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How time-weighted return works

Time-weighted return is the compound growth of one unit of money, with cash flows stripped out. On a stretch with nothing paid in or taken out it is the CAGR: $10,000 to $18,000 over 6 years is 10.29 percent a year.

Compound annual growth rate

10.29%

$10,000 reaches $18,000 in 6 years at that steady rate.

Growth multiple
1.80x
Total growth over the period
80.0%
Gain in money
$8,000.00

Balance at the end of each year

YearBalanceMultiple
1$11,0291.10x
2$12,1641.22x
3$13,4161.34x
4$14,7971.48x
5$16,3201.63x
6$18,0001.80x
$
$
yr

Count years of growth, not readings. Start of year one to end of year six is 6. A part year goes in as a fraction, so 18 months is 1.5.

On this page

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APR against APY

In short

  • On a stretch with no deposits or withdrawals, time-weighted return is the CAGR. $10,000 to $18,000 over 6 years is 10.29 percent a year.
  • The same two balances over 3 years are 21.64 percent a year. The window is part of the number.
  • Up 60 percent then down 37.5 percent leaves $10,000 where it started: a time-weighted return of 0 percent, against an 11.25 percent average of the two years.
  • Run the same two values backwards and $18,000 to $10,000 over 6 years is minus 9.33 percent a year. A negative time-weighted return is the same root on a ratio below 1.
  • Deposits in the middle are stripped out of a true time-weighted return. A CAGR taken from an account you were funding counts those deposits as growth, which is then a money-weighted mixture.

One unit of money, compounded

Time-weighted return asks what one unit of money did, period after period, with deposits and withdrawals taken out of the chain. Each sub-period is a holding-period return. Those returns compound. The result is the growth of a dollar that was never added to and never taken from.

On a stretch with no cash flows in or out, there is only one sub-period, and the time-weighted return is the CAGR:

TWR=(VtV0)1t−1\text{TWR} = \left(\frac{V_t}{V_0}\right)^{\frac{1}{t}} - 1

$10,000 growing to $18,000 over 6 years: the sixth root of 1.8 is 1.10292357. Subtract 1 and the rate is 10.29 percent a year. Grow $10,000 at that rate for 6 years and you land back on $18,000.

The CAGR calculator on this page is that identity. How the CAGR formula works owns the root. This page owns the reading of that root as a time-weighted return.

The CAGR explorer holds the start still and lets you drag the finish.

The window is part of the number

Hold the two balances still and change only the years. $10,000 to $18,000 over 6 years is 10.29 percent a year. The same two values over 3 years are 21.64 percent a year.

A time-weighted return quoted without its window is not a number anyone can use. Compare equal periods ending on the same date, or you are ranking two clocks.

The average that never happened

A holding gains 60 percent in year one and loses 37.5 percent in year two. Those two returns average 11.25 percent a year. The factors multiply: 1.6×0.625=11.6 \times 0.625 = 1. From $10,000 you still have $10,000. The time-weighted return is 0 percent.

That is volatility drag: the list of yearly percentages averaged to a number the money never earned. Arithmetic against geometric return is the same pair in a table.

A time-weighted return is a geometric chain. It is the only chain that reproduces the ending value of one unit.

Cash flows are the split from money-weighted

A true time-weighted return chains sub-period returns between cash-flow dates, so a deposit does not count as growth. A CAGR taken from an opening and a closing balance of an account you were funding does count it, because the formula only sees two numbers.

Hold the opening $10,000 still. Pay in the rest of the rise the day before the ending reading, and a CAGR still prints 10.29 percent over 6 years. Nothing grew at 10.29 percent. You supplied the rise. Time-weighted return would split the stretch at the deposit and would not credit that cash to the holding.

How money-weighted return works is the IRR of the dated series, which is the rate that wants those dates in. Money-weighted against time-weighted is the pair. The two teaching sheets are different on purpose: the IRR sheet has cash flows, the CAGR sheet does not.

The round trip can be negative

$18,000 falling to $10,000 over 6 years is a growth multiple of 10000/18000=0.555610000/18000 = 0.5556. The sixth root is 0.9067, and subtracting 1 leaves minus 9.33 percent a year. Grow $18,000 at that rate for 6 years and you land on $10,000.

