The Risk and Term
Structure of Interest Rates
Chapter 6
1
2
Why Do Bonds With Same
Maturity Have Different Prices?
Some might be riskier than others.
 Some might be more liquid than others.
 Some might have lower taxes than others.
 Collectively, these influences are called
“risk structure of interest rates.”
 Of course, if prices of various bonds differ
so do their yield to maturity.

3
Risk Structure of Interest Rates
Default risk - inability of the bond issuer
to pay interest or face value.
 Liquidity risk - inability to find a buyer
when one decides to sell her bond
before it matures.
 Income tax - interest earnings on
municipal bonds are free from federal
income tax.

4
Default Risk

US Treasury bonds are risk free.
Congress can raise taxes.
 Federal government can print money.

The interest difference between a defaultfree bond and one with default risk is called
“risk premium.”
 Buyers of bonds have to get higher interest
bonds (lower price bonds) to persuade
them to buy the riskier bonds.

5
Long-Term Bond Yields, 1919–2008
Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–
1970; Federal Reserve: www.federalreserve.gov/releases/h15/data.htm
.
6
Why Do Similar Bonds With Different
Maturities Have Different Prices?
Two bonds could be identical in their risk
structure but they may have different yield
to maturity if their maturities differ.
 This is called “term structure of interest
rates.”

7
Interest Rates on U.S. Government
Bonds with Different Maturities
Sources: Federal Reserve: www.federalreserve.gov/releases/h15/data.htm
.
8
Increase in Default Risk on
Corporate Bonds
9
Application: The Subprime
Collapse and the Baa-Treasury
Spread
Corporate Bond Risk Premium and Flight to
Quality
10
8
6
4
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Corporate bonds, monthly data Aaa-Rate
Corporate bonds, monthly data Baa-Rate
10-year maturity Treasury bonds, monthly data
10
Interest Rates
Interest Rate Differentials During
Recession
12
10
8
6
4
2
0
1990
Series1
Series2
Series3
1990.5 Months
1991 1991.5
1992
Series 1 is Moody’s Baa Corporate Bond Yield. Series 2 is 1-yr Treasury
Constant Maturity Rate. Series 3 is the difference between the two.
Source: http://www.stls.frb.org/fred/data/irates.html (Discontinued).
11
http://research.stlouisfed.org/fred2/
categories/22/1
During the 2001
recession, Baa yields fell
from 8.5% to 8%;
treasuries fell from 6% to
below 4%, adding 3.5% to
the risk premium.
12
Decline in Corporate Bond Risk
P1
P2
P2
P1
Q of US bonds
Q of corporate bonds
White arrow shows the risk premium initially. Red arrow is
the new risk premium.
13
Risk Premium
During recessions default risk generally
rises.
 Rating agencies evaluate single
companies and issue a rating indicating
the default risk of the company’s bonds.
 Rating agencies also evaluate the
default risk of foreign bonds.

14
15
http://www.economist.com/finance/displaystory.cfm?story_id=8628827
16
Liquidity

The more liquid an asset is, the quicker
and cheaper it can be converted to
cash.

Cheaper means lower transaction cost.
The more liquid an asset is the higher
the demand for it.
 What happens to the risk premium if
corporate bonds become less liquid?

17
Corporate Bonds Become Less Liquid
ii
P
P
i
i
Q of Corporate Bonds
Q of T-bonds
Initially, corporate bond market and T-bond market are at
equilibrium at the intersection of white S and D. Corporate bonds
have lower P and higher I. Less liquidity increases the D for Tbonds and reduces the D for corporate bonds. Interest rates on
corporate bonds rise, on T-bonds fall.
18
Municipal Bonds
Municipal bonds have lower interest
rates than T-bonds.
 Municipal bonds are not risk-free.

Cleveland defaulted in early 1970s.
 New York defaulted in late 1970s.
 Orange County, California defaulted in
1994.


Is there a contradiction?
19
Tax Advantage of Municipal Bonds




Earnings from municipal bonds are exempt from
federal income tax.
A person at 33% income tax bracket can earn a
higher after-tax return from a riskier municipal
bond than a risk-free T-bond.
$1000 face-value T-bond with 10% coupon rate
selling for $1000 would yield $67 after-tax
income to this person.
$1000 face-value muni-bond with 8% coupon
rate selling for $1000 would yield $80 after-tax
income to this person.
20
The Effect of Tax Elimination on
Municipal Bonds
i
P
P
P
i
i
Q of Muni Bonds
Q of T-bonds
Assuming similar risk and liquidity we start with same P and i.
Eliminating taxes for munis would increase the demand for them,
While reducing the demand for T-bonds.
21
What Would Happen If the Top
Tax Rate Were Increased?
D for munis will increase.
 D for T-bonds will decrease.
 P of munis will rise.
 P of T-bonds will drop.
 Interest rates on munis will fall.
 Interest rates on T-bonds will rise.

