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FRM Part II · FRM Exam Part II · Correlation Basics: Definitions, Applications, and Terminology

Two assets have returns that are jointly driven by a common shock only in extreme market sell-offs, while in normal times they are nearly unrelated. A risk manager estimates a full-sample Pearson correlation of 0.15 and uses it in a Gaussian-based portfolio VaR. What is the main weakness of this approach?

The weakness is that one linear correlation, averaged over all periods, can miss dependence concentrated in the tails. A Gaussian structure has no tail dependence, so the probability of joint extreme losses and portfolio VaR are understated. Copulas with tail dependence or stressed correlations would capture this better.

  1. APearson correlation is always biased upward in large samples
  2. BA single linear correlation can understate tail dependence, so joint extreme losses are underestimatedCorrect
  3. CGaussian models overstate diversification only when correlation is negative
  4. DPearson correlation cannot be computed when returns are not normal

Explanation

A full-sample Pearson coefficient averages over the whole distribution and is dominated by normal periods. A Gaussian dependence structure has no tail dependence, so joint extreme losses are understated. Pearson can be computed for any returns with finite variance, and is not systematically biased upward.

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