The economics of Money, Banking and Financial Markets Part 3 ppsx

120
PREVIEW
In our supply and demand analysis of interest-rate behavior in Chapter 5, we exam-
ined the determination of just one interest rate. Yet we saw earlier that there are enor-
mous numbers of bonds on which the interest rates can and do differ. In this chapter,
we complete the interest-rate picture by examining the relationship of the various
interest rates to one another. Understanding why they differ from bond to bond can
help businesses, banks, insurance companies, and private investors decide which
bonds to purchase as investments and which ones to sell.
We first look at why bonds with the same term to maturity have different inter-
est rates. The relationship among these interest rates is called the risk structure of
interest rates, although risk, liquidity, and income tax rules all play a role in deter-
mining the risk structure. A bond’s term to maturity also affects its interest rate, and
the relationship among interest rates on bonds with different terms to maturity is
called the term structure of interest rates. In this chapter, we examine the sources
and causes of fluctuations in interest rates relative to one another and look at a num-
ber of theories that explain these fluctuations.
Risk Structure of Interest Rates
Figure 1 shows the yields to maturity for several categories of long-term bonds from
1919 to 2002. It shows us two important features of interest-rate behavior for bonds
of the same maturity: Interest rates on different categories of bonds differ from one
another in any given year, and the spread (or difference) between the interest rates
varies over time. The interest rates on municipal bonds, for example, are above those
on U.S. government (Treasury) bonds in the late 1930s but lower thereafter. In addi-
tion, the spread between the interest rates on Baa corporate bonds (riskier than Aaa
corporate bonds) and U.S. government bonds is very large during the Great
Depression years 1930–1933, is smaller during the 1940s–1960s, and then widens
again afterwards. What factors are responsible for these phenomena?
One attribute of a bond that influences its interest rate is its risk of default, which
occurs when the issuer of the bond is unable or unwilling to make interest payments
when promised or pay off the face value when the bond matures. A corporation suf-

fering big losses, such as Chrysler Corporation did in the 1970s, might be more likely
Default Risk
Chapter
The Risk and Term Structure
of Interest Rates
6
to suspend interest payments on its bonds.
1
The default risk on its bonds would
therefore be quite high. By contrast, U.S. Treasury bonds have usually been consid-
ered to have no default risk because the federal government can always increase taxes
to pay off its obligations. Bonds like these with no default risk are called default-free
bonds. (However, during the budget negotiations in Congress in 1995 and 1996, the
Republicans threatened to let Treasury bonds default, and this had an impact on the
bond market, as one application following this section indicates.) The spread between
the interest rates on bonds with default risk and default-free bonds, called the risk
premium, indicates how much additional interest people must earn in order to be
willing to hold that risky bond. Our supply and demand analysis of the bond market
in Chapter 5 can be used to explain why a bond with default risk always has a posi-
tive risk premium and why the higher the default risk is, the larger the risk premium
will be.
To examine the effect of default risk on interest rates, let us look at the supply and
demand diagrams for the default-free (U.S. Treasury) and corporate long-term bond
markets in Figure 2. To make the diagrams somewhat easier to read, let’s assume that
initially corporate bonds have the same default risk as U.S. Treasury bonds. In this
case, these two bonds have the same attributes (identical risk and maturity); their
equilibrium prices and interest rates will initially be equal (P
c
1
ϭ P

T
1
and i
c
1
ϭ i
T
1
),
and the risk premium on corporate bonds (i
c
1
Ϫ i
T
1
) will be zero.
CHAPTER 6
The Risk and Term Structure of Interest Rates
121
FIGURE 1 Long-Term Bond Yields, 1919–2002
Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15/data/.
16
14
12
10
8
6
4
2
0

1950 1960 1970 1980 1990 2000
State and Local Government
(Municipal)
U.S. Government
Long-Term Bonds
Corporate Baa Bonds
Annual Yield (%)
Corporate Aaa Bonds
19401930
1920
1
Chrysler did not default on its loans in this period, but it would have were it not for a government bailout plan
intended to preserve jobs, which in effect provided Chrysler with funds that were used to pay off creditors.
www.federalreserve.gov
/Releases/h15/update/
The Federal Reserve reports the
returns on different quality
bonds. Look at the bottom of
the listing of interest rates for
AAA and BBB rated bonds.
Study Guide Two exercises will help you gain a better understanding of the risk structure:
1. Put yourself in the shoes of an investor—see how your purchase decision would
be affected by changes in risk and liquidity.
2. Practice drawing the appropriate shifts in the supply and demand curves when
risk and liquidity change. For example, see if you can draw the appropriate shifts
in the supply and demand curves when, in contrast to the examples in the text,
a corporate bond has a decline in default risk or an improvement in its liquidity.
If the possibility of a default increases because a corporation begins to suffer large
losses, the default risk on corporate bonds will increase, and the expected return on
these bonds will decrease. In addition, the corporate bond’s return will be more

