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Every performance figure has to solve one awkward problem: money moves in and out. If you deposit €10,000 the day before a 5% rally, your portfolio value jumps — but you did not earn that jump, you funded it. Separating the two is the entire subject of return measurement, and it has two standard answers.

The problem, concretely

Take a year with two halves and one deposit in the middle.

You ended with €90,000 having put in €95,000. You lost €5,000. And yet your holdings went up 50% and then down 10% — a combination that is comfortably positive. Both statements are true.

Time-weighted return: how good were the decisions?

Time-weighted return (TWR) chops the period at every cash flow, computes the return of each slice, and chains them together. Deposits and withdrawals are removed by construction, because they only ever happen at the boundary between slices.

In the example: (1 + 0.50) × (1 − 0.10) − 1 = +35%. That is the return of the strategy. If you had held a constant €1 in this portfolio all year, you would have ended with €1.35.

In practice you compute it daily. For each day, take yesterday's closing value, subtract the net cash flow that happened today, and measure the change:

where Ft is today's deposits minus withdrawals. Chain the daily (1 + r) factors and you have a return series that no deposit can contaminate. This is what fund managers are required to report, precisely because they do not control when clients hand them money.

Money-weighted return: how did the money do?

Money-weighted return (MWR) is the internal rate of return of your actual cash flows — the single discount rate that makes everything you paid in equal everything you have now.

In the example it is roughly −9%. Most of your money was only present for the losing half of the year, so the loss dominates. That is not a bug: MWR is the honest answer to "what did my capital earn?" and it is the number that determines whether you are richer.

There is no closed form; it is solved numerically. Bisection is the safest method — present value is strictly decreasing in the rate, so a simple binary search always converges, unlike Newton-Raphson which can shoot off to nonsense on lumpy cash flows.

Which one should you look at?

The gap between the two is the most interesting number nobody computes. TWR far above MWR means you consistently added money before drops. TWR far below MWR means you were lucky, or genuinely good at buying weakness. Either way it is a fact about your behaviour, not about your holdings.

Why BensTrack shows time-weighted

The annual returns, CAGR, volatility and maximum drawdown on your portfolio dashboard are all time-weighted. Three reasons:

• It is comparable to a benchmark. Money-weighted returns cannot be compared to an index, because the index has no cash flows.
• It is what the risk metrics require. A drawdown computed on raw account value would show a "crash" every time you withdrew money for a holiday.
• It answers the question you can act on. You cannot go back and change when you had savings available; you can change what you buy.

Your absolute profit in euros or dollars — which is a money-weighted concept — is shown right next to it, so both perspectives are on the same screen.

Two traps

Tiny denominators. A daily return of (V − Vprev − F) / Vprev explodes when Vprev is near zero — typically on the first days of a new portfolio. Any serious implementation clamps or skips those days; otherwise a single €5 starting balance produces a 4,000% annualised return.

Mis-timed cash flows. TWR assumes the flow happened at the boundary of the period. If you deposit mid-day into a volatile market and only measure daily, you attribute a few hours of market movement to the wrong bucket. Over a year it washes out; over a week it does not.

The short version

Time-weighted measures the investment. Money-weighted measures the investor. Look at the first to judge your strategy, the second to judge your wealth, and the difference between them to judge your timing.