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

The market portfolio has a standard deviation of 15% and the risk-free rate is 4%. Stock X has a standard deviation of 30% and a correlation of 0.6 with the market. The market risk premium is 6.75%. Which is the required return on X under CAPM?

The required return is 12.10%. Beta equals correlation times the ratio of standard deviations: 0.6 × 30/15 = 1.2. Required return is 4% plus 1.2 times 6.75%, which is 8.1%, giving 12.1%.

  1. A10.75%
  2. B12.10%Correct
  3. C8.05%
  4. D14.05%
  5. 16.15%

Explanation

Beta = 0.6 × 30/15 = 1.2. Required return = 4% + 1.2 × 6.75% = 4% + 8.1% = 12.1%. Option A uses beta 1.0 style error (4% + 6.75%). Option D uses beta of 1.5 mistakenly.

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