Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected revenue rate µ; with variance o? for i = 1, ..., n, and the covariance of the revenues of stocks i and j is given by Oij 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 T;H;, 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. for i + j, i, j = 1,..., n. The proportion

Suppose that you have to choose an optimal portfolio from a list of n stocks. Stock i has expected revenue rate µ; with variance o? for i = 1, ..., n, and the covariance of the revenues of stocks i and j is given by Oij 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 T;H;, 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. for i + j, i, j = 1,..., n. The proportion

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
See similar textbooks
icon
Related questions
Question
Please solve only part b in 1 hour to get a thumbs up
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.
Transcribed Image 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.
Expert Solution
steps

Step by step

Solved in 7 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS