FRM Part II · FRM Exam Part II · Portfolio Construction
A portfolio has expected return 10%, volatility 15%, and the risk-free rate is 2%. An investor wants volatility of 9% by combining this portfolio with the risk-free asset. What is the resulting expected return, and the weight in the risky portfolio?
Volatility scales linearly with the risky weight, so the weight is 9% divided by 15%, or 60%. Expected return is 2% plus 0.6 times the 8% excess return, giving 6.8%. The Sharpe ratio of 0.533 is unchanged along the capital allocation line.
- AExpected return 6.8%; weight 60%Correct
- BExpected return 7.2%; weight 60%
- CExpected return 6.8%; weight 40%
- DExpected return 8.0%; weight 90%
Explanation
Weight = 9/15 = 0.6. Expected return = 0.02 + 0.6(0.10 − 0.02) = 0.02 + 0.048 = 6.8%. Option 7.2% results from 0.6×10%+0.4×3%, an incorrect risk-free rate, or from ignoring the cash return; a 40% weight inverts the ratio.
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