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

A two-asset portfolio has equal weights, each asset with volatility 20%. Under normal conditions correlation is 0.30; under stress it rises to 0.90. What is the approximate ratio of stressed portfolio volatility to normal portfolio volatility?

The ratio is about 1.21. Portfolio variance equals 0.02 + 0.02ρ, giving 0.026 at ρ=0.30 and 0.038 at ρ=0.90. Volatilities are 16.12% and 19.49%, so stress raises portfolio volatility roughly 21%. The variance ratio of 1.46 would be incorrect.

  1. A1.21Correct
  2. B1.46
  3. C1.00
  4. D0.82

Explanation

Portfolio variance = 0.25(0.04)+0.25(0.04)+2(0.25)(ρ)(0.04) = 0.02+0.02ρ. Normal: 0.02+0.006=0.026, vol 16.12%. Stressed: 0.02+0.018=0.038, vol 19.49%. Ratio=19.49/16.12≈1.21. The 1.46 is the variance ratio (0.038/0.026), a mistake of not taking the square root.

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