IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
Under a one-factor arbitrage pricing theory (APT) with risk-free rate 6% and a factor risk premium of 5%, a security has factor sensitivity 1.4. What expected return does APT imply for the security?
APT implies an expected return of 13%. The risk-free rate of 6% is added to the sensitivity of 1.4 multiplied by the factor risk premium of 5%, which is 7%, giving 6% + 7% = 13%.
- A7.0%
- B11.0%
- C12.0%
- D13.0%Correct
- 14.0%
Explanation
Expected return = 6% + 1.4 x 5% = 6% + 7% = 13%. Check: 1.4 x 5 = 7. Using 1.4 x 6 = 8.4 would give 14.4%, wrongly applying the risk-free rate; omitting the risk-free rate gives 7%.
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