Prices and Yields on Coupon Bonds

This chapter is about prices and yields on coupon bonds. The vast majority of bonds pay coupon interest regularly to investors, mostly semiannually but sometimes quarterly or just once a year. Zero-coupon bonds like Treasury STRIPS might have an interesting history, but in the study of bond math, they really are just a convenient way to introduce terminology and basic calculations – yields to maturity, horizon yields, periodicity conversions, credit spreads, and default probabilities. With all due respect to Chapter 2, Chapter 3 is much more important.

There is a which-comes-first aspect to bond prices and yields: Do prices drive yields, or do yields drive prices? If we know an investor's required rate of return for a particular bond, we can calculate the bond price. If instead we observe the price, we can calculate the yield to maturity and thereby infer the required rate of return. This chapter addresses the timing question using demand and supply diagrams. Then we work on calculating, interpreting, and critiquing the various yield statistics that are used to summarize the many cash flows on a coupon bond.

Before starting, consider a simple problem. You are looking to buy a high-yield (don't call it “junk”) corporate bond for your loved one for Valentine's Day. The bond you're considering has an 8% coupon rate and semiannual payments on May 15 and November 15 – that means each coupon payment is $4 per $100 of par value. Now as February 14 nears, you observe that the bond's yield to maturity is exactly 8.00% (s.a.). Given that the coupon rate and yield are the same, will the bond be trading at a discount, at par value, or at a premium? If those terms are new to you, no problem – they are covered in this chapter. Also, don't worry about accrued interest. The price I'm asking about is the “flat” price to which the accrued interest will be added. That too is covered in the chapter.

Admit it: Your answer is that the bond will be trading at par value. You no doubt were once told, or memorized for an exam, the bond price rules: When the coupon rate is less than the yield, the bond is priced at a discount; when the coupon rate is equal to the yield, the bond is priced at par value; and when the coupon rate is above the yield, the bond is priced at a premium. Your answer, of course, is wrong – not by much but wrong nevertheless. The rules you remember strictly apply only to coupon dates, and you're shopping for the high-yield corporate bond in the middle of the coupon period. After going deeper into the bond math, you'll see why the flat price will be at a slight discount, a little below par value.