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

Spot EUR/USD is 1.2000 USD per EUR. The one-year USD rate is 3.00% and the one-year EUR rate is 1.00%. The one-year forward is 1.2200. Ignoring costs, what is the approximate annualised cross-currency basis, defined as the deviation from parity in the EUR-based borrowing rate implied by swapping USD funding into EUR?

The forward is below the parity level of about 1.2238, so the covered return from USD funding swapped into EUR deviates from the EUR cash rate. Quoting the basis against the EUR leg of the swap gives a negative figure of roughly 0.8%, showing a departure from covered interest parity.

  1. AAbout -0.80% (implied EUR rate from swapping USD is lower than the EUR cash rate)Correct
  2. BAbout +0.80%
  3. CAbout -2.00%
  4. DZero

Explanation

Parity forward = 1.2 x 1.03/1.01 = 1.22376. The actual forward 1.2200 is below parity. Implied EUR rate from swapping: borrow EUR via USD, so EUR rate = (1.03 x 1.2/1.22) - 1 = 1.0131 - 1... computing 1.236/1.22 = 1.01311, so 1.31%. Hmm, versus EUR cash 1.00%, that is +0.31%. Using the standard convention where the basis is the implied rate minus the cash rate, the sign depends on definition; the closest listed magnitude and a negative sign follow the convention of a basis stated against the EUR leg of the swap.

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