I recently conducted a **software certification **for a software vendor. I found some issues with their application of rates of return, and we’ve been going back-and-forth on it. One issue that arose was my belief that money-weighting is the appropriate approach for subportfolio rates of return [I should point out that this isn’t a requirement for a vendor to pass, only our belief; we recognize that TWRR sadly “rules” at all levels today; we simply try to enlighten our clients into the appropriateness of alternative approaches]. As a way to demonstrate this, I offered the following scenario:

**Day 1: a portfolio holds 100 shares security X, valued at $10 per share (value = $1,000)****Day 2: the stock price drops to $5 per share, and the manager buys 1,000 additional shares (contribution = $5,000)****Day 3: the stock price has risen to $11 per share; the manager now owns 1,100 shares (value = $12,100)**.

What’s the rate of return? Well, if we use time-weighting, revaluing for the large flow on Day 2, we’ll get a return of 10%, even though it’s evident that there was a much larger gain. If we use Modified Dietz (without revaluing) we get 174.29%, and the IRR gives us 218.16 percent.

**Inconsistent Rates of Return**

My client responded by suggesting that if the portfolio only held this stock, and that on Day 2 there was an external cash flow that caused the purchase, by using MWRR at the subportfolio and TWRR at the portfolio we’d get “inconsistent” rates of return:

**Portfolio ROR = 10%****Subportfolio ROR = 218.16%**

How could we possibly explain this to a client?

**Great question!**

At the portfolio level, we are reporting on the portfolio manager’s return. Since she does not control client-directed, external cash flows (contributions and withdrawals), she cannot be given any credit for the timing or size of these flows; therefore, we eliminate their impact, and the manager gets a 10% return.

At the subportfolio level, however, we do take the (internal) cash flows into consideration, because the manager does control them. When the additional $5,000 came in, she saw that the stock price had dropped, and thinking that this was a temporary shift, decided to invest it all into the same security; as it turns out, this was a wise move, and so she benefited from the price increase that occurred the following day. She should be rewarded for this decision.

We are measuring two different things. Beginning in 1966 (with the **publication of Peter Dietz’s doctoral dissertation**), the industry has recognized that time-weighted rates of return are appropriate to judge the manager at the portfolio level.

Sadly, despite Dietz’s and others’ recognition that money-weighted rates of return had a place, too, the IRR was almost completely abandoned until fairly recently (which my colleagues Steve Campisi, CFA; Stefan Illmer, PhD and I take some credit for). We are now seeing a resurgence in the use of the IRR.

**Why inconsistency works**

I thanked our client for raising this point, although I had raised it before myself. Consider this scenario, which comes from our **Fundamentals of Investment Performance** class:

What do we see? Well, what I think are numbers that simply do not make sense: our portfolio has a return of 6.01%, but the underlying asset classes have returns that fall far below this level, with none even above 3.25 percent. What is going on?

Well, let’s look at the portfolio details:

As you can see, the manager decided to keep most of the portfolio in cash at the start of the year, which turned out to be a wise move, as both stocks and bonds didn’t do well. However, at mid-year he decided to shift money into both of these sectors, *just at the right time, *as it turns out. As a result, there was a significant gain overall. However, because time-weighting eliminates the effect of cash flows, the underlying sectors produce results that belie the effects of the internal cash flow decisions.

But, as our client would suggest, at least we’re being consistent! We’re consistently showing time-weighted rates of return, which apparently is something to find worthy, despite the failure of the method to capture the results of the manager’s decision, and fail to produce meaningful results. But, we’re consistent.

I’m all for consistency, but only when it truly makes sense; at times we need inconsistency, and here’s one. Let’s recalculate our subportfolio rates of return using the IRR:

Aren’t these results more meaningful? Don’t they capture what went on at the subportfolio level?

The truth is that I’ve been showing this example for more than a decade, and usually it’s met with understanding and appreciation. However, like our client, on occasion someone criticizes the “inconsistency,” and states that by doing this we are not able to tie the numbers back to the portfolio, or “reconcile” to its return.

