CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio
A risky portfolio has an expected return of 12% and a standard deviation of 20%. The risk-free rate is 4%. An investor puts 60% of her wealth in the risky portfolio and 40% in the risk-free asset. The standard deviation of the combined portfolio is closest to:
The combined portfolio's standard deviation is 12%. With a risk-free asset, risk scales with the weight in the risky portfolio, so 0.60 multiplied by 20% gives 12%. The risk-free holding contributes no variance or covariance.
- A8%
- B12%Correct
- C20%
Explanation
The risk-free asset has zero variance and zero covariance with the risky portfolio, so portfolio standard deviation = w × σ = 0.60 × 20% = 12%. The 8% option uses the weight in the risk-free asset (0.40 × 20%) by mistake. The 20% option ignores the weighting.
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