Transcript Slide 1
Chapter 6
The Term Structure And
Risk Structure Of
Interest Rates
©Thomson/South-Western 2006
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The Term Structure Of Interest
Rates
The term structure of interest rates is the relationship at any given time
between the length of time to maturity and the yield on a debt security.
The yield curve graphically depicts the term structure of interest rates.
The length of time to maturity is on the horizontal axis and the yield on
the vertical axis.
Each point on a curve corresponds to the yield on a given day of a
particular type of bond for a particular maturity date.
Term structure exists for different types of debt instruments—usually bonds
US Treasuries
Corporate Bonds
State and Local Bonds
The yield curve is typically ascending, but can be flat, descending, or
humped.
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Figure 6-1
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Theories Of Term Structure
The pure expectations theory
The liquidity premium theory
The segmented markets theory
The preferred habitat theory
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Pure Expectations Theory
Market forces dictate that the yield on a long-term
bond of any particular maturity equals the geometric
mean (or average) of the current short-term yield
and successive future short-term yields currently
expected to prevail over the life of the long-term
security.
If transactions costs are zero, the investor would
expect to earn the same average return over the
long run if they:
purchase a long-term bond and hold it to maturity or
purchase a short-term bond and "roll it over" every time it
matures.
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Assumptions of the Pure
Expectations Theory
Investors seek to maximize holding period returns--the
returns earned over their relevant planning horizons.
Investors have no institutional preference for particular
maturities. They regard various maturities as perfect
substitutes for each other.
There are no transactions costs associated with buying and
selling securities. Hence, investors will always swap
maturities to respond to perceived yield advantages.
Large numbers of investors form expectations about the
future course of interest rates, and act aggressively on those
expectations.
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The Implicit Forward Interest Rate:
Two-Year Investment Horizon
The implicit forward interest rate is the rate on one-year
securities one year in the future that would leave you
indifferent between the two strategies.
R1 + t+1r1 = 2R2
R1 and R2 are the yields available today on one and
two-year Treasury securities, respectively.
t+1r1 is the implicit forward rate that would balance the
equation.
From there we can easily calculate this implicit forward rate:
t+1r1 = 2R2 - R1.
Considering compounding, the math becomes
(1 + R1)(1 + t+1r1) = (1 + R2)2
t+1r1 = (1 + R2)2/(1 + R1) – 1
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Implicit Forward Rate: 20 Year
Investment Horizon
Over the long run, compounding is more important, so:
(1 + tRL)n = (1 + tR1)(1 + t+1r1)(1 + t+2r1)...(1 + t+n-1r1)
where currently available yields are
tRL on long-term bonds
tR1 short-term (one-year) bonds
For a 20-year horizon let n=20
The r’s that make the two sides equal are unbiased estimates
of the market's expectation of future interest rates, such as:
tRL = ((1 + tR1)(1 + t+1r1)(1 + t+2r1)…(1 + t+n-1r1))1/n - 1
The current long-term bond yield is the geometric mean of the current
one-year bond yield (tR1) and future one-year bond yields (the r's)
currently expected to prevail over the life of the long-term bond.
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Implications of the Pure
Expectations Theory
If investors believe that short-term interest rates will be higher in the
future, the yield curve today slopes upward.
If investors think interest rates will decline in the future, the yield curve is
downward sloping or inverted.
In the pure expectations theory:
an ascending yield curve is evidence of market consensus that
interest rates are headed upward;
a downward-sloping or inverted yield curve implies that economic
agents expect that interest rates are headed lower, and
a flat yield curve implies a consensus that future yields will remain the
same as current yields.
In the pure expectations theory, nothing except the outlook for interest
rates affects the shape of the yield curve.
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Liquidity Premium Theory
The pure expectations theory of term structure is
correct, except for this issue: long-term bonds entail
greater market risk than short-term securities do.
Market risk is the risk of appreciable fluctuation in the price
of the security due to interest rate changes.
Investors may have to sell their assets prior to maturity,
exposing themselves to the possibility of losses as interest
rates and thus market prices change.
If bond buyers are risk averse, they must be
compensated with a term premium for the greater
market risk inherent in long-term bonds.
tRL = ((1 + tR1)(1 + t+1r1)(1 + t+2r1)…(1 + t+n-1r1))1/n -1 + TP
The Liquidity Premium Theory states that the term premium
(TP) is positive and increases with the length of term, so
the normal yield structure is ascending.
