Exam 9: Diversification depends on dependence, not only marginal risk
Aggregating risks requires a dependence assumption. Summing stand-alone capital numbers ignores diversification, while assuming independence can understate joint stress. Correlation alone may also miss tail dependence.
Worked example or practice scenario
Two toy zero-mean risks each have standard deviation 10. With correlation zero, the standard deviation of their sum is √200≈14.14. With correlation .8, it is √360≈18.97. Summing standard deviations to 20 is a different limiting assumption.
Try this next
Write the covariance term explicitly. Then describe a common catastrophe or market factor that could alter dependence during stress. Do not call a standard-deviation calculation a complete regulatory capital model.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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