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FRM Part II · FRM Exam Part II · Derivatives

A risk manager computes the expected exposure profile of a portfolio of interest rate swaps with a counterparty over a ten-year horizon. The profile rises initially, peaks around years three to four, then declines to zero at maturity. Which explanation best accounts for this shape?

The hump arises from two competing effects. Initially, growing uncertainty in rates (diffusion) raises potential exposure, but as payments are made, fewer cash flows remain (amortisation) and exposure falls to zero at maturity. Default probability is separate from the exposure profile.

  1. ADefault probability falls over time, which lowers exposure in later years
  2. BEarly on, uncertainty in market variables grows with time, but later the amortisation effect from remaining payments being fewer dominatesCorrect
  3. CThe swap notional amortises linearly from inception, so exposure only declines
  4. DCollateral thresholds increase steadily in later years, reducing exposure

Explanation

Exposure on a swap reflects two competing forces: the diffusion effect, where rate uncertainty widens with time, and the amortisation effect, where fewer remaining cash flows reduce the value at risk. Diffusion dominates early and amortisation later, giving a hump. Default probability does not enter an exposure profile.

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