Time-weighted return vs Modified Dietz: which one is right?

The short answer

The time-weighted return measures how your investments did. The Modified Dietz return measures how your money did. They only disagree when you add or take out money, and the bigger those deposits are next to the account, the more they can disagree. Use the time-weighted return to compare yourself with an index or a fund. Use Modified Dietz to see what your own money earned.

How is a time-weighted return worked out?

It cuts the period into pieces at every deposit and withdrawal, takes the return of each piece on its own, and chains the pieces together by multiplying (1 + each return). Because each piece is measured before the new money arrives, the size of a deposit never changes the answer. Each stretch of time counts the same, whether the account held $1,000 or $100,000 during it.

The cost is that it needs the account's value on the day of every deposit. Luck Filter values the account every trading day from your broker's history, so every day is its own piece.

How is a Modified Dietz return worked out?

It divides the money made by the average amount invested over the period:

Modified Dietz = money made ÷ (starting value + each deposit × the share of the period it was in the account)

Money made is the ending value minus the starting value minus what you put in (net of what you took out). A deposit made halfway through a year counts as half of itself in the average; one made on the last day barely counts at all. Withdrawals work the same way, in reverse. So a period counts for more when more of your money was in it.

Why do the two returns differ? A worked example

You start the year with $1,000 and it grows 50%, to $1,500. Halfway through the year you add $9,000. Then everything falls 20%, to $8,400.

• Time-weighted: +50% and then −20% chain to 1.5 × 0.8 = 1.2, a return of +20%. Your picks did well over the year as a whole.
• Money made: $8,400 − $1,000 − $9,000 = −$1,600.
• Modified Dietz: the average invested is $1,000 for the whole year plus $9,000 for half of it, $5,500. −$1,600 ÷ $5,500 = −29%. Most of your money arrived just in time for the fall.

Now swap the order: the $1,000 first falls 20% to $800, you add $9,000, and then everything rises 50%, to $14,700. The time-weighted return is the same +20% (0.8 × 1.5 = 1.2), because the picks did exactly the same things. But you made $4,700 on the same $5,500 average, a Modified Dietz return of +85%. Same investments, same +20%, and two very different outcomes for your money.

Neither number is wrong. They answer different questions.

To see it move, change the deposit and when it went in with the time-weighted vs Modified Dietz calculator. It starts with the first example's numbers.

Which one is more accurate?

Each is the accurate one for its own question:

• Comparing with an index, a fund or another investor: time-weighted. An index has no deposits, so the fair comparison takes the timing of yours out. This is why fund managers report time-weighted returns, and why the global standard for reporting investment performance (GIPS) asks for them in most cases. Luck Filter's skill check uses daily time-weighted returns for the same reason.
• Knowing what your own money earned: Modified Dietz. If your deposits landed before a fall, you really did lose money, whatever the picks did. Modified Dietz is a close, simple estimate of the money-weighted return (the internal rate of return), and it is the number to hold against a savings goal.
• If you rarely add or take out money, it hardly matters. With no deposits or withdrawals, the two come out the same.

Modified Dietz is an estimate: it treats the money in each period as growing at one steady rate. It is least exact when a deposit is large next to the account and markets swing hard inside the period. Looking at shorter periods (a month, a quarter) keeps it close. The time-weighted return is exact as long as the daily values are, so where a value is an estimate (an option that has not traded that day, for example), it carries that estimate.

Do you control the timing of your deposits?

Usually yes, and that is the honest case for looking at both. A fund manager does not choose when clients add money, so time-weighting is fair to them. A retail investor does choose. If you tend to add money after markets have risen, the time-weighted return will flatter you and Modified Dietz will show the cost. That gap between the two is a measure of your timing.

How does Luck Filter calculate them?

• The account's value every trading day is rebuilt from your broker's own history of trades, cash and holdings, read-only.
• Deposits and withdrawals come from the broker's records. Shares moved in from another account count as a deposit at their market value that day. Dividends and interest are not deposits: they are part of the return. Fees are not added back: they lower both returns.
• The time-weighted return chains every day's return. The Modified Dietz return weighs each deposit by the calendar days it was in the account during the period you pick.
• Both are shown side by side on the Performance page with the money made, and the page says which way your timing went. See every figure on the full list of what Luck Filter measures.