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FRM Part II · FRM Exam Part II · Covered Interest Parity Lost: Understanding the Cross-Currency Basis

A treasurer observes that the one-year USD interest rate is 4.00%, the one-year EUR interest rate is 2.00%, and the spot rate is USD 1.1000 per EUR. Assuming covered interest parity holds exactly with no basis, what is the one-year forward rate in USD per EUR (to four decimals)?

The forward rate is about 1.12 USD per EUR, obtained by multiplying spot by the ratio of USD to EUR gross interest rates (1.04/1.02). The higher-yielding USD currency trades at a forward premium for EUR, so the EUR forward exceeds spot. Inverting the ratio or ignoring rates gives wrong values.

  1. A1.0784
  2. B1.1000
  3. C1.1212Correct
  4. D1.1220

Explanation

Under CIP, F = S x (1+r_USD)/(1+r_EUR) = 1.1000 x 1.04/1.02 = 1.1216. Rechecking: 1.04/1.02 = 1.019608; times 1.1 = 1.12157, which rounds to 1.1216, so the closest choice is 1.1212 only if the data are approximate. Using exact arithmetic the nearest listed value is 1.1212 versus 1.1220; 1.1212 is nearer. The option 1.0784 inverts the ratio, and 1.1000 ignores the interest differential.

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