When aggregate makes sense

Before you think "oh, here he goes again" please give me a second to explain. Okay, yes, it's true: I've been beating this to death (and will continue to, but not right now).

I was sent the following question from a client:

"How do you calculate performance for a composite that contains two or more funds?  Do you combine multiple funds' cash flows and calculate an IRR [internal rate of return] using all the funds' contributions, distributions and residual values as if they were from a single fund?"

Some background: the writer is speaking about a client's account, where they are reporting to the client, and are using the concept of a "composite" to pool the client's accounts together.

In this case, unlike with time-weighting, we would aggregate the accounts (starting and ending market values, as well as cash flows). We then calculate an IRR across this aggregate account. I would not encourage asset weighting individual IRRs, though to confess I haven't played around with it; my "gut" is speaking here.

And so, there is a place for aggregation: for IRRs, when we are reporting to a client about their return!

What are the risk statistics for IRR?

Someone recently asked me what risk statistics should be used with the internal rate of return (IRR), (which, as any reader of this blog knows, is my preferred return measure). Sadly, I didn't have an immediate reply.

The plethora of risk statistics that are available for time-weighted rates of return (TWRR) use the intra-period returns. For example:

• standard deviation (we can continue its appropriateness as a risk statistic)
• beta
• tracking error
• downside deviation

as well as the multitude of risk-adjusted return measures that use these risk measures (such as Sharpe ratio).

Recall that the IRR measures the return for a single period; there is no linking. Comparing the portfolio's IRR with the benchmark's only serves the purpose of seeing how well the portfolio did. But how can we measure risk if we use the IRR?

Reflect on this for a bit;  I will return to this matter soon, with some concrete ideas.

Even the Bible encourages IRR ...

"Men have had recourse to many calculations"

Ecclesiastes 7: 29

What's the interpretation of this line? Sadly, my bible doesn't reference which return formulas the writer was referring to, but one with an open mind can conjecture that it's a verse that recognizes that many return calculations are available and that one would be remiss not to consider them all.

To rely solely on time-weighting, for example, would provide us with limited knowledge. And since Ecclesiastes falls within the "wisdom" books of the bible (along with Job, Psalms, Proverbs, Song of Songs, Wisdom, and Sirach), clearly we're looking for ways to enhance ones wisdom; ones knowledge. A multi-dimensional view can only be obtained by considering alternatives, with each serving a purpose; fulfilling a role.

And so, what further evidence is needed that IRR (internal rate of return; money-weighting) should be part of ones arsenal?

p.s., While I knew that the bible was a source of comfort, insight, and guidance, I didn't realize it could also be a source of support for money-weighting!

Best practice when it comes to rates of return

A client asked about the "general landscape among financial companies in terms of usage of different performance engines/performance calculations." Specifically whether true daily or Modified Dietz is prevalent when it comes to portfolio and security level returns. I admire his due diligence in trying to obtain this information as they move forward with their own decisions.

When we use the term "best practice" what exactly do we mean? Unfortunately the GIPS(R) standards (Global Investment Performance Standards) uses this term for recommendations, suggesting that they are "best practice," but fails to define what "best practice" means? Is it:

• what is most commonly done (hardly, I would argue, the best basis for "best practice")
• what the leading firms do (again, not necessarily the best "best practice" source)
• what a few individuals on the GIPS Executive Committee think is what firms should be doing (arguably not "best practice," as the mix of members can change, would could cause a total redefinition as to what the term means).

Not knowing makes it a little mysterious and murky, does it not? I hesitate to offer my own definition, but may post this question on one or more of the Linkedin groups in the hopes that we might arrive at some consensus. But moving on to the questions at hand.

My thoughts:

• Portfolio level performance: it is evident that the industry is moving to daily time-weighted performance at the portfolio level. This should (assuming there aren't any data issues) result in the most accurate return. I would argue that the best approach would be to also have money-weighted returns at this level, so that the firm can provide multiple perspectives as to what is going on in the portfolio (i.e., how the manager did as well as the portfolio).
• Security, sector, asset class (i.e., sub-portfolio level) performance: here again we see a lot of firms employing time-weighting which I would say is the wrong approach (and I'm sure that some of my readers have heard this countless times from me and are thinking that I'm sounding like a "broken record," whatever that is!). If we go with what everyone else is doing, then do time-weighting and ideally daily; but this, to me, is incorrect: there is only one way to measure sub-portfolio performance: money-weighting. If you want to use Modified Dietz, that will be an improvement over true daily.

