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

A mean-reverting correlation model is written as dρ = a(μ − ρ)dt + σ dz. The long-run mean μ is 0.40, the current correlation is 0.60 and a = 2.0 per year. Ignoring the random term, what is the expected change in correlation over a very short interval, expressed per year?

The expected drift is a(μ − ρ) = 2.0 × (0.40 − 0.60) = −0.40 per year. Because the current correlation lies above the long-run mean, the drift is negative and pulls correlation downward toward 0.40.

  1. A+0.40
  2. B−0.40Correct
  3. C−0.20
  4. D+0.20

Explanation

Drift = a(μ − ρ) = 2.0 × (0.40 − 0.60) = 2.0 × (−0.20) = −0.40 per year. The negative sign shows correlation is pulled down toward the mean. A distractor of −0.20 omits the speed parameter a, and the positive signs reverse μ − ρ.

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