Instructions: This is an individual assignment. For each optimization model below you need to (1) formulate the model by hand (typed is better) with all variables de…ned and the model objective and constraints fully written out and (2) print out the MATLAB …le that contains the data (e.g. through the vec-tors/matrices) and call to linprog used to compute the model in MATLAB and the output from calling linprog that shows the optimal values for the variables and objective function value.
Do not just dump the MATLAB …le, comment it and highlight the optimal values. You must use MATLAB linprog function but you can call the function from python in which case you must print out your python code. Your project should be contained in a single pdf …le (DO NOT MAKE THIS FILE TOO LARGE) and when you send me the …le via e-mail (rkwon@mie.utoronto.ca) MAKE THE SUBJECT OF YOUR E-MAIL exactly as APS 502 Computa-tional Project 1. (I will not accept an e-mail that contains a link to your assignment, you must send me the assignment directly). Write your full legal name and student number on your assignment. Due Nov. 6 by 5PM (EST). Late assignments will incur penalty.
Problem 1
A bond portfolio manager has $100,000 to allocate to two di¤erent bonds; a corporate bond and a government bond. These bonds have the following yield, risk level, and maturity:
Bond
Yield
Risk Level
Maturity
Corporate
4%
2
3 years
Government
3%
1
4 years
The portfolio manager would like to allocate the funds so that the average risk level of the portfolio is at most 1.5 and the average maturity is at most 3.6 years. Any amount not invested in the bonds will be kept in a cash account that is assumed to generate no interest and does not contribute to the average risk level or maturity. In other words, assume cash has zero yield, zero risk level, and zero maturity.
How should the manager allocate funds to the two bonds to maximize yield?
Assume that the manager can only buy bonds i.e. selling bonds is prohibited.
You can assume that the unit price of each bond is $1 (one dollar).
Formulate the portfolio managers problem as a linear program and solve using MATLAB.
Problem 2
Part 1
Formulate a linear programming model and solve using MATLAB to …nd the lowest-cost dedicated bond portfolio that covers the stream of liabilities given in the table below (allow cash to be carried forward at no-interest):
Date
1
2
3
4
5
6
Required
500
200
800
400
700
900
1
with the set of bonds below:
Bond
1
2
3
4
5
6
Price
Rating
1
10
10
10
10
10
110
108
B
2
7
7
7
7
7
107
94
B
3
8
8
8
8
8
108
99
B
4
6
6
6
6
106
92.7
B
5
7
7
7
7
107
96.6
B
6
6
6
6
106
95.9
B
7
5
5
5
105
92.9
A
8
10
10
110
110
A
9
8
8
108
104
A
10
6
6
106
101
A
11
10
110
107
A
12
7
107
102
A
13
100
95.2
A
Part 2
Now consider a version of the problem where at most 50% of the bond portfolio’s value (value is in dollars) can be in bonds rated B. Solve this model using MATLAB and compare with optimal bond portfolio from Part 1.
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