Consider the multifactor APT with two factors. Stock A has an expected return of 14%, a beta of 1.2 on factor 1, and a beta of .8 on factor 2. The risk premium on the factor-1 portfolio is 3%. The risk-free rate of return is 4%. What is the risk-premium on factor 2 if no arbitrage opportunities exist?
A) 2%
B) 4%
C) 6%
D) 8%

Question

Quizplus · Accepted Answer

The expected return on a stock according to the Arbitrage Pricing Theory (APT) can be calculated using the formula: $E(R_i) = R_f + \beta_{i1}RP_1 + \beta_{i2}RP_2 + ... + \beta_{in}RP_n$, where $E(R_i)$ is the expected return on asset i, $R_f$ is the risk-free rate, $\beta_{ij}$ is the sensitivity of the ith asset to factor j, and $RP_j$ is the risk premium for factor j. For Stock A, we have $E(R_A) = 14\%$, $R_f = 4\%$, $\beta_{A1} = 1.2$, $RP_1 = 3\%$, and $\beta_{A2} = 0.8$. Plugging these into the APT formula gives us $14\% = 4\% + 1.2(3\%) + 0.8(RP_2)$. Solving for $RP_2$ gives us $RP_2 = 8\%$.

Consider the Multifactor APT with Two Factors