uncertain as well. The theory of asset demand predicts that because the expected
return on the corporate bond falls relative to the expected return on the default-free
Treasury bond while its relative riskiness rises, the corporate bond is less desirable
(holding everything else equal), and demand for it will fall. The demand curve for
corporate bonds in panel (a) of Figure 2 then shifts to the left, from D
c
1
to D
c
2
.
At the same time, the expected return on default-free Treasury bonds increases
relative to the expected return on corporate bonds, while their relative riskiness
122 PART II
Financial Markets
FIGURE 2 Response to an Increase in Default Risk on Corporate Bonds
An increase in default risk on corporate bonds shifts the demand curve from D
c
1
to D
c
2
. Simultaneously, it shifts the demand curve for
Treasury bonds from D
T
1
to D
T
2
. The equilibrium price for corporate bonds (left axis) falls from P

c
1
to P
c
2
, and the equilibrium interest rate
on corporate bonds (right axis) rises from i
c
1
to i
c
2
. In the Treasury market, the equilibrium bond price rises from P
T
1
to P
T
2
, and the equilib-
rium interest rate falls from i
T
1
to i
T
2
. The brace indicates the difference between i
c
2
and i
T

2
, the risk premium on corporate bonds. (Note: P
and i increase in opposite directions. P on the left vertical axis increases as we go up the axis, while i on the right vertical axis increases as
we go down the axis.)
Quantity of Corporate Bonds
Quantity of Treasury Bonds
Price of Bonds,
P
(
P
increases
↑
)
Interest Rate,
i
(
i
increases )
↑
Interest Rate,
i
(
i
increases )
↑
Price of Bonds,
P
(
P
increases

↑
)
(a) Corporate bond market
(b) Default-free (U.S. Treasury) bond market
Risk
Premium
P
c
2
P
c
1
S
c
D
c
1
D
c
2
i
c
1
P
T
2
P
T
1
i

c
2
S
T
D
T
1
D
T
2
i
T
1
i
T
2
i
T
2
declines. The Treasury bonds thus become more desirable, and demand rises, as
shown in panel (b) by the rightward shift in the demand curve for these bonds from
D
T
1
to D
T
2
.
As we can see in Figure 2, the equilibrium price for corporate bonds (left axis)
falls from P

c
1
to P
c
2
, and since the bond price is negatively related to the interest rate,
the equilibrium interest rate on corporate bonds (right axis) rises from i
c
1
to i
c
2
. At the
same time, however, the equilibrium price for the Treasury bonds rises from P
T
1
to P
T
2
,
and the equilibrium interest rate falls from i
T
1
to i
T
2
. The spread between the interest
rates on corporate and default-free bonds—that is, the risk premium on corporate
bonds—has risen from zero to i
c

2
Ϫ i
T
2
. We can now conclude that a bond with
default risk will always have a positive risk premium, and an increase in its default
risk will raise the risk premium.
Because default risk is so important to the size of the risk premium, purchasers
of bonds need to know whether a corporation is likely to default on its bonds. Two
major investment advisory firms, Moody’s Investors Service and Standard and Poor’s
Corporation, provide default risk information by rating the quality of corporate and
municipal bonds in terms of the probability of default. The ratings and their descrip-
tion are contained in Table 1. Bonds with relatively low risk of default are called
investment-grade securities and have a rating of Baa (or BBB) and above. Bonds with
CHAPTER 6
The Risk and Term Structure of Interest Rates
123
Rating
Standard Examples of Corporations with
Moody’s and Poor’s Descriptions Bonds Outstanding in 2003
Aaa AAA Highest quality General Electric, Pfizer Inc.,
(lowest default risk) North Carolina State,
Mobil Oil
Aa AA High quality Wal-Mart, McDonald’s,
Credit Suisse First Boston
A A Upper medium grade Hewlett-Packard,
Anheuser-Busch,
Ford, Household Finance
Baa BBB Medium grade Motorola, Albertson’s, Pennzoil,
Weyerhaeuser Co.,

