$\begin{array}{l}
\text { The following information relates to Questions } 15 - 17\
\begin{array} { l c c c c }
\hline \text { Bond } & \text { Coupon Rate } & \text { Time-to-Maturity } & \text { Time-to-Maturity } & \text { Spot Rates } \
\hline \mathrm { X } & 8 \% & 3 \text { years } & 1 \text { year } & 8 \% \
\mathrm { Y } & 7 \% & 3 \text { years } & 2 \text { years } & 9 \% \
\mathrm { Z } & 6 \% & 3 \text { years } & 3 \text { years } & 10 \% \
\hline
\end{array}
\end{array}$
All three bonds pay interest annually.
-based upon the given sequence of spot rates, the yield-to-maturity of bond Z is closest to:
A) 9.00%.
B) 9.92%.
C) 11.93%

Question

$\begin{array}{l}
\text { The following information relates to Questions } 15 - 17\
\begin{array} { l c c c c } 
\hline \text { Bond } & \text { Coupon Rate } & \text { Time-to-Maturity } & \text { Time-to-Maturity } & \text { Spot Rates } \
\hline \mathrm { X } & 8 \% & 3 \text { years } & 1 \text { year } & 8 \% \
\mathrm { Y } & 7 \% & 3 \text { years } & 2 \text { years } & 9 \% \
\mathrm { Z } & 6 \% & 3 \text { years } & 3 \text { years } & 10 \% \
\hline
\end{array}
\end{array}$ 
All three bonds pay interest annually.
-based upon the given sequence of spot rates, the yield-to-maturity of bond Z is closest to:
A) 9.00%.
B) 9.92%.
C) 11.93%

Quizplus · Accepted Answer

The yield-to-maturity (YTM) of bond Z can be approximated by the average of the spot rates for its cash flows since it has a 3-year maturity and the spot rates for 1, 2, and 3 years are 8%, 9%, and 10% respectively. The average of these rates gives a rough approximation of the YTM. The calculation is (8% + 9% + 10%) / 3 = 9%. However, because bond Z has a lower coupon rate than the spot rates, its YTM will be slightly higher than the average spot rate to compensate for the lower coupon payments. Therefore, the closest estimate is 9.92%.

All Three Bonds Pay Interest Annually