Chapter 6 APPENDIX B - Pearsoncmg.com

Chapter 6 Bonds 181
To summarize, for the three-year bonds considered:
Coupon Rate 0% 4% 10%
YTM 4.50% 4.47% 4.44%
◗ Evaluate
Note that even though the bonds all have the same maturity, they have different yields. In fact, holding constant
the maturity, the yield decreases as the coupon rate increases. We discuss why below.
Example 6.11 shows that coupon bonds with the same maturity can have different
yields depending on their coupon rates. The yield to maturity of a coupon bond is a
weighted average of the yields on the zero-coupon bonds. As the coupon increases, earlier
cash flows become relatively more important than later cash flows in the calculation of
the present value. The shape of the yield curve keys us in on trends with the yield to maturity:
1. If the yield curve is upward sloping (as it is for the yields in Example 6.11), the
resulting yield to maturity decreases with the coupon rate of the bond.
2. When the zero-coupon yield curve is downward sloping, the yield to maturity will
increase with the coupon rate.
3. With a flat yield curve, all zero-coupon and coupon-paying bonds will have the
same yield, independent of their maturities and coupon rates.
Treasury Yield Curves
As we have shown in this section, we can use the zero-coupon yield curve to determine
the price and yield to maturity of other risk-free bonds. The plot of the yields of coupon
bonds of different maturities is called the coupon-paying yield curve. When U.S. bond
traders refer to “the yield curve,” they are often referring to the coupon-paying Treasury
yield curve. As we showed in Example 6.11, two coupon-paying bonds with the same
maturity may have different yields. By convention, practitioners always plot the yield of
the most recently issued bonds, termed the on-the-run bonds. Using similar methods to
those employed in this section, we can apply the Law of One Price to determine the zerocoupon
bond yields using the coupon-paying yield curve. Thus, either type of yield curve
provides enough information to value all other risk-free bonds.