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

For a mean-reverting correlation process with rate a, the half-life of a deviation from the long-run mean is ln(2)/a. Analyst A estimates a = 1.39 per year for equity correlation and Analyst B estimates a = 0.35 per year. Using ln(2) = 0.693, which statement is correct?

Half-life is ln(2)/a. Analyst A gives 0.693/1.39 ≈ 0.50 years and Analyst B gives 0.693/0.35 ≈ 1.98 years. A larger reversion rate means deviations decay faster, so A's estimate implies a much quicker return to the mean.

  1. AA's half-life is about 0.50 years and B's is about 1.98 years, so A implies faster return to the meanCorrect
  2. BA's half-life is about 1.98 years and B's is about 0.50 years, so A implies faster return to the mean
  3. CBoth half-lives are about 0.69 years because half-life does not depend on a
  4. DA's half-life is about 2.0 years and B's about 0.5 years, so B's correlation is reverting more slowly

Explanation

Half-life A = 0.693/1.39 ≈ 0.50 years; B = 0.693/0.35 ≈ 1.98 years. A higher a means faster reversion, so A implies quicker return. The second option swaps the values, the third ignores a, and the fourth is internally inconsistent with its own inversion.

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