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Distinguish between expected exposure, expected positive exposure, current exposure and peak exposure.

FRM® Part II · Credit Risk Measurement and Management · The Evolution of Stress Testing Counterparty Exposures · FRM2.CR.21.a

The idea

Four measures describe how much a derivatives counterparty could owe you. Current exposure is today's replacement cost. It is the larger of the netting set's mark-to-market value and zero, because you lose only when the value is positive to you. Expected exposure, EE(t), is the average of the positive part of portfolio value at a future date t across simulated scenarios. Expected positive exposure, EPE, is the time average of the EE profile over a horizon, usually one year, and is used for capital and pricing. Peak exposure, also called potential future exposure, is a high percentile of the exposure distribution at a given date, such as the 95th or 99th, and is used for limits. The usual mistake is taking EE as the expected MTM, which can be zero, instead of the expected value of its positive part. Suppose the MTM is normal with mean zero and standard deviation σ. The expected exposure is then EE = 0.399 × σ. The 95% peak exposure is Peak = 1.645 × σ, which is far larger because it looks at the tail rather than the average.

Formulas

Current exposure of a netting set

CE = max(MTM, 0)

MTM
the netting set's mark-to-market value today, after netting all its trades

Net first, then floor at zero, under an enforceable netting agreement. Summing only the positive trades ignores netting.

Expected exposure when MTM is normal with mean zero

EE = 0.399 × σ

σ
the standard deviation of the value at that date

EE is the mean of the positive part of MTM, not the mean MTM, which is zero here. Using 0.798 × σ counts negative values as exposure.

Peak exposure at 95% when MTM is normal with mean zero

PFE = 1.645 × σ

σ
the standard deviation of the MTM at the future date

A one-tailed percentile at a single date, used for limits. Using 1.96 gives the 97.5% level, not the 95%.

A practice question

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

Which statement defines current exposure to a derivatives counterparty?

  1. The larger of the netting set's mark-to-market value today and zero - correct
  2. The average of the positive part of portfolio value at a future date across simulated scenariosWhy not: Describes expected exposure at a future date, not the replacement cost today.
  3. A high percentile, such as the 99th, of the distribution of portfolio value at a future dateWhy not: Describes peak (potential future) exposure, a future percentile measure rather than today's value.
  4. The time average of the expected exposure profile over the first yearWhy not: Describes expected positive exposure (EPE), a time average rather than today's replacement cost.

Current exposure is what would be lost today if the counterparty defaulted and there were no recovery: max(MTM of the netting set, 0). EE, EPE and peak exposure all look forward.

A harder one

A 1-year expected exposure profile for a counterparty, taken at equally spaced quarter-ends, is USD 2.0, 3.5, 4.5 and 2.0 million; today's exposure is USD 1.0 million. Taking EPE as the simple average of the four quarterly EE values, what is EPE?

  1. USD 4.5 millionWhy not: Uses the maximum of the EE profile (peak EE) instead of its time average.
  2. USD 2.0 millionWhy not: Takes the last EE value instead of averaging the profile.
  3. USD 3.0 million - correct
  4. USD 2.6 millionWhy not: Adds today's USD 1.0 million as a fifth equally weighted point: (1.0 + 2.0 + 3.5 + 4.5 + 2.0) / 5.

EPE = (2.0 + 3.5 + 4.5 + 2.0) / 4 = 3.0. EPE is the time average of EE, so it is below the maximum EE and does not include today's current exposure as a data point.

The hardest tier

A bank compares the expected exposure profiles of a 5-year interest rate swap and a 5-year FX forward, both at inception with zero value. Which statement is most accurate?

  1. Both profiles keep rising until maturity because the volatility of the market factors keeps growing with time and nothing offsets that growthWhy not: Ignores amortisation on the swap: as payments are exchanged, remaining exposure falls.
  2. The forward's expected exposure tends to keep rising toward maturity, while the swap's rises and then falls as remaining payments shrink, giving a hump - correct
  3. The swap's expected exposure is largest at inception, when the notional at risk is largestWhy not: Confuses notional with exposure; a swap starts at zero value and exposure builds as rates move.
  4. Both profiles have zero expected exposure throughout because their value at inception is zeroWhy not: Treats a zero starting value as zero future exposure; future MTM is random and its positive part is not zero.

Diffusion makes exposure grow with time, but a swap amortises as cash flows are settled, so its profile humps and declines. A forward has a single final payment and no amortisation.

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