Large Bank Examination Workshop February 2026

Tranche Losses and Correlation • The expected loss on a CDO tranche clearly depends on the default probabilities and recovery rates on the loans. But it also depends on the correlation or dependence among defaults. • Suppose that we own a 0-1% equity tranche, with a maturity of 5 years, and that all 100 mortgages in the pool have a probability of default of 0.2 (20%) in that period.

• Suppose that the default correlation among the mortgages is 1. This means that, if they default, they will all default together.

Source: This example is based on one in Morini, M., Understanding and Managing Model Risk: A Practical Guide for Quants, Traders and Validators, Chicheseter: Wiley, 2011.

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Tranche Losses and Correlation • The loss distribution on the 0-1% equity tranche is therefore:

ì í î

0 with probability 0.8 100 with probability 0.2

Loss 0%,1% =

• The expected loss on the tranche is 20 (per 100 nominal).

• Now suppose instead that the default correlation were 0. The probability of zero defaults over five years is , so the loss distribution on the 0-1% equity tranche is: 0.8 100 » 0

ì í î

0 with probability 0.0 100 with probability 1.0

Loss 0%,1% =

• The expected loss on the tranche is 100 (per 100 nominal).

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