Transcript Risk and Term Structure

The Structure of Interest Rates
Risk Structure
1
Risk Structure in Interest Rates
• The risk structure of interest rates refers to
difference in the yields on instruments that
have the same term to maturity.
• Why do securities with the same term to
maturity have different interest rates?
– Default risk
– Liquidity
– Tax considerations
2
Interest Rate Differences
• Yields differ because of differences in default risk,
liquidity, and tax treatment
– Default risk
• You lose your asset.
– Liquidity
• Your ability to convert your asset into cash is less than that of
another asset.
– Tax treatment
• Favorable tax treatment for your security results in lower interest
rates.
3
Default Risk
• Default occurs when there is a failure to
fully meet the terms of a contractual
agreement.
– Failure to pay the full interest specified.
– Failure to redeem the bond at face value at
maturity.
– Delay in the receipt on interest.
• A premium for default risk is embedded in a
security’s yield.
4
Default Risk
Price
S
Yield
0
P1c
i1c
P2c
i2c
Price
S
P2t
i2t
P1t
i1t
Risk
Premium
D2c
D1c
0 Quantity of Corporate Bonds
Corporate Bond
Market
Yield
0
D2t
D1t
0 Quantity of Treasury Bonds
U.S. Treasury Bond
Market
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Default Risk Premium
• Let the default risk on corporate bonds rise.
– The demand for corporate bonds falls from D1c
to D2c.
• The price of corporate bonds falls from P1c to P2c,
and the yield on corporate bonds rises from i1c to i2c.
– Simultaneously, the demand for Treasury bonds
increases from D1t to D2t.
• The price of Treasury bonds rises from P1t to P2t,
and the yield on Treasury bonds falls from i1t to i2t.
– The risk premium is i2c - i2t.
6
Liquidity
• Liquidity is defined as the ability of an asset
to be quickly and cheaply converted into
cash.
– Other things remaining the same, the more
liquid an asset is the more attractive it is.
• U.S. Treasury bonds are the most liquid of all long
term bonds because they are the easiest and least
costly of all bonds to sell.
– They are widely traded.
• Corporate bonds are less liquid.
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Liquidity
Price
S
Yield
0
P1c
i1c
P2c
i2c
Price
S
P2t
i2t
P1t
i1t
Risk
Premium
D2c
D1c
0 Quantity of Corporate Bonds
Corporate Bond
Market
Yield
0
D2t
D1t
0 Quantity of Treasury Bonds
U.S. Treasury Bond
Market
8
Liquidity
• Assume that corporate bonds and Treasury
bonds are equally liquid and that all their
other attributes are the same.
– Equilibrium prices and yields are identical.
• Let the liquidity of the corporate bond
decrease because it is less widely traded.
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Liquidity
• Let the liquidity on corporate bonds fall.
– The demand for corporate bonds falls from D1c
to D2c.
• The price of corporate bonds falls from P1c to P2c,
and the yield on corporate bonds rises from i1c to i2c.
– Simultaneously, the demand for Treasury bonds
increases from D1t to D2t.
• The price of Treasury bonds rises from P1t to P2t,
and the yield on Treasury bonds falls from i1t to i2t.
– The risk premium is i2c - i2t.
10
Income Tax Considerations
Price
Yield
0
S
P1m
Price
S
i2m
i1m
P2m
D2m
P1t
i1t
P2t
i2t
D1t
m
D1
0
Yield
0
Quantity of Municipal Bonds
Municipal Bond
Market
D2t
0
Quantity of Treasury Bonds
U.S. Treasury Bond
Market
11
Income Tax Considerations
• Let municipal bonds be given tax-free
status.
– The demand for municipal bonds increases
from D1m to D2m.
• The price of municipal bonds rises, and the yield
falls.
– The demand for Treasury bonds falls from D1t
to D2t.
• The price of Treasury bonds falls, and the yield
rises.
