1. A portfolio is diversified into three assets A (i = 1, 2, 3), two of which are risk-free (assets Aj and A2) and one risky (A3). The risk-free assets do not correlate with each other but they have non-zero covariances 013 and 023 with the risky asset. Wi are the respective weights of these assets and Mi their returns; 03 is the standard deviation of the risky asset. (a) Write down expressions for the expected return and variance of this 3- asset portfolio, clearly defining any relevant constraint(s). (2 marks) (b) f the investor stipulates a maximum of 20% for the risky asset, derive the corresponding expected return and risk of this portfolio. Precise logic should be given as to the nature of the derived forms. (3 marks) (c) For the case of 013 = 023, derive the return-risk formula and then plot the corresponding diagram (expected portfolio return along the y-axis and risk along the x-axis). Explain the implication of the result obtained. (4 marks) (d) Derive the return-risk description for 013 + 023. What conic section does the return-risk profile correspond to? Draw the return-risk plot, clearly identifying the relevant quantities. (6 marks) (e) Derive the condition for short selling of asset A1. Then explain why such a short selling is unlikely to be of any economic benefit. (5 marks) 1. A portfolio is diversified into three assets A (i = 1, 2, 3), two of which are risk-free (assets Aj and A2) and one risky (A3). The risk-free assets do not correlate with each other but they have non-zero covariances 013 and 023 with the risky asset. Wi are the respective weights of these assets and Mi their returns; 03 is the standard deviation of the risky asset. (a) Write down expressions for the expected return and variance of this 3- asset portfolio, clearly defining any relevant constraint(s). (2 marks) (b) f the investor stipulates a maximum of 20% for the risky asset, derive the corresponding expected return and risk of this portfolio. Precise logic should be given as to the nature of the derived forms. (3 marks) (c) For the case of 013 = 023, derive the return-risk formula and then plot the corresponding diagram (expected portfolio return along the y-axis and risk along the x-axis). Explain the implication of the result obtained. (4 marks) (d) Derive the return-risk description for 013 + 023. What conic section does the return-risk profile correspond to? Draw the return-risk plot, clearly identifying the relevant quantities. (6 marks) (e) Derive the condition for short selling of asset A1. Then explain why such a short selling is unlikely to be of any economic benefit
