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

Which statement about the Pearson correlation coefficient as a measure of dependence in financial applications is most accurate?

Pearson correlation measures only linear dependence, so two variables can be strongly nonlinearly dependent and still show a correlation near zero. It also does not capture tail dependence, is sensitive to outliers, and need not equal one under perfect nonlinear dependence.

  1. AIt captures only linear dependence and can be near zero even when variables are strongly nonlinearly dependentCorrect
  2. BIt captures all forms of dependence, including tail dependence
  3. CIt is unaffected by outliers in the data
  4. DIt always equals one when two variables are perfectly dependent

Explanation

Pearson correlation measures linear association. Variables such as X and X squared can be strongly dependent yet have near zero correlation. It is sensitive to outliers, and perfect nonlinear dependence need not give a correlation of one.

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