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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 over a long sample. Which conclusion is most appropriate?

Zero Pearson correlation means no linear relationship, but nonlinear dependence can still exist. Independence implies zero correlation, but zero correlation does not imply independence, because Pearson's measure 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 fall in value at the same time
  4. DThe covariance must be equal to one

Explanation

Pearson correlation measures only linear dependence. Zero correlation does not imply independence, since variables such as X and X^2 (with X symmetric about zero) have zero correlation yet are fully dependent. Independence implies zero correlation, but the reverse does not hold.

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