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S4: The Term Structure of Interest Rates – Background Reading
1
The Term Structure of Interest Rates
Objectives:
Use the term structure of interest rates to
i)
infer risk free interest rates and
ii) forward interest rates
Learning Outcomes
appreciate the demand for risk free assets by the retail investors and how this
demand is met by the income stripping exercise carried out by the financial
institutions
appreciate the need to estimate market expectations of future interest rates for
the purpose of investment decisions
learn from the expectation and liquidity premium hypotheses
(i)
the relationship between forward interest rates and market expectations
of future interest rates
(ii)
the choice of bonds with different maturities
appreciate the arguments for the demand for liquidity premium by retail
investors and the willingness of corporations to offer additional returns beyond
market expectations
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2
Are Fixed Coupon Bonds Risk Free Assets?
Let’s refer to the
5.75% May 2021
CGS that we priced before on Thu, 11/11/10 using a
YTM of
5.530%
and a settlement date on
Mon, 15/11/10
.
2.875x(1+
?
)
20
2.875x(1+
?
)
19
2.875x(1+
?
)
18
2.875x(1+
?
)
17
…….
2.875 x(1+
?
)
1
($
101.735
)
$2.875
$2.875
$2.875
$2.875
…..
$2.875
$
2.875+$100
15/11/10
15/05/11
15/11/11
15/05/12
15/11/12
…..
15/11/20
15/05/21
holding period
Since the YTM is 5.5.30% p.a. compounded semiannually, investors would expect their
investment of $101.735 to grow to $180.393 when the bond matures on 15/05/21.
21
)
2
%
530
.
5
1
(
735
.
101
180.393
To achieve this, all the coupon interests have to be reinvested at the same initial yield of
5.530% in the future, i.e.,
CI
15/05/21
=
2.875
x(1+
5.530
/2)
20
+
2.875
x(1+
5.530
/2)
19
+ … +
2.875
x(1+
5.530
/2)
1
+
2.875
=
80.393
FV
15/05/21
=
100.000
In summary,
fixed coupon bonds are
not
risk free  the yield is only an expected return for holding the
bond to maturity as investors may not be able to reinvest all the coupon interests at the
same rate as the initial yield.
there is an implicit (though unrealistic) assumption about the YTM that that investors can
reinvest all the future coupon interest at the same rate as the initial yield.
S4: The Term Structure of Interest Rates – Background Reading
3
How do we measure expected return if we don’t hold the bond to maturity?
We know what to expect if we were to hold a bond to maturity, but what if our investment
horizon doesn’t match the bond’s maturity? For example, if we have a 2year investment
horizon, which of the following choices should we choose?
0
1
2
3
4
.
.
.
n
roll over two 1year bonds
buy and hold a twoyear bond to maturity, or
buy a nyear bond and sell it after two years, where n > 2.
We should first compare the “expected” return, rather than the YTM, of these alternatives
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This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.
 One '09
 Nicole

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