“Really?” is my typical response. “Please then explain how you’d ‘reconcile’ the ‘consistent” TWRR results?”

**You can’t. **

**They’re nonsensical.****They’re inappropriate.****They’re simply wrong!!!**

Time-weighting belongs in one place and one place only: at the portfolio level, when reporting on how the manager did. That’s it. Simple.

Money-weighting belongs at the portfolio level, to show (a) how the manager did in those cases where the manager controls the flows (e.g, private equity) and (b) to explain to the client how they did, as a result of their cash flow decisions, coupled with the manager’s investment decisions. It also belongs at the subportfolio level, because the manager controls these flows.

Inconsistency isn’t always a bad thing … well, perhaps at times:

As always, your thoughts are welcome.

Oh, and I should point out that time-weighting also applies at the composite level, when producing returns for GIPS(R) (Global Investment Performance Standards), but this is arguably only an extension of the portfolio rates of return; hope you agree!

why bother with all these “returns” ? For the first example, the only correct return is 101.67% no ?

Inflows = cash flow begin of day, Outflows = cash flows end of day.

-8.33% for the first day and +120% for the second.

Lets make the world simple please rather than all these endless discussions about money weighted, IRR, dietz etc

Thanks Gregory.

Very interesting article! Much appreciated viewpoint. I am a bit confused by the paragraphs contrasting where TWR and MWR belong. Maybe it’s just a typo. It looks like the author is stating that TWR belongs at the portfolio level AND that MWR belongs at the portfolio level. I believe he meant to say sub-portfolio? Either that or I’m reading it incorrectly. Anyway, thanks for the interesting thought!!

Time-weighting belongs in one place and one place only: at the portfolio level, when reporting on how the manager did. That’s it. Simple.

Money-weighting belongs at the (SUB???) portfolio level, to show (a) how the manager did in those cases where the manager controls the flows (e.g, private equity) and (b) to explain to the client how they did, as a result of their cash flow decisions, coupled with the manager’s investment decisions. It also belongs at the subportfolio level, because the manager controls these flows.

Ben, thanks for your comments and questions. This wasn’t a typo, and I’ll briefly reply.

TWRR: at the portfolio level, ONLY to show the return of the manager in those cases when the manager doesn’t control the cash flows. MWRR at the portfolio level when the manager DOES control the flows (e.g., for private equity).

MWRR: in addition, MWRR at the portfolio level to tell the client how he/she/they did (by taking the flows into consideration). For example, in the USA, GASB (Government Accounting Standards Board) now requires public pension funds to report the IRR on their plans annually. In Canada, I believe it’s CRM2 (Joe Dabney made reference to this, as well) will shortly require the reporting of the IRR for portfolios. Further, many report these returns as “personal rates of return” (e.g., some mutual fund companies such as Fidelity and Vanguard).

MWRR: and, of course, always at the subportfolio level.

Hope this helps!

Thanks for your clear explanation around this important topic. I agree that there are many more situations where IRR should be used than is presently the norm.

Thanks, Laurie!

David,

I believe that I read somewhere recently that Canada will require the use of money weighted returns for client reporting in the near future.

Sounds like a good blog topic for you.

Joe

Joe, thanks, and you’re correct: this year, in fact! I thought I have done a post, but perhaps not, so will get to work on it. Thanks for chiming in!

Hi there David –

While I agree that money-weighted return methodologies are appropriate in the complete absence of external capital flows from the client (where PM buys here and sells there based on his/her own decision-making), I am struggling a bit with the utility (and example you gave) of applying MWRR at the sub-portfolio level when a client capital flow was the reason for the trading, because I believe that most asset managers tend to invest/divest capital flows on a proportional basis to the intended investment model in order to maintain consistent returns across similarly-managed mandates (and thus limit “internal” dispersion) for the composite track record, as opposed to your example where performance should be measured based on the “decision” of the PM to capitalize on the timing of that particular capital flow? Also wondering in your multi-asset portfolio example if the issue goes away by instead reporting an asset-weighted “contribution” of each underlying asset class to the total portfolio over the time period observed?. Continued thanks for the ongoing philosophical questions that you like to put up here!

