Reference no: EM132172955
Question - A local bank wants to build a bond portfolio from a set of five bonds with $1 million available for investment. The expected annual return, the worst-case annual return, and the duration (a measure of the bond's sensitivity to changes in interest rates) of each bond are given in the following table.
|
Expected Return
|
Worst Case return
|
Duration
|
|
Bond 1
|
12.5 %
|
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 bank wants to maximize the expected return from its bond investments, subject to three conditions: the average worst-case return for the portfolio must be at least 7.2%; the average duration of the portfolio must be at most 6; and at most 40% of the total amount invested can be invested in a single bond. Construct and solve a Linear Optimization model to determine the amount invested in each of the 5 bonds for this problem in Excel. You will have some blending style fractional constraints when initially formulating this model, please make sure that you perform the necessary algebra to make these constraint linear as discussed in class (other methods for implementing these constraints that differ from the method used in class may result in lost points).
a. Answer the following questions about your optimal solution (for parts iii-v, you will need to make some additional calculations to find the answers):
i. Which constraints are binding?
ii. Which constraints are non-binding? What does a non-binding constraint mean in the context of this problem?
iii. What is the rate of return for this investment portfolio?
iv. What is the actual average worst-case return for this investment portfolio?
v. What is the actual average duration for this investment portfolio?