Time-weighted against money-weighted

The conceptual spine of this subject. Once you have it, performance disputes mostly dissolve.

Two questions, not one

"How well did this investment perform?" A question about the investment. The answer must not depend on when anybody happened to put money in, because the manager did not choose that.

"How well did I do?" A question about you. The answer must depend on when you put money in, because that was your decision and it affected your outcome.

These are different questions and they have different correct answers. Expecting one number to serve both is the mistake.

Time-weighted return

A time-weighted return measures the growth of a unit of money held throughout, with contributions and withdrawals stripped out. Computationally you break the period at every cash flow, compute the return of each sub-period, and chain them:

$1 + R_{tw} = (1+r_1)(1+r_2)\cdots(1+r_n)$

Each sub-period gets equal weight regardless of how much money was present in it — which is the whole point. A manager who did well in a month when you had ₹1,000 invested and badly in a month when you had ₹10,00,000 invested is not penalised, because the amounts were not their decision.

This is what published fund returns are. SEBI requires scheme performance against the benchmark's Total Return Index as CAGR over 1, 3, 5 and 10 years and since inception — computed NAV to NAV, which is inherently time-weighted. The factsheet is answering the first question, correctly.

Money-weighted return

A money-weighted return is the single rate that reconciles all your dated flows with your current value. That is XIRR, from chapter 3.

Here the amounts matter enormously. A period in which you held a lot influences the answer more than one in which you held little, because more of your money was exposed to it.

This is what your return is. It answers the second question, correctly.

Why they differ

They coincide only when there were no flows after the start. Any contribution or withdrawal in between opens a gap, and the gap has a sign:

You beat the time-weighted return if you happened to hold more money during the good stretches — adding before a rise, or simply having accumulated more by the time the good years arrived.

You lag it if you held more during the bad stretches — adding after a run-up, or stopping during a fall.

Neither outcome implies an error. Both figures can be computed perfectly and still disagree, because they are measuring different things.

What the gap actually measures

This is the useful part. The difference between the fund's time-weighted return and your money-weighted return is, mostly, the effect of your own timing.

The Risk subject documents this as the behaviour gap, and Behavioural finance explains the mechanism: Attention and what gets bought shows money arrives after things have risen and been noticed, and Recency and reinforcement learning shows contributions increase after good outcomes. Both push in the same direction, which is why the gap is usually negative for individual investors rather than randomly signed.

So the gap is a measurement of your behaviour, available for free from your own statement. If it is persistently negative, the investments are not the problem.

One honest complication: a long-running SIP produces a negative gap even with perfect behaviour, purely because money accumulates over time and a late-period fall therefore hits a larger balance. Not all of the gap is a mistake, and distinguishing the arithmetic part from the behavioural part requires looking at whether you also changed your contributions.

Which to use when

Purpose	Measure
Judging a fund or manager	Time-weighted — they did not choose your flows
Comparing two funds	Time-weighted — flows would contaminate the comparison
Judging your own outcome	Money-weighted (XIRR)
Checking whether you are on track for a goal	Money-weighted
Judging your own timing decisions	The gap between them

And one rule that prevents most errors: never compare a time-weighted figure with a money-weighted one and conclude that somebody underperformed. That comparison is only meaningful as a measure of the gap, never as a verdict on either party.

Working the problem

Fund reports 12% a year over five years; your XIRR is 7%.

Three explanations with no error by anybody:

1. You invested progressively, and the good years came early. A SIP means little money was present in years one and two and most of it by years four and five. If the fund's 12% was earned disproportionately in the early years, your money largely missed it. The fund's figure is right; so is yours.

2. You added after rises and paused during falls. The classic behaviour pattern — contributions increase after good news and stop when markets fall. This weights your money toward expensive entry points. Nobody made an arithmetic mistake; the timing did the damage.

3. Costs that the published figure legitimately excludes. NAV-based performance is net of expenses but not of exit load or taxes. If you switched schemes, paid an exit load, or realised gains along the way, your after-everything outcome is lower than the NAV-to-NAV figure, which was never claiming to include those.

Which you could detect from your own statement: the third, directly and unambiguously — exit loads and redemptions are line items with dates and amounts, so you can total them.

The first two are harder, and the honest answer is that you can separate them but not fully diagnose them from the statement alone. Your statement gives every contribution date and amount, so you can see whether contributions were level or lumpy. Level contributions through the whole period point to explanation 1 — arithmetic, not behaviour. Lumpy contributions clustered after good stretches point to explanation 2 — behaviour. What the statement cannot tell you is what you were thinking, which is why writing down the reason at the time, as Designing around yourself recommends, converts an unanswerable question into a checkable one.

The practical next step is not to abandon the fund. A 12% time-weighted return means the investment did its job. The 5-point gap is about when your money was present, and the fix for that is in the Behavioural finance subject rather than in a different fund.

The point

Time-weighted return strips out contributions to measure the investment, which is why published fund returns are computed that way and why they are correct for judging a manager. Money-weighted return — XIRR — includes contributions to measure your outcome, which is why it is correct for judging yourself. They coincide only when nothing was added or withdrawn, and the gap between them is mostly the effect of your own timing, reliably negative for individuals because money tends to arrive after good news. Comparing one against the other to conclude someone underperformed is the single most common error in reading performance.