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FRM Part II · FRM Exam Part II · Margin (Collateral) and Settlement

A bank settles FX trades through a PvP system and also bilaterally. Bilateral settlement for a given day covers 100 trades averaging USD 20 million each with a failure probability of 0.1% per trade, and failure causes loss of 100% of the principal paid in advance, though the loss is 50% of the principal in expectation in aggregate because of partial recoveries. Using the 50% loss and assuming independent trades each with the stated failure probability, what is the expected daily settlement loss?

Expected loss is 100 trades times USD 20 million times 0.1% failure probability times 50% loss given failure, which equals USD 1.0 million per day. Using full principal would double it to USD 2.0 million, but the stated expected loss severity is half the principal.

  1. AUSD 1.0 millionCorrect
  2. BUSD 2.0 million
  3. CUSD 0.5 million
  4. DUSD 10.0 million

Explanation

Expected loss per trade = 20m × 0.001 × 0.5 = 0.01m. Over 100 trades this is 1.0m, which is also the sum of expectations, so independence is not needed for the mean. USD 2.0m ignores the 50% loss. USD 0.5m halves it again. USD 10m multiplies by 10 erroneously.

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