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Figure 6-3
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Segmented Markets Theory
Securities of different maturities are very poor substitutes for one another.
From lenders’ vantage point:
Short-term securities possess liquidity and great stability of principal.
Long-term securities provide stability of income over time, but higher market
risk.
A lender who prefers income stability would clearly prefer long-term bonds,
whereas a lender who values principal protection prefer short-term securities.
From borrowers’ vantage point:
Firms borrowing to finance inventories prefer short-term loans.
Families buying homes prefer long-term fixed rate mortgages.
Municipalities and corporations may prefer to finance long-term capital
projects on a longer-term .
Individuals and firms are strongly motivated to match the maturities of
their assets with the maturities of their liabilities.
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Implications of the Segmented
Markets Theory
Yields in any maturity sector are determined strictly by supply
and demand conditions in that sector.
Corporate and U.S. Treasury debt management decisions
significantly influence the shape of the yield curve.
If firms and the government are currently issuing
predominantly long-term debt, the yield curve will be
relatively steep.
If they are issuing principally short-term debt, short-term
yields will be high relative to long-term yields.
Treasury debt management is a potential tool of economic
policy because it can influence the yield curve.
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Figure 6-4
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Preferred Habitat Theory
This hybrid theory combines elements of the other
three.
Borrowers and lenders do hold strong preferences
for particular maturities.
The yield curve will not conform strictly to the
predictions of the other three theories.
If expected additional returns to be gained by deviating
from their preferred maturities become large enough,
institutions will deviate from their preferred maturities.
Institutions will accept additional risk in return for
additional expected returns.
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Term Structure Theories: How Well
Do They Explain The Facts?
The facts:
The yield curve slopes upward most of the time.
The yield curve typically shifts up and down over
time rather than twisting or rotating about some
point along the curve.
While both short-term and long-term interest rates
exhibit a pro-cyclical pattern, short-term yields
exhibit considerably greater amplitude over the
business cycle than long-term yields do.
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Fact 1: Upward-Sloping Yield
Curve Predominates
Upward-sloping yield curves are much more
prevalent than inverted yield curves.
In periods when inverted yield curves do
occur, short-term interest rates exceed longterm rates by only small margins.
The predominance of the upward-sloping
yield curve is consistent with all of the
theories except the pure expectations theory.
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Fact 2: Yields of Various Maturities
Typically Move in the Same Direction
The yield curve normally shifts upward or
downward each week or month rather than
twisting or rotating about some point along the
yield curve.
The pure expectations theory, the liquidity
premium theory, and preferred habitat theory
easily explain this empirical regularity.
The segmented markets theory cannot
account for this.
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Fact 3: Yield Curve Exhibits A
Regular Cyclical Pattern
Both short-term and long-term interest rates move
pro-cyclically over the course of the business cycle:
rising during expansions and
falling during recessions.
Short-term rates exhibit much greater amplitude
than long-term rates over the cycle.
The pure expectations theory, the liquidity premium
theory, and preferred habitat theory easily explain
this empirical regularity.
The segmented market theory's explanation is
plausible if Fed engages in counter-cyclical policy.
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Figure 6-5
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The Risk Structure Of Interest
Rates
A security issuer defaults if it fails to meet the terms of the contractual
agreement (indenture) in full.
For a bond, default is either the borrower's failure to make full interest
payments at stated dates or to redeem the bond at face value at maturity.
Embedded in the yields of risky securities is a premium to compensate
lenders for default risk.
The magnitude of this premium varies widely among different securities.
The magnitude of the risk premium is the difference between the yield
on a risky security and a risk-free security (like a Treasury bill).
Moody's and Standard and Poor's, provide ratings of the quality of
corporate and municipal bonds in the United States (ranging from
investment grade bonds to junk bonds.)
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Risk Premiums
The magnitude of risk premiums increases during
recessions and other times when firms experience
financial distress.
The risk premium increased during the severe recessions
of 1973-1975 and 1981-1982 as the incidence of
corporate financial distress escalated sharply.
It decreased modestly during the economic boom of the
1990s.
The risk premium increased again in 2001 and 2002:
recession of 2001
September 11, 2001
the corporate scandals of 2002
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Figure 6-6
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Default-Free Market
Sd1
Interest rate
Interest rate
Figure 6-7
Risky Market
Sr2
Sr1
ir2
Sd2
ir1
id1
Dr1
id2
Dd1
Loanable Funds (Q)
Loanable Funds (Q)
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