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

A risk manager compares two dependence measures for the returns of two assets. One asset's returns are transformed by a strictly increasing nonlinear function (for example, taking the exponential of returns), while the other is unchanged. Which statement is correct?

Spearman rank correlation is unchanged while Pearson correlation generally changes. A strictly increasing transformation preserves the ordering of observations, which is all rank correlation uses, but it alters the linear relationship that Pearson measures.

  1. ABoth Pearson correlation and Spearman rank correlation are unchanged
  2. BPearson correlation is unchanged, but Spearman rank correlation changes
  3. CSpearman rank correlation is unchanged, but Pearson correlation generally changesCorrect
  4. DBoth measures generally change because the marginal distribution changes

Explanation

Rank correlation depends only on the ordering of observations, and a strictly increasing transformation preserves ordering, so Spearman is unchanged. Pearson measures linear association and generally changes under nonlinear transformations. Option B reverses this.

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