Tommy Hilfiger
Ba BB Lower medium grade Royal Caribbean, Levi Strauss
B B Speculative Rite Aid, Northwest Airlines Inc.,
Six Flags
Caa CCC, CC Poor (high default risk) Revlon, United Airlines
Ca C Highly speculative US Airways, Polaroid
C D Lowest grade Enron, Oakwood Homes
Table 1 Bond Ratings by Moody’s and Standard and Poor’s
ratings below Baa (or BBB) have higher default risk and have been aptly dubbed
speculative-grade or junk bonds. Because these bonds always have higher interest
rates than investment-grade securities, they are also referred to as high-yield bonds.
Next let’s look back at Figure 1 and see if we can explain the relationship between
interest rates on corporate and U.S. Treasury bonds. Corporate bonds always have
higher interest rates than U.S. Treasury bonds because they always have some risk of
default, whereas U.S. Treasury bonds do not. Because Baa-rated corporate bonds have
a greater default risk than the higher-rated Aaa bonds, their risk premium is greater,
and the Baa rate therefore always exceeds the Aaa rate. We can use the same analysis
to explain the huge jump in the risk premium on Baa corporate bond rates during the
Great Depression years 1930–1933 and the rise in the risk premium after 1970 (see
Figure 1). The depression period saw a very high rate of business failures and defaults.
As we would expect, these factors led to a substantial increase in default risk for bonds
issued by vulnerable corporations, and the risk premium for Baa bonds reached
unprecedentedly high levels. Since 1970, we have again seen higher levels of business
failures and defaults, although they were still well below Great Depression levels.
Again, as expected, default risks and risk premiums for corporate bonds rose, widen-
ing the spread between interest rates on corporate bonds and Treasury bonds.
124 PART II
Financial Markets
The Enron Bankruptcy and the Baa-Aaa Spread
Application

In December 2001, the Enron Corporation, a firm specializing in trading in the
energy market, and once the seventh-largest corporation in the United States,
was forced to declare bankruptcy after it became clear that it had used shady
accounting to hide its financial problems. (The Enron bankruptcy, the largest
ever in the United States, will be discussed further in Chapter 8.) Because of the
scale of the bankruptcy and the questions it raised about the quality of the infor-
mation in accounting statements, the Enron collapse had a major impact on the
corporate bond market. Let’s see how our supply and demand analysis explains
the behavior of the spread between interest rates on lower quality (Baa-rated) and
highest quality (Aaa-rated) corporate bonds in the aftermath of the Enron failure.
As a consequence of the Enron bankruptcy, many investors began to
doubt the financial health of corporations with lower credit ratings such as
Baa. The increase in default risk for Baa bonds made them less desirable at
any given interest rate, decreased the quantity demanded, and shifted the
demand curve for Baa bonds to the left. As shown in panel (a) of Figure 2,
the interest rate on Baa bonds should have risen, which is indeed what hap-
pened. Interest rates on Baa bonds rose by 24 basis points (0.24 percentage
points) from 7.81% in November 2001 to 8.05% in December 2001. But the
increase in the perceived default risk for Baa bonds after the Enron bank-
ruptcy made the highest quality (Aaa) bonds relatively more attractive and
shifted the demand curve for these securities to the right—an outcome
described by some analysts as a “flight to quality.” Just as our analysis predicts
in Figure 2, interest rates on Aaa bonds fell by 20 basis points, from 6.97%
in November to 6.77% in December. The overall outcome was that the
spread between interest rates on Baa and Aaa bonds rose by 44 basis points
from 0.84% before the bankruptcy to 1.28% afterward.
Another attribute of a bond that influences its interest rate is its liquidity. As we
learned in Chapter 4, a liquid asset is one that can be quickly and cheaply converted
into cash if the need arises. The more liquid an asset is, the more desirable it is (hold-
ing everything else constant). U.S. Treasury bonds are the most liquid of all long-term

bonds, because they are so widely traded that they are the easiest to sell quickly and
the cost of selling them is low. Corporate bonds are not as liquid, because fewer bonds
for any one corporation are traded; thus it can be costly to sell these bonds in an
emergency, because it might be hard to find buyers quickly.
How does the reduced liquidity of the corporate bonds affect their interest rates
relative to the interest rate on Treasury bonds? We can use supply and demand analy-
sis with the same figure that was used to analyze the effect of default risk, Figure 2,
to show that the lower liquidity of corporate bonds relative to Treasury bonds
increases the spread between the interest rates on these two bonds. Let us start the
analysis by assuming that initially corporate and Treasury bonds are equally liquid
and all their other attributes are the same. As shown in Figure 2, their equilibrium
prices and interest rates will initially be equal: P
c
1
ϭ P
T
1
and i
c
1
ϭ i
T
1
. If the corporate
bond becomes less liquid than the Treasury bond because it is less widely traded, then
(as the theory of asset demand indicates) its demand will fall, shifting its demand
curve from D
c
1
to D

