Benchmarking

Time-weighted vs money-weighted return: what each number tells you

Two investors buy the same fund over the same period and pay the same fees. One reports a return of +12%, the other +4%. Both numbers are correct. They answer different questions.

Every portfolio has two return numbers. The time-weighted return measures how the investments did. The money-weighted return measures how your money did, including the timing of your deposits and withdrawals.

This article explains what each number measures, how it is calculated, and why the two can point in opposite directions for the same account.

The two questions

How good were my investments? That is the time-weighted return (TWR). It removes the effect of when you added or withdrew money and chains together the returns of what you held. Fund factsheets report TWR, and it is the number you can compare with an index.

How good was my outcome? That is the money-weighted return (MWR, also called the internal rate of return or IRR). It includes timing. A large deposit shortly before a rally raises your MWR above your TWR. A deposit shortly before a fall lowers it.

The distinction exists because a private investor makes two kinds of decisions: what to hold, and when the money goes in and out. TWR grades the first decision. MWR grades both together. Neither number is more correct than the other. They measure different things.

How the time-weighted return is calculated

Cut your history into sub-periods at every deposit and every withdrawal. Within each sub-period no money moved, so the percentage change in value is investment performance only. Calculate that percentage for each sub-period, multiply the factors (1 + return) together, and subtract 1.

Each sub-period's return is calculated on whatever was in the account at the time, so the size of the account does not matter. A 5% gain counts as 5% whether it happened on €1,000 or on €100,000.

This is how TWR removes your deposit timing from the result. What remains is a number you can lay next to an index, which has no deposits either.

How the money-weighted return is calculated

The money-weighted return treats your portfolio as a series of cash flows. Money went in on certain dates, money came out on certain dates, and a balance is left today.

MWR is the single annual rate that, applied to every cash flow for the time it was invested, reproduces today's balance. Accountants know it as the internal rate of return, and spreadsheets calculate it with the XIRR function.

Each euro is weighted by how long it was invested, so large late deposits dominate the number. If most of your money arrived last year, your MWR mostly reflects last year, whatever happened in the years before. That is what the number is for. Your result in euros depends most on what your largest amounts did.

A worked example

One fund, two years, round numbers. You start with €10,000. In year one the fund gains 20%, so you have €12,000. You then deposit another €12,000, which brings the account to €24,000. In year two the fund loses 10%, leaving €21,600.

The time-weighted return chains the two years: 1.20 × 0.90 = 1.08, or +8% over the period. The fund did well, and so did your choice of fund.

The money-weighted return looks different. You put in €22,000 in total and finished with €21,600, a loss of €400. Your MWR is slightly negative. Same account, same fund: +8% by one measure, a loss by the other. The €12,000 you added at the top was invested only during the losing year, and MWR counts that.

Now reverse the order. The fund loses 10% first (€10,000 becomes €9,000), you deposit €12,000 anyway (€21,000), and year two gains 20%, ending at €25,200.

TWR is the same: 0.90 × 1.20 = 1.08, still +8%. But €22,000 in became €25,200 out, a profit of €3,200. The only difference between losing €400 and making €3,200 was the timing of one deposit.

What the gap between the two numbers means

The difference between your TWR and your MWR is, roughly, the cost or the profit of your timing. Research on fund flows keeps finding the same pattern. The average investor's money-weighted return trails the funds they hold by 1 to 1.5% per year, because people add money after rallies and stop during dips. The funds did fine. The timing did not.

If your MWR is consistently below your TWR, your selection may be fine while your timing is expensive. A fixed monthly purchase takes the timing decision out of the process, which is one reason the gap is smaller for investors who automate. The arithmetic of steady contributions is in investing €500 a month.

If instead your TWR trails a fair benchmark while your MWR looks respectable, your timing has been compensating for your selection. You cannot tell which of the two you have from a single blended percentage.

What your broker shows you

Usually neither number, cleanly. Most broker apps show a simple percentage, current value against something, and it is often unclear against what. DeGiro's "Totale w/v" is a cash-flow-based figure. Robinhood's chart is close to a TWR but has no benchmark next to it. Almost no broker shows both numbers side by side.

The consequence is that two people comparing returns are rarely comparing the same quantity. One quotes an app's cash-flow figure, the other a chart percentage, and both round generously.

The raw material for the correct numbers does exist. It sits in the transaction export every broker provides, the file described in guides like the DeGiro export guide: every deposit, every trade and every dividend, with a date. A tracker can read that file without your password, as explained in why we'll never ask for your broker login.

Which number to look at

Both, for different questions. TWR answers whether your selection did its job. It is the number an index comparison can fairly be laid against, which is why the method in how to check if you beat the S&P 500 is built on it.

MWR answers what your money did. It is the number your account balance reflects, and the one your timing shows up in.

Reporting whichever number is higher is a common habit. A portfolio with a good TWR and a lagging MWR year after year shows a pattern in when the money went in, and that pattern is only visible when both numbers are on the screen.

In short

The time-weighted return (TWR) measures your investments and ignores the timing of your deposits. It is the number to compare with an index.
The money-weighted return (MWR or IRR) measures your outcome and includes the timing of your deposits. It is the number your balance reflects.
The gap between the two is the cost or the profit of your timing.
Both are calculated from your transaction history: every deposit, trade and dividend, with a date.

BullBenchmark reads the transaction export from your broker and shows your return next to the S&P 500 and the Nasdaq 100, fed with the same deposits on the same dates, in your own currency. The first two weeks are free and no card is needed.