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Returns - TWRR & MWRR - And the Canadians!
Old 02-05-2019, 05:21 AM   #1
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Returns - TWRR & MWRR - And the Canadians!

I've always known and understood the difference in Time Weighted Returns vs. Money Weighted Returns. However, I've been digging into the details recently and come across some interesting things. For those that need a refresher, this link is a really good summary in cartoon format: Making Sense of Your Investment Performance

Interesting #1: Since summer of 2016, Canada has required firms to report client personal performance using Money Weighted numbers. That is, it reflects the actual gain/loss for each client.

Interesting #2: I can find no such regulation (or even recommendation) for USA. In fact it would appear some companies report TWR and others MWR. I can confirm that TRowe Price uses TWR for their "Personal rate of return" as detailed at this link. I have read that others use MWR.

Interesting #3: MWR can easily be calculated using the XIRR function in Excel or Google Sheets. Of course, you need to have all transactions and their dates for the desired time period

Interesting #4: I have automatically invested in one particular fund for the past 20 years. TRowePrice are reporting that my personal rate of return (using TWR) is 7%. My calculation - it really is easy using XIRR - is over 10%.

TWR is very useful for comparing different investments. However, MWR is your actual return. It is very interesting and useful to know your actual return for planning purposes.
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Old 02-05-2019, 07:01 PM   #2
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Yes, our government likes to make sure we get good value for our tax dollars, including universal healthcare.

The reports you refer to also include investment costs, although the cost calculation is limited to trading commissions and fees paid to the broker, but not the entire MER on funds.

If you like using XIRR to calculate MWR, here is a good thread with tips on how to use it to calculate return for multiple years and multiple accounts:
https://www.canadianmoneyforum.com/s...calculate-XIRR

And the Bogleheads return spreadsheet is great for TWR:
https://www.bogleheads.org/wiki/Calc...rsonal_returns

Interesting that your MWR on the TRP fund was so much higher than the TWR reported by the fund. Did you use dollar cost averaging over that time period?
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Old 02-05-2019, 07:23 PM   #3
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Interesting that your MWR on the TRP fund was so much higher than the TWR reported by the fund. Did you use dollar cost averaging over that time period?
Yes, contributions made on the first business day (or close) of every month for that time period. I do wonder how that affected the results. Did it cause me to inadvertently time the market in a positive way?
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Old 02-05-2019, 10:38 PM   #4
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Yes, contributions made on the first business day (or close) of every month for that time period. I do wonder how that affected the results. Did it cause me to inadvertently time the market in a positive way?
I've been looking at this further. I'm convinced that my decision to start investing when I did using dollar cost averaging, to be followed by the so-called lost decade (2000-2009) caused me to make many years of cheaper purchases than what TWRR would dictate. After all TWRR is effectively just a straight line connecting the beginning price and ending price. The strategy forces a "buy low" mentality, and the "lost decade" compounded that, resulting in the significant difference in TWRR and MWRR.
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Old 02-06-2019, 05:02 AM   #5
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Yes, consistent monthly purchases results in buying more units when the price is lower and fewer units when the price is higher.
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Old 02-06-2019, 02:12 PM   #6
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I can't really wrap my head around this but it appears that the Making Sense article is mischaracterizing the TWR method, at least according to TRowe. TRowe clearly states that it takes into account buys and sells, and calculates the performance of every period between buys and sells and sums them. The Making Sense article is comparing the MWR calculation to the simple performance of a portfolio with no buys or sells, that's not apples to apples.
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Old 02-06-2019, 05:13 PM   #7
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I can't really wrap my head around this but it appears that the Making Sense article is mischaracterizing the TWR method, at least according to TRowe. TRowe clearly states that it takes into account buys and sells, and calculates the performance of every period between buys and sells and sums them. The Making Sense article is comparing the MWR calculation to the simple performance of a portfolio with no buys or sells, that's not apples to apples.
Thanks for taking the time to look at that in such detail.

T. Rowe Price's verbiage is completely confusing to me. They make two statements:

1 - "Personal rate of return is an individualís investment performance, or the return on individual investments and transactions, based on the transaction history and resulting cash flows, minus any fees." - I agree!

2 - "Time-Weighted Rate of Return (TWRR) is widely used by financial analysts. It takes into account the amount of time you held investments in your account, the overall portfolio performance, as well as external cash flows, such as purchase and redemption transactions into and out of your account." - I don't think it does. It uses all those things, but for the purpose of negating the cash flows.

