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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

Under CAPM, the market has expected return 10% and standard deviation 15%; the risk-free rate is 4%. Portfolio P is 60% in the market portfolio and 40% in the risk-free asset. What are the expected return and standard deviation of P, and its beta?

Expected return is 7.6%, standard deviation 9% and beta 0.6. Return is the weighted average 0.6 x 10% + 0.4 x 4%. Risk-free holdings add no variance or covariance, so risk and beta both scale by the 0.6 market weight.

  1. A7.6%, 9%, 0.6Correct
  2. B7.6%, 15%, 0.6
  3. C6.4%, 9%, 0.6
  4. D7.6%, 9%, 1.0
  5. 10%, 9%, 0.6

Explanation

Expected return = 0.6 x 10% + 0.4 x 4% = 7.6%. The risk-free asset has zero variance and zero covariance with the market, so sigma = 0.6 x 15% = 9%. Beta = 0.6 x 1 + 0.4 x 0 = 0.6, and the CAPM check 4% + 0.6 x 6% = 7.6% agrees.

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