The problem time-weighting solves
Suppose a portfolio starts the year at $100,000, rises to $110,000 by June, receives a $50,000 deposit, and finishes December at $168,000. The account gained $18,000 on $150,000 of money that passed through it. Is that a 12% year? A 15.5% year? Neither figure comes from a single obvious division, and the two answers mean different things.
The investments earned 10% in the first half and 5% in the second. That is the manager's record, and it does not depend on the deposit at all. Chain the two: 1.10 × 1.05 = 1.155, a time-weighted return of 15.5%. Meanwhile, your money did worse than that, because the larger balance was invested during the weaker half — the internal rate of return on the actual cash flows is 14.50% a year. Both numbers are correct. They answer different questions.
Time-weighted return answers: how did the investments perform? It deliberately strips out the size and timing of deposits and withdrawals, because a manager does not control when clients add money. That is why it is the basis of the Global Investment Performance Standards and why every published fund return is a time-weighted figure.
Money-weighted return — the internal rate of return — answers: how did my money do? It weights each sub-period by the capital exposed to it, so it reflects your own timing decisions. For an individual investor deciding whether they are on track, that is often the more relevant number, and it is what the IRR calculator and XIRR calculator compute directly.
How the chaining works, and where the flow goes
The recipe is mechanical. Break the measurement period at every date on which external money entered or left. Value the portfolio on each of those dates. Compute a holding-period return for each sub-period. Multiply the growth factors together and subtract one.
The only genuinely fiddly part is where the cash flow sits. If the portfolio is valued on the flow date — which is what modern custodians do — the flow belongs at the start of the following sub-period, so the return is
HPR = EMV / (BMV + CF) − 1
because the flow was available to be invested for the whole sub-period. If instead the flow arrives at the very end of a sub-period, it earned nothing during it, and the correct treatment is HPR = (EMV − CF) / BMV − 1. This calculator uses the first convention; the difference between the two is small for a small flow near a period boundary and material for a large one.
Where daily valuation is not available — a private fund, a property partnership — the Modified Dietz method approximates the sub-period return by weighting each flow by the fraction of the sub-period it was invested for. It is an approximation to the same quantity, and its error grows with the size of the flow and the volatility inside the sub-period.
The chained result is a geometric mean, not an arithmetic one, and geometric chaining has a property worth internalising: volatility reduces the compounded result relative to the average. Sub-periods of +10% and −10% average zero but chain to 1.10 × 0.90 = 0.99, a cumulative −1%. That is not an artefact of the method; it is what actually happened to the money.
Worked example: a deposit before a weaker half-year
Take the portfolio from above. It starts at $100,000. No money moves in the first half, and it is worth $110,000 at the end of June. On 1 July you deposit $50,000. It finishes December at $168,000.
- First sub-period. No flow, so HPR = 110,000 ÷ 100,000 − 1 = +10.00%. Growth factor 1.10.
- Second sub-period. The deposit is available for the whole half, so the base is 110,000 + 50,000 = $160,000. HPR = 168,000 ÷ 160,000 − 1 = +5.00%. Growth factor 1.05.
- Chain them. 1.10 × 1.05 = 1.155, so the time-weighted return is 15.50% for the year.
- Annualise. The two sub-periods cover one full year, so (1.155)1/1 − 1 = 15.50% — unchanged, because the period is already a year.
- Compare with the money-weighted return. Solve 100,000x² + 50,000x = 168,000 for x = 1 + r per half-year. That gives x = 1.0700379, a half-yearly IRR of 7.0038%, and annualised (1.0700379)² − 1 = 14.4981%.
The gap of 15.50 − 14.50 = 1.00 percentage point is the cost of your timing: $160,000 was exposed to the 5% half and only $100,000 to the 10% half, so the weighted experience of your money is pulled toward the weaker number. Reverse the deposit — put the $50,000 in at the start and let the good half act on the larger balance — and the money-weighted return would exceed the time-weighted one instead. The manager's 15.50% would be identical in both cases, which is exactly the point of time-weighting.
Check the dollar arithmetic too: ending value $168,000 less the $100,000 start less the $50,000 deposit leaves an $18,000 gain. That gain is 18,000 ÷ 150,000 = 12.0% of the money that passed through the account, a third figure that is neither of the two returns and should not be quoted as either.
