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Fin221: CHAPTER 6
THE STRUCTURE OF
INTEREST RATES
Why interest rate vary among different financial
claims?
Interest Rate Changes & Differences Between
Interest Rates (yield) among financial claims
Can Be Explained by Several Variables :
• Term to Maturity.
• Default Risk.
• Tax Treatment.
• Marketability.
• Special features : Call or Put Options &
Convertibility.
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The Term structure of interest rate
• Term to maturity of a financial claim is the length of time
until the principal amount borrowed becomes payable.
• The term structure of interest rate refers to the
relationship between yield (interest rate) and term to
maturity on securities that differ only in length of time to
maturity.
• May be studied by plotting a Yield Curve at a point in
time
• The yield curve may be ascending, flat, or descending.
• Several theories explain the slope and the shape of the
yield curve, including the Expectations Theory and
Market Segmentation Theory.
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Yield Curves in the 2000s Exhibit 6.1
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The Expectations Theory of the Term Structure
• The shape and slope of the yield curve is
determined by expectations of future interest rate
movements, and changes in these expectations
lead to changes in the shape of the yield curve:
– Ascending: future interest rates are expected to increase.
– Descending: future interest rates are expected to decrease.
• Investors are assumed to be profit maximizers and that
they are indifferent towards interest rate risk (indifferent
about holding short-term or long-term securities).
• The theory implies a strong relationship between long
and short-term interest rates. Long-term interest rates
represent the geometric average of the current and a
series of expected future (implied, forward) interest rates.
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Term Structure Formula from Expectation Theory
1 t Rn   1 t R1 1 t 1f1 1 t 2 f1  1 t n1f1  n
1
where :
R  the observed market rate,
f  the forward rate,
t  time period for which the rate is applicable ,
n  maturity of the bond.
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The Term Structure Formula and The Implied Forward Rate
The term structure formula can be used to calculate the implied
forward rate (f1) given any two adjacent spot rates (tRn) and (tRn-1).
The formula used to calculate the implied forward rate is :
 1 t Rn  
f


1


t n 1 1
n 1
 1 t Rn1  
n
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Finding a One-Year Implied Forward Rate
• Using term structure of interest rates from January 29, 1999,
find the one-year implied forward rate for year three.
– 1-year Treasury bill
– 2-year Treasury note
– 3-year Treasury note
4.51%
4.58%
4.57%
 1  .0457 3 

1

0
.
0455
or
4.55%

3 f1  
2
 1  .0458  
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Term Structure and Liquidity Premium Theory
• Investors however know that long-term securities
have greater price variability (price risk) and have
less marketability, than short-term securities.
• Since long-term securities have greater risk,
investors require greater premiums to give up
liquidity.
• The yield curve therefore must have liquidity
premium added to it. The liquidity premium explains
an upward sloping yield curve, and that it will be
more upward sloping than that predicted by the
expectation theory.
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The Market Segmentation Theory
• Maturity preferences by investors may affect security
prices (yields), explaining variations in yields by time
• Market participants have strong preferences for securities
of particular maturity and buy and sell securities
consistent with their maturity preferences.
• As a result of these preferences, the yield curve is
determined by interaction of supply and demand for
securities at or near a particular maturity, and thus the
curve is segmented.
• If market participants do not trade outside their maturity
preferences, then discontinuities are possible in the yield
curve.
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The Market Segmentation and the Preferred
Habitat Theory
• The Preferred Habitat Theory is an extension of the
Market Segmentation Theory.
• The Preferred Habitat Theory allows market
participants to trade outside their preferred habitat
(maturity preferences) if adequately compensated for
the additional risk by a risk premium.
• Investors will reallocate their security holding in
response to the expected risk premium. This allows
for humps or twists in the yield curve, but limits the
discontinuities possible under Segmentation Theory.
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Which Theory is Right?
• Day-to-day changes in the term structure are
most consistent with the Preferred Habitat
Theory.
• However, in the long-run, expectations of
future interest rates and liquidity premiums
are important components of the position and
shape of the yield curve.
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Economic implications of the Yield Curve
Yield Curves are directly related to the level of
economic activity (the Business Cycle) and profits of
financial institutions:
 An ascending (upward sloping) yield curve
indicates the market expectations of higher
interest rates, higher periods of economic
expansion and/or higher inflation levels.
 The yield curve starts sloping upwards at the
beginning of the business cycle.
 Banks and financial institutions are expected to
make better profits. The more the steeper the yield
curve, the higher are the expected profits
 A descending (downward sloping) yield curve
forecasts the opposite indications.
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Interest-Rate and Yield-Curve Patterns Over the
Business Cycle
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Uses of the Yield Curve
• At any point in time, the slope of the yield curve
can be used to assess the general expectations
of borrowers and lenders about future interest
rates!
• Investors can use the yield curve to identify
under-priced securities for their portfolios.
• Issuers may use the yield curve to price their
securities.
• Investors use the yield curve for a strategy
known as riding the yield curve.
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Default Risk
• It is the probability of the borrower not honoring the
security contract. Losses may range from “interest a
few days late” to a complete loss of principal.
• Risk averse investors want adequate compensation
for expected default losses.
• Investors charge a Default Risk Premium for added risk of
default. It is measured as:
DRP = i - irf
• The DRP is the difference between the promised or
nominal rate and the yield on a comparable (same term)
risk-free securities.
• Investors are satisfied if the default risk premium is equal
to the expected default loss.
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Default Risk: Risk Premiums (May 2004)
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Default Risk, cont.
• Default Risk Premiums Increase (Widen) in Periods of
Recession and Decrease in Economic Expansion
• In good times, risky security prices are bid up; yields
move nearer that of riskless securities.
• With increased economic pessimism, investors sell risky
securities and buy “quality” widening the DRP.
• Credit Rating Agencies Measure and Grade Relative
Default Risk Security Issuers
• Cash flow, level of debt, profitability, and variability of
earnings are indicators of default riskness.
• As conditions change, rating agencies alter rating of
businesses and governmental debtors.
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Corporate Bond-Rating Systems
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Tax Effects on Yields
• The Taxation of Security Gains and Income Affects
the Yield Differences Among Securities
• The after-tax return, iat, is found by multiplying the
pre-tax return by one minus the marginal tax rate.
iat = ibt(1-t)
• Municipal bond interest income is tax exempt.
• Coupon income and capital gains have been taxed
differently in the past, but are now both taxed at
the same rate as ordinary income for individuals.
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To Buy a Municipal or a Corporate Bond?
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