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Locate the owner movement
The portfolio starts at 100. Immediately before a 90 deposit it is worth 110; immediately after, it is worth 200. It ends at 180. These before/after values distinguish investment changes from new capital.
Calculate the subperiod rates
The first rate is 110/100−1 = 10%. The second is 180/200−1 = −10%. Link them as 1.10×0.90−1 = −1%. The time-weighted result does not include the deposit as a return.
| Interval | Starting base | Ending value | Return |
|---|---|---|---|
| Before transfer | 100 | 110 | 10% |
| After transfer | 200 | 180 | −10% |
Reconcile the money change separately
Ending wealth 180 minus initial capital 100 minus deposit 90 gives a money loss of 10. That amount and the −1% linked rate describe different objects. The larger capital was exposed during the negative-return subperiod.
Do not annualize without durations
The case supplies two measured intervals but does not label their lengths. The cumulative time-weighted rate is defined. An annual equivalent requires actual durations or an explicit equal-period frequency assumption.