Chapter 20
Bond Markets
Investments
© K. Cuthbertson and D. Nitzsche
Learning Objectives
 Relationship between various measures of return on
a bond



Spot rates
YTM
Holding period return
 Bond price and spot interest rates on a coupon
paying bond
 Key features of government bond markets
 Pricing of Corporate bonds
© K. Cuthbertson and D. Nitzsche
Intro to Fixed Income Securities

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Coupon paying bond

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Pricing of bond
 M=1000; C=80; n=5; S1=4.5%; S2=5.1%; S3=5.5%
S4=5.8% S5=6.1%
1
2
3
4
5
0.045
80
0.051
80
0.055
80
0.058
80
0.061 1080
P=
© K. Cuthbertson and D. Nitzsche
76.555
72.424
68.129
63.848
803.24
1084.2
Figure 1 : Coupon-paying bond
100
P
0
C
C
C
1
2
3
...
C
n
n = time to maturity of bond
100 = redemption value, or par value, of bond
P = bond price
C = coupon on bond
© K. Cuthbertson and D. Nitzsche
Time
Yield to Maturity of the Bond
 M=1000; C=80; n=5; S1=4.5%; S2=5.1%; S3=5.5%
S4=5.8% S5=6.1%
1 0.045
80
2 0.051
80
3 0.055
80
4 0.058
80
5 0.061 1080
P=
 YTM=6.0011
© K. Cuthbertson and D. Nitzsche
76.555
72.424
68.129
63.848
803.24
1084.2
Table 4 : Yield and price relationship
Bond sells at
Relationship
Par
when coupon rate = YTM
Discount
when coupon rate < YTM
Premium
when coupon rate > YTM
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Holding Period Return
 P0= 1000; C=100; n=5 years; If you sell in two years
when r=9% you will get P2= 1025.3 (FV=1000; N=3; r=9;
PMT=100; PV=?)
 Then your holding period return=11.11 based on the
following cash flows PV=-1000;
FV=1025.3+209.5=1234,8, n=2; r=? ( return for coupon
payments 100 paid in year 1 is reinvested @9.5 and
makes 109.5 at year two plus 100 for second year =209.5)
 I would rather not worry about reinvestment of coupon
and set it up as PV=-1000; PMT =100; n=2; FV = 1025.3
and find the return; note FV depends on interest rate
when you sell the bond before maturity!
© K. Cuthbertson and D. Nitzsche
Figure 2 : Holding period return (two years)
5 year, 10% coupon (annual)
Par = $1000
P0 = $1000 (YTM = 10%)
Reinvestment rate = 8%
P2 = $1025.30
(YTM = 9%)
Capital
gain
M = $1000
P0 = $1000
(YTM = 10%)
$100
$100
9.5%
0
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1
2
3
4
5
Time
Figure 3 : Gilts outstanding
11%
2%
87%
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Conventional
Index linked
Undated
Figure 4 : Gilts prices
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Figure 5 : Shareholder and bondholder pay-offs
Payoff
0
S
Payoff
M
Value of firm
Shareholder Payoff
© K. Cuthbertson and D. Nitzsche
M
Value of firm
Bondholder Payoff