Tue. Dec 7th, 2021

All investors care deeply about their returns and with good reason. If you are an active investor, you will want to compare the performance of your portfolio with a benchmark to see if you (or your advisor) have added value to your stock selection or market schedule. Even if you are an indexer, you may want to compare your personal rate of return with that of a model ETF portfolio.

As surprising as it may seem, if you’ve made contributions or withdrawals during the year (as most of us do), determining your rate of return isn’t easy. In addition, there are several ways to perform the calculations and the results can vary significantly.

My partner Justin Bender and I wrote a white paper on this topic in 2015. In a couple of new videos this month, Justin reviews these ideas and explains how to calculate a time-weighted rate of return (TWRR) and rate of money-weighted return (MWRR). Use 2020 as a case study: the severe recession and the surprisingly rapid recovery provided a real example of how the timing of contributions and withdrawals could have produced very different results using these two methods.

This week our partner Shannon Bender debuts on YouTube with her own video on calculating the rate of return. Shannon delves into a third method: Modified Dietz, which includes features from both TWRR and MWRR and offers DIY investors the opportunity to compare their personal performance with a benchmark.

In the following summary, I have set aside the technical details of how each rate of return is calculated. Instead, I’ve provided an overview of each method, considered its strengths and weaknesses, and explained where you’re most likely to find it.

Time Weighted Return Rate (TWRR)

The goal of a time-weighted rate of return is to eliminate the effect of cash flows (contributions or withdrawals) from your portfolio.

To understand why this is important, consider Rick and Morty, who are both clients of the same advisor. They have the same ETF portfolio and hold it throughout 2020. However, Rick received an unforeseen in early February and added it to his account. Around the same time, Morty needed to buy a car, so he sold some ETF units and withdrew the proceeds.

Then came the market crash in March. Rick felt like a fool for adding new cash just before the recession, while Morty believed he was a genius for making money. However, when they received their performance report for 2020, Rick and Morty found that they were getting identical performance rates.

This is because his advisor used a TWRR. Because they had identical wallets, Rick and Morty’s performance was considered to be the same, regardless of the decision to add or withdraw cash in February.

Strong points

  • TWRR is a more accurate way to measure the performance of a portfolio manager or mutual fund compared to a benchmark. Since the decision to add or withdraw money is often made by the investor, the money manager should not be rewarded or penalized for the time.

Weaknesses

  • Your TWRR may not reflect your personal experience. Rick and Morty got weighted returns at identical times in 2020, but you can be sure they weren’t equally happy with their results.
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  • Using TWRR makes it more difficult to assess your skill (or lack thereof) at the time of market. Whether you add money to the bottom of the market (good time) or panic and withdraw money after an accident (bad weather), your TWRR would be the same as a buy and hold investor.
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  • The TWRR calculation requires that you know the value of your portfolio each day that there was a contribution or withdrawal. If you get monthly extracts from your brokerage, this information is simply not available, making the TWRR impractical for DIY investors.

Who uses TWRR?

ETFs and mutual societies background. Mutual funds always have time-weighted returns. If a popular fund sees an influx of new money or if bearers of shares panic and produce large redemptions, none of these events will affect the fund’s published return.

Portfolio managers who compare their returns. Money managers should only be accountable for the decisions they can control. The use of TWRR ensures that clients with the same portfolios report similar rates of return, regardless of whether they choose to add or withdraw funds during the period.

Our portfolio models. ETF portfolio models in the Canadian Couch Potato and Canadian Portfolio Manager blogs use TWRR when reporting historical returns. If you have the same ETFs and are wondering why our publications are not based on your own experience, it may be because you have made significant contributions or withdrawals.

Money-weighted rate of return (MWRR)

While a TWRR eliminates the effect of cash inflows and outflows, a money-weighted rate of return does the opposite: it is designed to measure the effect of your contributions and withdrawals. The MWRR is sometimes referred to as the dollar-weighted rate of return or internal rate of return (IRR).

To see our example again, Rick made a significant contribution to his portfolio just before the March 2020 market crash, while Morty made a withdrawal at the same time. Using the MWRR, Morty would report a higher return than Rick, due to the fortunate moment of his retirement.

Strong points

  • The MWRR is likely to better reflect your individual situation. The timing of your contributions or withdrawals may make it unfair to compare your performance to a benchmark, but it will continue to have a significant effect on your account balance, which is what investors usually focus on.
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  • If you’re a market timer that moves in and out of your portfolio, the MWRR will keep you honest. You can compare your money-weighted performance with an index benchmark to see if you’ve outperformed your buy and hold strategy. (Note that this means that you are actually contributing to or withdrawing from the accounts you are measuring. If you sell shares and leave cash in your account, a TWRR is more appropriate to calculate your rate of return.)

Weaknesses

  • Because the client makes many decisions about cash flows, the MWRR is not an appropriate measure for a portfolio manager whose performance is based on an index.
  • There is no simple formula for calculating the MWRR of a portfolio: in the past, the only way to do this was to do an iterative process, testing different rates until you found what worked. This is a debatable point now that you can use Excel.

Who uses MWRR?

Your brokerage. When you view your portfolio returns on your online brokerage board or in your annual statements, they are all money-weighted rates of return. In 2017, Canadian securities managers demanded that investment firms use the MWRR to report returns, because they felt it more accurately reflected people’s experience.

Modified diet

Both time- and money-weighted rates of return have advantages and disadvantages, so if you are interested in analyzing the performance of your portfolio, it would be ideal to use both methods. But, as we’ve seen, the TWRR formula isn’t feasible for most investors to do, as it requires you to have access to daily account valuations.

Fortunately, there is a practical method that minimizes the effect of cash flows and usually gives a good approximation to a true TWRR: it’s called Modified Dietz. (What Shannon describes in the video is more appropriately said linked Modified Dietz method.)

In this formula, you still need the dates and amounts of the contributions or withdrawals. But it is not necessary to know the total value of the portfolio in each of these days. Instead, you only need the end-of-month values, which are easy to obtain from your brokerage extracts. The use of monthly values ​​softens the effect of modest cash flows, which produce a return more similar to a TWRR.

Modified Dietz uses a complex formula, but don’t worry – all you have to do is gather your statements and download Justin’s easy-to-use Modified Dietz calculator from your Canadian wallet manager site. The 2021 version will run for any leap year.

Strong points

  • If you don’t have the data to calculate a true TWRR, the linked modified Dietz method can get you very close. This will allow you to compare the performance of your portfolio with a benchmark (such as an index or model portfolio), even if you made contributions or withdrawals during the period.

Weaknesses

  • If your cash flows are very large in relation to the overall value of the portfolio, the modified Dietz method can be broken down. If you open the year with $ 100,000 and add $ 1,000 a month, it works great. But if you start with $ 100,000, add $ 75,000 earlier in the year, and then withdraw $ 90,000 in the fall, it’s less useful as an approximate TWRR. In the latter case, the return of modified Dietz is likely to be closer to the MWRR.
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  • If cash flows occur during an unusual period of volatility, Modified Dietz may exaggerate or underestimate your performance relative to a TWRR. In the video, Shannon explains how this could have happened during the recession and subsequent recovery in 2020.

Who uses modified Dietz?

Many investment managers. While fund and money managers generally prefer to use time-weighted real returns, this may not be possible. For example, managers may not be able to obtain daily valuations of their portfolio, as some assets (such as real estate or equity) are not priced daily. In this case, they can use modified Dietz with monthly or even quarterly assessments.

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