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CHAPTER 2 Zero-Coupon Bonds

Bonds are in many ways easier to analyze than money market instruments.

There are no antiquated “discount rates” that misrepresent an investor's rate of return. The yield to maturity on the bond will reflect the growth path over time for the investment under some reasonable assumptions. But the many cash flows received on a typical coupon-bearing bond cause a problem known as coupon reinvestment risk. The problem is that we have to estimate the rates at which we will be able to reinvest the coupons that we receive in the future, so the total return over the time to maturity is uncertain. We ignore that for now and focus in this chapter on a simple zero- coupon bond. There are just two cash flows, one at purchase and the other at redemption more than a year into the future.

Zero-coupon bonds do exist, although they are not nearly as common as standard fixed-income bonds that pay semiannual coupons. The most developed market for “zeros” is U.S. Treasury STRIPS, the acronym for Separate Trading in Registered Interest and Principal Securities. Why and how the Treasury first created STRIPS back in the 1980s is a great illustration of the process of financial engineering.

Before getting to the STRIPS story, first consider a 10-year zero-coupon corporate bond that is priced at 60 (percent of par value). The investor pays $600 now and gets $1,000 in 10 years – simple enough. A bit of bond math covered in this chapter produces a yield to maturity of 5.174% (s.a.) for this bond. The “s.a.” tag, commonly used in bond markets, means that the yield is stated on a semiannual bond basis and is an annual percentage rate that has a periodicity of 2.

This yield statistic of 5.174% is the investor's rate of return over the 10 years assuming that the investor holds the bond until maturity, there is no loss arising from default by the corporate issuer, and there are no taxes. Later in this chapter we relax the first two assumptions. What is the investor's “horizon yield” if the holding period is less than 10 years? What is the implied probability of default if an otherwise comparable risk-free government bond trades at a price higher than 60? We defer the implications of taxation until Chapter 4.

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