Cash Flows
Cash Flow Sign Convention
- Negative (-): Money you invest/put in
- Positive (+): Money you withdraw/take out
- Final value: Enter as positive inflow
- Period (t): 0 = start, 1 = after period 1, etc.
Money-Weighted Return (IRR)
Strong dollar-weighted return above market average
MWR vs TWR
MWR (IRR) measures your actual dollar return including timing effects. TWR measures manager performance (cash-flow neutral). If MWR > TWR, your timing helped; if MWR < TWR, timing hurt.
Formula Breakdown
Understanding the Results
Your Actual Return
MWR (IRR) reflects your real dollar-weighted experience, including the impact of when you added or withdrew money. It's personal to your timing.
Newton-Raphson Method
IRR has no closed-form solution. We use iterative Newton-Raphson method to find the rate that makes NPV = 0.
MWR Performance Interpretation
| Return | Rating | Interpretation |
|---|---|---|
| > 15% | Excellent | Outstanding dollar-weighted return |
| 10% - 15% | Good | Strong performance above market |
| 5% - 10% | Moderate | In line with market returns |
| 0% - 5% | Low | Below market average |
| < 0% | Negative | Net loss on investment |
Understanding Money-Weighted Return
What is Money-Weighted Return?
Money-weighted return (MWR), also known as Internal Rate of Return (IRR), measures your actual investment performance including the impact of cash flow timing. Unlike TWR, it captures whether your timing decisions helped or hurt.
MWR is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. It weights returns by the amount of money invested at each point in time.
MWR vs TWR: A Practical Example
Consider a fund with these quarterly returns: +20%, -10%, +15%, +5%
| Investor | Strategy | TWR | MWR |
|---|---|---|---|
| A (Lucky Timing) | $10K at start, +$20K before +15% quarter | ~30% | ~35% |
| B (Unlucky Timing) | $10K at start, +$20K before -10% quarter | ~30% | ~22% |
Both investors experienced the same manager (same TWR), but their personal returns (MWR) differ substantially because of when they added money.
How IRR is Calculated
IRR solves the equation: NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ = 0
Since this is a polynomial equation with no closed-form solution, we use iterative methods:
- Initial guess: Start with r = 10%
- Calculate NPV: Sum all discounted cash flows
- Newton-Raphson: Adjust r based on NPV and its derivative
- Repeat: Until NPV ≈ 0 (within tolerance)
When to Use MWR
- Personal portfolio evaluation: When you want to know your actual return
- Cash flow timing assessment: To see if your timing helped or hurt
- Private investments: PE funds, real estate, and other illiquid investments often report IRR
- Project finance: Capital budgeting decisions typically use IRR
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only and does not constitute financial advice. Past performance does not guarantee future results. Always consult with a qualified financial advisor before making investment decisions.
