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IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns

A two-factor APT model for an Indian equity portfolio has a risk-free rate of 6%, factor risk premiums of 4% for factor 1 (say, market) and 2% for factor 2 (say, interest-rate change), and a portfolio with sensitivities 1.2 and -0.5. What is the expected return under the APT?

The expected return is 9.8%. Under APT it equals the risk-free rate plus each sensitivity times its factor risk premium: 6% + 1.2×4% − 0.5×2% = 6% + 4.8% − 1.0% = 9.8%.

  1. A9.8%Correct
  2. B10.6%
  3. C7.8%
  4. D11.8%
  5. 8.8%

Explanation

E(R) = 6% + 1.2×4% + (-0.5)×2% = 6 + 4.8 - 1.0 = 9.8%. Using +0.5 for the second factor gives 11.8%. Omitting the risk-free rate gives 3.8%, and ignoring factor 2 gives 10.8%, so none of these is correct.

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