CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I
Asset X has a standard deviation of 20% and Asset Y has a standard deviation of 10%. The correlation between them is 0.5. A portfolio is invested 50% in each asset. The portfolio standard deviation is closest to:
The portfolio standard deviation is about 13.2%. Portfolio variance is 0.01 plus 0.0025 plus 0.005, giving 0.0175, whose square root is 13.2%. This is below the 15% weighted average because the correlation of 0.5 is less than 1, providing diversification.
- A12.2%
- B13.2%Correct
- C15.0%
Explanation
Variance = 0.25(0.04) + 0.25(0.01) + 2(0.5)(0.5)(0.5)(0.2)(0.1) = 0.01 + 0.0025 + 0.005 = 0.0175. Square root = 13.2%. The 15.0% figure is the weighted average, which ignores diversification (it assumes correlation of +1).
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