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

A risk analyst reviews historical equity returns and notes that the correlation between two stock indices computed over calm periods is 0.35, while over crisis periods it is 0.75. Which description best characterizes this empirical observation?

Correlations typically rise during stressed markets, so the jump from 0.35 to 0.75 reflects state-dependent correlation rather than a stable relationship or sampling noise. Pearson correlation measures linear dependence and is not constant across market regimes.

  1. ACorrelation is stationary, so the difference is only sampling noise
  2. BCorrelations tend to rise in stressed markets, indicating correlation is state-dependentCorrect
  3. CCorrelation is constant but volatility changes, which alters the measured coefficient
  4. DCorrelation measures only nonlinear dependence, which grows in crises

Explanation

Empirical studies show correlations are not constant; they tend to increase during market stress or downturns. This is state dependence. Treating the difference as noise ignores the systematic pattern, and Pearson correlation captures linear, not nonlinear, dependence.

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