A local bank wants to build a bond portfolio to maximize the expected return from a set
Question:
A local bank wants to build a bond portfolio to maximize the expected return from a set of five bonds with $1 million available for investment. The expected annual return, the worst-case annual return on each bond, and the ‘‘duration’’ of each bond are given in the following table. (The duration of a bond is a measure of the bond’s sensitivity to interest rates.)
Expected Rate of Return | Worst-Case Rate of Return | Duration | |
Bond 1 | 15.0% | 8.0% | 8 |
Bond 2 | 11.5% | 7.5% | 7 |
Bond 3 | 10.5% | 6.8% | 6 |
Bond 4 | 9.5% | 7.0% | 5 |
Bond 5 | 8.5% | 7.4% | 3 |
The average worst-case return for the portfolio must be at least 7.2 percent. The average duration of the portfolio must be at most 6. Because of diversification requirements, at most 40 percent of the total amount invested can be invested in a single bond.
Write down the mathematical formulation of the optimization problem using a linear programming model, specifying the decision variables, objective function, and constraints.
Expert Answer:
Formulate the Linear Programming Model as shown below Let the amount invested in ... View the full answer
