Question

Consider an APT model with independent economic factors $F_1$ and $F_2$. The risk-free rate is 2%. The following table shows the factor sensitivities ($b_1$ and $b_2$) for two well diversified portfolios A and B and their corresponding expected returns. \begin{tabular}{|c|c|c|c|} \hline Portfolio & $b_1$ & $b_2$ & Returns \\ \hline A & 0.6 & 0.4 & 10.8 \\ B & 1.2 & 0.7 & 18.6 \\ \hline \end{tabular} (a) Compute the factor risk premiums for both factors. [5 marks] (b) Suppose that there is a new portfolio C with factor sensitives of $b_1 = 1$ and $b_2 = 0.8$. What is the expected return for this portfolio ? [3 marks] (c) Suppose that that this portfolio (C) is currently earning a return of 20% in the market. Are arbitrage opportunities possible ? [2 marks] (d) Explain how you can construct a portfolio that has an exposure of $b_2 = 1$ with respect to the second factor. What is the expected return for this portfolio ? [5 marks]

          Consider an APT model with independent economic factors $F_1$ and $F_2$. The risk-free rate is 2%. The following table shows the factor sensitivities ($b_1$ and $b_2$) for two well diversified portfolios A and B and their corresponding expected returns.

\begin{tabular}{|c|c|c|c|}
\hline
Portfolio & $b_1$ & $b_2$ & Returns \\
\hline
A & 0.6 & 0.4 & 10.8 \\
B & 1.2 & 0.7 & 18.6 \\
\hline
\end{tabular}

(a) Compute the factor risk premiums for both factors. [5 marks]
(b) Suppose that there is a new portfolio C with factor sensitives of $b_1 = 1$ and $b_2 = 0.8$. What is the expected return for this portfolio ? [3 marks]
(c) Suppose that that this portfolio (C) is currently earning a return of 20% in the market. Are arbitrage opportunities possible ? [2 marks]
(d) Explain how you can construct a portfolio that has an exposure of $b_2 = 1$ with respect to the second factor. What is the expected return for this portfolio ? [5 marks]

Consider an APT model with independent economic factors F1 and F2. The risk-free rate is 2%. The following table shows the factor sensitivities ($b1$ and $b2$) for two well diversified portfolios A and B and their corresponding expected returns.

Portfolio b1 b2 Returns

A 0.6 0.4 10.8

B 1.2 0.7 18.6

(a) Compute the factor risk premiums for both factors. [5 marks]
(b) Suppose that there is a new portfolio C with factor sensitives of b1 = 1 and b2 = 0.8. What is the expected return for this portfolio ? [3 marks]
(c) Suppose that that this portfolio (C) is currently earning a return of 20% in the market. Are arbitrage opportunities possible ? [2 marks]
(d) Explain how you can construct a portfolio that has an exposure of b2 = 1 with respect to the second factor. What is the expected return for this portfolio ? [5 marks]

Added by Sara I.

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