Key takeaways
– The money-weighted rate of return (MWRR) measures the actual return you earned on an investment, taking into account the timing and size of your cash flows (contributions, withdrawals, dividends, sale proceeds).
– MWRR is mathematically the same as the internal rate of return (IRR).
– Use MWRR to evaluate an investor’s real experience. Use time-weighted rate of return (TWRR) when you need to measure the manager’s performance independent of client cash flows.
– Spreadsheets (IRR/XIRR) or a financial calculator make computing MWRR straightforward. Non‑conventional cash flows can produce multiple IRRs — be careful.
What MWRR measures and why it matters
– Definition: MWRR is the discount rate (IRR) that sets the net present value of all cash flows (into and out of the investment) equal to zero. It answers: “What single interest rate would turn my initial investment and subsequent cash flows into the final value I observed?”
– Why it’s useful: MWRR reflects the effect of your decisions (timing and amount of deposits/withdrawals). It tells you the return you actually experienced as an investor, not the return of the underlying fund if you had not added or removed money.
– When to use: personal portfolio performance, comparing alternate savings/withdrawal strategies, or measuring the outcome for a specific investor.
The core formula
The MWRR (IRR) r solves the equation:
CF0 + CF1/(1+r) + CF2/(1+r)^2 + … + CFn/(1+r)^n = 0
where:
– CF0 = initial cash flow (typically negative for an investment),
– CF1…CFn = subsequent cash flows (negative for contributions, positive for withdrawals or sale proceeds),
– r = MWRR (periodic rate),
– n = number of periods.
Note: For irregular dates, the same principle applies but discounting uses exact day-counts; spreadsheet XIRR handles that.
Step-by-step: calculating MWRR by hand or with trial-and-error
1. List all cash flows in chronological order. Include the initial investment (negative), every deposit/withdrawal (negative for money into the investment, positive for money out), and the final market value (positive).
2. Choose a period (annual, monthly, etc.). If cash flows occur at irregular dates, use XIRR (see spreadsheet section).
3. Solve for r that makes the sum of discounted cash flows equal to zero.
• By hand: use trial-and-error (try plausible rates until NPV ≈ 0).
• With a financial calculator: use the IRR function.
• With spreadsheet: use IRR (periodic) or XIRR (irregular dates).
Practical spreadsheet steps (Excel / Google Sheets)
Periodic, evenly spaced cash flows:
– Put cash flows in consecutive cells (e.g., A1:A4) with signs: investments negative, returns/withdrawals positive.
– Use =IRR(A1:A4) to get the periodic MWRR. Optionally supply a guess: =IRR(A1:A4, 0.1).
Irregular dates (recommended for real portfolios):
– In column A, enter cash flow amounts (same sign convention).
– In column B, enter the corresponding dates.
– Use =XIRR(A1:An, B1:Bn) to compute the annualized MWRR.
Alternative: Use Goal Seek (if you want to see how r affects NPV)
– In one cell compute NPV(r) = SUM(CFi / (1+r)^(ti)) where ti is time in periods (or use exact days/365 for irregular).
– Use Goal Seek to set that NPV cell to 0 by changing the cell that contains r.
Worked numeric example (periodic cash-flow IRR)
– Cash flows by year:
• Year 0: -10,000 (initial investment)
• Year 1: -2,000 (additional contribution)
• Year 2: +5,000 (withdrawal)
• Year 3: +9,000 (final sale)
– Enter [-10000, -2000, 5000, 9000] into Excel and use =IRR(range).
– Result: IRR ≈ 9.1% (this is the money-weighted return that equates the present value of inflows and outflows).
Analyzing cash flows: inflows vs outflows
– Outflows (money going into the portfolio): initial purchase, additional contributions. Treat as negative cash flows.
– Inflows (money coming out to the investor): withdrawals, dividends taken as cash, sale proceeds. Treat as positive cash flows.
– Terminal market value should be included as an inflow on the final period if you’re measuring to a sale or valuation date.
Comparing MWRR and TWRR
– MWRR (money-weighted):
• Reflects both the investment performance and investor behavior (timing/size of flows).
• Good for showing an investor’s actual experience.
• Sensitive to large or poorly timed cash flows.
– TWRR (time-weighted):
• Removes the effect of external cash flows by chaining subperiod returns.
• Good for comparing investment managers because it isolates the manager’s performance independent of investor contributions/withdrawals.
– If there are no cash flows during the measurement period, MWRR ≈ TWRR.
Advantages of MWRR
– Provides a realistic measure of the investor’s realized return.
– Easy to compute with standard spreadsheet functions (IRR/XIRR).
– Useful for decision analysis (e.g., did adding money at a certain time improve realized performance?).
Limitations and pitfalls
– Sensitive to timing and size of cash flows: a large deposit just before positive performance inflates MWRR; a large withdrawal before gains reduces it.
– Not appropriate for comparing performance across managers or funds because it reflects investor-specific flows.
– Multiple IRRs can occur if cash flows change sign more than once (non‑conventional cash flows), making interpretation ambiguous.
– IRR assumes interim cash flows are reinvested at the IRR rate — that may be unrealistic.
– Requires careful sign convention; reversing signs yields wrong results.
Which should you use: MWRR or TWRR?
– Use MWRR when you want to measure your actual return as an investor (your performance given your deposits/withdrawals).
– Use TWRR when you want to evaluate a manager or compare funds, because it neutralizes the effect of client flows.
– Neither method is universally “better”; they answer different questions. Many reports present both.
Practical checklist before you compute MWRR
– Confirm you have all cash flows and the terminal value (market value) for the period.
– Check sign convention: contributions negative, withdrawals and ending market value positive.
– Determine whether flows are periodic or irregular (IRR vs XIRR).
– Be aware of non-conventional patterns (sign changes) that can yield multiple IRRs.
– If comparing to benchmarks, consider presenting both MWRR (investor experience) and TWRR (manager performance).
Bottom line
MWRR (the IRR of your cash flows) is the right tool to show the return you actually experienced because it incorporates the timing and magnitude of contributions and withdrawals. For evaluating fund managers or comparing investment strategies where you want to remove the influence of client flows, use time-weighted returns instead. Use spreadsheets (IRR/XIRR) or financial calculators to compute MWRR reliably, and be mindful of the method’s assumptions and sensitivities.
Source
– Investopedia — “Money-Weighted Rate of Return (MWRR)” by Zoe Hansen.
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.