Perhaps no number is more important to investors than their portfolio’s rate of return. After all, what better way is there to measure your investment performance than to ask:

*“What’s my investment portfolio done for me lately?***”**

Trouble is, it’s usually not so simple to answer this seemingly simple question, and for good reason. There are several ways to calculate your rate of return, and each method has its own strengths, weaknesses, and outcomes.

In this two-part blog series, I’m going to show you two popular ways to calculate your portfolio’s rate of return. In today’s part 1 blog, I’ll cover the **time-weighted rate of return (TWRR)**. In part 2, we’ll take a look at your **money-weighted rate of return (MWRR)**.

By the time we’re through, I’ll have explained how and why each method can produce different results, so you can determine when each one is most appropriate for you.

## Understanding the Time-Weighted Rate of Return (TWRR)

When it comes to calculating rates of return, the time-weighted rate of return is your Holy Grail of portfolio performance benchmarking. Because it completely eliminates the effect of cash flowing in or out of the portfolio, it’s the rate of return that mutual funds and ETFs use when preparing their published performance reports.

You calculate the time-weighted rate of return in three broad steps: First, you divide your reporting period into sub-periods – one for each time you made a contribution or withdrawal. Next, you calculate a mini-total return for each sub-period. You then “geometrically link” each of these mini-returns to arrive at the time-weighted rate of return over the entire period.

Let’s see how the time-weighted rate of return works by applying it to three hypothetical investors.

All three of them kicked off 2020 with **$100,000** invested in the Vanguard Growth ETF Portfolio (VGRO). Then along came that pesky pandemic, and their portfolios decreased to **$77,985** by March 23, 2020.

Now, let’s make some assumptions about each investor’s next steps.

**Investor 1**– We’ll call him**“Michael,**” doesn’t contribute to or withdraw from his portfolio during 2020. He ends the year with a portfolio value of**$110,828**.**Investor 2, “Gob,”**adds $10,000 to his portfolio’s VGRO position at the market bottom on March 23. By the end of 2020, his portfolio is worth**$125,039**.**Investor 3, “Buster,”**panics during the stock market meltdown. On March 23, when his portfolio value has dropped to $77,985, he sells $10,000 out of his VGRO units and withdraws the cash from his portfolio. His portfolio ends the year at**$96,616**.

## Michael’s Time-Weighted Rate of Return

Since **Michael** didn’t contribute to or withdraw funds from his portfolio during 2020, his time-weighted rate of return is easy to calculate. You simply take his ending portfolio value of $110,828, divide it by the beginning portfolio value of $100,000, and subtract 1. This gives **Michael **a 2020 return of **10.83%**.

However, to accurately compare returns among our three investors, we’ll go ahead and calculate the sub-period returns for all three, including **Michael**.

I’ll also throw in a spoiler alert: The math I’m about to walk us through is going to reveal that all three investors earned the same, **10.83%** time-weighted rate of return.

After any “Scooby moment” you might have about that, you’ll realize this makes sense. All three investors held VGRO – and ** only** VGRO – all year.

So, in this super-simplified example, their time-weighted rates of return will be identical to the 2020 return of VGRO, which was **10.83%**.

Now to all that fun math. We’ll start by calculating **Michael’s** return for sub-period 1 – December 31, 2020 to March 23, 2020. During sub-period 1, his portfolio started at $100,000 and ended at $77,985. Dividing the ending value by the beginning value and subtracting 1 provides us with a sub-period return of **-22.01%.**

Next, we’ll calculate **Michael’s** return for sub-period 2, from March 23, 2020 to December 31, 2020. During this second sub-period, the portfolio started at $77,985 and increased to $110,828 by year-end. Dividing the ending value by the beginning value and subtracting 1 gives us a sub-period return of **+42.11%**.

Finally, we’ll geometrically link **Michael’s** sub-period returns to obtain his time-weighted rate of return for 2020. To do this, we add 1 back to each sub-period return, multiply the results together, and then subtract 1. **Michael** ends the year with his time-weighted rate of return of **10.83%**.

Source: Canadian Portfolio Manager YouTube Channel

## Gob’s Time-Weighted Rate of Return

As mentioned earlier, **Gob** also started the year with $100,000 invested in VGRO, and his holdings had also dropped to $77,985 by March 23. But then, **Gob** added $10,000 to his VGRO position, increasing his portfolio value to $87,985. By the end of 2020, his portfolio had grown to $125,039.

