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FRM Part II · FRM Exam Part II · Risk Mitigation

A bank's annual expected operational loss from an event type is USD 8 million, and its 99.9% annual loss quantile is USD 120 million. It considers a policy that pays losses above a USD 20 million per-event deductible, up to USD 60 million per event, costing USD 6 million a year. In a single-event year at the 99.9% quantile, the loss is USD 120 million from one event. What is the bank's retained loss in that scenario, and how does the policy affect the tail?

The bank retains USD 80 million. The insurer pays the loss above the USD 20 million deductible but only up to its USD 60 million per-event limit, so the bank bears the deductible plus the 60 million excess. The limit leaves large tail exposure from a single severe event.

  1. AUSD 20 million; the policy removes almost all tail risk
  2. BUSD 60 million; the policy halves the tail loss exactly because the limit is half of the loss
  3. CUSD 80 million; the per-event limit leaves the bank exposed above the cap, with the deductible also retainedCorrect
  4. DUSD 120 million; the policy has no effect on single events

Explanation

Insurer pays min(120 - 20, 60) = 60 million. Bank retains 120 - 60 = 80 million, being the 20 deductible plus 60 above the 80 cap. The per-event limit therefore leaves substantial tail exposure; 20 ignores the cap and 60 ignores the deductible.

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