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

An analyst studies daily equity correlations across many stock pairs over several years and plots the distribution of correlation estimates. Which description best matches the empirical finding on the shape of such correlation distributions, as discussed by Hull-type empirical studies of correlation?

Correlations are bounded between -1 and 1 and their empirical distribution is usually skewed, particularly when the average correlation is high. A normal distribution is therefore inappropriate because it is unbounded and symmetric.

  1. ACorrelations are normally distributed around zero with no bounds
  2. BCorrelations are bounded between -1 and 1 and the distribution is typically skewed, so a normal assumption is inappropriateCorrect
  3. CCorrelations are uniformly distributed between -1 and 1
  4. DCorrelations are always constant and show no dispersion over time

Explanation

Correlation is bounded by -1 and +1, so its distribution cannot be normal, and empirical distributions are typically skewed, especially when the mean is high. A normal distribution would put probability mass outside the permitted range. Uniform or constant correlation contradicts observed behavior.

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