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

A CDO's mezzanine tranche is backed by a pool of BBB-rated subprime MBS tranches. Assume each underlying asset defaults with probability 10% over the horizon, and the CDO tranche suffers a loss only if at least two of three equally weighted assets default. Under independence, the probability of tranche loss is 2.8%. If defaults become perfectly correlated (all or none), what is the probability of tranche loss, and what does this illustrate?

With perfect correlation the three assets default together, so the tranche loss probability equals the single-asset default probability of 10%, versus 2.8% under independence. This shows that underestimating default correlation badly understated the risk of mezzanine CDO tranches.

  1. A10%; correlation assumptions can greatly understate risk of tranches that depend on joint defaultsCorrect
  2. B2.8%; correlation does not affect tranche risk
  3. C0.1%; higher correlation lowers the risk of mezzanine tranches
  4. D30%; defaults add across assets

Explanation

Check independence: P(2)=3(0.01)(0.9)=0.027 and P(3)=0.001, total 0.028. With perfect correlation, either all three default (prob 10%) or none do, so tranche loss probability is 10%. This shows that assuming low correlation understated the risk of tranches sensitive to joint defaults, as happened in the crisis when housing defaults became highly correlated.

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