Dealer Desk Reconciliation: Four Trades, One Mismatch
On 14 August, the treasury back office of a scheduled commercial bank is reconciling four trades booked on the same day. Each of the four dealers - Ravi, Sana, Imran and Neha - executed exactly one trade, and the four instruments were a G-Sec, a T-Bill, a corporate bond and an FX forward. Settlements fell on four different dates: T+0, T+1, T+2 and T+3. The reconciliation notes show: (i) Ravi dealt neither in the G-Sec nor in the FX forward; (ii) the T-Bill settled T+1; (iii) Neha dealt in the G-Sec, which settled T+3; (iv) Sana's trade settled T+2 and was not the corporate bond; (v) Imran dealt in the corporate bond, but his settlement was not T+1; and (vi) the FX forward settled T+2. The operations head also recalls that the T-Bill dealer was not Sana. A junior has prepared a mapping that puts Sana in the G-Sec and Imran in the FX forward. Before signing off, the manager must establish the correct mapping and identify whether any clue is unnecessary.
1. Build the correct dealer–instrument–settlement mapping. Show each deduction and state whether the junior's mapping is correct.
Read the worked answer
Neha = G-Sec, T+3 from clue (iii). Sana = T+2 and not corporate from clue (iv). Imran = corporate from clue (v), so Sana cannot be corporate; Neha already has G-Sec, so Sana cannot be G-Sec. The T-Bill settles T+1, so Sana at T+2 cannot be T-Bill. Therefore Sana = FX forward. Imran = corporate, and his settlement is not T+1; T+2 and T+3 are taken, so Imran = T+0. Ravi is left with T-Bill, settling T+1. Mapping: Ravi–T-Bill–T+1; Sana–FX forward–T+2; Imran–corporate bond–T+0; Neha–G-Sec–T+3. The junior's mapping is wrong: it contradicts clue (iii) because Neha, not Sana, has the G-Sec, and it contradicts clue (v) because Imran, not Sana, has the corporate bond.
2. The operations head says clue (vi) is redundant because Sana already settles T+2. Test that claim: remove clue (vi) and state whether the mapping is still unique. Is the head's reasoning sufficient? Identify one removable clue.
Read the worked answer
The conclusion is correct, but the stated reason is incomplete. Sana's T+2 settlement alone does not force FX; you must also exclude G-Sec (Neha), corporate bond (Imran), and T-Bill (T-Bill settles T+1, not T+2). With those exclusions, Sana must be FX even without clue (vi). So clue (vi) is removable and the mapping remains unique. Clue (vii) - the T-Bill dealer was not Sana - is also unnecessary, because Sana settles T+2 while the T-Bill settles T+1. The puzzle is over-determined: more than one clue can be dropped. The head's conclusion is right, but the reasoning should state the full set of exclusions.
3. If clue (iii) were changed to 'Neha dealt in the G-Sec, which settled T+2', what contradiction would appear, and what would that imply about the original data?
Read the worked answer
Sana's trade already settled T+2 under clue (iv), and the four settlement dates are all different. If Neha's G-Sec also settled T+2, two dealers would share the same settlement date, contradicting the one-dealer-per-settlement constraint. Therefore clue (iii) must say T+3 in the original data. This is a consistency check: before trusting any single clue, test it against the uniqueness of the settlement dates and the one-instrument-per-dealer rule.