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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

A stock has a beta of 1.2. The risk-free rate is 3%, and the expected market return is 9%. Under a zero-beta CAPM, the expected return on the zero-beta portfolio is 4.5% instead of the risk-free rate. What is the stock's expected return under the zero-beta model?

The expected return is 9.9%. Using the zero-beta CAPM, take 4.5% plus 1.2 times the market premium over the zero-beta rate (9% minus 4.5% = 4.5%), which is 5.4%. Using the 3% risk-free rate instead would wrongly give 10.2%.

  1. A10.2%
  2. B9.9%Correct
  3. C10.8%
  4. D9.0%

Explanation

Zero-beta CAPM: 4.5% + 1.2 × (9% − 4.5%) = 4.5% + 5.4% = 9.9%. Standard CAPM gives 3% + 1.2 × 6% = 10.2%, which is the distractor using Rf. Option C applies beta to the market return only partly wrongly, and D ignores beta.

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