Pure Discount Bonds% 41... Bonds Trading at Par – If a bond’s price equals its face value, then its yield-to-maturity = current yield = coupon rate... First Solution Method00... Second
Trang 1Chapter 8 Contents
• 1 Using Present Value Formulas to Value Known
Flows
• 2 The Basic Building Blocks: Pure Discount Bonds
• 3 Coupon Bonds, Current Yield, and
Yield-to-Maturity
• 4 Reading Bond Listings
• 5 Why Yields for the same Maturity Differ
• 6 The Behavior of Bond Prices Over Time
Trang 2Bond Prices Rise as the
Interest Rates Fall
as the sum terms
n n
n n
n j
j j
i
pmt i
pmt i
pmt i
pmt
i
pmt PV
+
+
+
+ +
+
+
+
=
+
=
−
−
=
∑
1
1
* 1
1
*
1
1
* 1
1
*
1
1
*
1 1
2 2
1 1
1
Trang 3US Treasury Yiled Curve, Jan 97
4.50
5.00
5.50
6.00
6.50
7.00
7.50
Years to Maturity
Trang 4Pure Discount Bonds
the present value of a lump sum
equation we analyzed in Chapter 4
pure discount bond is given by the
relationship:
1
−
=
⇒ +
P
F i
i P
F
Trang 5Pure Discount Bonds
1
−
=
⇒ +
P
F i
i P
F
– P is the present value or price of the bond – F is the face or future value
– n is the investment period
– i is the yield-to-maturity
Trang 6Pure Discount Bonds
% 41 5
1 9000
10000
1 1
=
−
=
−
P
F i
Trang 7Bonds Trading at Par
– If a bond’s price equals its face value, then
its yield-to-maturity = current yield =
coupon rate Proof:
F i
pmt P
i i
pmt i
P
F
P i
F i
i
pmt P
n n
n n
=
=
⇒
+
−
=
+
−
⇒
=
+
+
+
−
=
1
1 1
1
1 1
&
1
1 1
1 1
Trang 8First Solution Method
00 1076
$
100
1000 1000
810 100
1000
890 100
1000
960
=
+ +
+
=
P
P
Trang 9Second Solution Method
91 075 ,
1
$
0728
1
100
1000 0600
1
100 0417
1
100
% 28 7
1 810
000 ,
1
% 00 6
1 890
000 ,
1
% 17 4
1 960
000 ,
1
3 2
3 1
3
,
0
2 1
2
,
0
1 1
1
,
0
=
+ +
+
=
=
−
=
=
−
=
=
−
=
P
P
i
i
i
Trang 10The YTM of the Coupon Bond
Trang 11( )
( )
( )
( )
>
− +
−
−
− +
−
−
=
− +
− +
=
⇒
>
>
>
+
+
+
−
=
0 1
1
1 1
&
1 1
1 1
1
1 1
0
&
0
&
0
&
1
1 1
1 1
n
n n
n
n n
i p
p f
i p
p f
p
x
f i
p
i
x
i
x n
i i
f i
i
x
p
Trang 12( ) ( ) ( )
=
⇒
− +
=
−
⇒
>
>
>
+
+
+
−
=
−
−
ytm
1 yield
coupon
1 ytm
1 ytm
1 yield
current
1
1 1
1 1
1
0
&
0
&
0
&
1
1 1
1 1
n
f x n p
x
n n
i
i i
x n
i i
f i
i
x
p
Trang 13Yield Relationships
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
600.00 800.00 1000.00 1200.00 1400.00 1600.00 1800.00
Price
coupon_y current_y y_t_m
Trang 14Yield Relationships
0.07
0.09
0.11
0.13
Price
coupon_y current_y y_t_m
Trang 15Two Yield Curves (Pure Discount)
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
Trang 16Dymanic Yield Curve
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
Current 5-year 10-year 15-Year 20-Year
Trang 17Interest Rates
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
spot long_forward
Trang 1820-Year Bond Value Over Time
920 940 960 980 1000 1020 1040 1060