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

A risk manager wants a dependence measure that is unchanged when each variable is transformed by a strictly increasing nonlinear function, such as taking logarithms of prices. Which measure has this property?

Spearman rank correlation is unchanged by strictly increasing transformations because it uses only the ranks of the data. Pearson correlation is invariant only to linear changes, so applying logarithms or other nonlinear monotone transforms can alter it, as can covariance and regression beta.

  1. APearson correlation coefficient
  2. BCovariance
  3. CSpearman rank correlationCorrect
  4. DBeta from a linear regression

Explanation

Rank correlations such as Spearman depend only on the ordering of observations, and strictly increasing transformations preserve ordering, so they are invariant. Pearson correlation is invariant only to linear transformations, so a log transform generally changes it. Covariance and regression beta also change with scaling and nonlinear transformation.

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