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The term structure of
interest rates
Econ 230 Financial Markets and Institutions
Prof. Cahill
Fall 2009
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View Full Document The yield curve
Plot of the yield to maturity of bonds with
different terms to maturity
Standard:
use U.S. Treasury bonds
Elsewhere:
swap rate yield curve/LIBOR curve
Use securities with no default risk, high liquidity
Spreads represent maturity premium only
Ideally use zero coupon bonds
Swap rate yield curve
Generic (“vanilla” or “bullet”) interest rate swap
1 party pays a variable rate (usually tied to LIBOR)
Counterparty pays a fixed rate, the “swap rate”
Should be the avg. exp. variable rate over lifetime of swap
Different swap rates for different contract lengths
Not default or liquidity risk free, but close
Used as standard in most of rest of the world
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View Full Document Shapes of the yield curve
Normal
Flat
Inverted
i
Term to maturity
i
Term to maturity
i
Term to maturity
How to calculate with coupon bonds?
Bootstrapping method
z
t
is the rate on a zero coupon bond with maturity
t
e.g. 2 year bond w/ annual
CF
:
CF
1
,
CF
2
,
M
Text does 6month coupon payments
You observe 1 year zero coupon rate from market (
z
1
)
P = CF
1
/ (1+
z
1
) + (
CF
2
+
M
)/ (1+
z
2
)
2
Use known
P
,
CF
,
M
and
z
1
from market
Solve for
z
2
, the 2year spot rate
Repeat for every maturity
Yield curve uses these zerocoupon equivalent spot rates
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View Full Document How to calculate with coupon bonds?
Bootstrapping method example
CF
= 50,
M
= 1,000,
z
1
=3%,
i
2
= 6%,
n
= 2
P
= 981.67 = 50/1.06 + 1050/1.06
2
P = CF
1
/ (1+
z
1
) + (
CF
2
+
M
)/ (1+
z
2
)
2
981.67 = 50/(1.03) + 1050/ (1+
z
2
)
2
(1+
z
2
)
2
= 1050/933.12 = 1.125
(1+
z
2
) =1.061
z
2
=
6.1%
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This note was uploaded on 02/19/2010 for the course ECON 1313212 taught by Professor John during the Spring '09 term at The School of the Art Institute of Chicago.
 Spring '09
 John
 Interest Rates

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