%pylab inline
Populating the interactive namespace from numpy and matplotlib
Similar to our example in class, here is the table of future liabilities (in $millions):
Years | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|
Benefits($millions) | 24 | 26 | 28 | 28 | 26 | 29 | 32 | 33 | 34 |
And here is the set of bonds that can be invested in:
Bonds | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Price | 102 | 101.625 | 103 | 102 | 102 | 103 | 101 | 101.5 | 102 | 102.75 | 103 | 104 |
Coupon(%) | 1.25 | 1.5 | 2.5 | 1.75 | 2.125 | 2.5 | 2.625 | 3 | 3.125 | 3.5 | 3.75 | 4.5 |
Maturity(Years) | 1 | 2 | 2 | 3 | 4 | 5 | 5 | 6 | 7 | 8 | 8 | 9 |
Consider two excess cash scenarios: 1) not reused at each period. 2) reinvested at 1% interest rate and reused. Find the least cost portfolio of bonds so that the pension fund can meet its future liabilities. Please show your LP problem set up.