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

Two returns X and Y have Cov(X,Y) = 0.0018, standard deviation of X equal to 0.06, and standard deviation of Y equal to 0.05. What is the Pearson correlation, and what does it say about independence if the value were exactly zero?

The correlation is 0.60, computed as 0.0018 divided by the product 0.06 times 0.05, which is 0.003. A zero correlation would imply independence only if the variables were jointly normally distributed, not in general.

  1. A0.60; zero would prove independence
  2. B0.60; zero would not prove independence unless the variables are jointly normalCorrect
  3. C0.30; zero would prove independence
  4. D0.036; zero would not prove independence

Explanation

Correlation = 0.0018 / (0.06 x 0.05) = 0.0018 / 0.003 = 0.60. Zero correlation implies independence only under joint normality, not in general. Option D multiplies rather than divides.

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