TIME WEIGHTED RETURNS VS MONEY WEIGHTED RETURNS

I think probably 70% of the people here don't really calculate their returns.
Certainly not the traders with multiple transactions, cos it is a mammoth task doing so.
The vast majority of the remaining 30% are probably calculating it wrongly (Wrongly, that is, if you are using your ROI and comparing it to active managers)

Basic management 101 tells us that whatever doesn't get measured, doesn't get done/improved upon.
Cos if you don't have an accurate barometer of what you're doing, you wouldn't be able to tell what works and what doesnt. In fact, knowing human nature, you're more likely to over emphasis your wins, and try to shut off the nagging voice reminding you of your losers. And those who don't monitor, are very likely to have many losers to speak of. (cos no desire to know numbers to measure your performance, reeks of an unanalytical mind + laziness)

The novice who tries to measure return, would probably just take the difference between the portfolio value at the end of the period vs the start of the period, and divide that by the portfolio value at the start to get a raw return.
That's a resonably good estimate........ if you have ZERO infusions or withdrawals from the portfolio, and all dividends are automatically part of the cash portion of the portfolio. (highly unlikely to be the case for novices)

Things get complicated if there are multiple deposits and withdrawals.
Things get EVEN more complicated when the fund size varies, and the return varies (obviously) at various time points when you're holding different fund sizes.

Hence the need to understand and differentiate between the Time Weighted Return vs Money Weighted Return.

I won't, and probably can't do as good a job elucidating this as @bgting who wrote about this somewhere if I rem.
Anyway, many websites talk about the difference.

Retail investors calculating an IRR (Internal Rate of Return) using Excel, would be getting the Money Weighted Return (MWR).
That's realistically what's the easiest for retail investors to do, with the least hassle.
Basically, you input every cash deposit and withdrawal into Excel, and the returns take into account your fund size.

Now, for a long while, I've been using this MWR and comparing it to the returns of well known hedge funds to get a gauge of where I stand.

Professional funds though, don't use MWR, they use TWR.
So it's not a like for like comparison, the calculation is completely different.
Still, I postulated that, well, how different can it be? Perhaps within a 1% difference?

I'm wrong.
Interactive brokers now automatically calculates both the MWR and TWR for my US portfolio, so suddenly, I am now acutely aware of how different it can be.

Attached images are the 2 returns taken errr 2 minutes ago.
They are real time.
As one can see, the 1 year MWR and TWRs for my US portfolio is very very different.
Certainly significantly different.

How about the returns automatically calculated by numerous websites that are popular? Like stock cafe?
I dunno.
TTI's opinion is that.... well, if you're comparing to YOURSELF over multiple years, so say, you just want to know the rate of improvement or deprovement over time, then it doesn't matter what methodology you use, as long as it's consistent over the years.

But what use is that?
Since any dumb joker can throw into a passive index, or a dumb joker with some deep pockets can throw it to some active fund manager, so logically, if one is going to actively manage your own funds, it makes sense to compare to these alternatives.
An index.
And other professional fund managers.
And to do that, we need to calculate the TWR to be accurate.
A 4%, 5% difference between IRR (MWR) and TWR is no joke.
Compound that over the years, and you've heaven and earth... no wait. Heaven and Hell, in terms of results.

So, unless these websites automatically calculating your returns require you to input CASH deposits and withdrawals, portfolio size daily, and all transactions when they occur, including fees incurred...
otherwise, the ROI number you get....
is just not accurate.
And sorry to pop your bubble, in all likelihood, as most people wouldn't play by the same rules as professional hedgies, they wouldn't treat cash as an actual asset class in your portfolio, that is, cash is not going to have a dilutive effect on your portfolio.
In reality though, the professional hedgie doesn't have the luxury of asking for cash when, and ONLY WHEN, he needs it.
The cash sits there and from day 1, it's dragging on portfolio returns, as long as you don't deploy it. (May even drag more if you deploy it too!)

Of course, TTI here is just being very draconian.
Most of you will in all likelihood, don't give a damn.
So much methodology, so much calculation.
(I don't calculate TWR myself too, it's too much work. I do MWR though.)

This post is just to highlight:
- the difference between TWR and MWR may actually be very significant
- if you got your ROI figures calculated by some automated sites, it's very likely to be very much inflated. (assuming you play by the hedgie rules).

That's all.
Goodnight.

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30 likes 103 comments
theintelligentinvestor

StocksCafe calculates the portfolio TWRR everyday and that is compared to the STI ETF TWRR. I used that to gauge my performance.

Anyhow, I rather spend the time researching for new opportunities. There is no prize to figure out exactly if I beat or don't beat the index to 3 decimal points. My 2c.

ThumbTackInvestor

Reply to @theintelligentinvestor : yup, like I said, then you're just comparing internally, like what you need to get to reach a certain goal of $XX in a certain time period.
Then whatever methodology doesn't quite matter as long as you're comparing y-o-y and it's consistently used without changes.
Also, on the point on cash drag, my point is not that it's always going to drag on returns.
My point is that if one has to compare against external benchmarks (yes I know u said you don't, I mean "one" as in general), then the effects of a cash hoard has to be taken into consideration. If it's actually a "push" in a downturn, instead of a "drag", so be it, but it's still an actual asset class.
Finally, yea, for sure, focusing to be a better investor is more important, don't think anyone can argue with that.
But it's not mutually exclusive either.
Trying to track accurately doesn't make you do worse and not bothering to track to this extent, doesn't make you do better either.

