Money-Weighted Rate of Return

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Money-Weighted Rate of Return (MWRR)

What is MWRR?

The money-weighted rate of return (MWRR) measures investment performance by accounting for the timing and size of cash flows—contributions, withdrawals, dividends and sale proceeds. MWRR is mathematically equivalent to the internal rate of return (IRR) and reflects how an investor’s actions affect overall returns.

How it works

MWRR finds the discount rate that equates the present value of cash inflows to cash outflows for the investment. Because it weights returns by the amount of money invested at different times, larger flows have greater influence on the result.

Formula (conceptual)

Solve for IRR in the equation:
sum_{t=0}^n CF_t / (1 + IRR)^t = 0

  • CF_0 is typically the initial investment (negative value for an outflow).
  • CF_1 … CF_n are subsequent cash inflows (+) or outflows (−) at each period t.
  • IRR is the money-weighted return.

In practice you solve this equation numerically (no closed-form solution for most cases).

Calculating MWRR with a spreadsheet

  1. List cash flows by period (include the initial investment as a negative number).
  2. Use the spreadsheet IRR function:
  3. Excel/Google Sheets: =IRR(range_of_cashflows, [guess])
  4. The result is the MWRR as a periodic rate (annualize if necessary).

Example cash flows layout:
– Year 0: −50 (purchase)
– Year 1: +2 (dividend)
– Year 2: +2 (dividend)
– Year 3: +65 (sale + final dividend)

Applying IRR to these values yields an MWRR of about 12% (annual).

MWRR vs. Time-Weighted Rate of Return (TWRR)

  • MWRR: Reflects investor behavior—sensitive to the size and timing of cash flows. Useful for measuring how an investor’s decisions affected portfolio growth.
  • TWRR: Neutralizes the effect of external cash flows by breaking returns into subperiods. Preferred for comparing investment managers because it isolates manager performance from client-driven cash flows.

If there are no external contributions or withdrawals, MWRR and TWRR will produce the same or very similar results.

Advantages of MWRR

  • Shows the actual return experienced by the investor, incorporating the impact of deposits and withdrawals.
  • Useful for personal performance measurement and decision analysis.

Limitations and cautions

  • Sensitive to the timing and magnitude of cash flows; a large contribution just before a strong period inflates MWRR.
  • Not suitable for comparing managers because it reflects investor actions.
  • Can produce multiple or ambiguous IRRs when cash flows change signs more than once.
  • Requires numerical methods (spreadsheets or financial calculators) to compute.

When to use each metric

  • Use MWRR when you want to evaluate the return you personally achieved, including the effects of your contributions and withdrawals.
  • Use TWRR when you need a fair comparison of manager performance or want to measure the portfolio’s compound growth independent of cash flows.

Bottom line

MWRR (IRR) is a practical metric for understanding how your cash flow decisions influenced investment outcomes. It gives a personalized view of performance but can be misleading when used to compare managers or when cash flows are irregular. Use MWRR and TWRR together when you need both investor-level insight and manager-level comparability.