A negative time-weighted return is not a special case. It is the same root, on a ratio below 1. Annualised return is the family name. CAGR is the geometric member. Time-weighted return, on a no-cash-flow stretch, is that member.

What this page is not doing

It is not a money-weighted IRR, not a ranking of funds, and not a chain of sub-period returns with deposits in the middle: this calculator is the no-cash-flow identity. The three sheets are $10,000 to $18,000 over 6 years (10.29 percent), the same money over 3 years (21.64 percent), and up 60 percent then down 37.5 percent (0 percent against an 11.25 percent average). This is educational material, not financial advice.

Worked examples

\$10,000 to \$18,000 over 6 years

An investment was worth $10,000 at the start and $18,000 six years later, with nothing paid in and nothing taken out. What is the time-weighted return?

  1. Divide the ending value by the starting value: 18000/10000=1.818000 / 10000 = 1.8.
  2. Take the 6th root: 1.81/6=1.102923571.8^{1/6} = 1.10292357.
  3. Subtract 1: 1.10292357−1=0.102923571.10292357 - 1 = 0.10292357, which is 10.29 percent a year.
  4. Check it by growing the money back up: 10000×1.102923576=1800010000 \times 1.10292357^{6} = 18000.

The time-weighted return is 10.29 percent a year. With no cash flows in the stretch, that is also the CAGR. $10,000 compounding at that rate for 6 years lands on $18,000.

The same money in half the time

Take the same $10,000 to $18,000, but suppose it happened over 3 years rather than 6. What is the time-weighted return now?

  1. The growth multiple does not change: 18000/10000=1.818000 / 10000 = 1.8.
  2. Only the exponent moves: 1.81/3=1.216441.8^{1/3} = 1.21644.
  3. Subtract 1: 0.216440.21644, or 21.64 percent a year.
  4. Check it: 10000×1.21644310000 \times 1.21644^{3} comes back to 18000.

The time-weighted return is 21.64 percent a year, more than double the 10.29 percent that the same growth gives over 6 years. The window is part of the number.

The average return trap

A holding gains 60 percent in year one and loses 37.5 percent in year two. Those two returns average 11.25 percent a year. Starting from $10,000, what is the time-weighted return?

  1. Up 60 percent is a factor of 1.6. Down 37.5 percent is a factor of 0.625.
  2. The factors multiply: 1.6×0.625=11.6 \times 0.625 = 1.
  3. A total factor of 1 means the ending value equals the starting value: $10,000 in, $10,000 out, 2 years apart.
  4. Put that into the formula: (10000/10000)1/2−1=0(10000/10000)^{1/2} - 1 = 0.

The time-weighted return is 0 percent. The holding ends at $10,000, exactly where it started, while the average of the two yearly returns says 11.25 percent a year.

\$18,000 back to \$10,000 over 6 years

The holding was worth $18,000 at the start and $10,000 six years later, with nothing paid in and nothing taken out. What is the time-weighted return?

  1. Divide: 10000/18000=0.55555610000 / 18000 = 0.555556.
  2. Take the 6th root: 0.5555561/6=0.9066810.555556^{1/6} = 0.906681.
  3. Subtract 1: 0.906681−1=−0.0933190.906681 - 1 = -0.093319, which is minus 9.33 percent a year.
  4. Check: 18000×0.9066816=1000018000 \times 0.906681^{6} = 10000.

The time-weighted return is minus 9.33 percent a year. $18,000 compounding at that rate for 6 years lands on $10,000.

Common questions

When is time-weighted return not a CAGR?

When there are deposits or withdrawals in the stretch. Then you chain the holding-period returns between those dates rather than taking one root on the opening and closing balances. This calculator is the no-cash-flow identity, which is the CAGR.

Why does a fund quote time-weighted return?

Because it answers what one unit of money did, which is the manager's job, and not what a particular client earned after their own additions and withdrawals.

Is 10.29 percent a forecast?

No. It is the one steady yearly rate that turns $10,000 into $18,000 over 6 years on a teaching sheet with no cash flows in between.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.