Time-weighted vs money-weighted return: which one is yours?

Two returns, two different questions

"What was my return?" sounds like a question with one answer. It has two, because it hides two questions. One is how good the investments were. The other is how much your money grew, given when you happened to add it. If you invested everything on the first day and never touched it again, the two answers are the same number. Most people add money every month, take some out now and then, and move it between accounts, and from the first of those movements the two answers part ways.

A statement or an app that shows a single return without saying which kind it is has answered one of those questions and left you to assume it was the other. The same ambiguity sits under the headline figure when you track your net worth: growth from markets and growth from deposits look identical in a balance until they are pulled apart.

Time-weighted return: how the investments did

Time-weighted return cuts the history into stretches at every deposit and withdrawal. Within each stretch nothing moved in or out, so the change in value is pure investment result. Each stretch's growth is expressed as a factor, 1.05 for a 5% gain, and the factors are multiplied together. The product, less one, is the return over the whole period, and it does not care whether you had $1,000 or $1,000,000 invested during any particular stretch.

That indifference is the point. A fund manager does not decide when shareholders buy in or cash out, so judging the manager on the timing of other people's money would measure the wrong thing. The GIPS standards, the CFA Institute's rules for how investment firms present performance, require time-weighted returns for every portfolio except a narrow set: those where the firm itself controls when money comes in and goes out, and which are also closed-end, have a fixed life or a fixed commitment, or rely on illiquid investments for a significant part of the strategy.

Money-weighted return: how your money did

Money-weighted return is the internal rate of return of your own cash flows. Take every deposit with its date, every withdrawal with its date, and the value of the account today. The money-weighted return is the single annual rate at which every deposit, growing from the day it went in, and every withdrawal, counted from the day it came out, would arrive at exactly today's value.

Because a dollar that was invested for two years counts for more than a dollar invested for two weeks, the stretches when most of your money was in the account dominate the result. That is precisely what you want when the question is about you. You decided when to add money, so a return that includes those decisions is the one that describes your results rather than the fund's.

One fund, three investors, three results

Take one fund that gains 20% in its first year and loses 10% in its second. Chained, that is 1.20 times 0.90, or 1.08: an 8% gain over two years, about 3.9% a year. That is the fund's time-weighted return, and it is the same for everyone who owned it. Here are three people who did, each with their own timing.

1. The first puts $60,000 in on day one and leaves it. It grows to $72,000, then falls to $64,800: a gain of $4,800. With nothing added later, their money-weighted return is the fund's, about 3.9% a year.
2. The second starts with $10,000, which grows to $12,000. Encouraged, they add $50,000 at the start of the second year, making $62,000, and the 10% fall takes it to $55,800. They put in $60,000 and have $55,800: a loss of $4,200, and a money-weighted return of about -6.1% a year.
3. The third starts with $50,000, which grows to $60,000, and takes $40,000 out at the start of the second year. The $20,000 left falls to $18,000. They put in $50,000 and got back $58,000 in all: a gain of $8,000, and a money-weighted return of about 12.1% a year.

Same fund, same 3.9% a year, and results ranging from a loss to three times the fund's rate. The only difference was when the money moved. A time-weighted figure alone would have told all three that they earned 3.9%.

Which one to look at, and when

• Comparing a fund, a manager or a strategy with an index: time-weighted. An index has no deposits, so only a measure with your deposits taken out compares like with like.
• Asking whether your own money did well, timing included: money-weighted. It is the rate your actual dollars earned.
• Asking whether your additions are paying off at all: compare the account's value with the total you put in, net of what you took out. That is a dollar figure rather than a rate, and it is the plainest of the three.

Be wary of any yearly rate built on a short history. A 3% gain in one month, compounded as if it repeated, becomes about 42.6% a year. The arithmetic is right; the assumption that the month will repeat eleven more times is the problem.

Working out your own money-weighted return

Excel and Google Sheets both have a function for it, XIRR, which returns the internal rate of return for cash flows on irregular dates. It needs two columns, an amount and a date, and the signs have to be right.

1. List every deposit into the account as a negative number, on the date it arrived. Money going in is money leaving your pocket.
2. List every withdrawal as a positive number, on the date it left.
3. Add one final row: today's date and the account's current value, as a positive number, as if you sold everything today.
4. Use =XIRR(amounts, dates) on those two columns. The result is a yearly rate, and both programs need at least one negative and one positive amount to produce one.

Only money crossing the account's boundary counts. A dividend that is reinvested never left, so it is not a row; a dividend paid out to your bank account did leave, so it is a withdrawal. Fees taken from the account are not rows either: they are already in the lower value at the end. Transfers between your own accounts are the trap. Moving money from one brokerage to another is a withdrawal for one account and a deposit for the other, but for your portfolio as a whole it is nothing at all, which matters as soon as you track investments across more than one brokerage.

Where Net Worth Nexus shows each one

Both, in the places where each answers the question being asked. The Time Machine's yearly pace is time-weighted: it reads your recorded history day by day with deposits and withdrawals taken out, and with less than a year of history it shows your growth so far instead of stretching it into a yearly rate. A position's own sheet shows a money-weighted year, worked out from your tax lots or your buys and sales, and only when the entries with a date account for every share you hold. When they do not, the figure is left out rather than estimated. You can see both pages on the features page.