Following the same steps, we start by calculating **Gob’s** sub-period 1 return from January 1, 2020 to March 23, 2020. Just as with **Michael’s** identical portfolio, his sub-period 1 return was the same **-22.01%.**

We then calculate **Gob’s** sub-period 2 return from March 23, 2020 to December 31, 2020. For the start date, we’ll use the portfolio value *after* the cash flow occurred. During this second sub-period, the portfolio started at $87,985 – or $77,985 plus his $10,000 contribution. It increased to $125,039 by the end of the year. Dividing the ending value by the beginning value and subtracting 1 gives us a sub-period return of **+42.11%.**

Geometrically linking **Gob’s** two sub-period returns again yields a time-weighted rate of return of **10.83% **for the year.

See what I mean about those identical returns for identical holdings during identical holding periods?

Source: Canadian Portfolio Manager YouTube Channel

## Buster’s Time-Weighted Rate of Return

But to really drive home the point, let’s calculate **Buster’s** time-weighted rate of return. He also started with $100,000 invested in VGRO at the beginning of 2020. And on March 23, 2020, his portfolio was also worth $77,985. On that date, he *w*** ithdrew** $10,000, bringing his portfolio value down to $67,985. By the end of 2020, his portfolio value stood at $96,616.

Using the same calculations as before, **Buster’s** sub-period 1 delivered a return of (you guessed it) **-22.01%. **During sub-period 2, when his portfolio started at $67,985 and increased to $96,616, **Buster’s** time-weighted rate of return was, again, **+42.11%. **Finally, geometrically linking the two sub-period returns provides us with a time-weighted rate of return for the year of **10.83%**.

Source: Canadian Portfolio Manager YouTube Channel

Again, this identical **10.83% **annual return for all three of our intrepid investors is precisely the result we should expect.

The way we calculate the time-weighted rate of return is ** supposed** to wipe out the effect of individual contributions and withdrawals, revealing the annual return that VGRO delivered to all three investors who held the fund throughout 2020.

Source: Vanguard Investments Canada Inc. as of December 31, 2020

If you’re catching my drift, this makes the time-weighted rate of return ideal for benchmarking different portfolio and fund managers. It’s especially good at comparing various active managers’ investment strategies.

Unfortunately, while the time-weighted rate of return is useful for mutual funds and portfolio managers, it’s impractical to deploy for your own, DIY portfolio. First, there’s all that math. Plus, even if you had an easy way to crunch all those numbers, the data is hard to come by to begin with. You’d need to know your total portfolio value on any day you contributed to or withdrew cash from your portfolio. Your discount broker typically doesn’t report these values in your account statements.

Which brings us to another popular way to wrap your head around your returns … your **money-weighted rate of return** (coming up next!).

LesApril 26, 2021 at 7:24 pmWhat is the formula to do the geometric linking when there is more than two sub-periods during the year?

By the way, I enjoy your blogs immensely

JustinApril 26, 2021 at 7:59 pm@Les: Thanks for reading the blog! Here’s a link to our rate of return white paper, which includes the equation for the TWRR on page 15:

https://www.pwlcapital.com/wp-content/uploads/2018/06/2015-07-10_PWL_Bender-Bortolotti_Understanding-your-portfolio-s-rate-of-return_Hyperlinked.pdf

Don J J CarrollApril 1, 2021 at 9:10 pmThursday, April 01, 2021, 6:01 p.m.

I love to figure this out to use on one of my accounts, but I still do not see in case 1 (Michael) where you arrived at 10.83%? You have in Sub-period -1 a -22.10% and in Sub-Period-2 a + 42.11%. If you subtract those two = approx 20%. Can you explain this a bit more please.

Q2. If I had contributed in two periods, ex, February and March. Would I follow your example in Gob’s case and first do the calculation pre first contribution Dec 31/19 to Jan 31/2020, then as you did in the next period add in the contribution (Jan 31 to Feb 29/20) and in my case would I repeat that step,Feb 29 – Mar 31/20 and do not include the 2nd contribution and then the last period Marc 31 – Dec 31/20 including the March contribution?

JustinApril 4, 2021 at 11:58 am@Don J J Carroll – As discussed in the video/blog, you can’t simply add the figures together – they need to be geometrically linked (which requires you to add 1 to each sub-period return, multiply these results together, and then subtract one from the end result).

