(modelling) Consider the following portfolio selection problem. An investor must choose a portfolio (x1,x2, . . . , xn)T, where 2, 1s the proportion of the assets allocated to the j:th security. The return on the portfolio has the mean value cx and the variance xVx, where is the vector denoting mean returns and V is the matrix of covariances of the returns. The investor would (essentially) like to maximize his/her expected return, while at the same time minimize the variance and hence the risk. A portfolio is called efficient (or (weakly) Pareto optimal) if there is no other portfolio having both a larger expected return and a smaller variance. (2p) a) Formulate an optimization problem whose optimal solution corresponds to an efficient portfolio. (Different models are possible.) Motivate why your model leads to an efficient portfolio. (1p) b) Suggest a systematic way of generating multiple efficient solutions. (modelling) Consider the following portfolio selection problem. An investor must choose a portfolio (x1,x2, . . . , xn)T, where 2, 1s the proportion of the assets allocated to the j:th security. The return on the portfolio has the mean value cx and the variance xVx, where is the vector denoting mean returns and V is the matrix of covariances of the returns. The investor would (essentially) like to maximize his/her expected return, while at the same time minimize the variance and hence the risk. A portfolio is called efficient (or (weakly) Pareto optimal) if there is no other portfolio having both a larger expected return and a smaller variance. (2p) a) Formulate an optimization problem whose optimal solution corresponds to an efficient portfolio. (Different models are possible.) Motivate why your model leads to an efficient portfolio. (1p) b) Suggest a systematic way of generating multiple efficient solutions