Time-weighted vs. money-weighted returns: why your results differ

Ask two different questions: how did the invested portfolio perform, and what return did the investor earn on money committed at different dates? TWR and MWR are designed to answer those different questions.

For this guide, the measured portfolio is one whole account, including its cash, investments, and liabilities. A bank transfer into it is an external contribution; buying a security using cash already inside it is not.

A transfer between two accounts is external to each account considered separately. It is internal when both are inside the same consolidated portfolio. Define the boundary before labeling transactions.

Use one reporting currency and a consistent valuation and fee convention. The formulas below assume positive portfolio values. They do not calculate a tax return or prescribe any country's account rules.

[GIPS performance methodology](https://www.gipsstandards.org/standards/gips-standards-for-firms/gips-standards-handbook-for-firms/) distinguishes time-weighted returns from returns that reflect external cash-flow timing.

Consider an original hypothetical example with no fees, taxes, income payments, borrowing, or currency changes. Each interval below is exactly 365 days; the contribution occurs after the first year's valuation.

The first year's investment gain is 200. The second year's investment loss is 1,000. Net investment P/L is therefore −800, also equal to 9,000 − 1,000 − 8,800.

The balance increased from 1,000 to 9,000, but that is not an 800% investment return: most of the increase came from the contribution. These numbers are not a backtest or an actual account record.

• September 18, 2024: invest 1,000 in the account.
• September 18, 2025: the account is worth 1,200 before adding money.
• On that same date: deposit 8,800, bringing account value to 10,000.
• September 18, 2026: the account is worth 9,000, with no further flows.

Measure each sub-period without an external flow inside it. Use the value immediately before a contribution as the old period's ending value, and the value immediately after it as the next period's starting value.

First sub-period return = 1,200 ÷ 1,000 − 1 = 20%.

Second sub-period return = 9,000 ÷ 10,000 − 1 = −10%.

Link the growth factors: TWR = (1 + 0.20) × (1 − 0.10) − 1 = 8% over two years. Adding 20% and −10% instead would give the wrong cumulative result.

The comparable annualized TWR is (1.08)^(1/2) − 1 ≈ 3.9230%. Keep the two-year cumulative 8% separate from this annual rate.

[TWR calculation guidance](https://www.gipsstandards.org/standards/gips-standards-for-asset-owners/gips-standards-handbook-for-asset-owners/) describes linking sub-period returns around external flows.

An internal rate of return, or IRR, is a common way to calculate MWR. From the investor's perspective, contributions are negative cash flows, while withdrawals and the ending portfolio valuation are positive.

For this example the dated values are −1,000, −8,800, and +9,000. The last value is treated as a terminal receipt for measurement, even though the portfolio need not actually have been sold.

Let r be the annual IRR. Discount the three values to the initial date: −1,000 − 8,800 ÷ (1 + r) + 9,000 ÷ (1 + r)^2 = 0.

Equivalently, 1,000 × (1 + r)^2 + 8,800 × (1 + r) = 9,000. Solving gives r ≈ −7.4589% per year. The initial capital was invested for two years; the extra contribution for only one.

Substituting the unrounded result reproduces the 9,000 terminal value. The 1,200 interim valuation is needed for exact TWR here, but it is not a cash flow to insert into the IRR equation.

[IBKR's performance-measure explanation](https://www.ibkrguides.com/orgportal/performanceandstatements/pa_viewingaccountperformance.htm) also separates cash-flow-sensitive MWR from TWR.

In a spreadsheet, place the three example dates beside −1,000, −8,800, and +9,000. XIRR(values, dates) uses actual dates, while periodic IRR assumes equally spaced observations.

Microsoft specifies a 365-day year for XIRR. In this example its annual result matches the IRR because both intervals contain 365 days. Other day-count conventions can produce small differences.

[XIRR's official documentation](https://support.microsoft.com/en-us/excel/functions/xirr-function) explains the date inputs and cash-flow signs. Use real date values rather than ambiguous text dates.

Include the ending portfolio value once. If everything was liquidated and withdrawn at the end, use that withdrawal and zero residual value, not the withdrawal plus the old balance.

A negative XIRR is a valid result, not automatically a software error. Irregular flows with repeated sign changes can have multiple solutions; a failed solver or a convenient starting guess does not establish a return.

Only 1,000 was exposed to the first year's 20% gain, while 10,000 was exposed to the second year's 10% decline. The larger capital base in the losing year explains the negative personal result.

Without the additional deposit, the same percentage path would turn 1,000 into 1,080. With no intermediate external flows, annualized TWR and IRR would both be approximately 3.9230% under these assumptions.

Dividing −800 by total contributions of 9,800 gives about −8.1633%. That simple P/L ratio is neither the annual IRR nor a substitute for dated cash-flow analysis.

TWR is useful for comparisons that remove investor-driven cash-flow timing. MWR is useful for the investor's experience and when the timing of committed capital is itself part of the decision being evaluated.

Neither is universally better. Compare annualized TWR with annualized MWR for the same dates, not a cumulative TWR with an annual IRR. Neither measures drawdown or guarantees future performance.

Within a whole account, dividends retained as cash or reinvested are investment results, not fresh contributions from the investor. A later transfer to the bank is an external withdrawal from that account.

[Investor.gov's distribution explanation](https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins/fund-distributions-investor-bulletin) distinguishes cash and reinvestment.

At the individual fund level, a distribution paid out to the holder crosses that investment's boundary. At the consolidated account level, the same money may remain inside as cash. Do not mix those scopes.

Futures variation settlement is part of trading P/L, not a new investor deposit. A separate bank transfer made to meet margin requirements is external funding. Do not remove trading losses as though they were withdrawals.

[CME's mark-to-market guide](https://www.cmegroup.com/education/courses/introduction-to-futures/mark-to-market) explains daily settlement. Reconcile it once within account equity rather than adding it to an already complete P/L again.

Use futures return denominators for trade-level ratios. They do not replace whole-account returns that incorporate dated funding and open-position values.

Exact cash-flow-split TWR requires valuations around the flows. When only opening and closing balances are known, do not invent the missing intermediate valuations to force an exact result.

Daily conventions and cash-flow-weighted approximations can differ between reports. Check the provider's calculation method instead of assuming every figure labeled TWR or MWR uses identical inputs.

Averages and CAGR explain compounding. Price versus total return addresses income. Neither alone adjusts for dated external flows. [!TRYMARK] TryMark cash-flow reconciliation At the next statement review, target the reported ending equity. Reconcile dated deposits, withdrawals, and valuations, then recompute the comparable TWR and IRR when any fee or cash-flow classification changes. [!WARNING] A return label is not a risk limit Neither method makes losses safe or predicts recovery. At zero or negative equity, standard positive-capital return comparisons can break down. Report liabilities and cash flows rather than forcing a misleading percentage.

• Record portfolio scope, reporting currency, valuation dates, and external transfers.
• For TWR, check before-flow and after-flow values and link the sub-period returns.
• For IRR, check investor-perspective signs, dates, and one terminal valuation.
• Match annualization, income, fees, taxes, and liability treatment before comparing reports.