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Lecture 7
The Term Structure of Interest Rates Continued.
I.
Overview
A) Estimating implied forward rates from current rates
B) Using implied forward rates to hedge future debt assets and obligations
C) Trading strategies
II.
Estimating implied forward rates from current rates
A) Given spot rates z
1
, z
2
, … z
T
, we can estimate implied forward rates. Let
j
f
t
denote the t year spot rate j years from now.
Given z
j
and z
t+j
we can estimate the implied t year spot rate j years from
now,
j
f
t
.
Recall the implied forward rate
j
f
t
is the future spot rate that will make an
investor indifferent between investing in a t+j year zero coupon bond or
investing in a j year zero coupon bond and then reinvesting the money in
a tyear zero coupon bond j years from now.
(1+z
t+j
)
t+j
= (1+z
j
)
j
* (1+
j
f
t
)
t
or
j
f
t
= [(1+z
j
)
j
*(1+z
t+j
)
t+j
]
1/t
 1.
Example: The zerocoupon yield curve and implied forward yield curves
can be found in the following table
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Years to
maturity
Spot rates
10/13/00
Implied
forward
rates
10/13/01
Implied
forward
rates
10/13/02
Implied
forward
rates
10/13/05
Implied
forward
rates
10/13/15
1year
5.949%
5.6252%
6.6805%
2year
5.787%
6.1516%
6.436%
3year
6.084%
6.1651%
6.5464%
4year
6.111%
6.3154%
5year
6.242%
6.4701%
4.542%
10year
6.356%
6.5587%
4.9147%
15year
6.453%
5.8822%
4.8769%
20year
5.972%
5.7335%
25year
5.835%
5.5464%
30year
5.662%
These implied forward rates are poor predictors of actual future rates.
The implied forward rates can be used to hedge future interest rate assets and
liabilities.
II.
Using Forward Rates to Hedge Against Future Interest Rate Changes
A) Forward rates can be thought of as “break even” rates on interest rate
hedges.
Example: Suppose you run a bank that makes longterm ARM loans based
on the yield on 15year bonds and borrows money in the mediumterm portion
of the yield curve by issuing 5year CDs to your customers.
The yield on your ARM loans is equal to the yield on 15year gov’t bonds
plus a fixed premium. Your CD’s pay a yield slightly above the yield on a 5
year gov’t bond.
Thus your bank makes profits when the yield curve is upward sloping in the 5
15 year range. If the yield curve inverts your profits will be hurt. Thus, you
have an incentive to hedge in such a way that you will make money if the
yield curve inverts. The implied forward rates are the rates at which dynamic
hedging strategies break even.
To hedge against an inversion 5 years from now in the 515 year range of the
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 Winter '08
 CHABOT
 Interest Rates

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