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FRM Part I · FRM Exam Part I · Multivariate Random Variables

An analyst observes that the correlation between daily returns of two stocks is 0.80 in calm markets but the relationship becomes much stronger in a crisis. Which statement about correlation as a dependence measure is most accurate?

Correlation measures only linear dependence. It can miss nonlinear relationships and regime-dependent behavior such as stronger co-movement in crises. Zero correlation does not imply independence, and sample correlation is sensitive to outliers despite being standardized.

  1. ACorrelation captures any nonlinear dependence between two variables fully
  2. BA correlation of zero implies the two variables are statistically independent
  3. CCorrelation measures only linear dependence and may understate dependence that is nonlinear or varies across regimesCorrect
  4. DCorrelation is unaffected by outliers because it is standardized

Explanation

Correlation is a measure of linear association. Zero correlation does not imply independence, it does not capture nonlinear relationships, and it is sensitive to outliers and can change across market regimes.

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