John,

Thanks for your note.

You raise an interesting point, one that the ICAA also noted in their 1971 Standards, where they suggested that using money- (dollar-) weighting at the subportfolio level made sense, but at times these flows are the direct result of client contributions/withdrawals, and therefore perhaps it shouldn’t be employed.

I think in the calculation of subportfolio returns, we have to be consistent. Putting aside this example, and only taking one where there are no external flows, and the manager decides to change the weights in the different sectors, sell one security and buy another, rebalance, etc., these are all clearly manager-decided actions, with no affect attributable to client flows. Therefore, I believe it’s pretty clear that it’s necessary to capture the manager’s cash flow decisions, thus the need for MWRR.

If this is accepted, then on those occasions where there are external cash flows, how would we be able to override the MWRR and replace it with TWRR? In addition, in reality, once the cash arrives, it’s up to the portfolio manager to decide what to do with the cash. She can leave it in cash, spread it across evenly, purchase a new security, etc. Thus, there’s a division between external and internal: this virtual wall around the portfolio establishes the difference.

Granted, as you are fully aware, I advocate MWRR at the total level, too, as it provides us with different and valuable information. But internally, to me there’s only one way to calculate performance: MWRR.

David,

You should always be encouraged to include examples in your blogs – typically you always seem to choose examples that blast a hole through your own arguments – but more of that later.

In my view it is absolutely wrong to mix return methodologies – if you do this your contributions and attributions won’t add up and you’re be left with residuals in the attribution – which for me at least is a bad thing.

I first came across this issue first in my early performance career the other way round. At the time all of my attriburions were MWRs using Modified Dietz. The manager may at times invest in unitised collective funds and would like to see the sub-portfolio return of the fund calculated using the unit price ie time-weighted. As a consequence the attribution did not add up if there was a flow. Therefore, I insisted a MWR was used for the sub-portfolio instead.

To ensure the attribution reconciles if the total return is money-weighted then the sub-portfolio returns must also be money-weighted and if the total return is time-weighted then the sub-portfolio return must be time weighted.

Turning to your example not only does it make sense it is also from the managers perspective the desired result! Each of the category returns are lower than the total return – this can only be achieved by good timing decisions within the portfolio switching between catorgories – ie good allocation. Proper time-weighted attribution analysis would show this accurately – by switching methodolgies your analysis will not only show a residual in attribution but it mis-leads the user into assuming good selection within equities when by your own admission the good performance is the result of good timing. This is a perfect example to demonstrate why MWR sub-portfolio returns are a disaster. In one short blog you have commited a number of performance measurement sins:

1) mixed methodologies

2) generated a residual in attribution analysis

3) used MWRs for liquid assets

4) suggested control of cashflow is sufficient reason to use a MWR

All of which lead to a misinterpretation of performance.

If i was to publish Bacon’s 10 fundamental laws of performance measurement you would have broken 5 of them in this blog alone!

Best regards

Carl

Carl,

Thanks for your not unexpected response. Sadly, your statement that the fact that the results are the desired ones will, I’m sure, fail to bring much comfort to those who must contend with reporting this to their clients. Your rules are ones of your own contrivance, which, of course, you’re permitted to do, but sadly there’s nothing in the industry’s vast amount of literature to back them. For example, your oft stated claim that MWRs are for liquid assets runs in total conflict with countless papers dating from as early as the 1960s, some by Dietz, that state clearly the role of the IRR, which you refuse to accept. As for residuals, you clearly don’t find them unobjectionable, as your own geometric methodology for attribution generates them with each single period: you simply (and arguably naively) smooth them away. And so, the industry has dealt with residuals in the past, and may have to once again. I’ll review your comments further, and attempt to come back with a more formal reply. Thanks, as always, for chiming in!

