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

In a zero-beta (Black) version of the CAPM, where no risk-free borrowing and lending exists, the zero-beta portfolio has expected return 5% and the market portfolio has expected return 11%. A stock has beta 0.5. Its expected return is:

In the zero-beta CAPM the intercept is the zero-beta portfolio return. Expected return is 5% plus 0.5 times the 6% difference between market and zero-beta returns, giving 8%.

  1. A5.5%
  2. B6.0%
  3. C8.0%Correct
  4. D8.5%
  5. 10.0%

Explanation

Expected return = zero-beta return + beta x (market - zero-beta return) = 5% + 0.5 x 6% = 8%. Using 0.5 x 11% = 5.5% (ignoring the intercept) gives 5.5%, which is wrong; adding 5% to 0.5x11% gives 10.5%, also wrong.

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