Learning bond math involves building a set of analytical tools. That is what we've been doing for the most part in the first six chapters – rate conversions, pricing and yield calculations, after-tax cash flows, implied spot and implied forward rates, duration, and convexity. The payoff ultimately comes in analyzing bond portfolios and fixed-income strategies, as we see in Chapters 9 and 10. But first we can use the toolkit to look at types of debt securities other than the traditional fixed-rate and zero-coupon bonds we've been working with so far.

Floating-rate notes (floaters or FRNs) remind us that trying to minimize interest rate risk in the bond market is rather like squeezing one end of a balloon to make it smaller. Obviously, the future cash flows on a fixed-rate bond are known in advance (barring default, of course). Therefore, interest rate volatility is realized entirely in the fluctuation of current market value. Floaters aim to minimize price volatility, but at the expense of uncertain future cash flows. Interest payments typically are tied to a money market reference rate – for instance, 3-month LIBOR. By design, the duration of a floater is very low, typically close to zero, for changes in market interest rates regardless of the time to maturity.

Inflation-indexed bonds (or linkers) adjust future coupon and/or principal cash flows for realized inflation. The idea is to maintain real value in terms of the purchasing power of future cash flows. There are two designs: (1) The coupon rate is fixed while the principal changes with the consumer price index (CPI), and (2) the principal is fixed while the coupon rate adjusts for changes in the CPI. I like to call the first type P-Linkers because the link is to the principal and the second type C-Linkers because the link is to the coupon rate. Both designs provide the investor with inflation protection – their inflation durations are zero, or at least close to zero. However, their real rate durations can be quite high, even higher than those for traditional fixed-rate bonds of comparable time to maturity.

A theme, actually a subplot, to this chapter is negative duration. That's an oddity for a debt security that does not contain an embedded option. The idea is that the bond price goes up (or down) when interest rates go up (or down). It's the opposite reaction from the usual inverse relationship between bond price and yield. If you work with or have studied floating-rate notes, ask yourself what type of standard FRN (e.g., one paying 3-month LIBOR plus a fixed margin) might have negative duration – a floater trading at a discount or at a premium? If you know the answer to that, try this: When might an inflation- indexed bond, in particular a C-Linker, have negative inflation duration – when it's trading at a discount or at a premium? If you have no idea, read on.

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