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FRM Part I · FRM Exam Part I · Anatomy of the Great Financial Crisis of 2007-2009

A subprime mortgage pool of 1,000 loans backs a securitization with a 20% subordination below the senior tranche (the senior tranche is protected by 20% of pool principal in junior tranches). Each loan has equal principal and recovery is 50% of principal on default. Assuming losses are applied from the bottom up, what is the minimum number of loan defaults that causes the senior tranche to suffer its first loss?

The senior tranche first takes a loss when 400 loans default. Subordination absorbs 20% of pool principal, and each default loses only 50% of a loan after recovery, so N x 0.5 / 1,000 = 20% gives N = 400. Ignoring recovery would wrongly give 200.

  1. A200 defaults
  2. B400 defaultsCorrect
  3. C500 defaults
  4. D800 defaults

Explanation

Subordination of 20% of pool means losses must exceed 20% of principal. Loss per default is 50% of one loan's principal, so pool loss is defaults x 0.5 / 1,000. Setting 0.5 x N / 1,000 = 0.20 gives N = 400. Defaults beyond 400 hit the senior tranche. The 200 answer ignores the 50% recovery.

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