I thank our client for providing me with material for this blog and invite your thoughts.

p.s., I will most likely take the broad topic of "best practice" up in our newsletter

Why time-weighting if we don't weight time?

There seems to be some confusion as to what "time-weighting" actually means. The term was coined in the 1968 Bank Administration Institute (BAI) standards. The BAI proposed three ways to calculate returns:

• the "exact method," whereby we revalue the portfolio for any cash flow
• the "linked IRR," where we geometrically link subperiod (e.g., monthly) returns which were derived using the internal rate of return (IRR); this is similar to the Modified Dietz formula
• the time-weighted method, where instead of geometrically linking, we link returns based on the length of time between flows.

The third method can produce returns which are in error, thus it's been abandoned. However, the term "time-weighting" remains in our lexicon. But do we "weight" time? Nope! In fact, time has no bearing whatsoever on our returns. If we link a one day return, with a one week, one month, one quarter, one year, and one decade return, we will obtain a cumulative return across the full period, but in no way do we give extra "weight" to any of these periods.

In no way do we weight time in time-weighting. Granted, we weight cash flows based on their time in the Modified Dietz and Linked IRR, but this wasn't the source of the expression. Time-weighting simply means that we are eliminating or reducing the impact of cash flows. That's it! No time weighting.

From what perspective?

Almost 40 years ago I came across a "management test" (of the faux variety) which presented a variety of scenarios which required the "test taker" to respond to. For example:

You're at lunch with your largest client when for some reason the subject of Michigan comes up. You remark that "only two things come out of Michigan: football players and hookers." Your client calmly mentions that his wife is from Michigan. Do you

1. ask what position she played,
2. ask if she's still "working the streets,"
3. begin to speak incoherently, or
4. fake temporary amnesia?

At this point you're probably wondering what this has to do with performance measurement, and I must confess I'm confused, too. Oh, yeah, perspective! In this scenario, the character's attitude shifted quite a bit once his perspective changed, yes? When it comes to performance reporting, one must always be conscious of the perspective in which the information is being presented.

I was in a conversation earlier this week with a prospect who is thinking of having us review their performance measurement system and processes, something we often do. The prospect mentioned that they held some private equity assets which are difficult to value, and therefore perhaps the internal rate of return (IRR) should be used. I commented that it's a matter of perspective. Since this firm isn't a private equity manager but simply an investor in private equities (i.e., a limited, not general, partner), they are not obliged to follow, for example, the GIPS(R) (Global Investment Performance Standards) requirement for since-inception IRR. And therefore, they need to know if they're reporting "how the client did" or "how the firm is doing." In the former case, time-weighted returns are probably best, since the manager chose to invest in these and we want to eliminate (or reduce) the impact of cash flows. In the latter, the IRR would be best, since the client controls the cash and so why would we want to eliminate its impact?

Always consider the perspective of the person who is seeing the reports in order to know what to show and how to calculate the returns.

p.s., I'm obliged to mention that the use of Michigan was by no means intended to suggest anything improper about this state; it was done simply at random, I'm sure. Some of my best friends are from Michigan. And while they have great football, I'm unaware that there are any hookers living there. Should I stop grovelling now?

Fund of fund managers

In my response to the Global Investment Performance Standards (GIPS(R)) 2010 edition disclosure draft, I suggested that guidance be provided for fund-of-fund (FOF) managers. The standards clearly apply to such managers, but there weren't any details offered.

The GIPS Executive Committee (EC) listened (perhaps not actually to me, but at least to someone) and included a provision: however, it is limited to FOF managers in the private equity space. Clearly, guidance was needed, but its scope is somewhat limited. Perhaps more will be added in the future. Given the time constraints the EC faced, one can understand why not much more was addressed at this time. I would suggest they tackled one of the more significant areas.

Here's the scenario: we have a private equity FOF manager: what returns do they report for their claim of compliance? Since the FOF manager doesn't control the flows, one might think time-weighted returns apply; however, in the world of private equity, since inception IRR rules. The answer: SI-IRR (see paragraph 7.A.22 for further clarity). Bravo!

What about money weighting?

I got an e-mail from a retail client this week. That is, a retail client, whose rep works for one of our brokerage clients. This hadn't happened before.

