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Q 5. Suppose that investors care only about the mean up and the variance o of portfolio returns, and that they want to minimise o
Q 5. Suppose that investors care only about the mean up and the variance o of portfolio returns, and that they want to minimise o subject to a target portfolio return p. Let r be the risk-free interest rate, and suppose that there are N risky assets. Also let w=(wi, ..., WN) ERN be the risky asset portfolio weights vector, H = (H1,..., MN) ERN the risky asset mean returns vector, 1 = (1, ...,1) ERN an N-dimensional vector of ones, and 011 OIN = ONI ... ONN the N * N risky asset variance covariance matrix. (a) What percent of the portfolio is invested in the risk-free asset? (1 mark] (b) What are the expressions for up and o$ for a portfolio composed of risky assets and the risk-free asset? [2 marks] (c) State the mean-variance optimisation problem for a portfolio com- posed of risky assets and the risk-free asset. [3 marks]
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