Fixed Income Securities, 4th Edition

CHAPTER 6Regression Hedging and Principal Component Analysis

The risk metrics and hedges of Chapters 4 and 5 assume relationships across rates of different terms. The assumptions are typically motivated by a combination of economic theory, empirical analysis of historical data, and views about future economic and financial developments. This chapter introduces approaches that rely explicitly on historical data. It would be an oversimplification, however, to categorize the techniques of Chapters 4 and 5 as subjective, while categorizing the approaches of this chapter as objective. Empirical methods also require assumptions, such as the number of rates or instruments used in the analysis, the particular rates or instruments chosen, and the historical time period selected for estimation.

The first section of this chapter describes single‐variable regression hedging in the context of hedging a 40‐year Johnson & Johnson (JNJ) bond with a 30‐year Treasury. The second section describes two‐variable regression hedging in the context of a relative value trade of 20‐year versus 10‐ and 30‐year Treasuries. The third and fourth sections discuss two other issues that arise in the context of regression hedging, namely, the choice between level and change regressions, and reverse regressions.

One conceptual problem with using regression hedging in practice is that each regression is essentially a different model of the term structure of interest rates with different underlying assumptions. ...