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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