Quantitative Methods & Business Analytics

Assignment Scenario
You are a financial advisor and your client wishes to invest in two different types of stocks: high tech stocks and energy stocks. You need to advise your client on how many units of each type of stock he should invest in this year. The budget for investment is up to £2 million. Each unit of the high-tech stocks costs £80 and provides an annual rate of return of 10%; each unit of energy stocks £100 and provides an annual rate of return of 5%. The client requires that the annual income from the investments will be at least £80000. The client wants to minimise the diversification of the portfolio and has calculated a diversification index investment measure. Each unit invested in high tech stocks has a diversification index of 6. Each unit invested in the energy stocks has a diversification index of 2, because it has a smaller range of assets. The client has also specified that at least £400000 should be invested in the high-tech stocks.
A. The client wants to know how many units of each type of investments he should purchase to minimise the total diversity index for the portfolio. Formulate a linear programming model for this problem.
[30 marks]
B. Produce an appropriate graphical representation of the feasible region and determine the optimal portfolio that minimises the total diversity index, along with the total income generated by the optimal portfolio.
[15 marks]
C. Solve the linear programming problem formulated for question A using Excel and Solver.
[25 marks]
D. What would the increase in diversity of the portfolio be if the client decides to increase the minimum investment in high tech stocks by £50.
[10 marks]
E. The client has never heard of linear programming techniques. Use the academic literature to support your decision of adopting linear programming techniques. Find at least two different applications where linear programming techniques have been used in portfolio investment decision and briefly compare and contrast the approach that the authors have used. You must use appropriate sources and you must include a reference list and need to follow the APA 7th edition.