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

A risk manager models two loss variables with heavy tails and a nonlinear but monotonic dependence. She wants a dependence measure that is invariant under strictly increasing transformations of each variable, such as taking logarithms of losses. Which measure fits, and what is a key consequence?

Spearman rank correlation fits, because it depends only on the copula and not on the marginal distributions, so strictly increasing transformations like logarithms leave it unchanged. Pearson correlation changes under nonlinear transformations and is sensitive to heavy-tailed marginals.

  1. APearson correlation, because it is unchanged by any monotonic transformation
  2. BSpearman rank correlation, because it depends only on the copula and not on the marginalsCorrect
  3. CCovariance, because it scales with the transformation
  4. DPearson correlation of squared returns, because it removes the sign

Explanation

Rank correlations such as Spearman and Kendall depend only on the copula, so they are unchanged by strictly increasing transformations of the variables. Pearson correlation changes under nonlinear transformations such as logs and also depends on the marginal distributions. Covariance is even less suitable since it is scale-dependent.

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