Time-weighted return vs money-weighted return: which one is your return?
If you have ever added money to a portfolio or taken some out, it has two honest returns, and they can point in opposite directions. One tells you how the investments did. The other tells you how your money did. This guide shows how to calculate both, with the arithmetic written out.
The short answer
How did the investments do? It removes the effect of when you added or withdrew money, so a deposit is never counted as growth. Use it to compare with an index or a fund, because it measures what the investments didregardless of when money moved. Glossary entry
How did my money do? It counts how much you had invested at each moment, so it includes the effect of your own timing. It is also called the internal rate of return (IRR) or the dollar-weighted return. Glossary entry
How to calculate portfolio return with deposits and withdrawals
The simple formula, end value minus start value divided by start value, breaks the moment money moves in or out. A $10,000 deposit is not a $10,000 gain, but that formula counts it as one. There are two ways to fix it.
Time-weighted return
- Split the period at every deposit and withdrawal.
- For each piece, divide the value just before the next deposit or withdrawal by the value just after the previous one, and subtract 1.
- Chain the pieces together by multiplying.
TWR = (1 + r₁) × (1 + r₂) × … × (1 + rₙ) − 1It needs the portfolio’s value at the start, at the end, and just before each deposit or withdrawal, plus the amount of each.
Money-weighted return
It is the single yearly rate at which your starting value and each deposit, each grown from the day it went in, minus your withdrawals, each grown from the day it came out, come to exactly your final value. There is usually no formula that gives it directly: it is solved by trial and error, which is why a spreadsheet does it for you. In Excel or Google Sheets, list each deposit as a negative amount with its date, each withdrawal as a positive amount with its date, and your current value as a positive amount with today’s date, then use XIRR. It gives a yearly rate. If you are measuring from a date after you started, enter the portfolio’s value on that date as the first row, as a negative amount, and list only the deposits and withdrawals after it.
For a quick estimate by hand, the Modified Dietz method comes close. It gives the return over the whole period, not per year:
return ≈ gain ÷ (start value + the sum of each deposit × the share of the period it was invested)Gain here means end value minus start value minus net deposits. A withdrawal counts as a negative deposit.
A worked example
| When | What happened | Portfolio value |
|---|---|---|
| Start of year 1 | You invest $100,000 | $100,000 |
| During year 1 | The portfolio rises 10% | $110,000 |
| Start of year 2 | You add $200,000 | $310,000 |
| During year 2 | The portfolio falls 5% | $294,500 |
Time-weighted: 1.10 × 0.95 − 1 = +4.5% over the two years, about +2.2% a year. The investments went up.
Money-weighted: you put in $300,000 and ended with $294,500, a loss of $5,500. Solving for the yearly rate gives about −1.4% a year. Modified Dietz gets close by hand: −$5,500 ÷ ($100,000 + ½ × $200,000) = −2.75% over the two years, which is about −1.4% a year.
Both numbers are correct. Most of the money arrived just before the fall, so the investments gained while you lost. They answer different questions.
In a spreadsheet the example is three rows, with made-up dates: 1 Jan 2021, −100,000; 1 Jan 2022, −200,000; 1 Jan 2023, 294,500. With the dates in column A and the amounts in column B, =XIRR(B1:B3, A1:A3) gives about −1.4%.
A withdrawal works the other way. Suppose that instead of adding $200,000 at the start of year 2, you took $50,000 out. The time-weighted return is unchanged at +4.5%, because it takes the money moving in or out out of the calculation. The portfolio ends at $57,000: $110,000, less the $50,000 you took out, then down 5%. The money-weighted return rises to about +4.5% a year, above the time-weighted +2.2% a year, because less of your money sat through the fall.
Which one should you look at?
Compare the time-weighted return with a benchmark. That tells you whether the investments you chose did better or worse than the benchmark over the same period, without your deposits getting in the way.
Look at the money-weighted return to see what your money earned. The gap between the two is the effect of when, and how much, you added or took out, in either direction. Measured across everyone invested in the same fund, thatgap has a name: the behaviour gap.
A return over more than a year is easier to compare as a yearly rate. See CAGR for how a total return becomes a yearly one.
Where Olnest fits
The percentage on the Olnest Overview chart is time-weighted in one specific way: when a new holding enters your portfolio, its value counts as money you added, not as growth. But the chart is rebuilt from what you hold today. A later top-up of something you already own is treated as if you had held it since your first buy, anything you have sold is left out, and cash is drawn at today’s balance. So it shows how your current holdings performed, not the return on every deposit and withdrawal you made.
The TOTAL RETURN tile on the same screen shows your gain in money on what you hold now, with that gain as a percentage of what it cost beneath it. It is neither of the two returns on this page. The app does not calculate a money-weighted return; for that, use the XIRR method above.
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