LP Modeling
Cash Matching Problem:
We wish to match cash obligations over a 6-year period. We select 10 bonds for this purpose (and for simplicity all accounting is done on a yearly basis). The cash flow structure of each bond is shown in the corresponding column in the table below. Under this column is the bond’s current price. For example, the first column represents a 10% bond that matures in 6 years. This bond is selling at 109. The second to last column shows the yearly cash requirements (or obligations) for cash to be generated by the portfolio. Formulate the standard cash matching problem as a linear programming problem and solve for the optimal portfolio.
TABLE
|
Yr |
|
Bonds |
|
||||||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Required |
|
||
|
1 |
10 |
7 |
8 |
6 |
7 |
5 |
10 |
8 |
7 |
100 |
100 |
|
|
|
2 |
10 |
7 |
8 |
6 |
7 |
5 |
10 |
8 |
107 |
|
200 |
|
|
|
3 |
10 |
7 |
8 |
6 |
7 |
5 |
110 |
108 |
|
|
800 |
|
|
|
4 |
10 |
7 |
8 |
6 |
7 |
105 |
|
|
|
|
100 |
|
|
|
5 |
10 |
7 |
8 |
106 |
107 |
|
|
|
|
|
800 |
|
|
|
6 |
110 |
107 |
108 |
|
|
|
|
|
|
|
1,200 |
|
|
|
|
109 |
94.8 |
99.5 |
93.1 |
97.2 |
92.9 |
110 |
104 |
102 |
95.2 |
|
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|
|
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