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CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I

Two risky assets are combined in a portfolio. Asset A has a standard deviation of 20% and Asset B has a standard deviation of 30%. Weights are 50% each and the correlation between them is 0.5. The portfolio standard deviation is closest to:

The portfolio standard deviation is about 21.8%. Portfolio variance is 0.01 plus 0.0225 plus a covariance term of 0.015, totalling 0.0475, whose square root is 21.8%. The 25.0% weighted average would apply only with perfect positive correlation.

  1. A21.8%
  2. B22.9%Correct
  3. C25.0%

Explanation

Variance = 0.25×0.04 + 0.25×0.09 + 2×0.5×0.5×0.5×0.20×0.30 = 0.01 + 0.0225 + 0.015 = 0.0475. The square root is 21.8%. Checking: 0.0475 gives sqrt = 0.2179, so the answer is 21.8%. The weighted average of 25.0% applies only when correlation is +1.

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