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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 fits a mean-reverting model to the correlation between two equity indices: change in correlation over one month = a(μ − ρ_t) + noise, with a = 0.25 per month and long-run mean μ = 0.40. The current correlation is ρ_t = 0.80. Ignoring noise, what is the expected correlation after one month, and after the move what is the remaining gap to the mean?

The expected correlation after one month is 0.70, with a remaining gap of 0.30 to the 0.40 mean. The adjustment is 0.25 times the initial 0.40 gap, which is 0.10, so correlation falls from 0.80 to 0.70.

  1. A0.70; gap 0.30
  2. B0.60; gap 0.20Correct
  3. C0.65; gap 0.25
  4. D0.55; gap 0.15

Explanation

Expected change = 0.25 × (0.40 − 0.80) = −0.10, so expected correlation is 0.70. Check: the gap was 0.40, and 0.40 × (1 − 0.25) = 0.30. The gap is therefore 0.30 and the expected correlation is 0.70, which matches option 0; so verify: 0.70 − 0.40 = 0.30.

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