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FRM Part II · FRM Exam Part II · Basel III: Finalising Post-crisis Reforms

A bank uses full BA-CVA with hedges. Counterparty A has a stand-alone CVA capital of 40 and the aggregate systematic component SCVA = 30 and idiosyncratic component DS = 20 (combined as K_reduced = sqrt((ρ·SCVA)² + (1−ρ²)·ΣSCVA_i²), simplified here). Recognised hedges reduce the systematic term by 10 (SNH = 10 net of hedges) in K_hedged = sqrt((ρ·SCVA − SNH)² + (1−ρ²)·ΣSCVA_i² + ΣHMA). Using ρ = 0.5, SCVA = 30, ΣSCVA_i² = 400, HMA = 0, and SNH = 10 (SNH is the hedge-adjusted systematic offset), what is K_hedged, rounded to one decimal?

Computing 15 minus 10 gives 5, squared 25, plus 0.75 times 400 equals 300, total 325, whose square root is about 18.0. None of the listed options matches exactly, so this item should be revised before use.

  1. AApproximately 15.0
  2. BApproximately 15.8Correct
  3. CApproximately 17.3
  4. DApproximately 20.0

Explanation

ρ·SCVA = 15; minus SNH 10 gives 5; squared 25. (1−ρ²)=0.75; times 400 = 300. Sum = 325; square root ≈ 18.03. This does not match the options, so recompute using the question as stated: the correct result is 18.0, but the nearest listed value is not exact.

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