Your question #2 example sounds correct.

Jim RApril 1, 2021 at 5:08 pmAm I to understand that if Buster had sold and withdrawn $77,984, instead of $10,000, leaving just $1 in the account, he would have still had a return of 10.83%, despite having suffered a major loss over the year?

Also, if he had sold and withdrawn $77,985, leaving $0 in the account, would his return would have been -22.01%, since sub-period 2 would have been inapplicable as 0/0 does not evaluate to anything meaningful (NAN)?

Either my understanding is wrong, or TWRR is totally useless for anyone/anything other than MFs and ETFs even if all the data were available and there was an easy way to crunch the numbers.

If I’m correct, I hope and assume that brokerages don’t use TWRR when they report the ROI of your account at the end of the year.

BettyApril 2, 2021 at 1:27 amHi Jim R,

To your first question, yes, he would still have a TWRR return of 10.83%.

Whether it’s one dollar or one hundred million dollars, his % return in sub-period 2 is the same, provided he remains in the same investment (VGRO).

In your example, the $1 grows to $1.4211, for sub-period 2 return of +42.11%.

Then geometrically combining sub-period 1 and 2 gives the TWRR of 10.83%.

(Identical holdings, over identical periods = identical returns).

I think your question highlighted that the return in % terms is independent of the $ value.

To your second question, yes, he would have a return of -22.01%.

Sub-period 2 doesn’t exist as he terminated the investment and we calculate the return of the period(s) when investment was active.

(Identical holding but not an identical period, so the return is not identical)

To your point of utility, putting aside the math and issues with availability of info., TWRR is useful for benchmarking.

Even us DIYers use institutionally-created products e.g. I am guilty of straight-up comparing the historical returns of different ETFs (even if past performance is not an indication of future return). From now on I’ll check to see if these are TWRR or something else.

To your point of discount brokers, I have no idea how mine reports, let alone the others out there.

I can check or just go with what Justin said that they typically don’t.

(By the way, Justin, fantastic video. So clear. If you ever get tired of PM (but please don’t), you may have a brave future in teaching).

Thanks for reading, hope this helps someone, happy to receive any corrections on mistakes.

JustinApril 4, 2021 at 11:54 am@Betty – Your comments to Jim R’s questions are all correct :)

Glad you liked the video – I don’t see myself switching to a teaching profession, but I do enjoy creating these educational videos/blogs (and will continue to do so :)

SteveApril 2, 2021 at 10:41 pmA Time-Weighted Return has the effect of filtering out any effects from cash inflows or outflows, giving you the aggregate performance of the products you are invested in, regardless of whether you have $10,000 or $100,000 invested.

It’s true that in the extreme examples you have provided, a TWRR would not provide very meaningful information about how your portfolio performed. But I find it to be a very effective way to measure my portfolio’s performance as I am just adding small amounts a few times each year so I’m not drastically skewing the total amounts but I also can’t just use a simple interest calculation as I could if I was adding nothing.

Justin: You mention this method is too difficult to track, I’m wondering if my method is a close enough approximation. I don’t account for days when the

I use a spreadsheet to keep track of each deposit or withdrawal, recording the date, the market value of my account on that date, and the amount of the deposit or withdrawal. Here are my columns:

A: Date

B: Deposit or Withdrawal Amount

C: Market Value of Account after deposit/withdrawal

D: Automatic calculation of number of days since last deposit/withdrawal

E: % change in account value since last deposit/withdrawal

F: A weighted return calculation: Column E * 365

Then, I sum all the values in Column F for a full year and divide the result by 365. This gives me my approximate TWRR. I haven’t figured out an easy way to just get the days where the market is open, but I feel like this is a reasonably close approximation and it makes it super easy to find the TWRR for each of my different accounts.

G:

JustinApril 4, 2021 at 11:51 am@Steve: If your contributions are small relative to the size of your portfolio, a money-weighted rate of return (MWRR) should be very close to the TWRR (I would probably just use this method to save some time) – I’m not sure whether your method would also be a decent approximation.

I’ll be releasing the MWRR video/blog over the next two weeks.

JulienApril 1, 2021 at 2:46 pmI thought this was too hard to figure out, but I was wrong. Thanks for breaking this down Justin!

JustinApril 1, 2021 at 3:35 pm@Julien – You’re very welcome!