Assume that a 10-year Treasury bond has a 12% annual coupon, while a 15-year T-bond has an 8% annual coupon. Assume also that the yield curve is flat, and all Treasury securities have a 10% yield to maturity. Which of the following statements is CORRECT?

Question

Quizplus · Accepted Answer

We can tell by inspection that b, c, and d are all incorrect. That leaves answers a and e as the only possibly correct statements. Also, recognize that longer-term bonds, and ones where payments come late (like low coupon bonds) are most sensitive to changes in interest rates. Thus, the 15-year, 8% coupon bond should be more sensitive to a decline in rates. Finally, we can do some calculations to confirm that e is the correct answer:
  $ \quad $  $ \quad $ $\text { Current situation }$   $ \quad $   $ \quad $  $ \quad $  $ \quad $  $ \quad $ $ \quad $ $\text { Rates decline }$
$\begin{array}{rr}
&10 \text {-year } &15 \text {-year }&10 \text {-year } &15 \text {-year }\
\text {Par}&1000&1000&1000&1000\
 \text {Maturity}&10 & 15 &10 & 15\
\text {Coup rate}&12 \% & 8 \% &12 \% & 8 \%\
\text {YTM}&10.00 \% & 10.00 \% & 9.00 \%&9.00 \%\
\text {Ann coup}&120 & 80 &120 & 80\
\text {Price}&\$ 1,122.89 & \$ 847.88&\$ 1,192.53& \$ 919.39\
\text {\%Gain}&&&6.2\%&8.4\%
\end{array}$

Assume That a 10-Year Treasury Bond Has a 12% Annual