Here is another really good link on how these things are calculated and it matches T.Rowe Price's example on their site (previous link).
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Old 02-07-2019, 06:35 AM   #8
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2 - "Time-Weighted Rate of Return (TWRR) is widely used by financial analysts. It takes into account the amount of time you held investments in your account, the overall portfolio performance, as well as external cash flows, such as purchase and redemption transactions into and out of your account." - I don't think it does. It uses all those things, but for the purpose of negating the cash flows.
What about that sentence doesn't jive with you? It says it takes into account the cash flow. Taking into account could mean negating, they are specifically excluding cash flow from the changes in portfolio value.

That last article was helpful and I think I finally get it. TWR breaks up the total investment period into segments, and the geometrically averages the performance of those periods, weighing each period of equal length the same. But its possible, for example, you had much more money invested during the down periods and less during the ups, meaning you had more in the game to lose during the downs, and less during the ups, so the effective growth for your portfolio is not really weighted equally over each of those time periods, it's weighted by the amount you had in the game during each time period. MWR takes that into account (though I still haven't seen the math, just reference to Excel functions, I guess it must be complex).

It also makes sense that TWR would be widely used, and the only useful metric of the two for comparing performance among different funds. It doesn't matter how much money you had in the fund at different times if you are trying to compare how you fund did compared to a benchmark or some other.

I guess the argument for MWR is that it is a more accurate picture of your gains and losses, which could be useful for historical purposes, but I don't really get the argument that it is more useful for projecting long-term market returns. Yes that was a more accurate picture of your personal return in the past, but without knowing how the market is going to move and how much money you'll have in it at any given time in the future you can't predict if the MWR would deviate up or down from the TWR.

It's interesting you can use MWR vs TWR as a metric for how good you are at market timing.

Also another thought, it's confusing and perhaps counter-intuitive that TRowe provides a TWR and calls it your 'personal rate of return'. It would make more sense for the 'personal rate of return' to be the MWR, but I guess in this context by personal they mean return to you across all your holdings, not performance of a single fund. Maybe this is your point about TRowe's description not sounding right to you.

This was educational, thanks for sharing.
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Old 02-07-2019, 07:15 AM   #9
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I use TWR to compare to benchmarks. How well my portfolio did compared to a blend of index returns that has a similar asset allocation to my own holdings.

I use MWR to compare to my expected rate of return in my financial plan. I project x.x% return in my plan, and if my MWR drops below that for significant time I may need to reassess my projections.

I try not to overthink it. Usually they are close.


Here are a couple of articles that also explain rate of return calculations. They are by Canadian authors, but I believe they will also work with US$.

https://canadiancouchpotato.com/2015...ate-of-return/

https://www.pwlcapital.com/resources...turn/?ext=.pdf
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Old 02-07-2019, 07:29 AM   #10
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This was educational, thanks for sharing.
Agreed - it has been educational for me too. I think you are correct about assessing historical vs the future.

Still, in that second link I would not be happy if my personal return was reported as 146% when I was actually down 30%.Yes for comparing to other investments, but no for "personal." And it would be very good for me to know that I'm actually down.
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Old 02-07-2019, 02:29 PM   #11
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The change in portfolio value in the example with TWR = 146.5% and MWR = -30% is extreme.

The portfolio holdings went up 450% by June 1, then dropped 45% by the end of the year. And the investor had the misfortune of depositing 9 times the starting portfolio value at the market peak. Unlikely to happen, except perhaps in cryptocurrencies.

It is a good way to demonstrate how contributions and withdrawals that can have a large effect on MWR, and how that effect is filtered out in TWR to make it comparable to benchmarks, but unlikely to happen in any diversified portfolio.

And why didn't such a shrewd investor have the sense to market time his or her way out of the investments in June??
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Old 02-08-2019, 03:03 AM   #12
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That example is extreme just to demonstrate the point - which I think it does very well as you say. But as we all know, even 1,2,or3% difference in return can have a huge impact over an investing lifetime.

Ahh but - this did happen in many portfolios. Not on such a drastic scale. From roughly 2000 to 2010 the market was fairly flat (as measured by the S&P 500 gaining 0%) and then in turned in to the bull market. It's the same idea.
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