The limitations of using correlation in default prediction
Correlation as a concept has value when it comes to hedging risk, but users must also recognise its limitations in predicting the likelihood of outlier events.
Suppose you have a portfolio of 11 bonds, each with a 10% probability of default, and the defaults are uncorrelated. What is the probability of zero defaults; one default; or all 11 defaulting?
If you are careless, you’ll answer 0.911 = 31% for zero, 11 x 0.910 x 0.1 = 38% for one, and 0.111 = 0.000000001% for 10. These computations are correct if the defaults are independent events. But that is not what uncorrelated means. Two events are uncorrelated if the probability of both occurring is equal
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