CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I
A risky portfolio has an expected return of 11% and a standard deviation of 20%. The risk-free rate is 3%. An investor wants a combined portfolio with a standard deviation of 15% by investing in this risky portfolio and the risk-free asset. The expected return of the combined portfolio is closest to:
The combined portfolio's expected return is about 9.0%. Holding 75% in the risky portfolio gives the required 15% standard deviation, so return is 0.75 times 11% plus 0.25 times 3%, which equals 9.0%.
- A6.0%
- B9.0%Correct
- C10.0%
Explanation
Weight in risky portfolio = 15/20 = 0.75. Expected return = 0.25 x 3% + 0.75 x 11% = 0.75% + 8.25% = 9.0%. Check via CAL slope: (11-3)/20 = 0.4; 3% + 0.4 x 15% = 9.0%. A 6.0% answer comes from using only the excess return slope without adding 3%; 10.0% wrongly uses 0.75 weight on risk-free.
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