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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 observes that the average pairwise correlation among equities is high, around 0.75, in a stressed period. Which statement best describes the likely skewness of the cross-sectional distribution of pairwise correlations?

The distribution is negatively skewed. When the average correlation is high, values are squeezed against the upper bound of 1, so the long tail extends toward lower correlations rather than higher ones.

  1. APositively skewed, with a long right tail beyond 0.75
  2. BNegatively skewed, because values cannot exceed 1 and the mass piles against that upper boundCorrect
  3. CSymmetric, because averages near 0.75 imply normality
  4. DSkewness is undefined for bounded variables

Explanation

With the mean near the upper bound of 1, observations cluster close to 1 and the tail extends toward lower values, giving negative skew. A positive-skew tail to the right is impossible beyond 1. Symmetry is not implied, and skewness is defined for bounded variables.

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