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FRM Part II · FRM Exam Part II · VaR Mapping

A US bank is long a 1-year forward contract to buy GBP 10 million. The spot rate is USD 1.30 per GBP, the 1-year GBP interest rate is 3% and the 1-year USD interest rate is 4% (annual compounding). When the forward is mapped to risk factors, what is the USD-equivalent present value of the long GBP zero-coupon bond leg, which is the position exposed to the GBP/USD spot risk factor?

The long GBP leg equals GBP 10 million discounted at the GBP rate of 3%, giving GBP 9.7087 million, then converted at spot 1.30 to about USD 12.62 million. Discounting must use the foreign rate before conversion at spot.

  1. AUSD 13.00 million
  2. BUSD 12.50 million
  3. CUSD 12.62 millionCorrect
  4. DUSD 13.13 million

Explanation

The foreign leg is the PV of GBP 10m at the GBP rate: 10/1.03 = GBP 9.7087m. Converted at spot 1.30 this gives USD 12.62m. Using USD 13.00m ignores discounting. Discounting 13.00m at the USD rate gives 12.50m, which uses the wrong rate. USD 13.13m is the undiscounted forward-rate amount payable at maturity (1.3126 x 10m).

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