Time-weighted vs money-weighted return: what your timing cost you

Ask two questions about the same portfolio and you get two different returns. How did the investments do? And how did my money do? They sound identical. They are not, and the gap between them is the only part of a portfolio's result that is entirely yours to decide: when you paid in.

Two years, one deposit

Take a portfolio that starts with 1,000.

• Year one: the holdings rise 50%. The portfolio is worth 1,500.
• Then you add 10,000 — the year was so good that it seemed like the moment. The portfolio is worth 11,500.
• Year two: the holdings fall 30%. The portfolio is worth 8,050.

How did it do?

The holdings rose 50% and then fell 30%. Chained together, that is 1.50 × 0.70 = 1.05: a gain of 5% over two years, about 2.5% a year. That is the time-weighted return.

Your money went in as 11,000 and is now worth 8,050. You have lost 2,950. Expressed as a yearly rate on the money you actually had invested, and when you had it invested, that is −25.1% a year. That is the money-weighted return.

Same holdings, same two years. One figure says +2.5% a year, the other −25.1%. Neither is wrong: they answer different questions.

Time-weighted: what the holdings did

Time-weighted return cuts the history at every deposit or withdrawal, measures the return of each piece, and chains them together. The size of the deposits never enters the calculation.

• r_k — the return of the holdings during sub-period k, between two cash flows
• n — the number of sub-periods
• TWR — the return over the whole period; the annualised version spreads it over the number of years

This is the figure funds publish, and the right one to compare with an index, because it removes the one thing a fund does not control: when its investors put money in or take it out.

Money-weighted: what your money did

Money-weighted return is the single yearly rate that makes all your deposits and withdrawals, grown at that rate, add up to what the portfolio is worth today. It is the internal rate of return of your cash flows.

• CF_t — each amount you put in (or took out, as a negative) at time t
• V_T — the portfolio's value at the end
• T − t — how many years each amount was invested
• r — the money-weighted return, the rate that makes both sides equal

In the example: 1,000 × (1 + r)² + 10,000 × (1 + r) = 8,050, which gives r = −25.1%. The 10,000 was invested for one year only — the bad one — and it outweighs everything else.

The gap is your timing

The difference between the two, year by year, is the behaviour gap:

In the example it is about −27.6 points a year. The holdings were fine; the timing of the deposit was very costly.

In real portfolios the gap is usually negative and much smaller, and the reason is not stupidity but psychology: people add money after good years, when confidence is high, and hold back after bad ones. More of the money is invested near the tops than near the bottoms. Studies of fund investors have measured this for decades, and the typical result is that investors earn less than the funds they own.

The gap is not always negative, and a positive gap is not proof of skill: over a few years, adding money before a rise is often luck.

The demo portfolio, measured

The demo portfolio — four invented companies, six years of trades — shows what the two figures look like on a realistic history:

Here the gap is close to zero: the deposits were spread out and did not cluster before the falls, so almost all of the result came from what was held rather than when it was bought. That is a perfectly good answer — the point of measuring the gap is to know which case you are in.

Why a broker app shows neither clearly

Most broker apps show a "return" computed as the gain divided by the money put in. That is a third figure, and it mixes both effects: it rises when the holdings do well and when large deposits happen to precede a rally, and it cannot tell you which. It also has no time dimension — a 50% gain over one year and over ten years look the same.

Putting the time-weighted and money-weighted returns side by side separates the two effects cleanly: the first is about your holdings, the second about your money, and the difference is about you.

On your own portfolio

The Performance tab of the dashboard shows the three figures together — the portfolio, your money, and the gap between them, with a sentence that reads the gap for you. See it on the demo, or import your own trades.