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

An analyst estimates equity correlation using only days on which the market fell sharply (market return below its 5th percentile) and finds a correlation of 0.75 between two stocks, versus 0.50 using all days. The analyst concludes that correlation rises in bear markets. Which statement best evaluates this conclusion?

The conclusion is questionable because conditioning on extreme market moves mechanically raises measured correlation even when the true correlation is constant. Selecting only large-move days biases the sample, so the higher figure cannot alone prove that correlation truly increases in bear markets.

  1. AIt is valid, because conditioning on extreme returns removes all estimation bias
  2. BIt is invalid, because correlation can never differ between subsamples
  3. CIt is valid only if the stocks are bond-like, since equity correlation is constant
  4. DIt is questionable, because conditioning on extreme market moves truncates the sample and mechanically inflates measured correlation even when the true correlation is constantCorrect

Explanation

Selecting observations on the basis of extreme values of a variable creates a conditioning (truncation) bias; sample correlation conditional on high volatility rises even under a constant-correlation bivariate normal model. So the 0.75 does not by itself prove true correlation breakdown. Correlation can differ across subsamples, so the claim of impossibility is wrong.

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