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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. Currently ρ = 0.80, the long-run mean μ = 0.50, and the speed of mean reversion a = 0.40 per year. Ignoring the random shock, what is the expected change in correlation over the next 0.5 years using a one-step approximation (Δρ = a(μ − ρ)Δt)?

The expected change is −0.060. The drift is speed 0.40 times the gap between the mean 0.50 and current 0.80, which is −0.30, times 0.5 years. Correlation is above its long-run mean, so it is pulled downward.

  1. A+0.060
  2. B−0.060Correct
  3. C−0.120
  4. D−0.240

Explanation

Δρ = 0.40 × (0.50 − 0.80) × 0.5 = 0.40 × (−0.30) × 0.5 = −0.06. Choosing −0.12 forgets the time step of 0.5, and −0.24 additionally omits... multiplying only a by the gap without a. The positive sign results from reversing the gap.

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