FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?
Monthly correlation follows a mean-reverting AR(1) process: rho(t+1) - 0.40 = 0.80 x (rho(t) - 0.40) + noise. The current correlation is 0.65. What is the expected correlation in two months, ignoring noise?
The expected correlation is 0.56. The current deviation from the 0.40 mean is 0.25, which decays by a factor of 0.8 each month, giving 0.25 x 0.64 = 0.16 after two months, so the expected level is 0.40 + 0.16.
- A0.56Correct
- B0.60
- C0.52
- D0.48
Explanation
Deviation now = 0.65-0.40 = 0.25. After two steps: 0.25 x 0.8^2 = 0.25 x 0.64 = 0.16. Expected correlation = 0.40+0.16 = 0.56. Using 0.8 only once gives 0.60; 0.52 comes from subtracting 0.8 twice incorrectly; 0.48 uses 0.5 decay.
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