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

A risk analyst states that two assets have a Pearson correlation of zero based on 5 years of monthly returns. Which conclusion is most appropriate?

Zero Pearson correlation means there is no linear relationship, but nonlinear dependence may still exist. Independence implies zero correlation, yet zero correlation does not imply independence, because correlation captures only linear association between the variables.

  1. AThe assets are statistically independent
  2. BThere is no linear relationship, but a nonlinear dependence may still existCorrect
  3. CThe assets will never move in the same direction
  4. DThe covariance of the assets must be one

Explanation

Pearson correlation measures only linear dependence. Zero correlation does not imply independence, since a nonlinear relationship (for example Y = X squared with symmetric X) can give zero correlation. Independence implies zero correlation, but not the reverse.

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