The limitations of using correlation in default prediction

Market analysis: Correlation and default

Aaron Brown

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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