What Is the Money-Weighted Rate of Return (MWRR)?
The Money-Weighted Rate of Return (MWRR) measures an investment’s performance by accounting for the size and timing of cash flows (e.g., deposits, withdrawals). It calculates the rate of return that equates the present value of all cash flows to the initial investment. MWRR is synonymous with the Internal Rate of Return (IRR) and contrasts with the Time-Weighted Return (TWR), which excludes cash flow effects.
Key Takeaways
- MWRR evaluates performance by factoring in cash flow timing and magnitude.
- It solves for the discount rate where the net present value (NPV) of cash flows equals zero.
- Ideal for assessing personal portfolio returns, as it reflects investor behavior.
- Differs from TWR, which isolates investment performance from cash flows.
How MWRR Works
MWRR sets the initial investment equal to the sum of future cash flows (dividends, withdrawals, sale proceeds). This approach captures the real-world impact of investor decisions on returns.
Formula
The MWRR formula is:
PVO = PVI = CF₀ + (CF₁ / (1+IRR)) + (CF₂ / (1+IRR)²) + ... + (CFₙ / (1+IRR)ⁿ)
Where:
– PVO = Present Value of Outflows
– PVI = Present Value of Inflows
– CF₀ = Initial investment (negative value)
– CF₁–CFₙ = Cash flows per period
– IRR = Money-weighted rate of return
👉 Discover how to optimize your investment strategy with MWRR
Calculating MWRR: Step-by-Step
Example Scenario
You buy a stock for $50 (Year 1), receive $2 annual dividends (Years 2–3), and sell it for $65 (Year 3).
| Year | Cash Flow | MWRR Calculation |
|---|---|---|
| 1 | -$50 (Initial) | |
| 2 | +$2 (Dividend) | |
| 3 | +$2 (Dividend) | |
| 3 | +$65 (Sale) | IRR = 11.73% (via spreadsheet) |
Spreadsheet Tip: Use =IRR(B2:B5) in Excel or Google Sheets to automate calculations.
MWRR vs. Time-Weighted Return (TWR)
| Feature | MWRR | TWR |
|---|---|---|
| Cash Flow Impact | Includes deposits/withdrawals | Excludes cash flows |
| Use Case | Personal portfolios | Fund manager comparisons |
| Sensitivity | Affected by investor timing | Neutral to cash flow timing |
Why It Matters:
– MWRR shows how your actions (e.g., adding funds before a surge) affect returns.
– TWR isolates market performance, making it better for benchmarking.
👉 Learn how TWR can complement MWRR analysis
Limitations of MWRR
- Penalizes External Factors: Large deposits/withdrawals skew returns, which may misrepresent a manager’s skill.
- Dollar-Weighted Bias: Overweights periods with higher portfolio values.
- Not Ideal for Comparisons: TWR is preferred for apples-to-apples fund performance reviews.
FAQs
1. When should I use MWRR?
MWRR is best for evaluating personal investment performance, especially if you make frequent contributions or withdrawals.
2. Can MWRR be negative?
Yes, if cash outflows exceed gains (e.g., selling at a loss after multiple withdrawals).
3. How does MWRR handle dividends?
Dividends are treated as inflows and factored into the IRR calculation.
4. Why is MWRR equal to IRR?
Both solve for the discount rate where NPV = 0, aligning present values of inflows and outflows.
5. Which is more accurate: MWRR or TWR?
Neither is universally “better.” MWRR reflects personal behavior; TWR measures market performance.
6. How do I improve my MWRR?
Minimize untimely withdrawals and align contributions with market growth phases.
The Bottom Line
The Money-Weighted Rate of Return is a powerful tool for investors to assess how their decisions—like timing deposits or withdrawals—impact overall returns. While it has limitations for comparative analysis, MWRR provides a personalized snapshot of portfolio performance. Pair it with TWR for a holistic view of your investments.
Pro Tip: Use spreadsheet tools to simplify MWRR calculations and track trends over time.