How are your returns calculated?

A return is the amount of money earned or lost on an investment. If you began the year with $100 in your account and ended the year with $110, that shows a 10% return. Investors use these figures to assess how well their money has been working for them or to compare investment opportunities. 

But it gets a little more complicated when you factor in deposits and withdrawals. For example, if your money earned 0% and the extra $10 was a deposit you made, that’s not actually a return. To account for those issues, there are three different ways to calculate returns. They all have different levels of complexity and accuracy. And they are helpful in different scenarios, which is why we share all three with you to help you track your account progress. You’ll see the easiest metric, simple returns, on your main account view. If you’d like a more nuanced take on your performance, you can find time-weighted and money-weighted returns under your account’s “advanced” settings.

Here’s how the 3 different types of returns are calculated and the differences among them:

Simple rate of return (SRR)

This is an intuitive, transparent way to see how much money your money has made by comparing what you currently have to the net amount you’ve deposited over time. It accounts for how long you've been invested, the timing of your deposits and withdrawals, and what you chose to buy. 

Simple returns are calculated by subtracting your net deposits from your account balance, and dividing that number by your net deposits.

SRR is useful for thinking about whether your investing strategy has been working for you. But it isn’t that helpful when you want to compare the performance of one investment to another, since most investments are quoted with the assumption that all of the money is put in at the beginning of the year, and not many people invest that way. For an apples-to-apples comparison, you need a calculation that attempts to remove the influence of deposits and withdrawals from the return. 

Time-weighted return (TWR)

Although less intuitive than simple returns, time-weighted returns help you understand how much your investment would have made per year, assuming a constant amount of money was invested. It lets you look at the performance of an investment, independent of your deposit and withdrawal behaviour, which makes it useful for comparing one investment to another. Time-weighted returns are calculated by determining the returns of the periods between deposits and withdrawals and multiplying them. 

Here’s what the math looks like:

TWR = [(1+P_1) x (1+P_2) x ... x (1+P_N)] - 1

Where P_1 is the rate of return of the 1st sub period, P_2 is the rate of return for the second sub period, etc.

The rate of return for each sub period is:
[end value - (start value + net deposits for that period)] / (start value + net deposits for that period)

Divide the result by the total number of years, and you have a useful estimate of an investment’s per-year performance.

TWR can also be a useful starting point for thinking about what returns the investment may provide in the future, since it's an average of what it did over prior periods. That can be indicative of the future if you have a long enough sample.

One big drawback of TWR is that, in some situations it can be pretty divorced from your actual investing experience (i.e. whether your particular timing of deposits and withdrawals led to making or losing money). After all, it’s about the average return your money had while invested. If an investment happened to perform best when you had the most money invested, you could have a positive return and a negative TWR.

Money-weighted return (MWR)

Money-weighted returns are the most complicated returns to calculate (it’s pretty much impossible to do by hand), but they provide the purest way to isolate the impact of your (or your investment manager’s) choices by accounting for how long you were invested and the timing of your deposits and withdrawals. This makes MWR an excellent tool for many self-directed investors: it’s a useful calculation if you want to assess your deposit and withdrawal behaviour as part of your specific investment strategy.

MWRs work by weighing each day of your investing period by how much money you had invested that day, and putting the result in per-year terms. 

Say you put $1,000 in a fund that stays even for the first six months, then goes up 10% over the next six months. You’d have made $100 with an annual money-weighted return of 10%. But if you withdrew $500 at the six-month point, you would only be up $50 at the end of the year, and your money-weighted return would drop to 7%. If you’d started the year with a $500 investment then deposited another $500 at the halfway mark, you’d be up $100 for the year again, but your money-weighted return would be 12.75%, since you benefited from the timing of your second deposit. 

MWR tends to be more useful for clients trying to understand what each dollar of their money has made for them, taking into account their deposit/withdrawal behaviour (i.e. if they are trying to time the market).