Question

Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She up to $720,000 to invest, all of which may or may not be used depending on other factors. She does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund is 18% and for bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22% and for the bond fund is 5%. To reduce her risk, she wants to limit her potential losses to $100,000.

(a) Formulate an LP model to help Janet maximizing her profits.

(b) Solve the model using the graphical method presented in class and provide the optimal solution. What is the maximum amount of money Janet can lose from her portfolio? (6 + 1 = 7 marks)

(c) Determine the range for coefficient of Stock fund for which the current solution will remain optimal. Use graphical approach.

(d) Determine the range for coefficient of Bond fund for which the point (0, 720) will be optimal. Use graphical approach.

(e) Jane would like to put more money into her portfolio. The Branch Manager where Jane does her banking says she qualifies for a $30K loan for an annual interest rate of 3%. Should Jane take loan (show work)?

Answer 1

(a) LP model is following

Let x = amount (dollars) to invest in stock funds

y = amount (dollars) to invest in bond funds

Max 0.18x + 0.06y

s.t.

x + y <= 720000

x <= 0.65(x+y) or, 0.35x - 0.65y <= 0

0.22x + 0.05y <= 100000

x, y >= 0

(b) Solution of the model using graphical method is following