Time-Weighted vs Money-Weighted Return, Explained

Two statements about the same portfolio can both be true and disagree by double digits. A fund factsheet says the strategy returned 12.3% a year; your account page says you made minus 0.1%. Neither is lying. They are answering different questions, and knowing which question each number answers is the difference between diagnosing a bad decision and blaming a good one.

The two measures are the time-weighted return and the money-weighted return. This explainer builds a complete two-year example with every deposit and every intermediate value written down, calculates both numbers by hand, and shows exactly which cash flow makes them diverge.

Two Questions That Sound Identical

• Time-weighted return (TWR) asks: how did the investments perform per dollar invested, ignoring when you added or removed money? It measures the strategy, not your timing. Fund managers are judged on it because they do not control when investors arrive.
• Money-weighted return (MWR), also called the internal rate of return or IRR, asks: what constant annual rate would turn your actual deposits into your actual ending balance? It measures your experience, including the effect of putting money in at bad moments.

The difference is not academic. TWR strips out cash-flow timing; MWR keeps it. If you deposit a large sum right before a decline, your MWR falls even though the fund's TWR is unchanged - and the fund did nothing wrong.

The Example: Two Years, Two Deposits

Assume a single fund and an investor who starts with $10,000 on 1 January 2024. Four half-year periods, with the fund's return in each:

The only external flow: on 30 June 2024, at the end of the first half-year, the investor deposits $90,000. That is why the H2 2024 starting value is $103,000 - the $13,000 balance plus the new money. Everything else is the fund's own movement.

Time-Weighted Return, Step by Step

TWR multiplies the sub-period returns, so cash flows never enter the calculation at all. Each sub-period return is measured on the money that was actually invested during that sub-period:

• H1 2024: 13,000 ÷ 10,000 − 1 = +30.00%
• H2 2024: 90,640 ÷ 103,000 − 1 = −12.00%
• H1 2025: 96,078.40 ÷ 90,640 − 1 = +6.00%
• H2 2025: 99,921.54 ÷ 96,078.40 − 1 = +4.00%

Chain them: 1.30 × 0.88 = 1.144 for 2024, which is +14.40%. Then 1.06 × 1.04 = 1.1024 for 2025, which is +10.24%. Over two years: 1.144 × 1.1024 = 1.261146, or +26.11%. Annualised, that is 1.261146^1/2 − 1 = +12.30% a year.

Notice what the formula did not need: the size of the deposit, the date of the deposit, or the account balance between periods. Only the boundaries between periods mattered.

Money-Weighted Return, Step by Step

MWR solves for the rate r that makes the present value of all cash flows zero. Written out with the four dates, using half-year periods as t = 0, 0.5, 1.5 and 2.0:

−10,000 − 90,000 ÷ (1 + r)^0.5 + 99,921.54 ÷ (1 + r)² = 0

There is no rearrangement that isolates r, so it is found by trial: guess a rate, compute the expression, and move the guess until the result is zero. A spreadsheet does this with IRR or XIRR; doing it by hand takes four or five attempts:

• Try r = 0%: −10,000 − 90,000 + 99,921.54 = −78.46. Negative, so the true rate is slightly below zero.
• Try r = −1%: −10,000 − 90,452 + 101,940 ≈ +1,488. Positive, so the answer lies between −1% and 0%.
• Try r = −0.1%: −10,000 − 90,045 + 100,121 ≈ +76. Still slightly positive.

The root is r ≈ −0.10% a year. That is the honest description of the investor's experience: $100,000 went in, $99,921.54 came out, and the annualised rate is barely negative.

Same Portfolio, Two Stories

Put the numbers side by side and the disagreement is not a rounding difference:

The cause is one date. The $90,000 arrived at the top of the first year, immediately before a 12% decline, and it then sat through two modest up periods. Nine tenths of the money earned the weaker sequence. The fund compounded at 12.3% a year; the investor's dollars did not, because they were not present for the 30% half-year.

Reverse the flow and the result flips. Had the investor withdrawn $90,000 at the same moment instead of depositing it, the money that stayed would have ridden the −12% with a small balance, and the MWR would have come out above the TWR. Same fund, same dates, opposite conclusion - which is the proof that these numbers measure different things rather than one being more accurate.

