Bond Portfolio Optimisation

Problem: You need to develop a multi-period model that recommends bond purchases to minimise costs while providing a specified cash flow.

This multi-period problem is an example of dynamic modeling. "Dynamic" means that decisions made in this period affect not only this period's returns (or costs), but future decisions and returns as well. For this reason, multi-period problems cannot be treated as if they were merely a collection of single-period problems.

In many multi-period modeling problems, liquid or cash-like assets are treated like other commodities, so holding cash is just like keeping inventory. The following illustrates the major features of multi-period models in a financial context.

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You're a financial adviser for an investment firm. Your client needs enough cash to cover commitments for the next five years. You've concluded that to meet these financial obligations, he should invest in some very low-risk securities such as government bonds. You must recommend bonds to buy to minimise his total cost now, yet cover his cash flow requirements. This is also an example of how to defease debt - how to wipe it off the books.

You want to minimise your client's initial investment, while covering his cash flow needs over the next five years. In other words, what is the minimum amount of cash that should be allocated among all the available bonds which will maintain the required cash inflow over the next five years?

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