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MAT540 Week 8 Assignment: Optimizing Investment Portfolios: A Linear Programming Approach to Maximizing Returns and Managing Risk

A solved assignment using linear programming to optimize investment portfolios and manage financial risk.

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Running Head:MAT540Week8Assignment1MAT540Week8Assignment:OptimizingInvestmentPortfolios:ALinearProgrammingApproachtoMaximizingReturnsandManagingRiskName:Professor:Math 540Date:ProblemYou are a portfolio manager for the XYZ investment fund. The objective for the fund is tomaximize your portfolio returns from the investments on four alternatives. The investments

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Running Head:MAT540Week8Assignment2include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your totalinvestment portfolio is $1,000,000.Investment ReturnBased on the returns from the past five years, you concluded that the investment annual returnson stocks are 10%, on real estates are 7% onbonds are 4% and on CD is 1%.Risk ConstraintsHowever, you also have to analyze the risks associate with each investment category. A wildlyused risk measurement parameter is called Value at Risk (VaR). (Note: VaR measures the riskof loss on a specific portfolio of financial assets.) For example, given a million dollar stockinvestment, if a portfolio of stocks has a one-day 4% VaR, there is a 5% probability that thestock portfolio will fall in value by more than 1,000,000 * 0.004 = $4,000 over a one day period.In the portfolio, the VaR for stock investments is 6%. Similarly, the VaR for real estateinvestment is 2% and the VaR for bond investment is 1% and the VaR for investment in CD is0%. To manage the portfolio, you decided that at 5% probability, your VaR for stocks cannotexceed $25,000, VaR for real estate cannot exceed $15,000, VaR for bonds cannot exceed$2,500 and the VaR for CD investment is $0.Diversification and Liquidity ConstraintsAs a diversified investment portfolio, you also decided that each investment category must holdat least $50,000 of the total investment assets. In addition, you must hold combined CD andbond investment no less than $200,000 in orderto meet liquidity requirement.
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Document Details

University
Ashford University
Course
MAT 540
Subject
Mathematics

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