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. you lose money? Formulate an LP to find the portfolio that maximizes expected return subject to earning at least (b) Does your portfolio in (a) result in a profit under all scenarios? If not, under which scenarios do (c) Suppose that you want to have a profit of at least $2000 no matter which scenario occurs. $2000. Solve using MATLAB and show the optimal portfolio and its expected profit again. r ofit ironstraints (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. 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. you lose money? Formulate an LP to find the portfolio that maximizes expected return subject to earning at least (b) Does your portfolio in (a) result in a profit under all scenarios? If not, under which scenarios do (c) Suppose that you want to have a profit of at least $2000 no matter which scenario occurs. $2000. Solve using MATLAB and show the optimal portfolio and its expected profit again. r ofit ironstraints (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
