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FRM Part II · FRM Exam Part II · The US Dollar Shortage in Global Banking and the International Policy Response

A foreign central bank draws USD 2,000 million from the Fed under a swap line at a spot rate of 1.25 USD per unit of its local currency (LC), paying the Fed a rate of 1.00% for a 3-month term. At maturity the spot rate is 1.40 USD per LC. Assuming the swap reverses at the initial rate, how many LC does the central bank pay the Fed back as principal, and what is the interest in USD?

The central bank returns LC 1,600 million, which is USD 2,000 million divided by the initial rate of 1.25, and pays USD 5.0 million interest (1% for a quarter). The swap reverses at the original rate, so the later move to 1.40 does not change principal.

  1. ALC 1,428.6 million principal; USD 5.0 million interest
  2. BLC 1,600.0 million principal; USD 5.0 million interestCorrect
  3. CLC 1,600.0 million principal; USD 20.0 million interest
  4. DLC 1,428.6 million principal; USD 20.0 million interest

Explanation

Principal in LC is 2,000/1.25 = 1,600 million, and the reversal uses the initial rate, so the later spot of 1.40 is irrelevant (this is why the Fed has no exchange-rate risk). Interest is 2,000 x 1.00% x 3/12 = USD 5.0 million. Using 1.40 gives 1,428.6, the wrong-rate error; failing to scale for 3 months gives 20.

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