FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?
A risk manager fits a mean-reverting model to the change in correlation: ρ(t+1) − ρ(t) = a(m − ρ(t)) + ε, with a = 0.20 and long-run mean m = 0.40. The current correlation is 0.70. Ignoring the error term, what is the expected correlation next period?
Expected correlation next period is 0.64. The reversion speed of 0.20 times the gap of −0.30 to the mean of 0.40 gives a change of −0.06, which reduces 0.70 to 0.64.
- A0.64Correct
- B0.60
- C0.50
- D0.76
Explanation
Expected change = 0.20 × (0.40 − 0.70) = −0.06. Next-period correlation = 0.70 − 0.06 = 0.64. The 0.76 option gets the sign wrong (+0.06), and 0.50 applies the full gap times 1/3, not a = 0.20.
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