c
2
as in panel (a). The Treasury bond now becomes relatively more
liquid in comparison with the corporate bond, so its demand curve shifts rightward
from D
T
1
to D
T
2
as in panel (b). The shifts in the curves in Figure 2 show that the price
of the less liquid corporate bond falls and its interest rate rises, while the price of the
more liquid Treasury bond rises and its interest rate falls.
The result is that the spread between the interest rates on the two bond types has
risen. Therefore, the differences between interest rates on corporate bonds and
Treasury bonds (that is, the risk premiums) reflect not only the corporate bond’s
default risk but its liquidity, too. This is why a risk premium is more accurately a “risk
and liquidity premium,” but convention dictates that it is called a risk premium.
Returning to Figure 1, we are still left with one puzzle—the behavior of municipal
bond rates. Municipal bonds are certainly not default-free: State and local govern-
ments have defaulted on the municipal bonds they have issued in the past, particu-
larly during the Great Depression and even more recently in the case of Orange
County, California, in 1994 (more on this in Chapter 13). Also, municipal bonds are
not as liquid as U.S. Treasury bonds.
Why is it, then, that these bonds have had lower interest rates than U.S. Treasury
bonds for at least 40 years, as indicated in Figure 1? The explanation lies in the fact
that interest payments on municipal bonds are exempt from federal income taxes, a
factor that has the same effect on the demand for municipal bonds as an increase in
their expected return.
Let us imagine that you have a high enough income to put you in the 35% income

tax bracket, where for every extra dollar of income you have to pay 35 cents to the gov-
ernment. If you own a $1,000-face-value U.S. Treasury bond that sells for $1,000 and
has a coupon payment of $100, you get to keep only $65 of the payment after taxes.
Although the bond has a 10% interest rate, you actually earn only 6.5% after taxes.
Suppose, however, that you put your savings into a $1,000-face-value municipal
bond that sells for $1,000 and pays only $80 in coupon payments. Its interest rate is
only 8%, but because it is a tax-exempt security, you pay no taxes on the $80 coupon
payment, so you earn 8% after taxes. Clearly, you earn more on the municipal bond
Income Tax
Considerations
Liquidity
CHAPTER 6
The Risk and Term Structure of Interest Rates
125
after taxes, so you are willing to hold the riskier and less liquid municipal bond even
though it has a lower interest rate than the U.S. Treasury bond. (This was not true
before World War II, when the tax-exempt status of municipal bonds did not convey
much of an advantage because income tax rates were extremely low.)
Another way of understanding why municipal bonds have lower interest rates than
Treasury bonds is to use the supply and demand analysis displayed in Figure 3. We
assume that municipal and Treasury bonds have identical attributes and so have the
same bond prices and interest rates as drawn in the figure: P
m
1
ϭ P
T
1
and i
m
1

ϭ i
T
1
. Once
the municipal bonds are given a tax advantage that raises their after-tax expected return
relative to Treasury bonds and makes them more desirable, demand for them rises, and
their demand curve shifts to the right, from D
m
1
to D
m
2
. The result is that their equilib-
rium bond price rises from P
m
1
to P
m
2
, and their equilibrium interest rate falls from i
m
1
to
i
m
2
. By contrast, Treasury bonds have now become less desirable relative to municipal
bonds; demand for Treasury bonds decreases, and D
T
1

shifts to D
T
2
. The Treasury bond
price falls from P
T
1
to P
T
2
, and the interest rate rises from i
T
1
to i
T
2
. The resulting lower
interest rates for municipal bonds and higher interest rates for Treasury bonds explains
why municipal bonds can have interest rates below those of Treasury bonds.
2
126 PART II
Financial Markets
FIGURE 3 Interest Rates on Municipal and Treasury Bonds
When the municipal bond is given tax-free status, demand for the municipal bond shifts rightward from D
m
1
to D
m
2
and demand

for the Treasury bond shifts leftward from D
T
1
to D
T
2
. The equilibrium price of the municipal bond (left axis) rises from P
m
1
to
P
m
2
, so its interest rate (right axis) falls from i
m
1
to i
m
2
, while the equilibrium price of the Treasury bond falls from P
T
1
to P
T
2
and
its interest rate rises from i
T
1
to i

