On this page
Calculate the gain-first path
Start with 100. A +20% return raises it to 120. Deposit another 100, creating base 220. A −20% return then produces final wealth 176. Total owner contributions were 200, so the money change above contributions is −24.
Calculate the loss-first path
Start with 100. A −20% return reduces it to 80. Deposit another 100, creating base 180. A +20% return then produces final wealth 216. The money change above contributions is +16.
| Path | Before deposit | After deposit | Final wealth |
|---|---|---|---|
| Gain then loss | 120 | 220 | 176 |
| Loss then gain | 80 | 180 | 216 |
Keep the linked rate separate
The two subperiod return factors multiply to 0.96 in either order, so both time-weighted cumulative rates are −4%. They do not determine the same ending money once the contribution is included. The new contribution is exposed only to the second return.
Avoid assigning causation from the rate alone
This is a counterexample to equating equal linked rates with equal investor wealth. It does not establish who controlled the cash-flow timing or whether any timing decision was informed. Describe the supplied schedule and its arithmetic before judging the decision.