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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 compares two correlation series for equity pairs. Series X has a speed of mean reversion of 0.10 per year, and Series Y has 0.90 per year. Both have the same long-run mean. Which conclusion is correct?

Series Y reverts faster. A higher speed of mean reversion means deviations from the long-run mean decay more quickly, so Y's 0.90 pulls correlation back much sooner than X's 0.10, even though both share the same long-run mean.

  1. ASeries X returns to its long-run mean faster than Series Y
  2. BSeries Y deviations from the mean are expected to die out faster than those of Series XCorrect
  3. CBoth series revert at the same rate because the means are equal
  4. DSeries Y has no mean reversion because its speed is high

Explanation

The speed parameter a governs how quickly deviations decay; a larger a means faster reversion. Y at 0.90 reverts much faster than X at 0.10. Equal long-run means do not imply equal speeds.

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