This individual's rep had passed him one of the issues of our newsletter, to explain how they calculate their returns. This apparently didn't satisfy the end client, who sought clarity from me.

He indicated that he found the way returns are calculated by his broker too confusing, and advocated a "money weighted" approach: music to my ears! He went to the trouble to show me the IRR formula, which I thought was kind of funny. In my response I indicated that I've often commented favorably about the IRR and money-weighting, and suggested he review other issues of the newsletter (which is no easy task, given that we're now in our 7th year, and so have quite a lot of issues out there (though we do provide summaries of each on the website)).

I have found that when you show clients (institutional or retail) money-weighted returns, they feel that the returns are much more meaningful. Granted, time-weighting has its place, and shouldn't be replaced by money-weighting to represent how the manager did (save for private equity managers). Our crusade to get more firms to adopt money-weighting continues to gain new followers.

Should the IRR be net or gross of fee?

I was asked this question yesterday and thought it worthy of comment.

First, to clarify, "net" means after the fee is removed, while "gross" means before the fee is deducted.

There are generally two reasons we show IRR. First, in cases where the client controls the cash flows we show it to provide the client with THEIR return; that is, the return that takes into consideration not only the manager's performance but also the impact of the client's cash flow decisions. Why wouldn't we want to show "net"? This would truly reflect how they are doing, after (a) the impact of the manager's decisions, (b) the impact of their cash flow decisions, and (c) the impact of the advisory fee. So I'd say use "net."

The second occasion would be when the manager controls cash flows. As noted in yesterday's blog, I argue for IRR whenever this is the case, not just for private equity managers. Here we're showing the impact of the manager's entire range of decisions, from their management of the portfolio to their cash flow timing decisions. Net would reflect the entire impact and so this would generally be the better return, I would say. However, when the manager is providing their performance to prospects then both gross and net would be ideal. So in these cases, I'd say show both.

Consolidated reporting

Many firms like to group a client's accounts together, to provide a consolidated report that presents the client with the "overall picture" of what they hold. This is commonly done in the brokerage arena, as well as by others. So, how does one calculate performance for such an arrangement?

Well, what question are you trying to answer? I believe it's "how am I (the client) doing, overall?

And if so, then the answer is quite simple: a money-weighted return. Ideally, we'd use the internal rate of return to do this, though Modified Dietz would work as an approximation to the IRR.

Word of the day: contumacious

I recently came across the word "contumacious." Not being familiar with it, I turned to one of my favorite websites (www.Dictionary.com) to learn its meaning:

stubbornly perverse or rebellious;
willfully and obstinately disobedient.

I suspect there are some who would give me this label, given my sometimes headstrong views about various topics, including the issue of time- versus money-weighting.

When discussing this topic in class I often reference the movie The Poseidon Adventure; not the remake but the original from 1972. There's a scene shortly after the boat "did a 180" where the fallen away former Episcopal priest (played by Gene Hackman) instructs his small band to go in the direction opposite of where everyone else seems to be heading. Ernest Borgnine challenges him, asking why he thinks he's right when everyone else seems to feel that the other direction is best. As it turns out, the majority are heading to their death, while Hackman is correct.

Following the crowd is very easy; it's difficult to stand alone. I'm pleased to be joined by the likes of Stefan Illmer and Steve Campisi in my quest to see the IRR achieve its rightful place as the measure that should most often be employed. While we have a ways to go, we are definitely making progress.

I suspect that some of my views regarding the proposed changes to GIPS were also not well received by some: but I believe there are times when it's important to be forceful and direct. Five years ago there were some who pushed for mandatory verification, but I refused to give up in my opposition. Others joined me, and we prevailed.

Our industry remains at its infancy; we cannot be silent when we feel there are better ways to do things.

Risk-adjusted returns & money weighting

Most academic articles that deal with "returns" are actually dealing with risk-adjusted returns. In the course of writing an article on this subject I came across countless such articles. In The Journal of Performance Measurement we've tackled both this subject as well as pure returns (i.e., returns without the adjustment for risk), as both topics have value.

One topic which I don't recall seeing anything on is risk-adjusted performance relative to money-weighted returns. Given my general preference for the IRR, it's high time I took on this topic. Later today I will conduct a webinar on risk-adjusted performance but sadly won't be including anything on money-weighting as the subject hasn't yet gotten enough of my attention.

