Different questions need different denominators
The cash result shows how much was gained or lost in monetary units after contributions and withdrawals. Time-weighted return divides the history at external flows and links growth factors; it describes the path of one unit of capital without the size of later contributions. The money-weighted measure accounts for how much money participated and for how long, answering the owner’s experience with a specific calendar rather than a universal strategy return.
Two years and one extra contribution
A fictional account starts with 100 units. It grows 10% in the first year, reaching 110 before a new contribution. The owner adds another 100, and the second year declines 10%. Ending value is 189. Total contributions are 200, so the cash result is −11. Fees, taxes, payouts and other operations are excluded. Values are known immediately before each external movement, which matters for splitting the periods.
Time-weighted return is 1.10 × 0.90 − 1 = −1% over two years. It is not an annual rate and not cash loss divided by contributions. The large contribution before the negative year does not change the two local percentages, but it changes how many monetary units the owner loses.
The money-weighted rate
For the stated annual dates, internal rate r satisfies −100 − 100 / (1 + r) + 189 / (1 + r)² = 0. The economically admissible solution in this model is approximately −3.7126% per year. The first contribution participates for two years and the second for one. This is a different object from the −1% TWR. State method and horizon together; an IRR value alone does not prove a unique solution for arbitrary cash flows.
Data requirements
You need valuations immediately around external movements or a transparent approximation rule. With only opening and closing balances, an exact time-weighted path with several contributions usually cannot be recovered. Transfers between assets inside the observed portfolio are not external owner contributions. A distribution retained inside the portfolio differs from money withdrawn outside it. Define the boundary beforehand so one dividend is not counted both in value and again as return.
Read the report without a percentage contest
Compare like with like: methods, dates, currency, expense treatment and distribution treatment. Do not call a worse money-weighted result proof of poor security selection; it may reflect the owner’s calendar. But a high TWR does not mean that a particular person earned the same monetary share. Keep the cash result and both percentage definitions beside each other when data allow.
The money-weighted rate is annual here because flows are separated by equal years. Put the same figures into monthly rows and the root refers to a month; arbitrary dates require a calendar convention and year basis. A two-year TWR can be annualized conditionally, but the label must say so and it does not change the actual sequence or cash result.