Consider the multifactor APT. There are two independent economic factors, F₁and F₂. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios: $\begin{array} { | l | l | l | l | } \hline \underline { \text { Portfolio } } & \underline { B \text { on } } \mathbf { E } \underline { 1 } & \underline { \beta \text { on } } \mathrm { F } _ { 2 } & \underline { \text { Expected Return } } \\\hline \mathrm { A } & 1.0 & 2.0 & 19 \% \\\hline \mathrm { B } & 2.0 & 0.0 & 12 \% \\\hline\end{array}$
-Assuming no arbitrage opportunities exist,the risk premium on the factor F₂ portfolio should be ___________.

Question

Consider the multifactor APT. There are two independent economic factors, F₁and F₂. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios:

\begin{array} { | l | l | l | l | } \hline \underline { \text { Portfolio } } & \underline { B \text { on } } \mathbf { E } \underline { 1 } & \underline { \beta \text { on } } \mathrm { F } _ { 2 } & \underline { \text { Expected Return } } \\\hline \mathrm { A } & 1.0 & 2.0 & 19 \% \\\hline \mathrm { B } & 2.0 & 0.0 & 12 \% \\\hline\end{array}

-Assuming no arbitrage opportunities exist,the risk premium on the factor F₂ portfolio should be ___________.

Quizplus · Accepted Answer

Using the APT model, we can calculate the expected return on each portfolio as follows: For portfolio A: E(Ra) = Rf + β1f1 + β2f2 E(Ra) = 0.06 + (1.0)(-2%) + (2.0)(?) E(Ra) = 0.06 + 0.04f2 19% = 0.06 + 0.04f2 f2 = 325% For portfolio B: E(Rb) = Rf + β1f1 + β2f2 E(Rb) = 0.06 + (2.0)(-2%) + (0.0)(?) E(Rb) = 0.02 12% = 0.06 + 0.0 + 0.0 Thus, the risk premium on the factor F₂ portfolio can be calculated as: RP2 = (E(Ra) - E(Rb)) / β2 RP2 = (19% - 12%) / 2.0 RP2 = 3.5% Therefore, the closest option is C (5%).

Consider the Multifactor APT -Assuming No Arbitrage Opportunities Exist,the Risk Premium on the Factor