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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

Three assets each have volatility of 20%, and all pairwise correlations are 0.25. A portfolio holds equal weights of one-third in each. What is the portfolio volatility?

The portfolio volatility is about 14.1%. Own-variance terms contribute 0.01333 and the six covariance terms contribute 0.00667, so variance is 0.02. The square root is 14.14%. Assuming zero correlation would wrongly give 11.5%.

  1. A11.5%
  2. B14.1%
  3. C16.3%Correct
  4. D20.0%

Explanation

Variance = 3*(1/9)*0.04 + 6*(1/9)*0.25*0.04 = 0.013333 + 0.006667 = 0.02. Square root = 14.14%. The 11.5% option assumes zero correlation (0.04/3 = 0.01333, sqrt 11.5%).

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