T
2
. The result is that municipal bonds end up with lower interest rates than those on Treasury
bonds. (Note: P and i increase in opposite directions. P on the left vertical axis increases as we go up the axis, while i on the
right vertical axis increases as we go down the axis.)
Quantity of Treasury Bonds
Quantity of Municipal Bonds
Price of Bonds,
P
(
P
increases
↑
)
Interest Rate,
i
(
i
increases )
↑
Price of Bonds,
P
(
P
increases
↑
)
(a) Market for municipal bonds
(b) Market for Treasury bonds
Interest Rate,

i
(
i
increases )
↑
P
m
1
P
m
2
S
m
D
m
1
i
m
1
i
m
2
D
m
2
P
T
2
P
T

1
S
T
D
T
1
D
T
2
i
T
1
i
T
2
2
In contrast to corporate bonds, Treasury bonds are exempt from state and local income taxes. Using the analy-
sis in the text, you should be able to show that this feature of Treasury bonds provides an additional reason why
interest rates on corporate bonds are higher than those on Treasury bonds.
The risk structure of interest rates (the relationship among interest rates on bonds
with the same maturity) is explained by three factors: default risk, liquidity, and the
income tax treatment of the bond’s interest payments. As a bond’s default risk
increases, the risk premium on that bond (the spread between its interest rate and the
interest rate on a default-free Treasury bond) rises. The greater liquidity of Treasury
bonds also explains why their interest rates are lower than interest rates on less liquid
bonds. If a bond has a favorable tax treatment, as do municipal bonds, whose inter-
est payments are exempt from federal income taxes, its interest rate will be lower.
Summary
Term Structure of Interest Rates
We have seen how risk, liquidity, and tax considerations (collectively embedded in the

risk structure) can influence interest rates. Another factor that influences the interest
rate on a bond is its term to maturity: Bonds with identical risk, liquidity, and tax
characteristics may have different interest rates because the time remaining to matu-
rity is different. A plot of the yields on bonds with differing terms to maturity but the
same risk, liquidity, and tax considerations is called a yield curve, and it describes the
term structure of interest rates for particular types of bonds, such as government
bonds. The “Following the Financial News” box shows several yield curves for
Treasury securities that were published in the Wall Street Journal. Yield curves can be
classified as upward-sloping, flat, and downward-sloping (the last sort is often
referred to as an inverted yield curve). When yield curves slope upward, as in the
“Following the Financial News” box, the long-term interest rates are above the short-
term interest rates; when yield curves are flat, short- and long-term interest rates are
the same; and when yield curves are inverted, long-term interest rates are below
short-term interest rates. Yield curves can also have more complicated shapes in
which they first slope up and then down, or vice versa. Why do we usually see
CHAPTER 6
The Risk and Term Structure of Interest Rates
127
Effects of the Bush Tax Cut on Bond Interest Rates
Application
The Bush tax cut passed in 2001 scheduled a reduction of the top income tax
bracket from 39% to 35% over a ten-year period. What is the effect of this
income tax decrease on interest rates in the municipal bond market relative
to those in the Treasury bond market?
Our supply and demand analysis provides the answer. A decreased income
tax rate for rich people means that the after-tax expected return on tax-free
municipal bonds relative to that on Treasury bonds is lower, because the
interest on Treasury bonds is now taxed at a lower rate. Because municipal
bonds now become less desirable, their demand decreases, shifting the
demand curve to the left, which lowers their price and raises their interest

rate. Conversely, the lower income tax rate makes Treasury bonds more desir-
able; this change shifts their demand curve to the right, raises their price, and
lowers their interest rates.
Our analysis thus shows that the Bush tax cut raises the interest rates on
municipal bonds relative to interest rates on Treasury bonds.
upward slopes of the yield curve as in the “Following the Financial News” box but
sometimes other shapes?
Besides explaining why yield curves take on different shapes at different times, a
good theory of the term structure of interest rates must explain the following three
important empirical facts:
1. As we see in Figure 4, 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 interest rates are high, yield curves are more
likely to slope downward and be inverted.
3. Yield curves almost always slope upward, as in the “Following the Financial
News” box.
Three theories have been put forward to explain the term structure of interest
rates; that is, the relationship among interest rates on bonds of different maturities
reflected in yield curve patterns: (1) the expectations theory, (2) the segmented mar-
kets theory, and (3) the liquidity premium theory, each of which is described in the
following sections. The expectations theory does a good job of explaining the first two
facts on our list, but not the third. The segmented markets theory can explain fact 3
but not the other two facts, which are well explained by the expectations theory.
Because each theory explains facts that the other cannot, a natural way to seek a bet-
ter understanding of the term structure is to combine features of both theories, which
leads us to the liquidity premium theory, which can explain all three facts.
If the liquidity premium theory does a better job of explaining the facts and is
hence the most widely accepted theory, why do we spend time discussing the other
two theories? There are two reasons. First, the ideas in these two theories provide the

