sure we can come up with thoughts on time-weighting (e.g., the weighting of cash flows), but that was exogenous (another word-of-the-day) to the BAI’s intent. Their Linked IRR (Modified BAI) weights the timing of flows, but this wasn’t their meaning.

Again, it’s really about trivia. Thanks again for your comment.