Money-weighted rate of return is the internal rate of return earned by dated portfolio cash flows, including their timing and size.
The money-weighted rate of return (MWRR) is the discount rate that equates the present value of an investor’s dated cash outflows with the present value of cash inflows and ending value. It reflects both investment performance and the timing and size of external contributions and withdrawals.
MWRR is generally an internal rate of return (IRR) calculation applied to an investment account or portfolio. It answers, “What annualized return did these actual dollars earn on these dates?”
Using an investor-perspective sign convention, contributions are negative cash flows and withdrawals, distributions, and ending value are positive:
where:
For equally spaced annual cash flows, (\tau_i) can be 0, 1, 2, .... For actual dates, software commonly uses day-count fractions. The day-count convention should be consistent and disclosed.
Assume a one-year account history:
| Date | Event | Investor cash flow | Portfolio value around event |
|---|---|---|---|
| Start | Initial investment | -$100 | $100 |
| Midyear | Additional contribution | -$100 | $110 before contribution |
| Year-end | Liquidation value | +$189 | $189 |
The MWRR solves:
The solution is approximately:
Why is the result negative? The initial $100 earned 10% in the first half, increasing to $110. The investor then added another $100, so $210 was exposed to a 10% second-half loss and ended at $189. More money was invested during the losing subperiod.
The two subperiod returns are +10% and -10%. Time-weighted return is:
| Measure | Result | Interpretation |
|---|---|---|
| Time-weighted return | -1.00% | Performance of one unit invested through both subperiods |
| Money-weighted return | approximately -7.29% | Annualized return on the investor’s dated dollars |
Neither result is inherently more correct. They answer different questions.
MWRR is often informative for:
It can be less suitable for comparing public-market managers when clients control external cash flows the manager cannot influence.
The investor perspective commonly uses:
A fund perspective may reverse signs. Reversing every sign produces the same IRR, but mixing perspectives can produce an invalid equation.
The ending value should be included only once. If the portfolio is not liquidated, treat the ending fair value as a hypothetical terminal inflow for the calculation.
MWRR is generally the portfolio application of IRR. The terms can differ in presentation:
These labels require precise methodology. Subscription credit facilities, interim valuations, fee timing, and recycled distributions can materially affect private-fund IRR.
Conventional cash flows usually have one initial outflow followed by inflows. Nonconventional cash flows can change sign several times, such as:
contribution, distribution, later capital call, final distribution
The IRR equation can then have:
Net present value at stated discount rates and multiple-on-invested-capital measures can provide additional context.
MWRR changes when analysts use different:
Illiquid-asset values can be model-based and later revised. A precise IRR does not make uncertain valuations precise.
| Measure | External cash flows | Time value | Primary use |
|---|---|---|---|
| Simple holding-period return | Assumes none within period | No separate date discounting | One uninterrupted investment period |
| Time-weighted return | Neutralizes their effect | Geometrically links subperiods | Strategy or manager comparison |
| Money-weighted return | Includes timing and size | Yes | Investor’s actual cash-flow experience |
| Modified Dietz | Time-weights flows in capital base | Approximation within period | Period return without every cash-flow valuation |
The GIPS Standards Handbook for Firms defines money-weighted return as reflecting the change in value and timing and size of external cash flows, commonly using IRR. SEC staff guidance on gross and net performance stresses consistent return type, methodology, and period when those results are presented together.
This article provides general financial education. It is not personalized investment, private-fund, performance-reporting, tax, accounting, legal, or fiduciary advice.