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

A risk manager states that because two assets have a Pearson correlation of zero, they must be independent, so tail losses will not occur together. Which critique is most accurate?

The statement is flawed because Pearson correlation measures only linear dependence. Zero correlation implies independence only for jointly normal variables. Nonlinear relationships and tail dependence can exist with zero correlation, so tail losses may still occur together.

  1. ACorrect, because zero correlation implies independence for all distributions
  2. BIncorrect, because zero correlation implies perfect negative dependence
  3. CIncorrect, because Pearson correlation measures only linear dependence, so nonlinear or tail dependence can exist despite zero correlationCorrect
  4. DCorrect, provided both assets have equal volatility

Explanation

Zero correlation implies independence only in special cases such as joint normality. Pearson correlation captures only linear association, so for example Y=X² with symmetric X has zero correlation yet is fully dependent. Tail dependence can therefore be present.

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