Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected revenue rate u; with variance o? for i = 1, ..., n, and the covariance of the revenues of stocks i...

Please solve only part b in 1 hour to get a thumbs up

Extracted text: Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected revenue rate u; with variance o? for i = 1, ..., n, and the covariance of the revenues of stocks i and j is given by ơij for i + j, i, j = 1,..., n. The proportion of stock i in the portfolio is denoted by x;. a) Showing your working carefully, show that the expected revenue from the port- folio is E1 xili, and find an expression for the variance of the portfolio revenue, again showing your working carefully. b) Still for a general number of n 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, µ2 = 0.08, µz = 0.09, oỉ = 0.1, o = 0.3, ož = 0.6, 12 -0.1, 013 = 0.1 %3D and 023 = 0.2. Find the optimal portfolio (i.e. the one with the minimum variance) for the expected rate of return of 0.08. d) Now suppose that the target rate of return is reduced to 0.07. Find the optimal portfolio in this case.