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kc2024

Created a simple spreadsheet to play with the numbers to make sense of it.
This is what I think based on my observations.

1. MWRR (XIRR) magnifies the gain/loss due to timing of the cash flow.
2. The difference between the two measures can be huge!
3. TWRR is definitely the same as tracking return using NAV.

You can access the worksheet at this link https://bit.ly/mwrrtwrrnav to play with it. I have protected the sheet, so you can only change those values in yellow. Do let me know if there is any error.

Do share if any of you have further insight.

ThumbTackInvestor

Reply to @kc2024 : Oh I c
I take a slightly different approach
I Inject as and when it’s allocated for investment
If there’s nothing to buy, it’s kept as cash inside the portfolio and hence, I talk about the cash drag
Basically I’m trying to mimick the conditions that a fund manager faces in real life
He can’t tell his clients to keep their cash until he finds something... and he’s constantly pressured to deploy cash or it’d b a dead weight

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bgting

My post on Walter Schloss returns with comments. :-)

#shamelessplug

https://www.investingnote.com/posts/475948

@kc2024 : If I'm not wrong, I believe you mentioned using similar method to calculate returns, based on per unit NAV?

bgting

@ThumbTackInvestor : For the benefit of everyone, this is a paper on TWRR versus MWRR with illustrations on how difference in timing of cash injections and withdrawals will affect MWRR event though TWRR is the same for both.

https://www.pwlcapital.com/resources/under...

bgting

Reply to @ThumbTackInvestor : Ya ... Maybe if you extract the illustration, the essence of it and write a blog post, people will read. :-)

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Evilcrownofthorns

Think you all much more advanced than I. I am still trying to figure out how to accurately track my cash injections (i usually just monthly throw in some money) and the % of organic growth vs actual growth....if anyone has a good method, please share. :)

ThumbTackInvestor

Reply to @Evilcrownofthorns : I think if your portfolio value increases, it's important and necessary to try to be more accurate in tabulating returns.
Cos like I said, at the end of the day, we want to know where we stand with respect to other instruments.
If my TWR consistently is <<< some professionally managed hedge funds over a long time, at least over an entire economic cycle, then why bother? (aside from the fun)
I'd chuck it to them, and focus on my businesses.

Personally too, now, as I hold significant cash in my "proton cannon", I cannot just exclude the effects of cash. That'd be an unfair advantage for me.
That's like having the PC appear when, and only when I need it.
Even Tony Starks need to actually build the PC BEFORE the aliens/enemies/Thanos invades.

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bgting

Come to think of it ... let's say you're given $50k to invest. The return will be the portfolio value at the end of the period over $50k less one. It doesn't matter what you do. That's exactly what this stock challenge does. Anyone wants to cry foul and complain why MWRR is not used !? Haha ...

#banter

https://www.investingnote.com/simulation_c...

ThumbTackInvestor

Reply to @jeremyowtaip : eh no, we're not talking about risk here.
Nothing about risk at all.

We're talking about which methodology most accurately reflects a fund manager's real return.

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sysy

me just aunty retailer... not using any formula here... hehehe
too complicated for me to use also lah... somemore my capital tiny little only sia...

bgting

Reply to @sysy : Learning together. Big huat to you too! :-)

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bgting

Alternative presentation for calculation of TWRR would be this for @kc2024 example.
https://www.investingnote.com/comments/819361

I believe this may be clearer way for some to see how the returns for multiple periods are chained up based on what goes to the numerators and denominators.

TWRR = (End Portfolio Value for Period 1 / Starting Portfolio Value for Period 1) x (End Portfolio Value for Period 2 / Starting Portfolio Value for Period 2) - 1
= (8000 / 10000) x (24000 / 16000) - 1
= 0.8 x 1.5 - 1
= 1.2 - 1
= 20%

layers

i just use stockcafe. i nv include cash. too much of a hassle

ThumbTackInvestor

Reply to @layers : yea whichever works for u, but as long as you know that then, you can't really take your ROI from stockcafe and compare it to a benchmark, or to actually, anyone else, except yourself over time.

bgting

Copying over the TWRR calculation by @wellhandy in this comment as illustration :
https://www.investingnote.com/comments/819439

TWRR = (1 + return for 1st half year) x (1 + return for 2nd half year) - 1
= (1 - 0.2) x (1 + 0.5) - 1
= 0.8 x 1.5 - 1
= 1.2 - 1
= 20%

0.5 = $1.2 / $0.8

Let's say Investor A places $10000 with the Fund Manager at start of the year. And Investor B places $8000 with the Fund Manager only at half year mark.

Investor A will see his return of having invested in the fund through the year as 20%. Investor B will see his return as 50% for half a year (100% annualised, which is also his MWRR). Based on TWRR, the return of the fund for the year is 20%.

We can say that Investor B has timed his investment well, for eg, by putting money into the fund after a crash. The Fund Manager does not have discretion of when the money comes in or goes out.

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