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
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