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CMA Final · Strategic Financial Management · Asset Pricing Theories

Under a single-factor APT model, the risk-free rate is 7%. Portfolio A has a sensitivity of 1.0 to the factor and an expected return of 12%. Portfolio B has a sensitivity of 2.0 and an expected return of 17%. Both are well diversified. What is the position under no-arbitrage conditions?

No arbitrage exists. Portfolio A earns 5% over the risk-free rate per unit of factor sensitivity, and B also earns 5% per unit (10% divided by 2). Identical premiums per unit of sensitivity mean both lie on the same APT line.

  1. AArbitrage exists because the factor risk premium implied by A (5%) differs from that implied by B (5%) only by rounding
  2. BNo arbitrage exists because both portfolios imply the same factor risk premium of 5%Correct
  3. CArbitrage exists because B should earn 19%
  4. DArbitrage exists because A should earn 14%

Explanation

Risk premium per unit of sensitivity for A = (12% - 7%)/1.0 = 5%. For B = (17% - 7%)/2.0 = 5%. Both equal, so the points lie on the same APT line and no arbitrage exists. B earning 19% would require a 6% premium, which is not implied by the data.

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