On this page
- Start with the question the return should answer
- Put the contribution between two valuations
- Link the subperiods for time-weighted return
- Find the money-weighted rate from the dated cash flows
- Compare like periods before interpreting the gap
- A no-contribution comparison helps isolate the difference
- Keep the method's other choices visible
- Frequently asked questions
- Sources and scope
Adding money can increase an account balance without producing an investment gain. Time-weighted return separates external contributions and withdrawals from the investment return path. Money-weighted return also reflects how much money was invested and when. The two figures can therefore differ for the same investment path.
To compare them, keep the cash flows, valuations and return periods together. The example below follows one fictional account for two full years, then compares both methods on an annual basis.
Start with the question the return should answer
A time-weighted return, or TWR, links the investment's returns over subperiods. Valuing the portfolio around an external cash flow lets you separate a contribution from a gain, or a withdrawal from a loss. You then multiply the subperiod growth factors rather than adding their percentage returns.
A money-weighted return, or MWR, takes the timing and size of the investor's cash flows into account. In this guide, we calculate one specific version: the annual internal rate of return, or IRR, that makes the net present value of the stated investor cash flows zero. Read an actual report's method before assuming every figure labelled MWR uses exactly the same calculation.
Commonfund's explanation of TWR and IRR sets out this distinction between linked investment growth and the return on dated amounts invested and returned. Dynamic Funds' comparison also explains how contributions and withdrawals can change an investor's reported experience. These explanations do not make either measure universally better for every question.
Put the contribution between two valuations
Assume you invest $100 at T0. Exactly one full year later, at T1, the investment has gained 10%, so it is worth $110 immediately before you contribute another $100. Immediately after that contribution, the portfolio is worth $210.
During the second full year, the investment loses 10%. At T2, exactly two years after T0, the portfolio is worth $189. You then liquidate it and receive the entire $189, leaving no remaining portfolio balance.
All amounts are fictional US dollars. We assign the same +10% and −10% investment returns regardless of the amount invested. There are no other contributions or withdrawals, income distributions, fees, taxes, currency conversions, inflation adjustments, transaction effects or defaults. The values and liquidation are teaching assumptions, not a real account or an available investment.
| Time | Portfolio value and timing | External flow into or out of the portfolio | Investor cash flow |
|---|---|---|---|
| T0: start | $100 after the initial contribution | +$100 contribution | −$100 |
| T1: exactly one year later | $110 before the contribution; $210 immediately afterward | +$100 contribution | −$100 |
| T2: exactly two years after T0 | $189 before liquidation; $0 after the full payment | −$189 paid to the investor | +$189 |
The extra $100 at T1 is capital added by you, not investment profit. Keeping $110 before the contribution separate from $210 after it prevents that payment from inflating the first year's return.
The $189 at T2 appears once as the investor's terminal receipt. It is not both a receipt and another $189 still held in the portfolio.
Link the subperiods for time-weighted return
For the first year, use the value before the new contribution:
First-year return = $110 ÷ $100 − 1 = 10%.
For the second year, start with the value after that contribution:
Second-year return = $189 ÷ $210 − 1 = −10%.
The two-year time-weighted growth factor is 1.10 × 0.90 = 0.99. Subtracting one gives the cumulative TWR:
Two-year cumulative TWR = 0.99 − 1 = −1%.
The +10% and −10% do not cancel. They apply successively to different starting values. Nor does the calculation treat the $100 contribution as a return.
For comparison with an annual rate, find the constant positive annual growth factor whose square is 0.99:
Annual-equivalent TWR = √0.99 − 1 ≈ −0.501256%.
That is the compound-equivalent annual rate for this two-year path, not either actual year's return. Our annualized versus total return guide explains that period conversion separately.
Find the money-weighted rate from the dated cash flows
Now use the investor's payments rather than only the portfolio's subperiod returns. The investor pays $100 at T0, pays $100 one full year later, and receives $189 at the end of the second full year.
Let r be the annual IRR, expressed as a proportion. Its annual growth factor is x = 1 + r, and we require x > 0. With the signs shown in the timeline, the present-value equation is:
−100 − 100 ÷ (1 + r) + 189 ÷ (1 + r)² = 0.
The first contribution is at T0, so it is not discounted. The second is one year away and the final receipt is two years away. Under the stated USD units, every term represents a dollar amount discounted to T0.
Substituting x and rearranging gives:
100x² + 100x − 189 = 0, with x > 0.
The admissible solution is x = (√214 − 5) ÷ 10 ≈ 0.962873884. Subtract one to recover the rate:
r = (√214 − 15) ÷ 10 ≈ −0.037126116, or −3.712612% per year.
A growth factor below one can represent a valid negative return. The other algebraic solution has x < 0 and falls outside this example's positive-growth-factor domain; it is not rejected merely because a return is negative.
Using the unrounded admissible factor in −100 − 100 ÷ x + 189 ÷ x² gives zero. The displayed factors and percentages are rounded, so substituting those shortened decimals can leave a small rounding difference.