22
Term Structure of Interest Rates

Bonds with identical risk, liquidity and
tax considerations may have different
interest rates because of their maturity.

Typically, bonds with maturity far into the
future have higher interest rates than
bonds that will mature soon.
23
Yield Curves
Yields of different maturity but identical risk,
liquidity, tax characteristics are plotted.
 Yield curves typically move upwards, but
sometimes they are flat or downward
sloping.



When short term interest rates are high yield
curves may be inverted.
Yield curves at different dates usually show
that short and long term interest rates move
up and down together.
24
Term-structure of Interest Rates
Source: http://www.stls.frb.org/docs/publications/mt/2000/cover4.pdf
25
Term Structure of
Interest Rates

Bonds with identical risk, liquidity, and tax
characteristics may have different interest rates
because the time remaining to maturity is different

Yield curve—a plot of the yield on bonds with differing
terms to maturity but the same risk, liquidity and tax
considerations

Upward-sloping  long-term rates are above
short-term rates

Flat  short- and long-term rates are the same

Inverted  long-term rates are below short-term rates
26
Facts
1.
Interest rates on bonds of different
maturities move together over time
2.
When short-term interest rates are low,
yield curves are more likely to have an
upward slope; when short-term rates are
high, yield curves are more likely to slope
downward and be inverted
3.
Yield curves almost always slope upward
27
Explaining Yield Curves
The expectations theory
 The segmented markets theory
 The liquidity premium theory

28
Expectations Theory
Explains why interest rates move together.
 Explains why when short-term interest
rates are low, yield curves are more likely
to be upward sloping.
 Explains why when short-term interest
rates are high, yield curves are more likely
to be downward sloping.
 Doesn’t explain why yield curves are
usually upward sloping.

29
Expectations Theory


Assume bonds with different maturities are
perfect substitutes.
Demand for bonds with higher yield will be
higher.



Their prices will go up and their yields will decline.
Yields on different maturity bonds will be equal.
How can you have an upward (or downward)
sloping yield curve if the expected yields on
different maturity bonds is the same?
30
An Example




Suppose you consider to save your funds for a
period of four years.
You can put these funds in a four-year bond or you
can put them in four successive one-year bonds.
Expectations theory says the returns from these
two choices should be the same.
If the expected yearly returns for the next four
years are 6%, 7%, 8%, and 9%, then the return on
the four-year bond should be 7.5%.
31
Expectations Theory

If short term interest rates have been inching up
(down), people will expect them to increase
(decrease) in the future, too.


If short-term rates are unusually high (low), people
will expect them to move down (up) in the future.


Short and long-term rates will move together.
Inverted (regular) yield curve.
Chances of interest rates moving in either direction
are equal. We shouldn’t see primarily upward
sloping yield curves.
32
Segmented Markets Theory
Assumption: different maturity bonds are not
substitutes.
 People with a short holding period will buy
short-term bonds, people with a long holding
period will buy long-term bonds.
 Interest rates on these bonds will be
determined by the specific supply and
demand of the short and long bond markets.

33
Segmented Markets Theory

Why do yield curves usually have an upward
slope?


Why do interest rates move together?


Typically, long-term bonds will carry higher
interest rate risk so will have a lower demand,
lower price and higher interest rate.
Segmented Markets Theory cannot explain this.
Why when short-term interest rates are high,
yield curves are inverted?

Segmented Markets Theory cannot explain this.
34
Liquidity Premium Theory


Interest rate on a long-term bond will be
equal to the average of expected short term
returns plus a liquidity premium that reflects
the lower demand for long-term (high interest
rate risk) bonds.
Liquidity premium on a five-year bond will be
lower than a ten-year bond.

Bonds of different maturities are partial (not
perfect) substitutes
35
Liquidity Premium Theory
Even if the expected future interest
rates were to remain constant, liquidity
premium will show an upward sloping
yield curve.
 Yield curve will be mildly rising if future
short term rates were expected to fall.
 An inverted curve indicates a sharp fall
in the expected future short term rates.

36
Preferred Habitat Theory

Investors have a preference for bonds of
one maturity over another

They will be willing to buy bonds of
different maturities only if they earn a
somewhat higher expected return

Investors are likely to prefer short-term
bonds over longer-term bonds
37
Liquidity Premium (Preferred
Habitat) and Expectations Theory
38
Why the Yield Curve Became
Inverted in 2000?

Do we expect a lower inflation 10, 30 years in the
future?


Do we have a lower liquidity premium than before?


Perhaps; but a current inflation rate of 3-3.5% is already
low.
Unlikely.
Is there an unusual supply-demand condition in the
long-term bond market?


Yes. The federal government announced retirement of
debt.
Read the one-page explanation of St. Louis Fed at
http://research.stlouisfed.org/publications/mt/20000401/cover.pdf
39
40
Yield Curves for U.S. Government Bonds
Sources: Federal Reserve Bank of St. Louis; U.S. Financial Data, various issues; Wall Street Journal,
various dates.
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