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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: MAT540 Week 8 Assignment 1 MAT540 Week 8 Assignment : Optimizing Investment Portfolios: A Linear Programming Approach to Maximizing Returns and Managing Risk N ame: Professor : Math 540 Date: Problem You are a portfolio manager for the XYZ investment fund. The objective for the fund is to maximize your portfolio returns from the investments on four alternatives. The investments

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    Running Head: MAT540 Week 8 Assignment 2 include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your total inves tment portfolio is $1,000,000. Investment Return Based on the returns from the past five years, you concluded that the investment annual returns on stocks are 10%, on real estates are 7% on bonds are 4% and on CD is 1%. Risk Constraints However, you also have to analyze the risks associate with each investment category. A wildly used risk measurement parameter is called Value at Risk (VaR). (Note: VaR measures the risk of loss on a specific portfolio of financial assets.) For example, given a million dollar stock investment, if a portfolio of stocks has a one - day 4% VaR, there is a 5% probability that the stock 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 estate investment is 2% and the VaR for bond investment is 1% and the VaR for investment in CD is 0%. To manage the portfolio, you decided that at 5% probability, your VaR for stocks cannot exceed $25,000, VaR for real estate cannot exceed $15,000, VaR for bonds cannot exceed $2,500 and t he VaR for CD investment is $0. Diversification and Liquidity Constraints As a diversified investment portfolio, you also decided that each investment category must hold at least $50,000 of the total investment assets. In addition, you must hold combined CD and bond investment no less than $200,000 in order to meet liquidity requirement.

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