CFA Level I Exam · Returns of Financial Assets and Instruments

Money-Weighted vs Time-Weighted Return: Differences and Calculation

Updated 7 October 2026 · Fact-checked

Money-weighted return is the internal rate of return on an investment's cash flows, so it reflects the timing and size of deposits and withdrawals. Time-weighted return compounds sub-period returns and ignores cash flow timing. Use time-weighted return to judge a manager and money-weighted return to judge what the investor actually earned.

Understand Money-Weighted vs Time-Weighted Return

A portfolio can have money added or removed during the period. That creates a problem: how do you measure performance fairly? Two methods answer two different questions.

The money-weighted return (MWR) is the internal rate of return (IRR) of the cash flows. It finds the single discount rate that makes the present value of all inflows to the portfolio equal to the present value of all outflows, with the ending value treated as a final outflow. Because bigger balances count for more, MWR is pulled towards the returns earned when the account was largest. The investor decides when to deposit or withdraw, so MWR measures the investor's own experience.

The time-weighted return (TWR) removes the effect of cash flows. You split the period into sub-periods at every date when money goes in or out, compute the holding period return for each, and link them geometrically. Each sub-period counts equally, whatever the balance. The manager usually does not control client deposits and withdrawals, so TWR is the standard way to judge a manager and to compare managers.

The two figures are equal when there are no external cash flows. They differ when cash flows occur. If money is added before a strong period, MWR is higher than TWR. If money is added before a weak period, MWR is lower than TWR.

Dividends and interest paid out of the investment and received by the investor count as cash flows in MWR. In TWR they are part of each sub-period's holding period return.

Key formulas to remember

Money-weighted return (IRR): 0 = CF0 + CF1 ÷ (1 + r) + CF2 ÷ (1 + r)² + … + CFn ÷ (1 + r)ⁿ; Deposits into the portfolio are negative, withdrawals, income received and the ending value are positive. The r that solves it is the MWR for the whole period, per period of the cash flow spacing.
Sub-period holding period return: HPR = (Ending value + Cash flow received) ÷ Beginning value − 1; Use the value just before any new deposit or withdrawal at the end of the sub-period, and the value just after the previous one at the start.
Time-weighted return (total): TWR = [(1 + HPR1) × (1 + HPR2) × … × (1 + HPRn)] − 1; Geometric linking. Do not add or average the HPRs.
Annualized time-weighted return: Annualized TWR = (1 + TWR)^(1 ÷ years) − 1; Use when the total period is longer than one year. For example, two years gives a square root.
Which measure to use: Manager evaluation → TWR; investor's own return → MWR; If the manager controls the timing of cash flows, MWR can also be appropriate.

How to solve Money-Weighted vs Time-Weighted Return questions

Use this order for any MWR or TWR question. First decide which measure is asked for, then list the dates and cash flows.

1Read what is asked: money-weighted (IRR, investor's experience) or time-weighted (manager skill). Note whether the answer is needed per year or for the full period.
2Draw a timeline. Mark every date when money enters or leaves the portfolio, plus the start and end dates.
3For TWR, split the timeline at each cash flow date. Find the value at the start and the end of each sub-period, before the cash flow at its end.
4Compute each sub-period HPR as (ending value + income) ÷ beginning value − 1.
5Link the HPRs by multiplying (1 + HPR) and subtracting 1. Annualize with a root if the period exceeds one year.
6For MWR, set up cash flows from the investor's view: deposits negative, withdrawals, income and the final value positive. Enter them in the calculator and compute IRR.
7Check sense: with no cash flows the two are equal. Money added before a strong period should make MWR higher than TWR, and the reverse before a weak period.
8Match to the options and eliminate any option that is the simple arithmetic average of the HPRs.

Quickest way: Calculator IRR plus linked HPRs

When to use it: Use under time pressure when you have two or three sub-periods and clear dated cash flows.

TWR first: write each (1 + HPR) as a decimal factor, multiply them, and subtract 1. Take the root for annualizing.
MWR on the TI BA II Plus: press CF, then 2nd CLR WORK. Enter CF0 and press ENTER, then the down arrow. Enter C01, ENTER, down arrow, and F01 as the count of times (usually 1). Repeat for each cash flow. Press IRR, then CPT.
MWR on the HP 12C: enter the first outflow, press CHS, then g CFo. For each later flow enter it (use CHS for deposits) and press g CFj. Then press f IRR.
Remember the calculator returns IRR per period. If periods are years, that is the annual MWR.
Use the direction check: the MWR should be closer to the return of the period with the larger balance. This often eliminates two options at once.

