FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management
An investor has a risky portfolio with expected return 12% and volatility 20%. The risk-free rate is 4%. The investor wants a total portfolio volatility of 15% by combining the risky portfolio with cash. What is the expected return of the combined portfolio?
The combined portfolio expects a 10% return. To reach 15% volatility the investor holds 75% in the risky portfolio and 25% in cash, giving 0.75 times 12% plus 0.25 times 4%, which equals 10%.
- A8.0%
- B10.0%Correct
- C11.0%
- D9.0%
Explanation
Weight in risky portfolio = 15/20 = 0.75. Expected return = 0.75x12% + 0.25x4% = 9% + 1% = 10%. Check: 4% + 0.75x8% = 10%. Option A (8%) is the wrong weight guess; 9% omits the cash return.
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