Money-weighted return: Definition & Examples

Money-weighted return (MWR) measures investment performance while reflecting the amounts and timing of money paid in and taken out. It answers an investor’s question: “What return did my particular cash-flow history earn?” Two clients holding the same fund can have different money-weighted returns because they contributed or withdrew at different times.

The usual calculation is the internal rate of return of the investor’s dated cash flows. That is the convention used here. The GIPS Standards Handbook describes MWR in terms of value changes and external cash-flow timing and size, with IRR as a commonly used calculation method.

Start with the investor’s ledger

Choose the boundary of the account being measured. From the investor’s perspective:

A contribution to the account is negative: the investor pays money in.
A withdrawal or distribution received is positive: the investor receives money.
Remaining account value at the measurement date is a positive terminal amount, as though withdrawn then. If the account is actually fully withdrawn, count that receipt once; do not add the same terminal value again.

Buying a share with cash already inside the account is not an external contribution. Nor is a dividend retained inside it an external withdrawal. These transactions affect holdings and value within the chosen boundary. A distribution paid out to the investor crosses that boundary and enters the ledger.

For signed amounts $C_i$ occurring at times $\tau_i$ measured in years, the annual-effective MWR solves

\sum_{i=0}^{n}\frac{C_i}{(1+r)^{\tau_i}}=0,\qquad r>-1.

The rate makes the net present value of the complete schedule zero. The positive accumulation base,

1+r>0

, is part of this effective-rate convention.

Two contributions, one annual rate

Consider a synthetic account in USD. The investor contributes 100 at inception, adds 50 exactly one year later, and receives 176 on full withdrawal exactly two years after inception. There are no other flows, fees or taxes in this example.

Time from inception	Investor cash flow, USD
0 years	−100
1 year	−50
2 years	+176

The equation is

-100-\frac{50}{1+r}+\frac{176}{(1+r)^2}=0.

Its admissible solution is 10% effective annually. Check it by moving both contributions to the final date:

100(1.10)^2+50(1.10)=121+55=176.

The first contribution has two years of exposure; the second has one. The 26 USD cash profit alone does not encode that timing or provide an annual percentage return.

Investor cash flows are minus 100 USD at year 0, minus 50 USD at year 1 and plus 176 USD at year 2. At an equivalent 10% annual rate, the two contributions accumulate to 121 and 55 USD.

Synthetic USD schedule with exact one-year intervals. The lower panel reconstructs terminal wealth at the solved constant rate; it does not assert observed yearly portfolio returns.

There is also a useful root check. Set $x=1+r$ . Multiplication by $x^2$ gives

100x^2+50x-176=(10x-11)(10x+16)=0.

The roots are $x=1.10$ and $x=-1.60$ . The latter implies $r=-260\%$ and violates the positive-base convention. It is an algebraic root, not a second admissible investment return. More complicated schedules can have multiple admissible IRRs or none; a calculator’s single output does not settle that question.

Why this is not the fund’s time-weighted return

Time-weighted return divides the history at external cash flows, computes each flow-free subperiod return, and compounds those returns. It neutralises the effect of how much external capital arrived at each boundary. Money-weighted return retains that effect.

The three cash flows above do not determine a time-weighted return. We would also need the account’s value immediately before the year-one contribution, or equivalent flow-adjusted subperiod return data. We cannot infer that missing value by assuming the account earned 10% in each year: 10% is the equivalent rate solving the investor’s whole schedule.

When clients control contributions and withdrawals, TWR is generally the more useful starting point for comparing managers; MWR records the client’s particular investment experience. When the manager controls capital calls or distributions, their timing can itself be part of the investment decision being evaluated. Neither return alone establishes skill or adjusts for risk.

SelfMadeQuant’s Risk-Adjusted Performance Measures lesson starts with this return-measurement distinction before introducing risk-adjusted comparisons. The public page provides a preview; the full lesson requires membership.

Keep dates and costs visible

For irregular dates, state how actual dates become year fractions rather than treating every adjacent flow as one equal period. Microsoft’s IRR function uses regular intervals; its XIRR function uses dates and a 365-day year convention. That software convention should not be silently substituted for another declared time basis.

Also label the cost basis. Fees deducted inside the account already reduce its value; do not subtract them a second time. Costs paid outside it need appropriate treatment if the intended measure includes them. A quoted MWR should say what fees and taxes are included, alongside its horizon and rate convention.

Sources

CFA Institute, GIPS Standards Handbook for Firms, November 2020, discussion of Provisions 2.A.28–2.A.29: MWR, IRR and valuation requirements for time-weighted calculations.
Elton, Gruber, Brown and Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th ed., Wiley, 2014, Chapter 26, “Measures of Return,” pp. 661–662: external flows, linked returns and manager comparison.
Microsoft, IRR function and XIRR function: regular-period and dated cash-flow conventions.

Start with the investor’s ledger

Two contributions, one annual rate

Why this is not the fund’s time-weighted return

Keep dates and costs visible

Sources

Related terms

Internal rate of return

Net present value

Time-weighted return