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

A portfolio is made up of 60% in a stock with beta 1.5 and 40% in the risk-free asset. The market risk premium is 5% and the risk-free rate is 6%. What is the portfolio's expected return under CAPM?

The expected return is 10.5%. Portfolio beta is the weighted average of betas: 0.6×1.5 plus 0.4×0, which is 0.9. Applying CAPM gives 6% plus 0.9×5%, which equals 10.5%. Ignoring the risk-free holding would wrongly give 13.5%.

  1. A10.5%Correct
  2. B12.0%
  3. C9.0%
  4. D13.5%
  5. 10.0%

Explanation

Portfolio beta = 0.6 × 1.5 + 0.4 × 0 = 0.9. Expected return = 6% + 0.9 × 5% = 10.5%. Option D ignores the risk-free holding and uses beta 1.5 (6% + 7.5% = 13.5%).

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