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IAI Actuarial Core Principles · Economic Modelling · Capital Asset Pricing Model (CAPM)

In Black's zero-beta CAPM, where no risk-free asset exists, the expected return of a security i is E(Ri) = E(Rz) + βi[E(Rm) − E(Rz)]. If E(Rz) = 6%, E(Rm) = 12% and βi = 1.5, the expected return of security i is:

The expected return is 15%. The premium of the market over the zero-beta portfolio is 6%, multiplied by beta of 1.5 gives 9%, and adding the zero-beta return of 6% gives 15%.

  1. A15%Correct
  2. B18%
  3. C9%
  4. D13.5%
  5. 12%

Explanation

Market premium over zero-beta portfolio = 12% − 6% = 6%. Multiply by beta: 1.5 × 6% = 9%. Add E(Rz): 6% + 9% = 15%. Distractor 9% omits the zero-beta return; 18% applies beta to the whole market return (1.5×12%).

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