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Recognise the characteristic exposure profiles of the various derivative contracts and of combinations of them.

FRM® Part II · Credit Risk Measurement and Management · Future Value and Exposure · FRM2.CR.19.d

The idea

Each product has a characteristic profile. A plain interest rate swap starts at zero, rises to a peak in the first half of its life, then falls to zero at maturity. Diffusion dominates early and amortisation dominates late. In a simple model the exposure is proportional to the square root of t times (T − t), which peaks at one third of the life. An FX forward has no interim payments, so its exposure keeps rising to maturity. A cross-currency swap rises even more because of the final exchange of notional. A bought option has exposure equal to its value, while the seller has none once the premium is paid. A bond or loan gives the lender exposure of about the notional, and the borrower none. Combining trades produces profiles that blend these shapes, and offsetting positions cancel.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which exposure profile is typical of an uncollateralised plain vanilla interest rate swap?

  1. A steady rise through the life that reaches its maximum at the maturity dateWhy not: That is the profile of an FX forward, which has no interim payments to amortise it.
  2. A near-constant level close to the notional for the whole life of the contractWhy not: That is typical of a loan or bond held by the lender, not a swap.
  3. The highest level on day one, followed by a steady decline until the maturity dateWhy not: A par swap starts with zero value, so exposure builds up before it declines.
  4. A hump: zero at inception, a peak in the first half of the life, then back to zero at maturity - correct

Early on diffusion dominates and exposure builds; later, as payments are made and the remaining life shrinks, amortisation dominates and exposure falls to zero at maturity.

A harder one

A bank buys a five-year bond from a corporate. Which description fits the bank's exposure to the issuer, compared with a swap?

  1. A hump that peaks about one third of the way through the life and returns to zero at maturityWhy not: That is the profile of a swap; a bond's value is not a net, zero-start value.
  2. A profile that is zero at inception and grows with the square root of time like a forwardWhy not: A forward-like profile; a bond starts with exposure equal to its price.
  3. One-sided exposure near the bond value, about the notional, until principal is repaid - correct
  4. Two-sided exposure, in which the issuer also has exposure to the bankWhy not: The issuer has no claim on the bondholder, so the exposure is one-sided.

The lender is owed the notional and coupons, so its exposure starts near the bond value and stays high until repayment. The borrower has no exposure to the lender.

The hardest tier

In a simple model the expected exposure of a nine-year swap is proportional to sqrt(t) x (9 - t), with t in years. How does the exposure at year 3 compare with that at year 1?

  1. About 1.73 times higherWhy not: Uses diffusion alone, sqrt(3)/sqrt(1), and ignores amortisation.
  2. About 1.30 times higher - correct
  3. About 2.25 times higherWhy not: Scales exposure linearly in time, (3 x 6)/(1 x 8), missing the square root.
  4. About 25% lowerWhy not: Uses amortisation alone, 6/8, so treats the shorter remaining life as dominant.

Ratio = (sqrt(3) x 6)/(sqrt(1) x 8) = 10.39/8 = 1.30. Year 3 is one third of nine years, the peak of this profile.

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