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Tax Considerations
• Assume a 50% income tax bracket. You own a
bond that sells for $1,000 and pays a $100
coupon. Since half of your coupon is taxed
away, your after tax yield is $50 or 5%.
• Assume you own a tax-free municipal. It sells
for $1,000 and pays an $80 coupon. Since it is
tax-free, you receive the full coupon payment,
and your after-tax yield is 8%.
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Summary: Risk Structure of
Interest Rates
• The risk structure of interest is explained
by:
– Default risk, liquidity, and tax treatment.
• As a bond’s default risk increases and/or its liquidity
decreases, its price falls and its interest rate rises.
• If a bond receives favorable tax treatment, its price
rises, and its interest rate falls.
14
Interest Rate Determination
Becomes...
Nominal Rate
=
+
+
Real Rate
Expected Inflation
Risk Premium
15
The Structure of Interest Rates
Term Structure
16
The Term Structure of Interest
Rates
• The term structure of interest rates refers to
difference in the yields on instruments that
are identical except for term to maturity.
• Term structure is represented graphically by
a yield curve.
– Yield curves consider only the relationship
between maturity or term of a security and its
yield at a moment in time, otrs.
17
Term Structure
• Time to maturity affects interest rates
because
– Time increases exposure to risk, causing
investors to demand higher yields on securities
with longer maturities.
18
Yield Curves
• Shapes:
– Upward sloping
• Interest rates on securities with longer maturities
exceed interest rates on shorter term securities.
– Downward sloping
• Interest rates on securities with longer maturities are
less than interest rates on shorter term securities.
– Horizontal
• Interest rates on long and short term securities have
approximately the same interest rates.
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Treasury Yield Curve
February 4, 2005
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Treasury Yield Curve
Yields as of 4:30 p.m. on Wednesday
4.50
Feb 7, 2002
Jan 30, 2002
Dec 6, 2001
3.00
3.00
1.50
3mo 6mo 2yr
5yr 10yr 30yr
Maturities
21
Treasury Yield Curve
Yields as of 4:30 p.m. on Wednesday
6.00
5.50
Jan 17, 2000
Jan 10, 2000
Dec 9, 1999
5.00
4.50
3mo 6mo 1yr 2yr 5yr 10yr 30yr
Maturities
22
Understanding the Yield Curve
• Any theory that is used to analyze term
structure should be able to explain the
following:
– Why interest rates on bonds of different
maturities move together over time.
– Why yield curves slope up when short term
interest rates are low and down when short term
interest rates are high.
– Why yield curves almost always slope up.
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Yield Curve Theories
• Expectations hypothesis
– Explains facts 1 and 2, but not 3.
• Segmented markets hypothesis
– Explains facts 3, but not 1 and 2.
• Preferred habitat and liquidity hypotheses
– Explains facts 1, 2, and 3.
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Expectations Hypothesis
• Assumptions:
– All investors are wealth maximizers.
– No investor has a specific preference about the
maturity or term of a security.
• Bonds of different maturities are perfect substitutes.
– Investors try to achieve the highest possible rate
of return from holding one or more securities
and are willing to move freely from one
maturity to another.
25
Expectations Hypothesis:
Example
• Assume investors have only two options for
investing over a three year period.
– Option 1 is to buy a bond that matures in one
year, reinvest the proceeds from the bond at the
end of the year in another one year bond, and
follow the same procedure at the end of the
second year.
– Option 2 is to purchase a security that matures
in three years and hold it to maturity.
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Expectations Hypothesis:
Example
• To make a decision between option 1 and
option 2, an investor needs to know:
– The rate currently earned on one year bonds
and the expected rates on year 2 and year 3
bonds.
• Assume the following:
– A one year bond yields 4%
– One year bonds are expected to yield 5% in
year 2 and 6% in year 3.
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Expectations Hypothesis:
Example
• What is the minimum accepted yield on a
three year security?
