This chapter presents some of the most important concepts used to measure and hedge risk in fixed income markets, namely, DV01, duration, and convexity. These concepts are first presented in a very general, one-factor framework, meaning that the only significant assumption made about how the term structure changes is that all rate changes are driven by one factor. As an application used to illustrate concepts, the chapter focuses on a market maker who shorts futures options and hedges with futures, although the reader need not know anything about futures at this point.
The chapter then presents the yield-based equivalents of these more general concepts, i.e., yield-based DV01, duration, and convexity. Because these can be expressed through relatively simple formulas, they are very useful for building intuition about the interest rate risk of bonds and are widely used in practice. They cannot, however, be applied to securities with interest-rate contingent payoffs, like options.
The chapter concludes with an application in which a portfolio manager is deciding whether to purchase duration in the form of a bullet or barbell portfolio. As it turns out, the choice depends on the manager’s view on future interest rate volatility.
Denote the price-rate function of a fixed income security by , where y is an interest rate factor. Despite the usual use of y to denote a yield, ...