Money-Weighted Rate of Return

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?”

Key Takeaways

  • Larger cash balances have more influence on MWRR than smaller balances.
  • Contributions made before weak performance can reduce MWRR relative to time-weighted return.
  • MWRR is useful for the investor experience when the investor controls cash-flow timing.
  • Time-weighted return is usually more suitable for isolating a manager from client-controlled cash flows.
  • Irregular dates require date-based exponents rather than assuming equally spaced annual periods.
  • Multiple sign changes can produce multiple IRRs or no economically useful solution.
  • Gross and net MWRR must state which fees, expenses, distributions, and valuations are included.

Core Formula

Using an investor-perspective sign convention, contributions are negative cash flows and withdrawals, distributions, and ending value are positive:

$$ 0 = \sum_{i=0}^{n} \frac{CF_i}{(1+r)^{\tau_i}} $$

where:

  • (CF_i) is cash flow (i)
  • (\tau_i) is elapsed time from the initial date, expressed in years
  • (r) is the annualized money-weighted return

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.

Worked Example: Cash-Flow Timing Matters

Assume a one-year account history:

DateEventInvestor cash flowPortfolio value around event
StartInitial investment-$100$100
MidyearAdditional contribution-$100$110 before contribution
Year-endLiquidation value+$189$189

The MWRR solves:

$$ -100 - \frac{100}{(1+r)^{0.5}} + \frac{189}{1+r} = 0 $$

The solution is approximately:

$$ r\approx -7.29\% $$

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.

Comparison With Time-Weighted Return

The two subperiod returns are +10% and -10%. Time-weighted return is:

$$ (1.10)(0.90)-1 = -1.00\% $$
MeasureResultInterpretation
Time-weighted return-1.00%Performance of one unit invested through both subperiods
Money-weighted returnapproximately -7.29%Annualized return on the investor’s dated dollars

Neither result is inherently more correct. They answer different questions.

When MWRR Is Useful

MWRR is often informative for:

  • a personal account when the investor controls deposits and withdrawals
  • private equity or real estate with capital calls and distributions
  • a project with dated investments and proceeds
  • a total fund when the decision maker controls the timing of major allocations
  • evaluating progress from actual investor cash flows

It can be less suitable for comparing public-market managers when clients control external cash flows the manager cannot influence.

Cash-Flow Sign Convention

The investor perspective commonly uses:

  • contribution or purchase: negative
  • withdrawal or sale proceeds: positive
  • income paid out: positive
  • ending portfolio value: positive terminal cash flow

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 and IRR

MWRR is generally the portfolio application of IRR. The terms can differ in presentation:

  • MWRR: emphasizes investor cash-flow weighting
  • IRR: emphasizes the discount rate solving the cash-flow equation
  • Since-inception IRR: uses all cash flows from inception to the measurement date
  • Net IRR: reflects specified fees, expenses, and carried interest
  • Gross IRR: excludes specified investor-level deductions

These labels require precise methodology. Subscription credit facilities, interim valuations, fee timing, and recycled distributions can materially affect private-fund IRR.

Multiple or Missing Solutions

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:

  • more than one mathematical solution
  • no real solution
  • a solution that is economically misleading

Net present value at stated discount rates and multiple-on-invested-capital measures can provide additional context.

Valuation and Timing Choices

MWRR changes when analysts use different:

  • cash-flow dates
  • beginning- or end-of-day assumptions
  • day-count conventions
  • interim and ending valuations
  • treatment of fees and expenses
  • currency conversion dates
  • distributions classified as income versus external cash flow

Illiquid-asset values can be model-based and later revised. A precise IRR does not make uncertain valuations precise.

MWRR Versus Other Return Measures

MeasureExternal cash flowsTime valuePrimary use
Simple holding-period returnAssumes none within periodNo separate date discountingOne uninterrupted investment period
Time-weighted returnNeutralizes their effectGeometrically links subperiodsStrategy or manager comparison
Money-weighted returnIncludes timing and sizeYesInvestor’s actual cash-flow experience
Modified DietzTime-weights flows in capital baseApproximation within periodPeriod return without every cash-flow valuation

Common Mistakes

  • Calculating account-value growth instead of solving for dated cash flows.
  • Entering contributions and withdrawals with inconsistent signs.
  • Omitting ending value or counting it twice.
  • Treating irregular dates as equally spaced periods.
  • Comparing MWRR directly with TWR without explaining cash-flow control.
  • Reporting one IRR when the cash-flow pattern permits several.
  • Comparing gross and net IRRs with different dates or methodologies.
  • Treating a precise result as reliable when valuations are uncertain.
  • Assuming MWRR identifies whether the manager added value.

Authoritative Context

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.

FAQs

Is money-weighted return the same as IRR?

MWRR is generally calculated as the IRR of the investor’s dated portfolio cash flows. The specific presentation should state the dates, valuation, annualization, and fee conventions.

Why can money-weighted return differ from time-weighted return?

MWRR gives more influence to periods when more money was invested. TWR geometrically links subperiod returns and neutralizes the size and timing of external cash flows.

Can money-weighted return have more than one answer?

Yes. Cash flows that change sign multiple times can create multiple IRR solutions or no useful solution. The full cash-flow pattern and complementary measures should be reviewed.

Educational Use

This article provides general financial education. It is not personalized investment, private-fund, performance-reporting, tax, accounting, legal, or fiduciary advice.

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