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 Assignment1
MAT540 Week 8 Assignment: Optimizing Investment Portfolios: A Linear
Programming Approach to Maximizing Returns and Managing Risk
Name:
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
MAT540 Week 8 Assignment: Optimizing Investment Portfolios: A Linear
Programming Approach to Maximizing Returns and Managing Risk
Name:
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
Running Head:MAT540 Week 8 Assignment2
include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your total
investment 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 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.
include (1) stocks, (2) real estate, (3) bonds, and (4) certificate of deposit (CD). Your total
investment 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 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.
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University
Ashford University
Subject
Mathematics