Consider the multi-factor APT model with two-factors. The risk premium on factor 1 and 2 portfolios are 6% and 4% respectively. Stock A has a beta of 1.1 on factor 1 and a beta of 0.8 on factor 2. The expected return on Stock A is 15%. If no arbitrage opportunities exist, the risk free rate is
A) 5.2%
B) 4.6%
C) 3.7%
D) 4.1%

Question

Consider the multi-factor APT model with two-factors.  The risk premium on factor 1 and 2 portfolios are 6% and 4% respectively.  Stock A has a beta of 1.1 on factor 1 and a beta of 0.8 on factor 2.  The expected return on Stock A is 15%.  If no arbitrage opportunities exist, the risk free rate is
A) 5.2%
B) 4.6%
C) 3.7%
D) 4.1%

Quizplus · Accepted Answer

The risk-free rate is 5.2% because the expected return on Stock A is equal to the risk-free rate plus the risk premium on the two factors multiplied by the betas of Stock A on those factors.

Consider the Multi-Factor APT Model with Two-Factors