Money-Weighted Return Calculator
Calculate an annualized money-weighted return from irregular dated cash flows using the XIRR equation and a 365-day basis. Enter contributions as negative investor cash flows and withdrawals or the ending account value as positive cash flows. The solver withholds the result when no unique supported root is found.
Enter signed investor cash flows
Use a negative amount when money goes into the trading account. Use a positive amount when money comes back to the investor, including one final account value on the measurement date.
Dated-cash-flow money-weighted return
Derived from Cash-Flow-Adjusted Returns model 1.0.0.
How the dated cash-flow return is solved
Money-weighted return reflects both account performance and the size and timing of the investor’s external cash flows. A large contribution before a strong period has more influence than the same contribution after that period. This makes the result personal to the entered cash-flow path.
The page uses the investor perspective. Money contributed to the trading account leaves the investor and is negative. Money withdrawn from the account returns to the investor and is positive. The last row normally includes the ending account value as if it were liquidated on that date.
Each cash flow is discounted by its exact calendar-day offset divided by 365. The solver searches for an annual rate that makes the sum of discounted flows equal zero. Flows entered on the same date are combined before solving, and rows can be entered in any order.
The numerical search uses a governed range above −100% through a very high positive rate. It scans for sign-changing root brackets and then bisects them. If it finds no root, or more than one distinct root, the page withholds a percentage instead of selecting a convenient answer.
Multiple mathematical returns are possible when the cash-flow signs reverse more than once. The displayed sign-change count is a diagnostic, not proof of the exact number of roots. A single displayed result means one root was found inside the governed search range, not that every possible numerical method must agree.
The output is annualized even when the entered period is shorter or longer than a year. Extremely short spans can therefore create very large annualized rates. The result is descriptive of the entered dates and values; it is not a forecast, expected return or suitable target.
Worked example from the audited fixture
The audited fixture enters −10,000 on 1 January 2025, another −1,000 contribution on 1 January 2026, and a +13,200 ending value on 1 January 2027.
At a 10% annual rate, the discounted values are −10,000, −1,000 ÷ 1.10, and +13,200 ÷ 1.10².
Those discounted amounts sum to zero, so the unique supported annualized money-weighted return is +10.0000% over the 730-day entered span.
How to interpret the result
- Confirm the sign convention first. Reversing all investor-flow signs can change or invalidate the interpretation.
- Include a terminal positive value unless the final withdrawal already represents complete liquidation of the account.
- Read the percentage as annualized, not as the simple gain over the first-to-last span.
- Inspect the residual as a numerical audit. It should be near zero relative to the cash-flow magnitudes.
- Treat more than one sign change as a warning that IRR schedules can be ambiguous, even when one supported root is displayed.
- Compare MWR with TWR to separate the investor cash-flow experience from a cash-flow-neutral performance measure.
Choose the return method that matches the available records
These tools share one governed input and presentation layer, but the outputs are not interchangeable. TWR removes external-flow timing, MWR reflects the investor’s cash-flow experience, and Modified Dietz estimates one period when every boundary valuation is unavailable.
| Method | Records required | Output basis | Cash-flow treatment |
|---|---|---|---|
| Time-weighted return | Values around every external flow | Cumulative, not annualized | Removes external-flow timing |
| Money-weighted return | Signed investor flows with dates and terminal value | Annualized XIRR | Reflects flow size and timing |
| Modified Dietz | Period values plus dated account flows | Period estimate, not annualized | Daily-weighted approximation |
Assumptions and limitations
- No account, broker statement, deposit ledger, withdrawal ledger, ending balance, tax record or valuation source is connected.
- The solver uses a 365-day annualization convention and a disclosed finite search range; it is not claimed to reproduce every spreadsheet implementation.
- Schedules with no supported root or more than one detected root are withheld rather than forced to one answer.
- Cash-flow classification, fees, financing, taxes and whether the terminal value is realizable are outside the arithmetic.
- A money-weighted return can be dominated by cash-flow timing and does not isolate trading skill.
- No deposit timing, withdrawal plan, target return, strategy, account, broker or trade is recommended.
Sources and methodology
The arithmetic is independently fixture-tested. These primary references define the formulas and conventions; they do not verify the user’s account values, cash-flow classifications, statement policy, performance quality or future outcome.
- Microsoft Support — XIRR Function — Official XIRR syntax, positive-and-negative cash-flow requirement, 365-day discounting and iterative-solution description.
- Microsoft Learn — XIRR (DAX) — Official statement of the zero-NPV dated-cash-flow equation used by the local solver.
- GIPS Standards Handbook for Firms — Money-Weighted Returns — CFA Institute explanation of MWR, investor cash-flow signs, timing and terminal value treatment.
Frequently asked questions
- It is the annualized rate that makes the net present value of the entered dated investor cash flows equal zero, so timing and size affect the result.
- Use a negative value because money leaves the investor and enters the trading account under this page’s investor-perspective convention.
- Use a positive value because money leaves the account and returns to the investor. Enter the final account value the same way.
- Without a terminal positive value, an open account’s remaining investment is missing from the cash-flow schedule and a meaningful root may not exist.
- It uses the same dated-cash-flow equation and 365-day exponent convention, but this local bracket-and-bisection solver is not claimed to match every Excel convergence choice.
- Some schedules have no root in the supported range, while others can have multiple roots. Selecting one silently would be misleading.
- The rate is annualized. Extending a short-period gain or loss to a 365-day equivalent can magnify the displayed percentage.
- MWR reflects the timing and size of the investor’s cash flows. TWR splits at those flows and geometrically links performance between them.
Separate investor experience from cash-flow-neutral performance
Verify statement, cost and account conventions
Before comparing account performance, confirm how the broker statement timestamps deposits and withdrawals, records balance versus equity, includes spread, commission, financing and rebates, and converts values into the account currency.
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