Slide 7-3
Bond Basics
•
U.S. Treasury Securities
– Bills (maturity < 1 year), no coupons, sell at discount
– Notes (maturity: 1-10 years), coupons, sell at par
– Bonds (maturity: 10-30 years), coupons, sell at par
– STRIPS: Claim to a single coupon or the principal of a
government bond. (Don´t confuse this with the “forward strip”.)
•
U.S. Treasury yield curve: Constructed from STRIPS
– The yield of a bond equals the expected/actual return only for
zero-coupon bonds
•
Notation:
–
r
t
(
t
1
,
t
2
):
Interest rate from time
t
1
to
t
2
prevailing at time
t
.
–
P
t
(
t
1
,
t
2
):
Price of a bond quoted at time t, to be purchased at t =
t
1
maturing at t =
t
2
Slide 7-4
Yield to Maturity (YTM)
Section 7.1
•
Yield-to-Maturity,
y
(0,
T
), also called the internal rate of return (IRR), is
the rate of return of a zero-coupon bond if the bond is held until
maturity.
•
P
(0,
T
) is the price you would pay to receive $1 at time
T
= the present
value of $1 received at time T = discount factor for discounting at the
YTM.
•
Example: Coupon bond that pays an annual coupon of
c.
The bond will sell at par if
B(0,T,c)=$1
. The par coupon is:
T
,T
y
,T
P
)]
0
(
1
[
1
$
)
0
(
+
=
B
(0,
T
,
c
)
=
$
c
(1
+
y
)
t
t
=
1
T
∑
+
$1
(1
+
y
)
T
=
$
c
×
P
(0,
t
)
t
=
1
T
∑
+
P
(0,
T
)
c
=
1
−
P(0,T)
P(0,t)
t
=
1
T
∑