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FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

A portfolio manager observes that during a sharp market sell-off, the correlation between two equity indices rose from 0.40 to 0.75, while the volatility of each index doubled. She concludes that correlation and volatility are related. Which statement best describes the empirical relationship?

Empirically, correlation is positively related to volatility: in high-volatility regimes, particularly sell-offs, correlations rise. Correlation is normalized by volatilities, so no mechanical inverse relation exists. This is why diversification benefits tend to shrink exactly when markets are most turbulent.

  1. ACorrelation tends to be positively related to volatility, so higher-volatility regimes tend to have higher correlationsCorrect
  2. BCorrelation is unrelated to volatility because volatility is a scale effect
  3. CCorrelation tends to fall when volatility rises because dispersion increases
  4. DCorrelation and volatility are mechanically inversely related through the covariance formula

Explanation

Empirical evidence shows that correlations are higher in high-volatility regimes, especially in down markets. The covariance formula does not mechanically force an inverse link, because correlation is already normalized by volatilities. Hence the claim of no relationship or a negative one is inconsistent with the data.

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