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

An analyst ranks monthly returns of two funds and finds that the ranks of Fund A and Fund B are perfectly aligned, although the relationship between the actual returns is strongly convex. Which conclusion is correct?

Spearman rank correlation equals +1 while Pearson is likely below +1. Perfectly aligned ranks indicate a perfectly monotonic relationship, which rank measures capture fully, but a convex relationship is not linear, so Pearson understates the dependence.

  1. ASpearman rank correlation is +1 while Pearson correlation is likely below +1Correct
  2. BPearson correlation is +1 while Spearman rank correlation is below +1
  3. CBoth Pearson and Spearman correlations must equal +1
  4. DKendall's tau is +1 but Spearman must be below +1

Explanation

Perfectly aligned ranks imply a monotonic relationship, so Spearman and Kendall's tau both equal +1. Pearson measures only linear association, so a convex monotonic relationship gives Pearson below 1. Option D is wrong because Spearman is also +1 under perfect rank agreement.

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