FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
In a zero-beta (Black) version of the CAPM, the risk-free asset is unavailable for unlimited borrowing and lending. The zero-beta portfolio has an expected return of 4%, the market expected return is 10%, and a stock has beta 0.5. What is the stock's expected return?
In the zero-beta CAPM, the zero-beta portfolio return replaces the risk-free rate. Expected return equals 4% plus 0.5 times the 6% difference between market and zero-beta returns, giving 7%.
- A5.0%
- B7.0%Correct
- C8.0%
- D3.0%
Explanation
Replace the risk-free rate with the zero-beta return: E(R) = 4% + 0.5 × (10% − 4%) = 4% + 3% = 7%. Option 1 uses a 2% premium error; option 3 applies beta to the market return alone with an addition error (5%+3%).
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