Linear Programming Models Are Used by Many Financial Firms to Select

Essay

Linear programming models are used by many financial firms to select a desirable bond portfolio. The following is a simplified version of such a model. Abby is considering investing in four bonds; $1.5 million is available for investment. The expected annual return, the worst-case annual return on each bond, and the "duration" of each bond are given below (The duration of a bond is a measure of the bond's sensitivity to interest rates.) Abby wants to maximize the expected return from her bond investments, subject to the following three constraints:
∙ The worst-case return of the bond portfolio must be at least 8%.
∙ The average duration of the portfolio must be at most 6. For example, a portfolio that invests $600,000 in bond 1 and $400,000 in bond 4 has an average duration of [600,000(3) + 400,000 (9)]/1,000,000 = 5.4.
∙ Because of diversification requirements, at most 40% of the total amount invested can be invested in a single bond.
Determine how Abby can maximize the expected return on her investment.