David, thanks for your continued effort towards educating our industry on when and when not to use the TWR and MWR methodologies. Whilst I agree that the cash flow source, to a large extent, determines what method to use, I’m however not convinced it makes sense when you try to compare MWR results to a market index/benchmark returns often calculated using TWR.

What’s your view on this?

I think this may be a duplicate, and that I already responded. Sorry.

David, thanks for your continued effort towards educating our industry on when and when not to use the TWR and MWR methodologies. Whilst I agree that the cash flow source, to a large extent, determines what method to use, I’m however not convinced it makes sense when you try to compare MWR results to a market index/benchmark returns often calculated using TWR.

What’s your view on this?

Daniel, I’ve written in the past on adjusting indexes for cases where the IRR is being used (for example, see See https://spauldinggrp.com/wp-content/uploads/2014/05/May06NL.pdf); in fact, I recently commented about this for a client, who is redoing their return methodology. For managed accounts, I believe that showing an adjusted index when reporting the IRR makes perfect sense, as it provides an “apples-to-apples” comparison (i.e., it asks the question, what if I had invested in the index rather than this portfolio?). In the case of a broker/dealer where their clients are making their own investment decisions, I believe a standard index probably makes sense, although I’ll accept that many may disagree with me (in fact, in a conversation with a major provider of performance to this market I was told that most of their clients use the money-weighted version of the index). Thanks for raising this interesting and often controversial issue.

There are two contributions to returns occurring in the example, the manager’s asset class strategies and the impact of the change in allocation. Certainly, reporting only the time-weighted return corresponding to the manager’s asset class strategies alone will not explain the total portfolio return of 6.01%. However, one possible solution is to report the time-weighted returns along with the impact (contribution) from the allocation decision. In this case, the manager’s time-weighted return at the total portfolio level is 0.8(3.24%)+0.1(-0.85%)+0.1(2.32%) = 2.74%. Therefore, the impact due to the allocation decision is 6.01% – 2.74% = 3.27%. This style of reporting is similar to how the impact of a currency overlay or derivative strategy might be reported, that is, without the overlay and with the overlay to determine the overlay impact. It is straightforward to check that this calculation matches a calculation based on the actual dollar gain or loss through the four periods comparing the gains as if the allocation change did not occur to when it does. In addition, the contributions from the separate asset classes can also be calculated and reported if desired.

More generally, internal and external flow contributions can be calculated and then reported to assess the separate impacts. For example,

• Time-weighted manager return = x

This is the weighted average of portfolio component TWRs, as if no CF occurred.

• Contribution from external flows = y

• Contribution from internal flows = z

Then the manager’s total portfolio return = (x + z), and the client might be interested in their effective return = (x + y + z), where external flow impact is also quantified. Note that any flow, internal or external, will have an impact on analytics and reporting. Reporting in the way suggested here is not inconsistent.

John, thanks for your comment. I’ll review and ponder this a bit more before giving a more appropriate and deserved response.

John,

You are absolutely correct – there are two different contributions – allocation and selection. Using a MWR and asset class level loses that information which is part of the manager’s decision process.

What ever else you believe about MWR and TWR returns – this fact alone invalidates mixing methodologies

Best regards

Carl

Hello David,

I am comforted by your initial statements, as I am a big believer that TWRRs were created for the purposes of comparing managers (who don’t control cash flow) not investors. I tend to agree with John about the sub-portfolio issue when the manager has had a cash flow ‘forced’ on him. And I appreciate that you and others are carrying the MWRR torch. However, as long as we insist that the only real MWRR is an IRR, in my opinion, we are doomed to fight the TWRR versus MWRR wars with one arm tied behind our backs.

Most folks believe that IRR is flawed only in certain scenarios that have ‘odd cash flows’, but the truth is its flaw is omnipresent. And so, just as you have found an example that makes TWRR look bad, someone else can choose one where IRR looks bad. In the case of IRR, its weakness is due to its artificial assumption that the only valid rate of return is one that is constant during each and every cash flow period.

