Question Details

MAT 540 ASSIGNMENT 1 LINEAR PROGRAMMING CASE
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 include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your total investment portfolio is $1,000,000. Investment Returns 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 the 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. The total amount of real estate holding shall not exceed 30% of the portfolio assets. A. As a portfolio manager, please formulate and solve the investment portfolio problem using linear programming technique. What are the amounts invest in (1) stocks, (2) real estate, (3) bonds and (4) CD? B. If $500,000 additional investments are available to you in your portfolio, how would you invest the capital? C. Would you maintain the portfolio investment if stock yields lowered to 6%? How would you re-distribute your investment portfolio?



Points: 110 Assignment 1: Linear Programming Case Study Criteria
Unacceptable
Below 60% F
Meets Minimum Expectations
60-69% D
Fair
70-79% C
Proficient
80-89% B
Exemplary
90-100% A
Explain what type of problem this is and the approach you are taking (20%) Did not explain what type of problem this is and the approach taken, or did so insufficiently. Insufficiently explained what type of problem this is and the approach taken Partially explained what type of problem this is and the approach taken Satisfactorily explained what type of problem this is and the approach taken Thoroughly explained what type of problem this is and the approach taken
Objective function specified correctly in writeup (10%) Objective function is specified incorrectly, with both coefficients incorrect or missing. Objective function is specified, but one (1) coefficient is incorrect. Coefficients for objective function are correct, but whether this is a max or min problem is incorrect.
Objective function is specified correctly. Constraints are specified correctly in writeup (10%) Constraints are specified incorrectly or missing. Some constraints are correctly specified. Most constraints are correctly specified. All constraints are correctly specified, buy applicable nonnegativity constraints are omitted. All constraints are correctly specified, including nonnegativity constraints, if applicable. Specified L.P. Model is correctly translated to Excel (10%) Specified L.P. Model is incorrectly translated into Excel Specified model is translated to Excel in a partially correct manner Specified model is translated to Excel in a mostly correct manner
Specified model is correctly translated to Excel Correct Answer is Obtained (10%)
Correct optimum is not obtained
Correct optimum is obtained
Correctly answer the sensitivity analysis part of the problem. (15%)
Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness Insufficiently explained and/or provided a partially correct answer to the sensitivity analysis part of the problem Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem Satisfactorily explained and correctly answered the sensitivity analysis part of the problem Thoroughly explained and correctly answered the sensitivity analysis part of the problem Correctly answer the shadow price part of the problem. (15%)
Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness Insufficiently explained and/or provided a partially correct answer to the sensitivity analysis part of the problem Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem Satisfactorily explained and correctly answered the sensitivity analysis part of the problem Thoroughly explained and correctly answered the sensitivity analysis part of the problem 5. Writing / Grammar and mechanics
(10%)
Serious and persistent errors in grammar, spelling, and punctuation.
Numerous errors in grammar, spelling, and punctuation.
Partially free of errors in grammar, spelling, and punctuation.
Mostly free of errors in grammar, spelling, and punctuation.
Free of errors in grammar, spelling, and punctuation.

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