Please solve only c part in 2 hours and get a thumbs up Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock ihas expected revenue rate u; with variance o? for i = 1, ..., n, and the covariance ofthe revenues of stocks i and j is given by ơij for i + j, i, j = 1,..., n. The proportionof 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 problemusing Lagrange multipliers, and find a set of linear equations for the optimal valuesof 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%3Dand 023 = 0.2.Find the optimal portfolio (i.e. the one with the minimum variance) for the expectedrate of return of 0.08.d) Now suppose that the target rate of return is reduced to 0.07. Find the optimalportfolio in this case.

The minimum variance portfolio: A rational investor is a person who invests in a portfolio on the…

c) Now consider a problem with three stocks, where the means, variances and co- variances are as follows: fl1 = = 0.06, 2= 0.08, 3 = 0.09, 0 = 0.1, 02 = 0.3, o² = 0.6, 012 = -0.1, 013 = 0.1 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.

c) Now consider a problem with three stocks, where the means, variances and co- variances are as follows: fl1 = = 0.06, 2= 0.08, 3 = 0.09, 0 = 0.1, 02 = 0.3, o² = 0.6, 012 = -0.1, 013 = 0.1 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.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 13QTD

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