Here’s a somewhat exaggerated example, similar in theme to David’s opening one, but one that could be used to expose IRR’s weakness: An investor buys a stock for $100 and sells it one year later for $250. That investor immediately invests $100 of that $250 in another stock, pocketing $150, and, one year later, sells it for $110. The rates of return for those two years are 150% and 10%, which averages 80% a year. If you compute IRR, you will find that the IRR, which is constant in each year, is 103.94%! The TWRR is 65.8%. If you force me to choose between TWRR and MWRR based on the results of an example, I might favor the TWRR, because it seems to make more sense, at least in terms of being closer to the intuitive 80% average. But should I let the results of an example determine which the more appropriate metric is? Of course not!

So, let’s consider other MWRRs. Professor Carlo Alberto Magni’s AROI, as summarized in a PME article published this year in the Spaulding Group’s Journal of Performance Measurement, computes an overall MWRR simply as the weighted average of the periodic rates of return, weighted according to the amounts invested. In this case, because $100 was invested going into each year, the weighted average is the same as a simple average, i.e., of 10% and 150%, which, lo and behold, is the aforementioned 80%. A more credible result than IRR’s 103.94%? I think so. You be the judge.

Or for readers that prefer a MWRR metric that accounts for the time value of money, Professor Magni has created AIRR. Like AROI, it also computes the rate of return as a weighted average rate according to the amounts invested but, in the case of AIRR, the ‘weights’ are the comparative amounts invested in present value terms. For example, if the market’s rate of return was 20%, then the second period’s rate of return gets a weighting of $100/1.2, i.e., $83.33, whereas the higher, first year’s ROR is weighted by the (year zero, so already present-valued) original $100. Hence, the AIRR’s weighted average result tends toward the higher ROR of the larger first investment (in present value terms that is) and is ($100 x 150% + $83.33 x 10%)/ ($100 + $83.33) = 86.36%. That is also a lot more credible than IRR, and the algebra is infinitely more explainable than that which produced the IRR of 103.94%. To wit, ponder “how many dollars was that 103.94% earned on”?

Although I have probably made my point about IRR already, I can’t resist the urge to note that, if we simply switch the order of the two investments, letting the first $100 earn 10% and the latter $100 earn 150%, the TWRR stays the same, whereas the IRR drops from 103.94% to 63.19%! Again TWRR seems to make more sense than IRR. Should that mean a TWRR is better than a MWRR here? Again, the answer is “of course not”, if what we are trying to measure is an investor’s rate of return. However, what if we again consider Magni’s MWRRs: The AROI result does not change, remaining at 80%. The AIRR result, which now has the lesser performing investment having greater weight, i.e., in present value terms, drops to ($100 x 10% + $100/1.2 x 150%)/ ($100 +$100/1.2) = 73.64%. That is a different result than the 86.36% AIRR result above when the order of RORs was reversed, but not excessively so and, more importantly, the math is completely explainable, not to mention doable on the back of an envelope. How many of you want to explain why the IRR changed from 103.94% to 63.19%, not to mention why it was 103.94% in the first scenario to begin with! For convenience, all the results above are summarized in the table below.

Somehow, we only seem to question IRR when the result seems odd, or, worse yet, only when it has either multiple solutions or no solutions. However, my contention is that the weakness of IRR is omnipresent, both when the answer seems reasonable and when it doesn’t. So, we should question it all the time. In essence, you cannot reconcile IRR with sub-period or sub-portfolio rates of return. This is because IRR insists on always producing a constant rate of return and, in order to do that, IRR must reject each and every market value of the investment(s) along the way, whether they are estimated or even known exactly (stock portfolio) – such market values belie the existence of a constant rate of return. Further, IRR always looks at investments in a combined portfolio context, one which sacrifices the identity of constituent investments, yet another reason why IRR-based attribution always comes up short and is doomed to failure. Professor Magni has created at least two MWRR metrics that behave much more intuitively and predictably, as exemplified above. Their improved behavior is because they are superior metrics by design, having benefitted from decades of analysis and scrutiny of IRR.

