Money and Banking

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Learning Unit #13
Term Structure of Interest Rates

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Objectives of Learning Unit
• You have learned in the previous Learning
Unit how differences in characteristics of
financial instruments lead to different
market interest rates.
− Risk, liquidity, and tax attributes
• In this Learning Unit, you will learn one
more important characteristic of financial
instruments.
– Maturity

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Maturity and Interest Rates
• Although some financial instruments are
issued by the same borrowers and have the
same characteristics except for maturities,
they often have different interest rates.
• Example: How much are interest rates on 3
month maturity CD, 6 month maturity CD, 1
year maturity CD, and 3 year maturity CD at
your bonk? Are they same? These CDs are
identical (risk, tax treatment, etc.) except for
maturity.

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Maturity and Interest Rates of U.S.
Treasury Securities
• U.S. Treasury securities with different maturity have
different interest rates.
− In general, interest rates on three-month U.S. Treasury bills
are lower than those of 20-year U.S. Treasury bonds.
− A spread between Treasury bills and Treasury bonds
changes over time.

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Yield Curve
• Yield curve: A plot of the interest rates (yield
to maturity) for particular types of bonds with
different terms to maturity, but the same risk,
liquidity, and tax treatments.
• Yield curves are classified in terms of their
shapes and are used to explain the condition
in financial markets and the economy.

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Example of Yield Curve
• Interest rates on CDs are 3% on 1-year maturity, 4%
on 2-year maturity, and 5% on 3-year maturity.
– Click your mouse to see how a yield curve is drawn on this
example.
Maturity
Interest Rate
4%
2 year
3%
1 year
5%
3 year
Yield curve

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Variations of Yield Curves
• Yield curve may be upward-sloping, flat, downward-
sloping (inverted), or any shapes between.
– Different shapes appear under different economic
conditions.
– They are used to explain or predict an economic condition.

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Example of Yield Curve on Barron’s
• Dow Jones’ publishes a yield curve of U.S. Treasury
securities every day on the Wall Street Journal and
weekly on Barron’s.
• They compare the most recent yield curve with a yield
curve one month ago and another one year ago, and
examine
− Shape of yield curve
− Changes in yield curve
• Yield curve section from Barron’s, January 7, 2008
– See “How to Interpret Yield Curve of Barron’s” on
Blackboard

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Three Theories to Explain Yield Curve
• Why does a yield curve have different
shapes? Why does it change from time to
time?
• Three different reasons for yield curves
(different interest rates among financial
instruments with different maturities)
– Liquidity premium theory
– Segmented market theory
– Expectations theory

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Liquidity Premium Theory
• Normally, the yield curve is upward sloping.
– Interest rates on short-term securities are normally lower
than interest rates on long-term securities.
− Figure 4 on slide #4 shows that in most years interest rates
on three-month U.S. Treasury bills are lower than those of
20-year U.S. Treasury bonds.
• One important difference between short-term
securities and long-term securities is their liquidities.
− Liquidity of short-term securities is higher than liquidity of
long-term securities.
− Even if you cannot sell them, short-term securities will
mature sooner than long-term securities and owners of
short-securities will receive full payments sooner.

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Liquidity and Yield Curve
• Liquidity of short-term securities > liquidity of long-
term securities.
• Saver/lenders prefer liquidity.
• Demand for short-term securities > Demand for long-
term securities.
• Interest rates on short-term securities < Interest rates
on long-term securities.
Long-term
High interest rate
Short-term
Low interest rate
Upward-sloping
yield curve

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Liquidity Premium Theory and Actual
Yield Curve
• Although the liquidity premium theory can
explain the yield curve most time, it cannot
explain why a yield curve becomes
sometimes flat, downward-sloping, and any
shapes between.
• Segmented market and expectations theories
complement the liquidity premium theory.

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Segmented Market Theory
• The segmented market theory assumes
that the interest rate on each instrument
is determined in a separate market with
a separate market demand and supply.
− A short-term interest rate is determined by
demand for and supply of sort-term
securities in the short-term security market.
− A long-term interest rate is determined by
demand for and supply of long-term
securities in the long-term security market.