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Expectations Hypothesis:
Example
Yield
.
5
4
.
1
3
The yield curve slopes up when
expectations of future yields are rising
because long term interest rates equal
the average of short term interest rates
expected to occur over the life of the
long term bond.
Time
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The Shape of the Yield Curve
• The expectations hypothesis can explain why the
yield curve changes shape.
– Expectations of rising yields mean that investors expect
bond prices to fall.
– Since long-term bond prices fall by more than shortterm bond prices, wealth maximizing investors sell
long-term bonds and move into cash equivalents or
short-term bonds.
– The decrease in demand causes long-term bond prices
to fall and long term yields to rise.
– The yield curve slopes up and/or becomes steeper.
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Expectations of Rising Rates
Price
S
Yield
0
P1
i1
P2
i2
D2
Price
S
P2
i2
P1
i1
D2
D1
D1
0 Quantity of Long Term Bonds
Yield
0
0 Quantity of Short Term Bonds
Upward Sloping Yield Curve
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The Shape of the Yield Curve
• The expectations hypothesis can explain why the
yield curve changes shape.
– Expectations of falling yields mean that investors
expect bond prices to rise.
– Since long-term bond prices rise by more than shortterm bond prices, wealth maximizing investors buy
long-term bonds and move out of cash equivalents and
short-term bonds.
– The increase in demand causes long-term bond prices
to rise and long-term yields to fall.
– The yield curve slope flattens or inverts
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Expectations of Falling Rates
Price
S
P1
Yield
0
i1
Price
S
i1
P1
D1
D1
0 Quantity of Long Term Bonds
Yield
0
0 Quantity of Short Term Bonds
Downward Sloping Yield Curve
Your turn
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Expectations Hypothesis:
Summary
• The expectations hypothesis can explain
why….
– Interest rates on bonds with different maturities
move together over time.
• A rise in short-term rates raises people’s
expectations of future short term rates.
• Long-term rates are an average of expected short
rates so they rise when short-term rates rise.
34
Expectations Hypothesis:
Summary
• The expectations hypothesis can explain
why…
– Yield curves tend to have an upward slope
when short term rates are low.
• When short term rates are low, people expect them
to rise in the future. This causes the average of
future expected short rates to be high relative to
current short term rates. Consequently, long rates
will rise, and the the yield curve will slope up.
35
Expectations Hypothesis:
Summary
• The expectations hypothesis cannot explain
why…
– Yield curves usually slope upward.
• In reality, interest rates are just as likely to fall as to
rise, so the yield curve if determined by expectations
should be flat.
36
Segmented Markets Hypothesis
• Assumptions:
– All investors are wealth maximizers.
– Investors have specific preferences about the
maturity or term of a security.
– Investors do not stray from their preferred
maturity.
• Investors try to achieve the highest possible
rate of return from holding one or more
securities, but they do not move from one
maturity to another.
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Segmented Markets Hypothesis
• The slope of the yield curve is explained by
different demand and supply conditions for
bonds of different maturities.
– If the yield curve slopes up, it does so because the
demand for short term bonds is relatively greater
than the demand for long term bonds.
• Short term bonds have a higher price and a lower
yield as a result of the relatively greater demand. So
the yield curve slopes upward.
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Segmented Markets Hypothesis
Price
Yield
0
S
P2s
Price
S
Yield
0
i2s
i1s
P1s
D2s
P1l
i1l
P2l
i2l
D1l
D1s
0
Quantity of Short-term Bonds
D2l
0
Quantity of Long-term Bonds
Upward Sloping Yield Curve
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Segmented Markets Hypothesis
• The slope of the yield curve is explained by
different demand and supply conditions for
bonds of different maturities.
– If the yield curve slopes down, it does so because
the demand for short term bonds is relatively less
than the demand for long term bonds.
• Therefore, short-term bonds have a lower price and
a higher yield. So the yield curve slopes down.
