Chapter 3 Introduction to Fixed-Income Valuation 119
11
⎛
⎝
⎛⎛
⎛
⎛
⎝
⎝
⎛
⎛⎛⎛
⎞
⎠
⎞
⎞
⎠
⎠
+
1
⎛
⎝
⎛
⎛
⎝
⎝
⎞
⎠
⎞
⎞
⎞
⎞
⎠
⎠
⎞⎞
⎞⎞
AP
R
P
P
m
AP
R
P
P
n
m
RR
m
n
RR
n
1
0
0
3897
⎝
⎝
⎝
⎠
⎝
⎝
⎝
⎠
⎠
⎠
1
12
2
12
1
1
+
1
=
⎛
⎝
⎛
⎛
⎝
⎝
⎞
⎠
⎞
⎞
⎞
⎞
⎠
⎠
⎞⎞
⎞⎞
AP
R
1
P
1
1
12
12
12
+
1
=
⎛
⎝
⎛
⎛
⎝
⎝
⎞
⎠
⎞⎞
⎞
⎞
⎠
⎠
⎞
⎞⎞⎞
AP
R
1
P
P
1
12
12
2
1
.
+
1
=
⎝
⎝
⎝
⎠
⎠
⎠
1
P
1
1
12
12
+
1
=
⎛
⎝
⎛
⎛
⎝
⎞
⎠
⎞
⎞
⎞
⎞
⎠
⎞
⎞
⎞
⎞
AP
R
1
P
P
1
1
12
12
.
⎛
⎝
⎛⎛
⎛
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⎛⎛⎛
⎞
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⎞
⎞⎞⎞
AP
R
1
P
P
r
+
+
r
r
+
r
+
r
+
+
1
+
1
+
+
1
+
+
1
+
1
+
1
1
+
r
+
+
r
r
+
+
+
+
+
1
2
12
12
+
⎛
⎛⎛
⎛
⎛
⎛
⎛⎛⎛
⎞
⎞⎞
⎞
⎞
⎞⎞⎞⎞
+
1
=
⎛
⎛
⎛
⎞
⎞⎞
⎞
⎞
⎞
⎞⎞⎞
.
AP
R
1
P
P
120 Part II: Solutions
where:
P
V
=
present value, or the price of the bond
P
M
T
=
coupon payment per period
F
V
=
ca
ll
price pai
d
at ca
ll
d
ate
r
=
mar
k
et
d
iscount rate, or require
d
rate o
f
return per perio
d
10
1
3
3
3
3
3
102
=
()
1
+
+
()
1
1
+
+
()
1
+
++
()
1
1
+
+
+
)
(
1
+
)
(
1
+
()
1
1
+
=
=
=
()
+
()
+
+
()
()
+
+
+
+
+
()
+
+
PV
=
P
=
F
=
ll
d
ll
d
=
k
d
d
f
d
3
3
3
3
=
()
+
+
()
1
1
+
+
()
+
+
()
1
+
+
+
+
+
()
+
+
=
+
+
+
+
+
+
Chapter 3 Introduction to Fixed-Income Valuation 121
where:
P
V
=
present value, or the price of the oating-rate note
=
9
7
Inde
x
=
reference rate, stated as an annual percentage rate
=
0.01
QM
=
quote
d
margin, state
d
as an annua
l
percentage rate
=
0
.
0080
F
V
=
f
uture va
l
ue pai
d
at maturity, or t
h
e par va
l
ue o
f
t
h
e
b
on
d
=
100
m
=
periodicity of the oating-rate note, the number of payment periods per year
=
=
2
=
DM
=
d
iscount margin, t
h
e require
d
margin state
d
as an annua
l
percentage rate
Su
b
stituting given va
l
ues in:
1
00
()
00
10
0
080
×
0
10
()
00
1
+
+
×
1
00
100
()
00
10
+
0
..
0
10
+
080
0
0
×
00
1
+
+
+
00
1
00
1
+
0
1
00
1
0
1
00
1
+
+
+
+
+
+
+
+
0
1
00
1
0
1
00
1
0
0
1
+
1
+
9
0
0
9
0
0
1
+
0
0
1
+
r
00
1
0
.
+
DM
=
×
=
=
FV
=
=
=
=
=
122 Part II: Solutions
Chapter 3 Introduction to Fixed-Income Valuation 123
tax status, an
d
annua
l
yie
ld
s. A par curve is a sequence o
f
yie
ld
s-to-maturity suc
h
t
h
at eac
h
b
on
d
is price
d
at par va
l
ue.
36 . B is correct.
e spot curve, a
l
so
k
nown as t
h
e strip or zero curve, is t
h
e yie
ld
curve con
–
structe
d
f
rom a sequence o
f
yie
ld
s-to-maturities on zero-coupon
b
on
d
s.
e par curve is
a sequence o
f
yie
ld
s-to-maturity suc
h
t
h
at eac
h
b
on
d
is price
d
at par va
l
ue.
e
f
orwar
d
a
dd
-on rate (
b
on
d
equiva
l
ent yie
ld
) is a rate quote
d
f
or money mar
k
et instruments suc
h
as
b
an
k
certi
cates o
f
d
e
p
osit an
d
in
d
ices suc
h
as Li
b
or an
d
Euri
b
or. Yie
ld
-to-maturity is
t
h
e interna
l
rate o
f
return on t
h
e
b
on
d
’s cas
h
ows—t
h
e uni
f
orm interest rate suc
h
t
h
at
w
h
en t
h
e
b
on
d
’s
f
uture cas
h
ows are
d
iscounte
d
at t
h
at rate, t
h
e sum o
f
t
h
e
p
resent va
l
ues
e
q
ua
l
s t
h
e
p
rice o
f
t
h
e
b
on
d
. It is t
h
e im
pl
ie
d
mar
k
et
d
iscount rate.
ll
124 Part II: Solutions
is used to calculate the G-spread for euro-denominated corporate bonds, not UK bonds.
e G-spread is calculated as follows:
Y
ield-to-maturity on the UK corporate bond:
r
100.65
5
5
1
0
5
,
0.04
7
62 or
47
6bps
12
3
()
r
1
()
r
1
1
()
r
1
=
+
+
=
Yie
ld
-to-maturity on t
h
e UK government
b
enc
h
mar
k
b
on
d:
r
,
12
3
()
r
()
r
1
1
()
r
=
+
3
3
5
5
105
5
0720
5
15
1
5
3
0565
25
2
2
10
2