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Example of Segmented Market Theory #1
• Demand for short-term securities is relatively greater than
demand for long-term securities.
• Assume same supply in both short-term and long-term securities
markets.
P Short-term
Q
S
P
Q
Long-term
S
i
maturity
ii
Upward
sloping
Low interest rate High interest rate
is
iL
is
iL
Short-term Long-term

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Example of Segmented Market Theory #2
• Demand for short-term securities is relatively less than demand
for long-term securities.
• Assume same supply in both short-term and long-term securities
markets.
P Short-term
Q
S
P
Q
Long-term
S
i
maturity
ii
iS
Short-term
iS
iL
Long-term
iL
Downward
sloping
High interest rate Low interest rate

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Example of Segmented Market Theory #3
• Demand for short-term securities is equal to demand for long-
term securities.
• Assume same supply in both short-term and long-term securities
markets.
P Short-term
Q
S
P
Q
Long-term
S
i
maturity
ii
iS
iS
Short-term
iL
Long-term
iL
Flat
yield
curve

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Segmented Market Theory and Shapes of
Yield Curve
• Markets of securities can be divided into
three different maturities: short-term, mid-
term, and long-term. Then, depending on
relative demand and supply in each market, a
yield curve may have V-shape or Λ-shape.
• By segmenting into more markets, any
shapes of yield curve can be explained by
relative demand and supply in each maturity
market.

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Limitation of Segmented Market Theory
• Although the segmented market theory can
explain any shapes of yield curve, based on
relative demand and supply of each maturity
security, it cannot explain why demands and
supplies differ among markets.
• In reality, demand for each maturity securities
is not completely independent to each other,
so as supply.
• The expectations theory considers this
interdependency among securities and
provides a reason for different demands.

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Expectations Theory
• The expectations theory considers an
interdependency among securities and provides a
reason for different demands.
− If you want to save $1,000 for two years, you may purchase
either one-year CD today (and roll over to another one year
CD next year) or two-year CD today.
− Two strategies (1-year CDs or 2-year CD) are perfect
substitute.
− If one strategy provides a higher return the other strategy,
saver/lenders will prefer the former over the later and
change their demands, leading changes in an equilibrium in
to markets (1-year CD market and 2-year CD market).
− Both markets will be at an equilibrium only if both strategies
provide the same return.

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Example of Two Strategies
• You save $1,000 for two years.
• Strategy #1: You purchase 1-year CD today which
provides 3% annual interest rate.
• Strategy #2: You purchase 2-year CD today which
provides 4% annual interest rate.
• If you take Strategy #1, you will reinvest your saving
next year (purchase 1-year CD) at X% annual
interest rate which is unknown today.
• A rate of return from Strategy #1 is
FV = $1,000 x (1+3%) x (1+X%) = ???
– A return from this strategy depends on an interest rate on
one-year CD next year.
• A rate of return from Strategy 32 is
FV = $1,000 x (1+4%)2
= $1,081.60

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Expectation and Choice of Strategy
• If you expect that an interest rate on one-year CD is still 3%
next year, how much will be a return from Strategy #1? Which
strategy will you choose? How will your choice affect the market
of 2-year CD today and its interest rate?
– Strategy #1 will provide $1,060.90, so you should choose Strategy
#2. An increase in demand for 2-year CD will lower its interest rate.
• If you expect that an interest rate on one-year CD increases to
7% next year, how much will be a return from Strategy #1?
Which strategy will you choose? How will your choice affect the
market of 2-year CD today and its interest rate?
– Strategy #1 will provide $1,102.10, so you should choose Strategy
#1. A decrease in demand for 2-year CD will raise its interest rate.
• If you expect that an interest rate on one-year CD increases to
5% next year, how much will be a return from Strategy #1?
Which strategy will you choose? How will your choice affect the
market of 2-year CD today and its interest rate?
– Strategy #1 will provide $1,081.50, so it is indifferent to choose
either strategy. Since there is no needs to change your demand, its
interest rate will not change (equilibrium).

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Expectations and Equilibrium
• Both markets reach an equilibrium only
if no more changes in demand in both
markets.
• Only if saver/lenders expect that the
one-year CD will have 5% interest rate
next year, the markets are at an
equilibrium today.

