AS.440.640 Financial Economics
Lecture 2
Zhou, Nan
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2
Bonds
I
Bonds are a form of debt that are held for a fixed term,
expiring at the maturity date
I
Issued by sovereign governments, municipalities, and
corporations to finance investment projects
I
As with any debt, there is a risk of default if the borrower is
unable to meet repayment obligations
I
The greater the chance of default, the higher the rate of return
that prospective investors demand as compensation, or
equivalently the lower the market price of the bond
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2
Zero Coupon Bond
I
A zero coupon bond promises a single payment, known as the
par or face value, due at maturity
I
Market prices are quoted as a percentage of par value, a three
year bond priced at 90
3
/
8
sells for 90
.
375 per 100 par value
I
Assume that face value equals 100 unless otherwise specified
I
The yield to maturity is the discount rate that sets the bond
price equal to the present value of the promised payment
PV
=
100
(1 +
y
)
3
= 90
.
375
y
=
100
90
.
375
1
3

1
≈
0
.
0343
I
Zero coupon bonds are almost always sold at discount, or
below par, otherwise the yield would be negative
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2
Coupon Bond
I
A coupon bond promises periodic coupon payments in
addition to repayment of par value at maturity
I
Name derives from literal coupons printed on bond certificates
that could be clipped and redeemed for payment
I
Intended to be sold near par value with the coupon mimicking
an interest payment
I
However, the coupon rate is set by the terms of the bond and
does not necessarily relate to the bond’s actual yield which is
determined by market forces
I
Suppose that the same entity as the previous example issues a
three year bond with an annual coupon of 5
.
625
Year
1
2
3
Cash Flow
5
.
625
5
.
625
105
.
625
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2
Pricing a Coupon Bond
I
Suppose that the yield on this coupon bond is identical to the
that of the zero coupon bond considered earlier
y
= 0
.
0343
I
Can find the price by computing the present value, noting that
a coupon bond is simply the sum of an annuity and a zero
coupon bond
PV
=
T
X
t
=1
C
(1 +
y
)
t
+
F
(1 +
y
)
T
=
C
y
1

1
(1 +
y
)
T
+
F
(1 +
y
)
T
=
5
.
625
0
.
0343
1

1
1
.
0343
3
+
100
1
.
0343
3
≈
106
.
155
I
Note that this bond sells at a premium, or above par, why?
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2
U.S. Treasury Securities
I
Considered to be an extremely safe investment given
practically nonexistent default risk
I
Coupons on U.S. Treasury bonds are paid semiannually  every
six months
I
For example, suppose that a five year Treasury bond has a
yield of
y
= 0
.
0229 and an annual coupon of 2
.
13, this implies
that you are entitled to coupon payments of 1
.
065 twice a year
I
To find the price of this bond, use the compounding formula
with
n
= 2 periods per year
PV
=
C
n
y
n
"
1

1
(
1 +
y
n
)
nT
#
+
F
(
1 +
y
n
)
nT
=
1
.
065
0
.
01145
1

1
(1
.
0
.
01145)
10
+
100
(1
.
01145)
10
≈
99
.
2482
Zhou, Nan
AS.440.640 Financial Economics
Lecture 2