128 PART II
Financial Markets
Following the Financial News
The Wall Street Journal publishes a daily plot of the yield
curves for Treasury securities, an example of which is
presented here. It is typically found on page 2 of the
“Money and Investing” section.
The numbers on the vertical axis indicate the interest
rate for the Treasury security, with the maturity given by
the numbers on the horizontal axis. For example, the
yield curve marked “Yesterday” indicates that the interest
rate on the three-month Treasury bill yesterday was
1.25%, while the one-year bill had an interest rate of
1.35% and the ten-year bond had an interest rate of
4.0%. As you can see, the yield curves in the plot have the
typical upward slope.
Source: Wall Street Journal, Wednesday, January 22, 2003, p. C2.
Yield Curves
www.ratecurve.com/yc2.html
Check out today’s yield curve.
Treasury Yield Curve
Yield to maturity of current bills,
notes and bonds.
Source: Reuters
1
1.0
2.0
3.0
4.0
5.0%

3 6 2 5 10 30
mos. yrs. maturity
Yesterday
1 month ago
1 year ago
groundwork for the liquidity premium theory. Second, it is important to see how
economists modify theories to improve them when they find that the predicted results
are inconsistent with the empirical evidence.
The expectations theory of the term structure states the following commonsense
proposition: The interest rate on a long-term bond will equal an average of short-term
interest rates that people expect to occur over the life of the long-term bond. For
example, if people expect that short-term interest rates will be 10% on average over
the coming five years, the expectations theory predicts that the interest rate on bonds
with five years to maturity will be 10% too. If short-term interest rates were expected
to rise even higher after this five-year period so that the average short-term interest
rate over the coming 20 years is 11%, then the interest rate on 20-year bonds would
equal 11% and would be higher than the interest rate on five-year bonds. We can see
that the explanation provided by the expectations theory for why interest rates on
bonds of different maturities differ is that short-term interest rates are expected to
have different values at future dates.
The key assumption behind this theory is that buyers of bonds do not prefer
bonds of one maturity over another, so they will not hold any quantity of a bond if
its expected return is less than that of another bond with a different maturity. Bonds
that have this characteristic are said to be perfect substitutes. What this means in prac-
tice is that if bonds with different maturities are perfect substitutes, the expected
return on these bonds must be equal.
Expectations
Theory
CHAPTER 6
The Risk and Term Structure of Interest Rates

129
FIGURE 4 Movements over Time of Interest Rates on U.S. Government Bonds with Different Maturities
Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve: www.federalreserve.gov/releases/h15
/data.htm#top.
16
14
12
10
8
6
4
2
0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
20-Year Bond
Averages
Three-Month Bills
(Short-Term)
Three-to
Five-Year
Averages
Interest
Rate (%)
To see how the assumption that bonds with different maturities are perfect sub-
stitutes leads to the expectations theory, let us consider the following two investment
strategies:
1. Purchase a one-year bond, and when it matures in one year, purchase another
one-year bond.
2. Purchase a two-year bond and hold it until maturity.
Because both strategies must have the same expected return if people are holding

both one- and two-year bonds, the interest rate on the two-year bond must equal the
average of the two one-year interest rates. For example, let’s say that the current interest
rate on the one-year bond is 9% and you expect the interest rate on the one-year bond
next year to be 11%. If you pursue the first strategy of buying the two one-year bonds,
the expected return over the two years will average out to be (9% ϩ 11%)/2 ϭ 10% per
year. You will be willing to hold both the one- and two-year bonds only if the expected
return per year of the two-year bond equals this. Therefore, the interest rate on the two-
year bond must equal 10%, the average interest rate on the two one-year bonds.
We can make this argument more general. For an investment of $1, consider the
choice of holding, for two periods, a two-period bond or two one-period bonds.
Using the definitions
i
t
ϭ today’s (time t) interest rate on a one-period bond
i
e
tϩ1
ϭ interest rate on a one-period bond expected for next period (time t ϩ 1)
i
2t
ϭ today’s (time t) interest rate on the two-period bond
the expected return over the two periods from investing $1 in the two-period bond
and holding it for the two periods can be calculated as:
(1 ϩ i
2t
)(1 ϩ i
2t
) Ϫ 1 ϭ 1 ϩ 2i
2t
ϩ (i

