MAT

540 Week 8 Assignment 1

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 * 0.04 = $40,000 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?

******Your writeup should introduce your solution to the project by

describing the problem. Correctly identify what type of problem this is. For

example, you should note if the problem is a maximization or minimization

problem, as well as identify the resources that constrain the solution.

Identify each variable and explain the criteria involved in setting up the

model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the

problem. Include the objective function and all constraints, including any

non-negativity constraints. Then, you should present the optimal solution,

based on your work in Excel. Explain what the results mean.

Finally,

write a paragraph addressing the part of the problem pertaining to sensitivity

analysis and shadow price.

MAT

540 Week 8 Assignment 1

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 * 0.04 = $40,000 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?

******Your writeup should introduce your solution to the project by

describing the problem. Correctly identify what type of problem this is. For

example, you should note if the problem is a maximization or minimization

problem, as well as identify the resources that constrain the solution.

Identify each variable and explain the criteria involved in setting up the

model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the

problem. Include the objective function and all constraints, including any

non-negativity constraints. Then, you should present the optimal solution,

based on your work in Excel. Explain what the results mean.

Finally,

write a paragraph addressing the part of the problem pertaining to sensitivity

analysis and shadow price.

MAT

540 Week 8 Assignment 1

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 * 0.04 = $40,000 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?

******Your writeup should introduce your solution to the project by

describing the problem. Correctly identify what type of problem this is. For

example, you should note if the problem is a maximization or minimization

problem, as well as identify the resources that constrain the solution.

Identify each variable and explain the criteria involved in setting up the

model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the

problem. Include the objective function and all constraints, including any

non-negativity constraints. Then, you should present the optimal solution,

based on your work in Excel. Explain what the results mean.

Finally,

write a paragraph addressing the part of the problem pertaining to sensitivity

analysis and shadow price.

MAT

540 Week 8 Assignment 1

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

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

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 * 0.04 = $40,000 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

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.

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?

investments are available to you in your portfolio, how would you invest the

capital?

portfolio investment if stock yields lowered to 6%? How would you

re-distribute your investment portfolio?

describing the problem. Correctly identify what type of problem this is. For

example, you should note if the problem is a maximization or minimization

problem, as well as identify the resources that constrain the solution.

Identify each variable and explain the criteria involved in setting up the

model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

problem. Include the objective function and all constraints, including any

non-negativity constraints. Then, you should present the optimal solution,

based on your work in Excel. Explain what the results mean.

write a paragraph addressing the part of the problem pertaining to sensitivity

analysis and shadow price.