The PBOND.lng Model

Bond Portfolio Optimization

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In certain situations, a business or individual may be faced with financial obligations over a future number of periods. In order to defease (i.e., eliminate) this future debt, the debtor can determine a minimal cost mix of current assets (e.g., cash and bonds) which can be used to cover the future stream of payments. This problem is sometimes referred to as the cash flow matching problem or the debt defeasance problem.

You are the head of your state's lottery office. Lottery prizes are not paid out immediately, but are parceled out over a 15 year period. You know exactly how much your office needs to pay out in prizes over the next 15 years. You would like to set aside enough money from lottery receipts to invest in secure government bonds so as to meet this future stream of payments. All remaining lottery receipts will be turned over to the state's treasurer to help fund the education system. You would like to turn over as many of the receipts as possible to the treasurer, so your plan is to purchase a minimal cost mix of bonds that just meets your future cash needs.

There are two bonds currently being offered that you feel are of sufficient quality to guarantee the future stream of prize payments. If funds are not invested in bonds, they can be placed into shore-term money market funds. You conservatively estimate that short-term rates will be about 4 percent over the 15 year time horizon. How many of each bon should you buy, and how much additional cash should you allocate to money market funds to minimize your total outlay while still being able to meet all the future prize payments?


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