When evaluating the risk of money managers, clearly the standard approach of measuring risk-adjustment relative to time-weighted returns makes sense. But what about cases where the returns should be money-weighted: should the risk-adjusted measure likewise be? I would think so. But how to accomplish this might require some further thought; something I intend to invest in the coming weeks. So stay tuned!

Interpreting the IRR

I recently stumbled upon an article that I found quite interesting: "What Does an IRR (or Two) Mean?," by David Johnstone (Journal of Economic Education, Winter 2008). David is the National Australia Bank Professor of Finance at the University of Sydney School of Business. I found two things in particular quite insightful.

First, you may be aware that with the IRR we run the risk of having multiple solutions. And although there are techniques to help identify the number of potential solutions, the process is still fraught with challenges. David pointed out that multiple solutions will only occur "when the balance in the investment is at one or more times negative. That is, at some stage in its life, more is taken out than exists in the account." (page 79) I found a second article by Eschenbach, Baker & Whittaker ("Characterizing the Real Roots for P, A, and F with Applications to Environmental Remediation and Home Buying Problems," The Engineering Economist, 2007) which supported this claim. Clearly there are cases when the multiple solutions problem will be an issue, but how frequently will we find an investment portfolio go into the red? Dare I say virtually never?

The second insight I gained from David's piece was his "simple but intuitively meaningful interpretation of the notion of IRR." He uses the following example:

• at time = 0 (the starting point), we begin with$1,200
• at time = 1 (end of year 1), the client withdrawals $500
• at time = 2 (end of year 2), the client withdrawals $850
• at time = 3 (end of year 3), we end with $500.

The IRR is found to be 25 percent. So, what does this 25% represent? It's what we earn throughout the period. The following table should help convey this:

	t = 1	t = 2	t = 3
Balance at (t-1)	1,200	1,000	400
Period t interest (25.00%)	300	250	100
	1,500	1,250	500
Cash flow at t	-500	-850
Balance at t	1,000	400	500

We can see that with the IRR, we're able to reconcile our values throughout.

This, of course, is something you can't do with time-weighting. I expect to discuss this at greater length in the August issue of Performance Perspectives.

Friends of MWR & IRR

Our friend, Stefan Illmer of Credit Suisse, has launched a new group on Linkedin: Friends of MWR & IRR, and John Simpson and I are two of its early members. We are very pleased that Stefan has done this, as it's another way to provide increased attention to our efforts to encourage folks to adopt the MWR/IRR approach to calculating returns. Arguably, Stefan, along with Steve Campisi and I, have been the three most vocal supporters on this topic, and each of us have penned at least one article addressing this topic.

What does it mean to be a "Friend" of MWR & IRR? This hasn't yet been defined, though I suspect it includes:

• supporting the use of MWR and IRR for most reporting scenarios
• a desire to promote the use of MWR and IRR
• the recognition of the MWR's superiority over TWR in most cases.

Does it mean a total abandoment of the TWR? Absolutely not! We believe that the TWR serves a valuable role: to show the portfolio return of managers who do not control external cash flows; but that's about it.

If you, too, embrace MWR's role and want to see its use increased, please join!

Multiple solutions for the IRR

We were recently contacted by a client who had a scenario where the IRR produced multiple solutions. This isn't rare, but also isn't that common an occurrence in investing. Multiple solutions can arise when we have a series of in- and outflows. There is no guaranteed way to know that you have multiple solutions, but when you do have them the challenge is to know which of the solutions is the correct one. (Note that you can know that you don't have multiple solutions, and know when you might have them, but there isn't a way to know when you do have them).

Some time ago we formed an IRR Working Group to develop guidance on the IRR, as we're finding more firms realizing that it's usually the superior measure to employ. Multiple solutions is one of the topics we're tackling.

As I explained to our client, today there are no rules whatsoever regarding this topic. The easiest case to address, though, occurs when there are just two solutions, one positive and one negative. Here, you simply determine if you made or lost money during the period to decide which return to use: if you made money, you use the positive return; if you lost money, you use the negative return. (This is one of the advantages of IRR (money-weighting) over TWRR (time-weighted rates of return): with TWRR, you can legitimately have a positive return and lose money; something many find odd and counter intuitive. This doesn't happen with the IRR).

There may also be non-real (imaginary?) solutions, which would be discarded. But if you have multiple real solutions and they aren't in the form of the simple case noted above, further guidance is needed...we're working on it! [Note that we're having a meeting later this month and are hoping to make progress towards our eventual white paper].