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

A risk analyst compares two measures of dependence between the returns of two assets. Which statement about Pearson correlation is correct?

Pearson correlation captures only linear dependence, so two variables can be strongly related in a nonlinear way, such as Y equal to X squared with symmetric X, and still show a correlation near zero.

  1. AIt captures any form of dependence, including nonlinear relationships, between two variables
  2. BIt measures only the strength of linear dependence and can be near zero even when the variables are strongly dependentCorrect
  3. CIt is always equal to 1 if one variable is a deterministic function of the other
  4. DIt is unaffected by outliers because it is standardized by the standard deviations

Explanation

Pearson correlation measures linear association only. A variable such as Y = X^2 with X symmetric around zero is perfectly dependent on X yet has zero correlation. Deterministic nonlinear functions therefore need not give a correlation of 1, and outliers can distort the estimate.

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