o Question 2. For this question, consider an investment universe composed of the following risky assets: Assets 1 0.2 0.5 0.3 0.04 0.07 0.2 1 0.7 0.4 B 0.08 0.12 Corr 0.5 0.7 1 0.9 0.12 0.18 0.3 0.4 0.9 1 D 0.15 0.26 Consider optimization for a target return m, with the net of allocations invested (borrowed) in the risk-free asset argmin uT, . s.t. r + (n - r1?w=m (a) Formulate the Lagrangian function and its partial derivatives. Derive the analytical solution for optimal allocations w*. Provide handwritten or typeset mathematical working. (b) For the risk-free rate of 3% and a range of target return values m= 5%,7.5%, 10%, 12.5% compute optimal allocations w* (each portfolio), portfolio risk on = Vw"Sw, and plot the Efficient Frontier. Note: it is your task to determine the nature of yn and shape of the frontier. o Question 2. For this question, consider an investment universe composed of the following risky assets: Assets 1 0.2 0.5 0.3 0.04 0.07 0.2 1 0.7 0.4 B 0.08 0.12 Corr 0.5 0.7 1 0.9 0.12 0.18 0.3 0.4 0.9 1 D 0.15 0.26 Consider optimization for a target return m, with the net of allocations invested (borrowed) in the risk-free asset argmin uT, . s.t. r + (n - r1?w=m (a) Formulate the Lagrangian function and its partial derivatives. Derive the analytical solution for optimal allocations w*. Provide handwritten or typeset mathematical working. (b) For the risk-free rate of 3% and a range of target return values m= 5%,7.5%, 10%, 12.5% compute optimal allocations w* (each portfolio), portfolio risk on = Vw"Sw, and plot the Efficient Frontier. Note: it is your task to determine the nature of yn and shape of the frontier