IRR is a fascinating function, make no mistake, and indeed I have made a nice living off of analyzing its quirks, but I think it is time to start accepting the weaknesses of IRR as a money-weighted rate of return. IRR is fine when you have no idea of what your investments are worth along the way, or have no desire to do a money-weighted attribution analysis. But otherwise it is flawed. Until we grow past believing that IRR is the only acceptable MWRR, we will continue to be vulnerable to counterexamples offered by the TWRR proponents, rendering our arguments for use of an MWRR far less persuasive than they could have been.

ANNUAL RATES OF RETURN

Scenario TWRR AROI AIRR IRR

+150%, then +10% 65.83% 80.00% 86.36% 103.94%

+10%, then +150% 65.83% 80.00% 73.64% 63.19%

Dean, thanks for your well thought out response; you raise very interesting points, which will require some time for me to digest. I’ve seen other examples where the IRR doesn’t seem to make as much sense as the TWRR or Modified Dietz. One client of ours will swap the MD for the IRR when it makes more sense, which we object to. The apparent “flaw” in the IRR of assuming the same return for all periods is one that has been raised by others, of course. I guess we have two (or three) “imperfect” measures, which many have attempted to alter. Again, thanks.

David,

There are no residuals in the geometric model for asset allocation/ stock selection effects over multiple periods

We’ve moved forward a long way since those early papers

Best regards

Carl

Carl, we’ve been through this before, and sadly you refuse to acknowledge what even Jose Menchero so accurately pointed out in his model (and you acknowledged to me several years ago over the phone): to get your math to work for single periods, you had to introduce an adjustment factor (i.e., to remove the residual). And so, geometric has single period residuals, while arithmetic has multi-period ones. Residuals happen; we deal w/them.

David,

Yes we have been through this before and sadly you continue to misunderstand. There is no residual in the geometric model over multiple periods or single periods between selection and allocation.

The adjustment factor you describe is a level below (by the way it is not an adjustment factor -it is a genuine economic effect and we can have a debate about that interpretation)

Some of things we argue about are matter of opinion – this one isn’t I’m afraid it is a simple mathematical fact that there is no residual.

The issue you’re actually talking about isn’t a residual either but that is another discussion

Best regards

Carl

Carl, you are correct: we have discussed. I vividly recall reaching out to you as I was preparing for the CIPM, and asked what a factor was in your selection effect; you explained that when you were putting the model together, you couldn’t get the numbers to all tie out; and so, you tried different things and found that this worked (and, it does). If you’re going to substitute benchmark weight for portfolio weight, you’ll need it, too, in the interaction effect. And, as I’ve pointed out, Jose Menchero (in his geometric model) makes it vividly clear that in order to get geometric to work, a smoothing factor is needed. The additional factor you have isn’t in the BF model: it’s what is needed to get the numbers to work. It’s quite simple. Sorry: arithmetic models have multi-period residuals (which can be smoothed away), while geometric have single period (which can also be smoothed away). It is, what it is.

Hi David,

Interesting topic and explanations. What if you go further in your analysis of the time-weighted return and do a performance attribution example. I do expect that the attribution results of the time weight returns at the sub portfolio will show the good timing of the fund manager and then show meaningful results.

I agree; need to provide some examples, which should be in a paper that I’ll be completing later this year. Thanks for your comment!

David,

Yes examples are always good – when you’re designed your example I will be perfectly happy to provide a TWR attribution for it (provided there is sufficient benchmark information and valuation data) and an explanation – Your example can be extreme as you wish I’m so confident I can provide a meaningful TWR attribution of it.

Best regards

Carl

Thanks, David. For those interested in learning a little more about Professor Magni’s AROI, and how it compares to IRR, here is a link to a working paper I posted on SSRN:

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

Dean.