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Segmented Markets Hypothesis
Price
S
Yield
0
i1s
P1s
Price
S
P1l
i1l
D1l
D1s
0
Quantity of Short-term Bonds
Yield
0
0
Quantity of Long-term Bonds
Downward Sloping Yield Curve
Your turn!
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Segmented Markets Hypothesis
• The segmented markets hypothesis explains
why….
– Yield curves typically slope upward.
• On average investors prefer bonds with shorter
maturities that have less interest rate risk.
• Therefore, the demand for short term bonds is
relatively greater than the demand for long-term
bonds
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Segmented Markets Hypothesis
• The segmented markets hypothesis cannot
explain why…
– Interest rates on different maturities move together.
• The segmented markets hypothesis assumes that
short and long markets are completely segmented.
– Yield curves slope up when interest rates are low
and down when interest rates are high.
• It is not clear how demand and supply for short
versus long term bonds changes with the level of
short term interest rates.
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Preferred Habitat Hypothesis
• Assumptions:
– All investors are wealth maximizers.
– Bonds of different maturities are treated as
substitutes, but not perfect substitutes.
– Investors prefer one maturity over another
• Short-term bonds are preferred to long-term bonds
because investors are risk averse.
44
Preferred Habitat Hypothesis
• Investors try to achieve the highest possible
rate of return from holding one or more
securities.
• Investors are willing to move from one
maturity to another, but they have a
preferred habitat.
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Preferred Habitat/Liquidity
Premium Hypothesis
• Preferred Habitat Hypothesis
– Interest rates on long-term bonds equal an
average of short-term rates that are expected to
occur over the life of the bond plus a term
premium that responds to supply and demand
conditions for that bond.
• Liquidity Premium Hypothesis
– A positive term (liquidity) premium must be
offered to buyers of longer term bonds to
compensate them for their increased risk.
46
Preferred Habitat/Liquidity
Premium
• The preferred habitat and liquidity premium
theories can explain why…
– Interest rates on different maturity bonds move
together over time.
• A rise in short-term interest rates indicates that
short-term rates will, on average, be higher in the
future.
• The liquidity premium on long-term bonds ensures
an upward sloping yield curve.
47
Preferred Habitat/Liquidity
Premium
• The preferred habitat and liquidity premium
theories can explain why…
– Yield curves tend to have a steep upward slope
when short term interest rates are low.
• When short-term interest rates are low, investors
expect them to rise to some normal level.
• Therefore, the average of future expected short-term
rates will be high relative to the current short rates.
• Given the existence of a liquidity premium, long
rates must be substantially above current short rates.
48
Preferred Habitat/Liquidity
Premium
• The preferred habitat and liquidity premium
theories can explain why….
– Yield curves tend to slope down when short term
interest rates are high.
• When short-term interest rates are high, investors
expect them to fall to some normal level.
• Therefore, the average of future expected short-term
rates will be low relative to the current short rates.
• Given the existence of a liquidity premium, long
rates will be below current short rates, if rates are
expected to fall by more than the liquidity premium.49
Preferred Habitat/Liquidity
Premium
• The preferred habitat and liquidity premium
theories can explain why…
– Yield curves typically slope upward.
• The term premium rises with a bond’s maturity
because of investors’ preferences for short term
bonds.
50
Yield Curves
• Conclusions:
– A steeply rising yield curve indicates that shortterm interest rates are expected to rise in the future.
– A moderately rising yield curve indicates that
short-term interest rates are not expected to rise or
fall much in the future.
– A flat yield curve indicates that short-term rates are
expected to fall moderately in the future.
– An inverted yield curve indicates that short-term
interest rates are expected to fall sharply in the
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future.
Interest Rate Determination
Becomes...
Nominal Rate
=
+
+
+
+
Real Rate
Expected Inflation
Risk Premium
Maturity Premium
Liquidity Premium
52