Time-Weighted vs Money-Weighted Returns: Why a Rising Portfolio Can Lose You Money

A positive performance chart and a loss in your account can both be correct. The chart may describe the investment path without the effect of contributions and withdrawals. Your result also depends on how much money travelled through each part of that path. Time-weighted return, money-weighted return and cash profit answer different questions; choosing the most flattering number does not reconcile them.

For a stock or multi-asset portfolio, start with the account boundary and the cash ledger. Then calculate the measures on a consistent time basis. The following hypothetical example produces an 8% cumulative time-weighted gain alongside an actual loss, without contradictory prices or a hidden fee.

The cash ledger: where the loss of 820 comes from

Put 1,000 currency units into an account containing both investments and cash. It earns 20% over one full year and is worth 1,200 immediately before a new contribution of 9,000. The second year therefore starts with 10,200. A 10% loss over that full year leaves 9,180. There are no other external flows, taxes or fees in this example, and both periods are exactly one year.

The investor contributed 10,000 and ends with 9,180: a loss of 820. The same result appears in the annual profit ledger: a gain of 200 followed by a loss of 1,020. Dividing −820 by total contributions gives −8.2%, but that simple ratio ignores holding time. It is neither the time-weighted result nor the annual money-weighted return. Most of the capital was invested for only one year.

Time weighting follows the path, not the contribution size

Split the record at each external flow. The first subperiod return is 1,200/1,000−1, or 20%. The second starts after the contribution, so its return is 9,180/10,200−1, or −10%. The extra 9,000 is capital, not performance.

Cumulative TWR = (1 + 20%) × (1 − 10%) − 1 = 8%. A unit of capital left in this same investment path throughout would grow by 8%. With no additional contribution, an initial 1,000 following exactly those returns would finish at 1,080. Adding the two returns gives an incorrect 10%; their arithmetic average of 5% is not the compound annual growth rate either.

Over two complete years, the annualized TWR is √1.08−1, approximately 3.923%. The 8% cumulative result and 3.923% annualized result describe the same path at different time scales. Exact time weighting requires reliable valuations around every external flow. Month-end balances without intervening flow-date valuations do not justify labelling an approximation as an exact TWR.

Money weighting asks how long each contribution was invested

Calculate the money-weighted result here as an internal rate of return. Let r be the annual rate. The initial 1,000 compounds for two years, while the additional 9,000 compounds for one:

1,000 × (1 + r)² + 9,000 × (1 + r) = 9,180.

The economically meaningful solution with 1+r positive is approximately −7.506% a year. Compare that with the annualized TWR of 3.923%, not directly with the two-year cumulative 8%. The negative IRR arises because most of the money was present only during the losing year, not because a 10% decline somehow outweighs a 20% rise on an unchanged amount.

From the investor's perspective, the equivalent cash-flow series is −1,000 at inception, −9,000 one year later and +9,180 after two years. The last value can be a reliably marked ending portfolio, not an actual liquidation. For irregular flows, use actual dates and an explicit year convention rather than assuming each row is a year. Cash-flow patterns with repeated sign changes can produce multiple or unusable IRR solutions. A spreadsheet error is not a zero return.

Define the account boundary before classifying cash flows

Within a whole account that includes cash, selling a stock and retaining the proceeds changes the asset mix; it is not a withdrawal. Buying another stock with existing cash is not a contribution. Treating every trade as an external flow can conceal the effect of holding cash and distort the performance record.

A dividend retained in the account belongs in investment income and cash value, not in new investor capital. A subsequent transfer out crosses the boundary and becomes a withdrawal. Transfers of securities also need consistent valuation. Measuring a security sleeve rather than the whole account changes that boundary and may change the flow classification; state which one you mean.

New money can correct allocation drift, but funding a rebalance is not the same as generating a return. The mechanics are set out in calculating portfolio rebalancing weights and contribution amounts. Also align reporting currency, income treatment and costs. A stock with an unchanged local-currency price can still change the value of an account measured in another currency.

Choose the measure for the question—and know when to stop

For an investment path whose manager does not control client subscriptions, TWR is usually the starting point. MWR adds the experience of the actual capital committed. Cash profit reconciles wealth gained or lost. None alone establishes stock-picking skill, good timing or an appropriate level of risk.

This example demonstrates that a much larger contribution entered before the weaker period. It does not establish performance chasing or managerial failure: that contribution might have come from wages, an asset sale or a pre-agreed schedule. To investigate funding timing, construct a benchmark using the same contribution and withdrawal dates and amounts. Subtracting a random index's cumulative return from a personal annual IRR is not a valid timing test.

Missing valuations, mixed currencies, unrecorded costs or withdrawals counted as losses are reasons to suspend the conclusion. A fee deducted within the account already reduces net value; do not deduct it twice. If a fee was paid outside the account and the aim is the investor's all-in result, incorporate it consistently in the relevant cash flows and explain the treatment.

A six-step reconciliation you can reproduce

1. Specify the whole account or sleeve, whether cash and accrued income are included, and the reporting currency.
2. Export dated external flows. Separate contributions, withdrawals, internal trades and fees.
3. Reconcile ending value plus withdrawals minus starting value and contributions with the monetary gain or loss. Count contributions after the opening valuation only; do not deduct the initial 1,000 twice.
4. Calculate and geometrically link flow-delimited subperiod returns. Flag missing valuations and approximation error instead of inventing prices.
5. Solve the investor cash-flow IRR; check dates, terminal value and the usable solution. Put comparison returns on the same period basis.
6. Report the results together: a loss of 820, cumulative TWR of 8%, annualized TWR of about 3.923% and annual MWR of about −7.506%. Their relationship explains the experience better than any one headline percentage.