Numerous problems in the area of finance can be addressed by using the various
optimization techniques. These problems often involve attempting to maximize the return
on an investment while meeting certain cash-flow requirements and risk constraints.
Alternatively, we may want to minimize the risk on an investment while maintaining a
certain level of return. We’ll consider one such problem here and discuss several other
financial engineering problems throughout this text. Brian Givens is a financial analyst for
Retirement Planning Services, Inc., who specializes in designing retirement income
portfolios for retirees using corporate bonds. He has just completed a consultation with a
client who expects to have $750,000 in liquid assets to invest when she retires next month.
Brian and his client agreed to consider upcoming bond issues from the following six
companies:
The column labeled “Return” in this table represents the expected annual yield on each
bond, the column labeled “Years to Maturity” indicates the length of time over which the
bonds will be payable, and the column labeled “Rating” indicates an independent
underwriter’s assessment of the quality or risk associated with each issue. Brian believes
that all of the companies are relatively safe investments. However, to protect his client’s
income, Brian and his client agreed that no more than 25% of her money should be invested
in any one investment and at least half of her money should be invested in long-term bonds
that mature in 10 or more years. Also, even though DynaStar, Eagle Vision, and OptiPro
offer the highest returns, it was agreed that no more than 35% of the money should be
invested in these bonds because they also represent the highest risks (that is, they were
rated lower than “very good”). Brian needs to determine how to allocate his client’s
investments to maximize her income while meeting their agreed upon investment
restrictions.