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FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

A risk manager notes that the sample distribution of pairwise equity correlations in a stress year is clustered near 0.8 with a long tail toward lower values. How is this distribution best described, and what is the implication for using a single average correlation?

The distribution is negatively skewed: most pairs sit near 0.8 with a long lower tail, pulling the mean below the mode. A single average correlation therefore understates how highly correlated the typical pair is and hides dispersion.

  1. APositively skewed; the average overstates low-correlation pairs
  2. BNegatively skewed; the mean is below the mode so the average understates how many pairs are highly correlatedCorrect
  3. CSymmetric; the average fully describes the distribution
  4. DUniform; every correlation level is equally likely

Explanation

A cluster near the upper end with a long tail to lower values is negative skew, pulling the mean below the mode. A single average therefore understates the typical high-correlation pair and hides dispersion.

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