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

A risk manager estimates that the correlation between two equity indices is 0.30 when the market is calm and 0.70 in a high-volatility regime. Each index position is USD 10 million with daily volatility 1.0% for each. Assuming a two-asset portfolio of equal weights and normally distributed returns, what is the portfolio daily standard deviation in USD in the high-volatility regime if volatilities stay at 1.0%? (Use sqrt(3.4)=1.8439)

With USD 100,000 daily standard deviation per position and correlation 0.70, portfolio variance is 2 plus 1.4 times 10^10, or 3.4 times 10^10. The square root is about USD 184,390. Higher stress correlation raises risk well above the calm-regime figure.

  1. AUSD 184,390Correct
  2. BUSD 156,200
  3. CUSD 200,000
  4. DUSD 134,160

Explanation

Each position's daily sigma is USD 100,000. Variance = 100,000^2 + 100,000^2 + 2(0.70)(100,000)(100,000) = 3.4 x 10^10. The square root is about USD 184,390. USD 156,200 corresponds to the calm 0.30 correlation, sqrt(2.6)=1.612 giving 161,200, not exactly; the calm-regime answer is a different figure and the use of the wrong correlation is the mistake. USD 200,000 assumes perfect correlation.

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