Compare like periods before interpreting the gap
The account had more money invested during the assigned losing second year. The money-weighted result reflects that timing and amount; TWR links the two stipulated investment returns. Neither figure, by itself, measures manager skill or proves that a particular timing decision was right or wrong.
| Measure | Period or basis | Calculation | Result |
|---|---|---|---|
| Cumulative TWR | Whole two-year investment path | 1.10 × 0.90 − 1 | −1% |
| Annual-equivalent TWR | Constant annual rate for that two-year path | √0.99 − 1 | Approximately −0.501256% per year |
| Money-weighted annual IRR | Dated investor payments and terminal receipt across the two years | (√214 − 15) ÷ 10 | Approximately −3.712612% per year |
| Net cash result | Total received less total contributed | $189 − $100 − $100 | −$11; an amount, not an annual return |
Comparing the cumulative −1% directly with the annual −3.712612% would mix periods. On the matching annual basis, the comparison is approximately −0.501256% TWR versus −3.712612% IRR.
The $11 cash loss is another useful description, but dividing it by the $200 contributed does not solve the annual IRR equation. That shortcut ignores that the second $100 was invested for only one of the two years.
A no-contribution comparison helps isolate the difference
Consider a separate control case with the same assigned investment returns but no additional contribution at T1. The portfolio follows $100 → $110 → $99 across the same two full years, and the investor receives $99 at T2.
Its cumulative TWR remains −1%. Its annual IRR satisfies −100 + 99 ÷ x² = 0 with x > 0, so x = √0.99. The annual IRR therefore equals the annual-equivalent TWR, about −0.501256%. The cumulative two-year rate remains a different number.
This comparison shows how the additional contribution matters in our assigned path. It is not evidence that one return method is always higher, that real cash flows have no effect on investment decisions, or that an investor could have predicted the losing year.
Keep the method's other choices visible
External cash flows are payments into or out of the account by the investor. Investment income, changes in asset values and trades within the portfolio are different items. TWR does not mean those items disappear, and neither TWR nor MWR tells you by its name alone which fees or taxes have been deducted.
Real reports need consistent valuation times, income treatment, cost treatment and periods. An inflation-adjusted return answers another question; the nominal versus real return guide separates money growth from purchasing power.
This example fixes equal full-year spacing and a complete terminal payment. It does not calculate irregular-date methods, approximate cash-flow adjustments, uncertain asset valuations or arbitrary payment schedules with different possible solutions.
CFA Institute's public GIPS overview describes additional context for performance reporting and external-flow policies. A worked TWR or IRR calculation alone does not establish compliance with the full standards. The sources' discussions of fund types and reporting practices are not universal rules for every account.
Frequently asked questions
Does adding money count as an investment gain?
No. In the example, the portfolio is worth $110 before the additional $100 arrives and $210 afterward. The contribution changes invested capital. The first year's investment return is still $110 ÷ $100 − 1 = 10%.
Does time-weighted return ignore dividends and fees?
No. Separating external contributions and withdrawals does not mean excluding all investment income or costs. Check the report's income, reinvestment and gross-or-net conventions. This fictional example excludes distributions, fees and taxes to isolate the external contribution.
Is time-weighted return always higher than money-weighted return?
No fixed ranking follows from the two methods. Their relationship depends on the return path and the timing and size of cash flows. Compare matching periods and measurement choices rather than treating the larger percentage as automatically more correct.
Can time-weighted and money-weighted returns agree?
Yes. In the no-additional-contribution case here, $100 becomes $99 over two full years. Its annual IRR and annual-equivalent TWR are both √0.99 − 1, about −0.501256%. That agreement is on the annual basis, rather than an equality with the cumulative −1%.
Is an annual IRR a forecast or a guaranteed return?
No. The calculated rate summarizes the specified cash flows under the chosen timing convention. It does not promise the same result next year, prove manager skill or establish an investment offer. A real report must identify its method and inputs.
Explore HypaForecast
Browse market questions or visit the BTC 5-minute and 15-minute pages. These general navigation links are separate from the fictional investment account in this guide.
Sources and scope
- Commonfund: Time-Weighted Return vs. Internal Rate of Return. Practitioner explanation of linked investment growth and dated cash-flow IRR. Its publication date was not established; its rounded numerical case and flattened formula layout are not used for this example.
- Dynamic Funds: Time-weighted vs. money-weighted returns. Canadian issuer education on how investor cash flows affect the comparison. Its historical example, recommendations and blanket comparison restrictions are not adopted as universal rules.
- CFA Institute: Overview of the Global Investment Performance Standards. Public overview discussing provisions of the 2020 edition, not a reading of the full standard, all later guidance or a compliance assessment.
The saved source extracts were read on 21 October 2026. That reading date is separate from publication dates and does not establish an exact source-fetch time. The source PDF layouts and formula images were not inspected. The USD amounts, two-year timeline and assigned returns are original fictional teaching inputs, with the exclusions stated above; no current account results or future investment performance are reported.
HypaForecast publishes educational guides and operates a prediction market. This explanation of return measurement does not establish a HypaForecast investment account, an offered yield, future performance or your eligibility to use a service.
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