Exhibit 19.3
Use the Information Below for the Following Problem(S)
The following information is given concerning a pure yield pick-up swap: You currently hold a 20 year, Aa 8 percent coupon bond priced to yield 10 percent. As a swap candidate you are considering a 20 year, Aa 10 percent coupon bond priced to yield 10.75 percent. Assume a reinvestment rate of 12.00 percent, semiannual compounding, and a one-year workout period.
$\begin{array}{lcc}
& \text { Curent Bond } & \text { Candidate Bond } \
\hline \text { Dollar Investment } & \$ 828.41 & \$ 938.83 \
\text { Coupon } & 80.00 & 100.00 \
\text { i on One Coupon } & 2.4 & ? \
\text { Principal Value at Year End } & 831.32 & ? \
\text { Total Accrued } & 913.72 & ? \
\text { Realized Compound Yield } & & ?
\end{array}$
10.5547
-Refer to Exhibit 19.3.The value of the swap is ____ basis points in one year.

Question

Exhibit 19.3
Use the Information Below for the Following Problem(S)
The following information is given concerning a pure yield pick-up swap: You currently hold a 20 year, Aa 8 percent coupon bond priced to yield 10 percent. As a swap candidate you are considering a 20 year, Aa 10 percent coupon bond priced to yield 10.75 percent. Assume a reinvestment rate of 12.00 percent, semiannual compounding, and a one-year workout period.
 $\begin{array}{lcc} 
& \text { Curent Bond } & \text { Candidate Bond } \
\hline \text { Dollar Investment } & \$ 828.41 & \$ 938.83 \
\text { Coupon } & 80.00 & 100.00 \
\text { i on One Coupon } & 2.4 & ? \
\text { Principal Value at Year End } & 831.32 & ? \
\text { Total Accrued } & 913.72 & ? \
\text { Realized Compound Yield } & & ?
\end{array}$
                                                                                10.5547
-Refer to Exhibit 19.3.The value of the swap is ____ basis points in one year.

Quizplus · Accepted Answer

$$\begin{array} { l c c } 
& \text { Current Bond } & \text { Candidate Bond } \
\hline \text { Dollar Investment } & \$ 824.41 & \$ 938.83 \
\text { Coupan } & 80.00 & 100.00 \
\text { i an One Coupon } & 2.4 & 2.75 \
\text { Principal Value at Year End } & 831.32 & 939.81 \
\text { Total Accrued } & 913.72 & 1042.56 \
\text { Realized Compound Yield } & & 10.7554
\end{array}$$
                                                                                          10.5547 
Current prices:
 $ P_{\text {corent }} $
$$
\begin{array}{l}
=40\left(\mathrm{PVIFA}_{5 \%, 40}\right)+1000(\mathrm{PVIF} \
=40(17.40) \
=1000(0.1420)=\$ 824.41
\end{array}
$$
$\begin{aligned}
P_{\text {candidate }} &=50\left(\mathrm{PVIFA}_{5375 \%, 40}\right)+1000\left(\mathrm{PVIF}_{5.375 \%, 40}\right.\
&=50(16.3132)+1000(0.1323)=\$ 938.83
\end{aligned}$
 
Year-end prices:
 $P_{\text {curent }}$
$$
\begin{array}{l}
=40\left(\mathrm{PVIF} \mathrm{A}_{5 \% .38}\right)+1000(\mathrm{PVIF} 5 \% .38) \
=40(16.8679)+1000(0.1566)=\$ 831.32
\end{array}
$$
$\begin{aligned}
\mathrm{P}_{\text {cendidate }} &=50\left(\mathrm{PVIFA}_{5375 \%, 38}\right)+1000\left(\mathrm{PVIF}_{5.375 \%}, 38\right.\
&=50(16.0602)+1000(0.1368)=\$ 939.81
\end{aligned}$ 
Current Bond
Percentage gain = ($913.72 - $824.41)/$824.41 = 0.108332
Realized yield per period = (1 + 0.108332)¹/² - 1 = 0.0527773
Realized compound yield = 2(0.02773)= 0.105547 = 10.5547%
Candidate Bond
Percentage gain = ($1042.56 - $938.83)/$938.83 = 0.110446
Realized yield per period = (1 + 0.110446)¹/² - 1 = 0.053797
Realized compound yield = 2(0.053797)= 0.107594 = 10.7594%
Swap value = 10.7594 - 10.5547 = 0.2047 = 20.47 basis points

Exhibit 19 &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp; &Nbsp;