2t
)
2
Ϫ 1 = 2i
2t
ϩ (i
2t
)
2
After the second period, the $1 investment is worth (1 ϩ i
2t
)(1 ϩ i
2t
). Subtracting
the $1 initial investment from this amount and dividing by the initial $1 investment
gives the rate of return calculated in the previous equation. Because (i
2t
)
2
is extremely
small—if i
2 t
ϭ 10% ϭ 0.10, then (i
2t
)
2
ϭ 0.01—we can simplify the expected return
for holding the two-period bond for the two periods to
2i
2t

With the other strategy, in which one-period bonds are bought, the expected
return on the $1 investment over the two periods is:
(1 ϩ i
t
)(1 ϩ i
e
tϩ1
) Ϫ 1 ϭ 1 ϩ i
t
ϩ i
e
tϩ1
ϩ i
t
(i
e
tϩ1
) Ϫ 1 ϭ i
t
ϩ i
e
t
ϩ i
t
(i
e
tϩ1
)
This calculation is derived by recognizing that after the first period, the $1 investment
becomes 1 ϩ i

t
, and this is reinvested in the one-period bond for the next period,
yielding an amount (1 ϩ i
t
)(1 ϩ i
e
tϩ1
). Then subtracting the $1 initial investment
from this amount and dividing by the initial investment of $1 gives the expected
return for the strategy of holding one-period bonds for the two periods. Because
i
t
(i
e
tϩ1
) is also extremely small—if i
t
ϭ i
e
tϩ1
ϭ 0.10, then i
t
(i
e
tϩ1
) ϭ 0.01—we can sim-
plify this to:
i
t
ϩ i

e
tϩ1
Both bonds will be held only if these expected returns are equal; that is, when:
2i
2t
ϭ i
t
ϩ i
e
tϩ1
130 PART II
Financial Markets
Solving for i
2t
in terms of the one-period rates, we have:
(1)
which tells us that the two-period rate must equal the average of the two one-period
rates. Graphically, this can be shown as:
We can conduct the same steps for bonds with a longer maturity so that we can exam-
ine the whole term structure of interest rates. Doing so, we will find that the interest
rate of i
nt
on an n-period bond must equal:
(2)
Equation 2 states that the n-period interest rate equals the average of the one-
period interest rates expected to occur over the n-period life of the bond. This is a
restatement of the expectations theory in more precise terms.
3
A simple numerical example might clarify what the expectations theory in
Equation 2 is saying. If the one-year interest rate over the next five years is expected

to be 5, 6, 7, 8, and 9%, Equation 2 indicates that the interest rate on the two-year
bond would be:
while for the five-year bond it would be:
Doing a similar calculation for the one-, three-, and four-year interest rates, you
should be able to verify that the one- to five-year interest rates are 5.0, 5.5, 6.0, 6.5,
and 7.0%, respectively. Thus we see that the rising trend in expected short-term inter-
est rates produces an upward-sloping yield curve along which interest rates rise as
maturity lengthens.
The expectations theory is an elegant theory that provides an explanation of why
the term structure of interest rates (as represented by yield curves) changes at differ-
ent times. When the yield curve is upward-sloping, the expectations theory suggests
that short-term interest rates are expected to rise in the future, as we have seen in our
numerical example. In this situation, in which the long-term rate is currently above
the short-term rate, the average of future short-term rates is expected to be higher
than the current short-term rate, which can occur only if short-term interest rates are
expected to rise. This is what we see in our numerical example. When the yield curve
is inverted (slopes downward), the average of future short-term interest rates is
5% ϩ 6% ϩ 7% ϩ 8% ϩ 9%
5
ϭ 7%
5% ϩ 6%
2
ϭ 5.5%
i
nt
ϭ
i
t
ϩ i
e

tϩ1
ϩ i
e
tϩ2
ϩ
. . .
ϩ i
e
tϩ(nϪ1
)
n
Today
0
Year
1
Year
2
i
t
i
e
tϩ1
i
2t
ϭ
i
t
ϩ i
e
tϩ1

