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

A risk team computes the correlation between two assets using only observations from days when the market index moved by more than 2% in absolute terms. They find a correlation of 0.80, while the full-sample correlation is 0.50. A colleague concludes that correlation truly jumps in turbulent markets. Which comment best reflects the statistical concern?

Selecting only days with large market moves is conditioning on extreme values, which can bias estimated correlation upward even when true correlation is unchanged. The observed jump from 0.50 to 0.80 may therefore partly be a statistical artifact, so heteroskedasticity-adjusted tests are needed before concluding correlation truly rises.

1. AConditioning on high-volatility observations can bias the estimated correlation upward even if the true correlation is constant, so the jump may be partly an artifactCorrect
2. BConditioning on large index moves always biases estimated correlation downward, so the true jump is even larger
3. CSub-sample correlations cannot differ from full-sample correlation unless the data are non-stationary
4. DThe result is invalid because correlation cannot be computed on a truncated sample under any circumstances