Which Number to Trust, and Where to Find It

• Fund factsheets, ETF pages and manager letters quote TWR, because a manager cannot control investor flows. When comparing two funds, this is the number to use.
• Brokerage "personal rate of return" and retirement-plan statements usually quote MWR. It is the right number for judging your own decisions about when to add money.
• Performance standards such as GIPS require TWR for reporting, precisely because MWR can be improved by cash-flow timing that has nothing to do with skill.
• Your own spreadsheet should use XIRR (which handles irregular dates) for MWR, and a chained product of sub-period returns for TWR. Both are one formula each.

A practical rule: use TWR to choose what to own, and MWR to check whether your behaviour is costing you. The gap between them is a direct measure of timing cost - the same phenomenon described qualitatively in the behaviour gap explainer.

Where the Sub-Period Boundaries Come From

The example uses half-years because they are easy to follow, but the choice of boundary is a real decision, not a presentation detail. TWR is only exact when a valuation exists at every cash flow; the more often you value the portfolio, the closer the chained product gets to the true figure.

• Daily valuation. This is the standard for funds, and the reason published returns are reproducible to two decimals. Every flow creates a boundary automatically because the manager knows the net asset value that day.
• Monthly valuation. Good enough for a personal account. The error from mis-timing a mid-month flow is small if the flow is small relative to the balance, and shrinks further when the flow is near a month boundary.
• Annual valuation only. Once a year is too coarse once contributions exceed roughly 10% of the balance. A $90,000 deposit into a $13,000 account, valued only at year end, cannot be attributed correctly to either period.

When valuations are missing, the common workaround is the Modified Dietz method, which approximates the sub-period return by weighting each flow for the fraction of the period it was invested. For a flow arriving exactly at the boundary - as in the example above - Modified Dietz and the exact calculation agree. For a flow arriving mid-period, it drifts, and the drift grows with both the size of the flow and the volatility of the period.

For a personal portfolio, the practical recipe is: record the balance on the first of each month, note every deposit and withdrawal with its date, and let a spreadsheet compute the chained monthly returns. Ten minutes a month produces a TWR that will match a fund factsheet within a few basis points, and an XIRR that matches the broker's personal rate of return.

One warning about comparing your own TWR to a fund's: your sub-period returns include cash drag, trading costs and any advisory fee deducted from the account, while the fund's published figure is calculated before those. A one-point gap between the two is normal and is not evidence of a mistake.

The Three Mistakes That Produce Wrong Numbers

• Treating deposits as returns. Adding $90,000 to a $13,000 account is a 590% increase in balance, not a 590% return. Every sub-period return must be measured against the balance at the start of that sub-period, before the flow.
• Timing the flow on the wrong side of the boundary. A deposit on 30 June can belong to the end of H1 or the start of H2. Both give the same TWR if applied consistently, but mixing conventions produces small, persistent errors that compound.
• Annualising a period shorter than a year. A 3% gain in one month annualises to 42.6% by the same formula. It is arithmetically correct and practically meaningless; report short periods as cumulative, and annualise only beyond twelve months.

If your statements disagree with your own tracking, the first thing to check is whether a dividend or a fee was booked as a flow. Reinvested dividends are a return, not a deposit; advisory fees paid from the account are a flow out that reduces MWR without changing TWR. The arithmetic of fees themselves is covered in the expense ratio walkthrough, and the tax side of selling is in the capital gains arithmetic.

What to Do With the Gap

Compute both numbers once a year. If the gap is small - under a percentage point - your deposits are roughly neutral and there is nothing to fix. If MWR lags TWR by several points a year, the cause is almost always clustered buying after strong runs and selling after weak ones. The corrective is mechanical rather than clever: fixed automatic contributions on set dates, which turns a timing decision into a schedule. The comparison between scheduled and one-off investing is worked through in the dollar-cost averaging analysis.

This article is educational and uses hypothetical figures with all assumptions stated. It is not investment advice, a recommendation of any security or fund, or a projection of future returns. Your own returns will differ. Consider consulting a licensed adviser about your circumstances.