Nonlinear assignment 
Assume that you are a management scientist, and advice one of your client on diversifying his/her investments. This client has invested significant amount of his/her gratuity in the stock of company A. Since the rate of return of company A’s stock is moderate, s/he wants to earn more from the investments, and at the same time, s/he is reluctant to involve in risk-taking activities. So s/he expects your advice on portfolio investments which will guarantee the client minimum 13 percentage of return in an average with bearable risk.
Your job is to select three companies’ stock that are listed in NASDAQ/NYSE and gather 15 years stock and calculate rate of return on each year. Assume that the company A has lowest average rate of return among the three companies.
1) Formulate a mathematical model for this portfolio selection problem.
2) Determine how much portion of your client’s investments can be distributed to each of these companies’ stock price, and at the same time, s/he has to expect minimum 15% rate of return while minimizing total risk.
3) Create sensitivity report and explain practical implications.
1) According to the question, I choose COCA-COLA, NIKE and APPLE as the three companies from the NASDAQ/NYSE by searching the stock price from the website. And we can see the price in the excel. Formulate a mathematical model for this portfolio selection problem.
Defining the Decision Variables: p1 = proportion of funds invested in COCA-COLA p2 = proportion of funds invested in NIKE p3 = proportion of funds invested in APPLE
Objective Function:
Minimize the portfolio variance (risk)
Defining the Constraints:
1. Expected Return 0.0283p1 + 0.1674p2 + 0.5489p3 >= 0.15
2. Proportions p1 + p2 + p3 = 1 p1, p2, p3 >= 0 p1, p2, p3 <= 1
3) the sensitivity report:
From the sensitivity report, we can see the portion of investment in COCA-COLA, NIKE and APPLE should be 32.06%, 60.82% and 7.12%. While we can achieve our
Your job is to select three companies’ stock that are listed in NASDAQ/NYSE and gather 15 years stock and calculate rate of return on each year. Assume that the company A has lowest average rate of return among the three companies.
1) Formulate a mathematical model for this portfolio selection problem.
2) Determine how much portion of your client’s investments can be distributed to each of these companies’ stock price, and at the same time, s/he has to expect minimum 15% rate of return while minimizing total risk.
3) Create sensitivity report and explain practical implications.
1) According to the question, I choose COCA-COLA, NIKE and APPLE as the three companies from the NASDAQ/NYSE by searching the stock price from the website. And we can see the price in the excel. Formulate a mathematical model for this portfolio selection problem.
Defining the Decision Variables: p1 = proportion of funds invested in COCA-COLA p2 = proportion of funds invested in NIKE p3 = proportion of funds invested in APPLE
Objective Function:
Minimize the portfolio variance (risk)
Defining the Constraints:
1. Expected Return 0.0283p1 + 0.1674p2 + 0.5489p3 >= 0.15
2. Proportions p1 + p2 + p3 = 1 p1, p2, p3 >= 0 p1, p2, p3 <= 1
3) the sensitivity report:
From the sensitivity report, we can see the portion of investment in COCA-COLA, NIKE and APPLE should be 32.06%, 60.82% and 7.12%. While we can achieve our