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

A risk team tests whether correlation breakdown is real by comparing correlations conditional on large market moves with unconditional correlations. Returns are bivariate normal with true constant correlation 0.50. They compute correlation using only observations where one market's return exceeded a high threshold. Which result is expected, and what does it imply?

Conditioning on extreme values of one variable truncates the sample and mechanically lowers the measured correlation even when true correlation is constant at 0.50. Apparent tail correlation changes can therefore be statistical artifacts, so tests of breakdown must adjust for this conditioning bias.

  1. AThe conditional correlation will be lower than 0.50 purely from truncation, so apparent breakdown in the tails can be a statistical artifact of conditioning on one variableCorrect
  2. BThe conditional correlation will equal 0.50 exactly, so conditioning is irrelevant
  3. CThe conditional correlation will be higher than 0.50, proving real contagion
  4. DThe conditional correlation will be undefined because normality is violated

Explanation

Selecting samples on the extreme values of one variable truncates its variance and mechanically biases the estimated correlation downward under constant-correlation normality. Thus conditional estimates must be interpreted carefully before inferring regime change. Observed higher stress correlations therefore need tests that adjust for this bias.

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