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

A portfolio manager observes that a stock index and a volatility index have a Pearson correlation of -0.80 over a calm period, and states that the correlation fully describes how the two behave together in a crisis. What is the best critique?

Pearson correlation is only a single linear summary estimated over a sample, so it may miss nonlinear and state-dependent dependence, such as stronger co-movement in stress. It is not a slope or causal effect, so a calm-period value cannot fully describe crisis behavior.

  1. ACorrelation of -0.80 implies that a 1% fall in the stock index causes an 0.80% rise in the volatility index
  2. BPearson correlation is a single linear summary and may not capture nonlinear or state-dependent dependence, such as stronger co-movement in stressed marketsCorrect
  3. CCorrelation is invalid for any two variables with different units
  4. DA negative correlation always means the two variables are statistically independent in the tails

Explanation

Pearson correlation measures average linear association over the sample and is not a regression slope or causal effect. Dependence can change with market conditions, so a calm-period estimate may not describe crisis behavior. Option A confuses correlation with beta; option C is wrong because correlation is unit-free.

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