Linear Programming Model for Investment Portfolio

Note: You must use MATLAB for the project and must include the code, data, and output in MATLAB in an appendix. You must write up the formulation for each part and show results of solving the model using tables or graphs with reasonable formatting (please do not just give me the dump of the computational output from MATLAB, this as mentioned should go in an appendix).

Making your report readable is VERY important and is part of the mark for this assignment.

Suppose that you have $20,000 to invest. Stock ABC sells at $20 per share today. A European call option to buy stock ABC for $15 in 6 months is available and this option is for 100 shares of stock ABC and costs $1000. You can either buy OR sell this option. In addition, a six-month riskless zero-coupon bond with face value of $100 sells now at $90 per unit. You have decided to limit the number of call options that you buy or sell to at most 50.

There are three scenarios (possibilities) for the price of stock ABC six months from now. Scenario 1 is that the price of stock ABC will be the same as today. Scenario 2 is that the price will go up to $40.

Scenario 3 is that price will go down to $12. Assume that each of these scenarios are equally likely.

(a) Formulate a linear program to determine the portfolio of stock ABC, Bond, and Call Option that maximizes the expected profit. Solve for the optimal portfolio using MATLAB and describe the optimal portfolio and its expected profit.

(b) Does your portfolio in (a) result in a profit under all scenarios? If not, under which scenarios do you lose money?

(c) Suppose that you want to have a profit of at least $2000 no matter which scenario occurs. Formulate an LP to find the portfolio that maximizes expected return subject to earning at least $2000. Solve using MATLAB and show the optimal portfolio and its expected profit again.

(d) A riskless profit is defined as the maximum possible profit that a portfolio is guaranteed to earn no matter which scenario occurs. Formulate an LP to find the maximum riskless profit under the three scenarios and solve using MATLAB (show optimal portfolio and riskless profit) For each model you must define all variables and explain all constraints.

Please highlight the optimal decisions and objective function clearly in your report.