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Expectations Theory
• The interest rate on a long-term bond is equal to an
average of short-term interest rates that savers expect to
occur over the life of the long-term bond.
• Formula: in
= (i1+i2+..+in)/n
in
: Interest rate on n-year maturity bond today
i1: Interest rate on 1-year maturity bond today
i2: Interest rate on 1-year maturity bond next year
in: Interest rate on 1-year maturity bond n-1 year later
0 1 2 3 n-1 n
i1 i2 i3 in
PV
FV

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Numerical Example of Expectations
Theory
• Saver/lenders expect 1-year interest rate in next three
years as
1-year Interest
ratethis year 3%
next year 5%
two year later 7%
Then, long-term interest rates today are
One year rate:
i1
=3%
Two year rate:
i2
=(3%+5%)/2=4%
Three year rate:
i3
=(3%+5%+7%)/3=5%

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Yield Curve and Expectations
• When the short-term interest rate is expected to increase in
future,
⇒ The long-term interest rate is higher than the short-term
interest rate today.
⇒ yield curve is upward-sloping today.
• For example, when one-year interest rate is 3% today, and is
expected to rise to 5% next year and 7% two years later, then
interest rates today are 3% on 1-year maturity, 4% on 2-year
maturity, and 5% on 3-year maturity.
Maturity
Interest Rate
4%
2 year
3%
1 year
5%
3 year
Yield
curve

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Reasons for Changes in Interest Rate
Over Time
• There are many reasons for changes in interest rates
in future.
– A change in real interest rate in future (r)
– A change in inflation rate in future (π)
i = r + π
• If an economic condition changes in future (e.g.
changes in wealth and income, changes in risk,
changes in profitability of business investment
opportunities), demand or supply of bonds will
change in future and a equilibrium real interest rate
will also change in future.

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Changes in Expected Inflation and Yield
Curve
• If Saver/lenders anticipate the inflation rate to
increase in future.
⇒ The short-term interest rate is expected to
increase in future for a given real interest
rate (π↑ ⇒ i↑).
⇒ The long-term interest rate is higher than
the short-term interest rate today.
⇒ yield curve is upward-sloping today.

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Yield Curve and Market Expectations
• A yield curve today tells you how professional traders
in markets anticipate future inflation (π) and
economic conditions (r).
− If they expect the U.S. economy to be in an expansion
phase of business cycle, they should expect interest rates to
rise in future, so the yield curve today should be upward-
sloping.
− If they expect the inflation rate to rise in U.S. economy, they
should expect nominal interest rates to rise in future, so the
yield curve today should be upward-sloping.
− Thus, an upward-sloping yield curve today may indicate
traders’ expectation of either an expansion or inflation in the
U.S. economy near future.

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Interpreting Actual Yield Curve
• Three theories of yield curve are complement. When
we interpret an actual yield curve, we must apply all
three theories.
• Due to the liquidity premium theory, even though we
expect no change in short-term interest rates near
future, the yield curve should be slightly upward-
sloping.
– Expectations theory indicates a flat yield curve.
– Liquidity premium theory indicates an upward-sloping curve.
– Two factors together produces a slightly upward-sloping
yield curve.

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Expectations Theory with
Liquidity Premium

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Expectations of Future Short-Term
Interest Rates
Fall moderately
Fall sharply
Rise
Stay the same
Yield to Maturity
Terms to Maturity
When short-term interest
rates in future are expected
to

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Interpreting Yield Curve
• Steep upward-sloping yield curves in 1985 and 2011 indicate traders’ expectations
of rising future interest rates.
• Moderately upward-sloping yield curves in 1980 and 1997 indicate traders’
expectations on no change in future interest rates.
• A flat yield curve in 2006 indicates traders’ expectations of falling future interest
rates.
• A downward-sloping (inverted) yield curve in 1981 indicates traders’ expectations
of sharply falling future interest rates.

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Disclaimer
Please do not copy, modify, or distribute this presentation
without author’s consent.
This presentation was created and owned by
Dr. Ryoichi Sakano
North Carolina A&T State University