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Investments,
8th
editionBodie,
Kane
and
MarcusSlides
by
Susan
HineMcGraw-Hill/IrwinCopyright
©
2009
by
The
McGraw-Hill
Companies,
Inc.
All
rightsreserved.CHAPTER
15The
TermStructure
ofInterest
Rates
Information
on
expected
future
short
termrates
can
be
implied
from
the
yield
curve
The
yield
curve
is
a
graph
that
displays
therelationship
between
yield
and
maturity
Three
major
theories
are
proposed
to
explainthe
observed
yield
curve15-2Overview
of
Term
StructureFigure
15.1
Treasury
Yield
Curves15-3BondPricing15-4
Yields
on
different
maturity
bonds
are
not
allequal–
Need
to
consider
each
bond
cash
flow
as
astand-alone
zero-coupon
bond
whenvaluing
coupon
bondsTable
15.1
Yields
and
Prices
toMaturities
on
Zero-Coupon
Bonds($1,000
Face
Value)15-5Yield
Curve
Under
Certainty
An
upward
sloping
yield
curve
is
evidencethat
short-term
rates
are
going
to
be
highernext
year
When
next
year’s
short
rate
is
greater
thanthis
year’s
short
rate,
the
average
of
thetwo
rates
is
higher
than
today’s
rate15-6Figure
15.2
Two
2-Year
InvestmentPrograms15-7Figure
15.3
Short
Rates
versus
SpotRates15-8fn
=
one-year
forward
rate
for
period
nyn
=
yield
for
a
security
with
a
maturity
of
nForward
Rates
from
Observed
Rates15-9Example
15.4
Forward
Rates15-104
yr
=
8.00%
3yr
=7.00%fn
=?(1.08)4
=
(1.07)3
(1+fn)(1.3605)
/
(1.2250)=
(1+fn)fn
=
.1106
or
11.06%Downward
Sloping
Spot
Yield
CurveExample15-11Zero-Coupon
RatesBond
Maturity12%111.75%211.25%310.00%49.25%5Forward
Rates
for
Downward
SlopingY
C
Example15-121yr
Forward
Rates1yr[(1.1175)2
/
1.12]
-
1=0.1150062yrs[(1.1125)3
/
(1.1175)2]
-
1=0.1025673yrs[(1.1)4
/
(1.1125)3]
-
1=0.0633364yrs[(1.0925)5
/
(1.1)4]
-
1=0.063008Interest
Rate
Uncertainty
What
can
we
say
when
future
interest
ratesare
not
known
today
Suppose
that
today’s
rate
is
5%
and
theexpected
short
rate
for
the
following
year
isE(r2)
=
6%
then:
The
rate
of
return
on
the
2-year
bond
is
riskyfor
if
next
year’s
interest
rate
turns
out
toabove
expectations,
the
price
will
lower
andvice
versa15-13Interest
Rate
Uncertainty
Continued15-14
Investors
require
a
risk
premium
to
hold
alonger-term
bond
This
liquidity
premium
compensates
short-term
investors
for
the
uncertainty
about
futurpricesExpectationsLiquidity
Preference–
Upward
bias
over
expectations15-15Theories
of
Term
StructureExpectations
Theory15-16
Observed
long-term
rate
is
a
function
oftoday’s
short-term
rateand
expected
futureshort-term
rates
Long-term
and
short-term
securities
areperfect
substitutes
Forward
rates
that
are
calculated
from
theyield
on
long-term
securities
are
marketconsensus
expected
future
short-term
ratesLong-term
bonds
are
more
risky
Investors
will
demand
a
premium
for
therisk
associated
with
long-termbonds
The
yield
curve
has
an
upward
bias
builtinto
the
long-term
rates
because
of
the
riskpremium
Forward
rates
contain
a
liquidity
premiumand
are
not
equal
to
expected
future
short-term
rates15-17Liquidity
Premium
TheoryFigure
15.4
Yield
Curves15-18Figure
15.4
Yield
Curves(Concluded)15-19Interpreting
the
Term
Structure15-20
If
the
yield
curve
is
to
rise
as
one
moves
tolonger
maturitiesA
longer
maturity
results
in
the
inclusion
oa
new
forward
rate
that
is
higher
than
theaverage
of
the
previously
observed
ratesReason:Higher
expectations
for
forward
rates
orLiquidity
premiumFigure
15.5
Price
Volatility
of
Long-Ter15-21Treasury
BondsFigure
15.6
Term
Spread:
Yields
on
10-Year
Versus
90-Day
Treasury
Securities15-22Forward
Rates
as
Forward
Contracts15-23
In
general,
forward
ra
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