CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio
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 holds 50% in each. The portfolio standard deviation is closest to:
The portfolio standard deviation is about 13.2%. Portfolio variance is 0.0175, found by adding the weighted variances and the covariance term, and its square root is 13.2%. The weighted average of 15% overstates risk because the correlation is below one.
- A11.6%
- B13.2%Correct
- C15.0%
Explanation
Variance = 0.25(0.04) + 0.25(0.01) + 2(0.5)(0.5)(0.5)(0.20)(0.10) = 0.01 + 0.0025 + 0.005 = 0.0175. The square root is 13.23%. The 15.0% figure is the weighted average, which ignores diversification.
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