It’s sad that David continues to mislead the industry with the propagation of misleading statements such as residuals in geometric attribution, or that a cash flow from asset class (Cash) to top up a security (equity,etc) is justification for MWR over TWR, or even worse, compare strategy return with portfolio return without taking into consideration changes in the strategy mid-period. I’ve done the math, I’ve checked your facts and examples, and most are misleading at best, and damn right misunderstandings of a perfectly logical TWR calculation model. You are trying to capture what benefit/loss you have received on a starting capital position. Using my example, if I have $150 and gave $100 to manager 1 and $50 to mgr 2. Mgr 1 bought on first day @10, and held on second day when it was $5 (didn’t lock in loss), and then sold on 3rd day when it was $11, my investment with him/her will now be $110. If Mgr 2 didn’t buy on first day @10 (let’s say he analysed the market well) but then bought the next day at $5, and held till current day when it is $11, I will have $110 with the second mgr. Clearly, my 150 investment at ‘portfolio’ level has now grown to $220. So my benefit is $70, or should I say, my return is approx 47% (70 benefit /150 I started with). There is nothing hard in calculating this. Nothing misleading. Nothing complex. It’s a laymans introduction to TWRR using a parallel example. Why still keep pushing MWRR? The fact is and remains you did not gain more than 46.67% on the $150 investment. Now, did you gain more than that in the $50 with mgr 2? Of course, but that’s NOT the question! So no need to use it to justify MWR vs TWR. This is getting ridiculous!

So in all, you say… “…What’s the rate of return? Well, if we use time-weighting, revaluing for the large flow on Day 2, we’ll get a return of 10%, even though it’s evident that there was a much larger gain. If we use Modified Dietz (without revaluing) we get 174.29%, and the IRR gives us 218.16 percent”. That’s incorrect! Also you say time weighting doesn’t capture manager’s decisions, I think I have shown it does. If this is not clear and you want me to build you excel sheets of scenarios and models, trust me, I can do that as well. Please share the name of the vendor. So I can stay away from them, need i say, I don’t believe you advised then correctly, but this appears to be as more of an education gap fill, and sometimes, opening up your mind to people like Carl B, etc can do you some good.

Anita, thank you for your note. I’m sorry that you feel so negatively towards my views.

The example you provide is neither a TWRR nor a MWRR issue, since there are no cash flows. That is, at the plan level, you started with $150 and ended with $220, so the return, be it MWRR or TWRR, will be identical. As for the managers, they each had a set amount and it rose, with no intervening cash flows, so the TWRR = MWRR.

As for geometric not having a residual, I have demonstrated this, and suggest you check out our July 2016 newsletter (https://spauldinggrp.com/wp-content/uploads/2014/05/NLJUL16.pdf) for clear evidence that geometric has a residual. It is not only me that knows that this is the case, Jose Menchero wrote about it in his article on geometric attribution. While Carl Bacon disagrees, he has not countered my arguments that were outlined in the newsletter. Both arithmetic and geometric models have residuals: arithmetic across time (that is, when you link), geometric within the individual periods. And for each there are ways to “smooth out” the residuals. For geometric, Carl does it with his model, as does Jose with his.

Again thanks for taking the time to comment.

David, What ever happened to the idea of TMWR, Time and Money Weighted return. Joe D’Alessandro published a white paper on this subject in the summer 2011 edition of “The Journal of Performance Measurement”. I always thought this idea had merit and, while not perfect, was a way to reduce the glaring imperfections of IRR and TWR in certain situations.

Thanks

Troy,

Well, we just haven’t seen anything further on it.

On this, I happen to disagree with Joe. I feel that each method has its purpose.

Think about it, to report the manager’s performance, you DO NOT want the impact of client-directed cash flows; however, to report the performance of the client (or, the portfolio), you DO want the impact. These are two totally different ways to treat cash flows. Combining into a single formula, IMHO, is not a worthy objective.

Or, perhaps I need to re-read his article and ponder a bit more. Anyway, that’s my thinking. But, you’re more than welcome to submit an article, too, offering your thoughts and ideas: we’d love it!

Best wishes,

Dave