Which number to use, and when
Use time-weighted return when you are judging an investment or a manager. It is the only fair basis for comparing two funds, or a portfolio against a benchmark, because it removes a variable the manager does not control. Every published mutual fund return, every index return, and every GIPS-compliant composite is time-weighted, so a time-weighted figure is the only one that can be compared with them.
Use money-weighted return when you are judging your own outcome. If you want to know whether your retirement account is on track, what matters is the return on the dollars you actually had invested, including the consequences of when you chose to add or withdraw. A financial plan that assumes 7% needs the money-weighted figure to test against, not the fund's headline return.
The gap between the two is itself informative. When the money-weighted return sits below the time-weighted one, more capital was exposed to the weaker sub-periods — the classic pattern of adding after a rally and pausing after a fall. When it sits above, the timing helped. Over long periods and many flows, the gap tends to be small for disciplined, regular contributors, which is one of the quieter arguments for automatic contributions.
Two practical cautions. First, time-weighted return is only as precise as your valuation points: chaining four quarterly sub-periods approximates what daily valuation would give, and the approximation degrades as flows get larger relative to the portfolio. Second, an annualised figure from a period shorter than a year extrapolates — a 5% quarter annualises to 21.55%, which describes a rate rather than a result, and quoting it as though the year had happened is misleading.
The same portfolio under three different measures
| Measure | Calculation | Result | Answers |
|---|---|---|---|
| Time-weighted return | 1.10 × 1.05 − 1 | 15.500% | How the investments performed |
| Money-weighted return (IRR) | 1.0700379² − 1 | 14.498% | What your money earned |
| Simple gain on cash in | 18,000 ÷ 150,000 | 12.000% | Nothing useful — avoid quoting it |
The third row divides the gain by all money that passed through the account, giving no weight to how long each dollar was invested. It is the figure people compute by instinct and the one that misleads most often.
Mistakes that produce a wrong time-weighted return
- Not breaking the period at a cash flow. A deposit inside an unbroken sub-period contaminates that sub-period's return with money the investments did not earn. This is the whole error the method exists to prevent.
- Putting the flow on the wrong side of the valuation. Adding a start-of-period flow to the denominator is correct; treating it as end-of-period and subtracting it from the numerator gives a different, and in that case wrong, answer.
- Counting internal transfers as external flows. Moving cash between holdings inside the same portfolio is not an external flow. Only money crossing the portfolio boundary breaks the period.
- Forgetting that dividends and interest are internal. Income earned by the holdings is part of the return, not a contribution, unless it is physically withdrawn.
- Averaging sub-period returns arithmetically. Chaining is multiplicative. The arithmetic mean of +10% and −10% is zero; the actual result is −1%.
- Annualising a short period without saying so. A 5% quarter annualises to 21.55%, which is a rate, not an outcome. Quoting it as a year's return overstates what happened.
- Comparing a time-weighted portfolio return with a money-weighted benchmark. Both sides of a comparison must use the same method, or the difference measures methodology rather than performance.
Why GIPS requires time-weighting
The Global Investment Performance Standards, maintained by CFA Institute, require firms to present time-weighted rates of return for composites precisely because managers do not control client cash flows. If money-weighted returns were reported, a manager whose clients happened to fund before a rally would look better than an identical manager whose clients did not. The standards do permit money-weighted returns in specific circumstances — notably where the manager controls the timing of flows, as in private equity, where the IRR is the industry convention. The choice of measure follows the question of who controls the cash.
Related measures and what to reach for next
Once you have an annualised time-weighted return, the natural next question is what it cost in risk. The Sharpe ratio calculator divides the excess return by volatility, and the standard deviation calculator produces the denominator from a return series.
For a single investment with no interim flows, time-weighted return collapses to the compound annual growth rate, which the CAGR calculator computes from just a start value, an end value and a number of years. For irregular flows on specific calendar dates, the XIRR calculator gives the money-weighted return with day-count precision rather than the equal-sub-period approximation used here. And where reinvestment at the IRR is implausible, the modified IRR calculator lets you specify a separate reinvestment rate.
One last framing. Neither return measure is a judgement about a portfolio until it is compared with something — a benchmark of the same asset mix over exactly the same dates. A 15.5% time-weighted year is excellent against a benchmark that returned 9% and disappointing against one that returned 22%. Compute the benchmark the same way, over the same window, before drawing any conclusion at all.