On this page
Compare two fictional sequences
Sequence A earns +20% then −20%; sequence B earns −20% then +20%. Both multiply initial wealth by 1.2×0.8 = 0.96. The multiplication is commutative for this no-flow endpoint calculation.
Retain the intermediate values
From initial index 100, A follows 100→120→96 while B follows 100→80→96. One first reaches a higher peak and the other first reaches a lower wealth level. An endpoint rate does not contain those path differences.
| Sequence | After first period | Final |
|---|---|---|
| A: +20%, −20% | 120 | 96 |
| B: −20%, +20% | 80 | 96 |
Understand why cash-flow timing changes the comparison
If an owner contributes or withdraws between the periods, the amount exposed to each return can differ. The commutative product still describes linked subperiod rates, but it no longer suffices to determine the investor’s ending money without the cash-flow schedule.
Use the path for its own question
Intermediate wealth matters for drawdowns, funding needs and decisions made between dates. A reordered fictional series does not prove the same investment experience or risk. Report the endpoint and path without treating either as a complete performance appraisal.