Fin 448: FixedIncome Securities
Homework Solution 6
Wei Yang
1
Interest rate swap
(1.1)
Since it is immediately after an exchange, the FRN will trade at par. The
value of the floating rate side is thus $100M.
(1.2)
The fixed rate side is a 3.5year bond paying semiannual coupons at a
coupon rate
c
=4.5%, while the yield curve is flat at
y
= 4.2%.
P
=
Z
c
y
"
1

1
(
1 +
y
2
)
2
n
#
+
Z
1
(
1 +
y
2
)
2
n
The price is $100.967M.
(1.3)
As a buyer you have a long position in FRN and a short position in the
fixed rate bond, so you have realized a loss of $0.967M.
2
Hedging bond position with swaps
(2.1)
A long position in swaps implies that you have bought an FRN and sold a
fixed rate bond. To hedge a long position in bonds, you need to long a swap.
The swap rate is just 5%, the same as the par yield of the Libor quality bonds.
(2.2)
The
DV
01 of a $1M face value par bond is $779.458.
For the FRN, which is priced at par
P
= 10
6
DV
01 =
1
2
1 +
l
2
×
P
×
1
10
4
= 49
.
0196
(2.3)
Our swap position implies buying floating and paying fixed, and thus a
total
DV
01 of 49
.
0196

779
.
458. The
DV
01 of the bond holdings cancel with
1
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the
DV
01 of the fixed side of the swap.
We are left with a positive
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 Spring '10
 WeiYang
 Finance, Interest, Interest Rate, Yield Curve, Interest rate swap

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