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Explain how correlation helped bring about the 2007-2009 global financial crisis.

FRM® Part II · Market Risk Measurement and Management · Correlation Basics: Definitions, Applications, and Terminology · FRM2.MR.8.b

The idea

Correlation helped cause the 2007-2009 crisis through the pricing and rating of structured credit. Mortgage-backed securities and CDOs were priced mainly with the Gaussian copula, which ties the default times of the underlying loans together through a correlation input. That input was low, held constant and calibrated on a calm history of regionally diverse mortgages. When US house prices fell across the whole country, defaults became strongly correlated and losses reached tranches thought to be safe. Higher default correlation raises the value of the equity tranche and lowers the value of senior tranches, because losses cluster in bad states instead of being spread thinly. Models that understated correlation therefore understated senior tranche risk, and those tranches carried AAA ratings. Exam point: expected pool loss does not depend on correlation, but tranche losses do, and the senior tranche is short correlation.

A practice question

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

As US house prices fell from 2006 onward, what happened to the correlation of defaults across mortgages and mortgage-backed securities?

  1. It fell, because geographic diversification of the pools began to take effect.Why not: Reverses the observed outcome; diversification across regions failed when prices fell nationwide.
  2. It stayed unchanged, because correlation is a fixed property of a pool.Why not: Correlation is not constant; it rises in stress, which is the point of correlation risk.
  3. It became negative, because defaults in one region were offset by gains elsewhere.Why not: There were no offsetting gains; losses were broad and simultaneous.
  4. It rose sharply, because borrowers in all regions were hit by the same national decline. - correct

Default correlation increased in the downturn as house prices fell almost everywhere. Models calibrated to a low correlation understated the probability of many simultaneous defaults.

A harder one

A bank holds a senior (AAA) CDO tranche, and the market-implied default correlation of the underlying pool rises from 20% to 60%. What is the effect on the value of its senior tranche and on an equity tranche of the same CDO?

  1. The senior tranche loses value and the equity tranche gains value. - correct
  2. Both tranches lose value, because correlated defaults add to the expected pool loss.Why not: Correlation does not change expected pool loss; it redistributes losses across tranches.
  3. The senior tranche gains value and the equity tranche loses value.Why not: Reverses the signs: higher correlation makes many-default scenarios likelier, which hurts the senior tranche.
  4. Neither changes, because the attachment points are fixed.Why not: Attachment points are fixed, but the probability that losses reach them depends on correlation.

Higher correlation fattens both tails of the pool loss distribution. The equity tranche gains because losses are bunched into fewer scenarios, and the senior tranche loses because the many-default scenarios become more likely.

The hardest tier

In 2006 a bank values its CDO tranches with a constant default correlation of 0.20, but the correlation that prevailed in the 2008 stress was much higher. Relative to a model using the higher correlation, the 2006 model:

  1. Understated expected losses on both senior and equity tranches.Why not: Applies one direction to both; higher correlation lowers the expected loss of the equity tranche.
  2. Overstated expected losses on senior tranches and understated them on equity tranches.Why not: Reverses the effect: low correlation makes senior losses look too unlikely and equity losses too likely.
  3. Left tranche expected losses unchanged, but overstated their volatility.Why not: Pool expected loss is independent of correlation, but expected losses of individual tranches are not.
  4. Understated senior tranche losses and overstated equity tranche losses. - correct

Lower correlation puts probability on moderate loss scenarios, which makes equity expected loss too high and senior expected loss too low. A model with too low correlation therefore misprices both ends.

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