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Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected revenue rate li with variance o for i = 1, ...,

n, and the covariance of the revenues of stocks i and j is given by oij for i + j, i, j = 1, ..., n. The proportion of stock i in the portfolio is denoted by ;. a) Showing your working carefully, show that the expected revenue from the port-folio is E1 xifli, and find an expression for the variance of the portfolio revenue,again showing your working carefully. b) Still for a general number ofn stocks, formulate this as an optimization problem using Lagrange multipliers, and find a set of linear equations for the optimal values of the x,s. You do not need to solve the problem at this stage. c) Now consider a problem with three stocks, where the means, variances and co-variances are as follows:0.06, µ20.04, µ3 =0.07, o? = 0.3, ož = 0.1, o3 :0.6, o 12 = -0.1, ơ 13 = 0.2and o23 = 0.1.Find the optimal portfolio (i.e. the one with the minimum variance) for the expectedfo 06 d) Now portfolio in this case and comment.(24 marks)suppose that the target rate of return is increased to 0.065. Find the optimal

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