Money-Weighted Return Calculator
Compute IRR or XIRR from irregular cash flows with dates: measure your personal rate of return accounting for deposit timing.
How It Works
Money-Weighted Return (MWR) measures your portfolio's performance while accounting for exactly when and how much money you deposited or withdrew. This is the same calculation your brokerage shows as your personal rate of return. If you deposited a large sum right before a market rally, MWR will be higher than time-weighted return because your timing added value.
This calculator uses the Newton-Raphson iterative method to find the internal rate of return (IRR) that makes the net present value of all your cash flows equal to zero. When you provide dates for each cash flow, it computes XIRR (the annualized version using exact day counts). Without dates, it assumes equal periods between flows. The solver converges within 100 iterations to within 0.01% accuracy.
The Formula
NPV(r) = Σ(CF_t / (1 + r)^t) + FV / (1 + r)^T = 0
Newton-Raphson: r_new = r_old - NPV(r) / NPV'(r)
XIRR: NPV(r) = Σ(CF_i / (1 + r)^(d_i/365)) + FV / (1 + r)^(D/365) = 0
Total Gain = Final Value + Withdrawals - Deposits
Total Return = Total Gain / Total Invested
The Newton-Raphson method iteratively solves for the rate that makes NPV equal zero. XIRR uses actual day counts divided by 365 for annualized rates.
FAQ
What is Money-Weighted Return?
Money-Weighted Return (MWR) is the internal rate of return (IRR) that accounts for the timing and magnitude of all cash flows into and out of a portfolio. Unlike time-weighted return, MWR reflects the actual investor experience because large deposits or withdrawals directly affect the result.
What is the difference between IRR and XIRR?
IRR assumes equal time periods between cash flows. XIRR uses the actual dates of each cash flow to compute an annualized return, making it more accurate when contributions and withdrawals happen on irregular dates.
How does the Newton-Raphson solver work?
The solver uses the Newton-Raphson method to find the discount rate that makes the net present value of all cash flows (including the final portfolio value) equal to zero. It iterates up to 100 times until the solution converges within 0.01% tolerance.
Should deposits be negative or positive?
Use negative amounts for deposits (money going into the portfolio) and positive amounts for withdrawals (money taken out). The final portfolio value is treated as a terminal positive cash flow.
Why did the solver fail to converge?
The solver may fail to converge when cash flows are all the same sign, when the return is extremely negative (below -99%), or when the data is inconsistent. Check that deposits are negative, withdrawals are positive, and the final value is reasonable.
Related Tools
More calculators: Time-Weighted Return, Sharpe/Sortino Ratio, Total Return, Compound Interest Comparator.