All investors care deeply about their returns, and with good reason. If you’re an active investor, you’ll want to compare the performance of your portfolio to an index benchmark to see whether you (or your advisor) added value with stock selection or market timing. Even if you’re an indexer, you may want to compare your personal rate of return against that of a model ETF portfolio.
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 straightforward. What’s more, there are several ways to perform the calculations, and the results can differ significantly.
My colleague Justin Bender and I co-wrote a white paper on this subject way back in 2015. In a pair of new videos this month, Justin revisits these ideas and explains how to calculate a time-weighted rate of return (TWRR) and a money-weighted rate of return (MWRR). He uses 2020 as a case study: the sharp downturn and surprisingly swift recovery provided a real-world example of how the timing of contributions and withdrawals could have produced very different results using these two methods.
This week our colleague Shannon Bender makes her YouTube debut with her own video on calculating your rate of return. Shannon takes a deep dive into a third method: Modified Dietz, which includes features of both the TWRR and MWRR and gives DIY investors an opportunity to compare their personal performance against a benchmark.
In the summary below, I’ve left out 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 encounter it.
Time-Weighted Rate of Return (TWRR)
The goal of a time-weighted rate of return is to remove the effect of cash flows (contributions or withdrawals) in 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 they hold it throughout 2020. However, Rick received a windfall in early February and added it to his account. Around the same time, Morty needed to purchase a car, so he sold some ETF units and withdrew the proceeds.
Then along came the market crash in March. Rick felt like a fool for adding new cash right before the downturn, while Morty thought he was a genius for taking money out. Yet when they received their performance report for 2020, Rick and Morty discovered that they earned identical rates of return.
This is because their advisor used a TWRR. Since they held identical portfolios, Rick and Morty’s performance was deemed to be the same, regardless of the decision to add or withdraw cash in February.
- The TWRR is a more accurate way to measure the performance of a portfolio manager or investment fund against 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 timing.
- Your TWRR may not reflect your personal experience. Rick and Morty had identical time-weighted returns in 2020, but you can be sure they weren’t equally satisfied with their results.
- Using the TWRR makes it harder to assess your skill (or lack thereof) at market timing. Whether you add money near the market bottom (good timing) or sell in a panic and withdraw money after a crash (bad timing), your TWRR would be the same as a buy-and-hold investor.
- The TWRR calculation requires you to know the value of your portfolio on every day there was a contribution or withdrawal. If you get monthly statements from your brokerage, that information just isn’t available, making the TWRR impractical for DIY investors.
Who uses TWRR?
ETFs and mutual funds. Investment funds always report time-weighted returns. If a popular fund sees an influx of new money, or if unitholders panic and make huge redemptions, neither of these events will affect the fund’s published return.
Portfolio managers who benchmark their returns. Money managers should only be accountable for decisions they can control. Using TWRRs ensures that clients with the same portfolios will report similar rates of return, regardless of whether they choose to add or withdraw funds during the period.
Our model portfolios. The model ETF portfolios on the Canadian Couch Potato and Canadian Portfolio Manager blogs use TWRRs when reporting historical returns. If you hold the same ETFs and you’re wondering why our published returns don’t jibe with your own experience, it may be because you made significant contributions or withdrawals.
Money-Weighted Rate of Return (MWRR)
While a TWRR removes the effect of cash inflows and outflows, a money-weighted rate of return does the opposite: it’s designed to measure the effect of your contributions and withdrawals. The MWRR is sometimes called the dollar-weighted rate of return, or the internal rate of return (IRR).
To revisit our example, Rick made a significant contribution to his portfolio just before the market crash of March 2020, while Morty made a withdrawal around the same time. Using the MWRR, Morty would report a higher return than Rick, because of the fortunate timing of his withdrawal.
- The MWRR is likely to better reflect your individual situation. The timing of your contributions or withdrawals might make it unfair to compare your performance to a benchmark, but it will still have a significant effect on your account balance, which is what investors usually focus on.
- If you’re a market timer who moves cash in and out of your portfolio, the MWRR will keep you honest. You can compare your money-weighted return to an index benchmark to see whether you outperformed a buy-and-hold strategy. (Note that this implies cash is actually contributed to or withdrawn from the accounts you are measuring. If you sell equities and leave the cash proceeds in your account, then a TWRR is more appropriate for calculating your rate of return.)
- Since many cash flow decisions are made by the client, the MWRR is not an appropriate measure for a portfolio manager whose performance is benchmarked to an index.
- There’s no simple formula for calculating a portfolio’s MWRR: in the olden days, the only way to do it was to use an iterative process, trying different rates until you found the one that worked. This is a moot point now that you can use Excel.
Who uses MWRR?
Your brokerage. When you view the returns of your portfolio on your online brokerage’s dashboard, or on your annual statements, those are all money-weighted rates of return. Back in 2017, the Canadian Securities Administrators mandated that investment firms use the MWRR to report returns, because they felt it more accurately reflected the experience of individuals.
Both time-weighted and money-weighted rates of return have pros and cons, so if you’re keen on analyzing your portfolio’s performance, it would be ideal to use both methods. But as we’ve seen, the TWRR formula is not feasible for most do-it-yourself investors, because 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 of a true TWRR: it’s called Modified Dietz. (What Shannon describes in the video is more properly called the linked Modified Dietz method.)
In this formula, you still need the dates and amounts of any contributions or withdrawals. But you don’t need to know the portfolio’s total value on each of these days. Instead, you only need the month-end values, which are easy to obtain from your brokerage statements. Using monthly values smooths out the effect of modest cash flows, which produces a return more closely resembling a TWRR.
Modified Dietz uses a complex formula, but fear not: all you need to do is gather your statements and download Justin’s easy-to-use Modified Dietz calculator from his Canadian Portfolio Manager site. The 2021 version will work for any non-leap year.
- 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 your portfolio’s performance to a benchmark (such as an index or model portfolio) even if you made contributions or withdrawals during the period.
- If your cash flows are very large relative to the overall portfolio value, the Modified Dietz method can break down. If you open the year with $100,000 and add $1,000 a month it works extremely well. But if you start with $100,000, add $75,000 early in the year, and then withdraw $90,000 in the fall, it’s less useful as an approximate TWRR. In the latter case, the Modified Dietz return is likely to be closer to the MWRR.
- If cash flows are made during a period of unusual volatility, Modified Dietz can overstate or understate your performance relative to a TWRR. In the video, Shannon explains how this could have happened during the downturn and subsequent recovery in 2020.
Who uses Modified Dietz?
Many investment managers. While funds and money managers generally prefer to use true time-weighted returns, this might not be possible. For example, managers might not be able to obtain daily valuations for their portfolio, because some assets (such as real estate or private equity) are not priced every day. In this case, they may use Modified Dietz with monthly or even quarterly valuations.