Common mistakes in Money-Weighted vs Time-Weighted Return

Averaging the sub-period returns to get the time-weighted return.
Arithmetic mean feels natural, and the average is often offered as a distractor.
Fix: Always link with (1 + HPR) factors. Use the arithmetic mean only when the question asks for it.
Using MWR to rank managers.
IRR is familiar from capital budgeting and looks like a complete performance measure.
Fix: MWR is distorted by client cash flows the manager does not control. Use TWR for manager comparison unless the manager controls flow timing.
Getting the signs wrong in the IRR cash flows.
Students enter deposits as positive because they add to the account.
Fix: View it as the investor: money put in is negative, money received and the ending value are positive. Keep the sign convention consistent.
Using the wrong value at the sub-period boundary.
Mixing values before and after a deposit.
Fix: End each sub-period with the value before the new cash flow. Start the next with the value after it.
Forgetting the interim income in the cash flows.
Dividends are treated as part of price change or are skipped.
Fix: In MWR, put each dividend at its date as a positive flow. In TWR, add it to the numerator of that sub-period's HPR.
Reporting a multi-year TWR without annualizing, or annualizing MWR again.
The question wording on periods is skipped.
Fix: Check the unit. TWR over several years needs a root. IRR from annual cash flows is already annual.

Worked examples

Example 1

An investor buys one share at $100 today. After one year the share pays a $2 dividend and is worth $120, and the investor buys a second share. After the second year each share pays a $2 dividend and is worth $130, and the investor sells both. The time-weighted annual return is closest to: A. 13.9%, B. 15.8%, C. 16.0%

Show the solution

Year 1 HPR: (120 + 2) ÷ 100 − 1 = 22%.
Value at the start of year 2 is two shares at $120 = $240, after the purchase.
Year 2 end value including dividends: 2 × 130 + 2 × 2 = $264.
Year 2 HPR: 264 ÷ 240 − 1 = 10%.
Link: (1.22 × 1.10) = 1.342.
Annualize over two years: √1.342 − 1 = 1.1584 − 1 ≈ 15.8%.
For comparison, the MWR uses flows −100, −118 (that is +2 − 120), +264. Solving gives about 13.9%, which is option A. The simple average of 22% and 10% is 16%, which is option C. Both are traps.

Answer: B. The time-weighted return is about 15.8% a year.

Example 2

A fund starts the year at €100,000 and earns +20% in year 1. At the end of year 1 the client adds €400,000. In year 2 the fund returns −10%. The money-weighted annual return is closest to: A. −5.4%, B. 3.9%, C. 5.0%

Show the solution

End of year 1 value before the deposit: 100,000 × 1.20 = €120,000. After the deposit: €520,000.
End of year 2 value: 520,000 × 0.90 = €468,000.
Investor cash flows: t0 = −100,000; t1 = −400,000; t2 = +468,000.
Set the IRR equation: −100,000 − 400,000 ÷ (1 + r) + 468,000 ÷ (1 + r)² = 0.
Let x = 1 ÷ (1 + r): 468,000x² − 400,000x − 100,000 = 0.
x = [400,000 + √(400,000² + 4 × 468,000 × 100,000)] ÷ (2 × 468,000) = (400,000 + 589,237) ÷ 936,000 ≈ 1.0569.
1 + r = 1 ÷ 1.0569 ≈ 0.9462, so r ≈ −5.4%.
Check: the TWR is √(1.20 × 0.90) − 1 = √1.08 − 1 ≈ 3.9%. The simple average of +20% and −10% is 5.0%. MWR is far lower than TWR because most money was invested in the losing year.

Answer: A. The money-weighted return is about −5.4% a year, even though the manager's time-weighted return is about 3.9%.

Exam tips

If a question asks about the manager's skill or comparing managers, the answer is almost always time-weighted return.
Predict direction before calculating: big deposit before a good period makes MWR above TWR, before a bad period makes it below.
Expect the arithmetic average of sub-period returns as a wrong option. Eliminate it and then check the other two.
With three options, calculating TWR is quick and uses no calculator cash flow keys. Do TWR first if both are in the options.
If you need IRR, clear the calculator worksheet first (2nd CLR WORK on the TI BA II Plus). Old entries are a common cause of wrong answers.

Practice questions from Returns of Financial Assets and Instruments

Money-Weighted vs Time-Weighted Return in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

FRM Part IIReturn Measurement and Manager Skill Evaluation

Money-Weighted vs Time-Weighted Return: frequently asked questions

What is the difference between IRR and time-weighted return?

IRR (money-weighted return) weights each period by the amount invested, so cash flow timing changes the result. Time-weighted return gives every sub-period equal weight and removes the effect of deposits and withdrawals.

When are money-weighted and time-weighted returns equal?

They are equal when there are no external cash flows during the period. They can also be close when flows are small relative to the portfolio.

Which return should I use to evaluate a portfolio manager?

Use time-weighted return, because the manager usually does not control when clients add or withdraw money. Use money-weighted return to show the investor's own experience.

How do I calculate money-weighted return on a financial calculator?

Enter the cash flows in the cash flow worksheet from the investor's view: deposits negative, withdrawals and the ending value positive. Then compute IRR. On the TI BA II Plus use CF, then IRR, then CPT. On the HP 12C use g CFo, g CFj and f IRR.