Practical Financial Optimization: Decision Making for Financial Engineers

Chapter 4

Portfolio Models for Fixed Income

There is no idea, however ancient and absurd, that is not capable of improving our knowledge.

Paul Feyerabend, Against Method

4.1 Preview

In this chapter we develop optimization models for fixed-income portfolios when the sources of risk are the level and shape of the term structure of interest rates. Models for structuring portfolios dedicated to matching a stream of cashflows are given first. These are followed by immunization models to protect portfolio returns from changes in the term structure. Additional models for factor immunization protect the portfolio returns from changes in convexity and steepness in addition to parallel shifts. These models are finally extended to immunize portfolios of corporate bonds from simultaneous changes in the term structure of interest rates and credit spreads.

4.2 Portfolio Dedication

Financial intermediaries, as well as nonfinancial institutions, are often faced with liability streams that stretch well into the future. In such cases the cashflows are uncertain and best represented by random variables. Sometimes, however, the streams may be known with certainty: the obligations arising from the sale of a guaranteed investment contract (GIC, see Section 8.3.1) are known with certainty; the liabilities of a defined benefits pension fund are known with the accuracy of mortality rate estimates and since the law of large numbers applies and average mortality rates provide sufficient accuracy so that ...