2
i
2t
ϭ
i
t
ϩ i
e
tϩ1
2
CHAPTER 6
The Risk and Term Structure of Interest Rates
131
3
The analysis here has been conducted for discount bonds. Formulas for interest rates on coupon bonds would
differ slightly from those used here, but would convey the same principle.
expected to be below the current short-term rate, implying that short-term interest
rates are expected to fall, on average, in the future. Only when the yield curve is flat
does the expectations theory suggest that short-term interest rates are not expected to
change, on average, in the future.
The expectations theory also explains fact 1 that interest rates on bonds with dif-
ferent maturities move together over time. Historically, short-term interest rates have
had the characteristic that if they increase today, they will tend to be higher in the
future. Hence a rise in short-term rates will raise people’s expectations of future short-
term rates. Because long-term rates are the average of expected future short-term
rates, a rise in short-term rates will also raise long-term rates, causing short- and long-
term rates to move together.
The expectations theory also explains fact 2 that yield curves tend to have an
upward slope when short-term interest rates are low and are inverted when short-
term rates are high. When short-term rates are low, people generally expect them to

rise to some normal level in the future, and the average of future expected short-term
rates is high relative to the current short-term rate. Therefore, long-term interest rates
will be substantially above current short-term rates, and the yield curve would then
have an upward slope. Conversely, if short-term rates are high, people usually expect
them to come back down. Long-term rates would then drop below short-term rates
because the average of expected future short-term rates would be below current short-
term rates and the yield curve would slope downward and become inverted.
4
The expectations theory is an attractive theory because it provides a simple expla-
nation of the behavior of the term structure, but unfortunately it has a major short-
coming: It cannot explain fact 3, which says that yield curves usually slope upward.
The typical upward slope of yield curves implies that short-term interest rates are usu-
ally expected to rise in the future. In practice, short-term interest rates are just as
likely to fall as they are to rise, and so the expectations theory suggests that the typi-
cal yield curve should be flat rather than upward-sloping.
As the name suggests, the segmented markets theory of the term structure sees mar-
kets for different-maturity bonds as completely separate and segmented. The interest
rate for each bond with a different maturity is then determined by the supply of and
demand for that bond with no effects from expected returns on other bonds with
other maturities.
The key assumption in the segmented markets theory is that bonds of different
maturities are not substitutes at all, so the expected return from holding a bond of one
maturity has no effect on the demand for a bond of another maturity. This theory of
the term structure is at the opposite extreme to the expectations theory, which
assumes that bonds of different maturities are perfect substitutes.
The argument for why bonds of different maturities are not substitutes is that
investors have strong preferences for bonds of one maturity but not for another, so
they will be concerned with the expected returns only for bonds of the maturity they
prefer. This might occur because they have a particular holding period in mind, and
Segmented

Markets Theory
132 PART II
Financial Markets
4
The expectations theory explains another important fact about the relationship between short-term and long-term
interest rates. As you can see in Figure 4, short-term interest rates are more volatile than long-term rates. If inter-
est rates are mean-reverting—that is, if they tend to head back down after they are at unusually high levels or go
back up when they are at unusually low levels—then an average of these short-term rates must necessarily have
lower volatility than the short-term rates themselves. Because the expectations theory suggests that the long-term
rate will be an average of future short-term rates, it implies that the long-term rate will have lower volatility than
short-term rates.
if they match the maturity of the bond to the desired holding period, they can obtain
a certain return with no risk at all.
5
(We have seen in Chapter 4 that if the term to
maturity equals the holding period, the return is known for certain because it equals
the yield exactly, and there is no interest-rate risk.) For example, people who have a
short holding period would prefer to hold short-term bonds. Conversely, if you were
putting funds away for your young child to go to college, your desired holding period
might be much longer, and you would want to hold longer-term bonds.
In the segmented markets theory, differing yield curve patterns are accounted for
by supply and demand differences associated with bonds of different maturities. If, as
seems sensible, investors have short desired holding periods and generally prefer
bonds with shorter maturities that have less interest-rate risk, the segmented markets
theory can explain fact 3 that yield curves typically slope upward. Because in the typ-
ical situation the demand for long-term bonds is relatively lower than that for short-
term bonds, long-term bonds will have lower prices and higher interest rates, and
hence the yield curve will typically slope upward.
Although the segmented markets theory can explain why yield curves usually
tend to slope upward, it has a major flaw in that it cannot explain facts 1 and 2.

Because it views the market for bonds of different maturities as completely segmented,
there is no reason for a rise in interest rates on a bond of one maturity to affect the
interest rate on a bond of another maturity. Therefore, it cannot explain why interest
rates on bonds of different maturities tend to move together (fact 1). Second, because
it is not clear how demand and supply for short- versus long-term bonds change with
the level of short-term interest rates, the theory cannot explain why yield curves tend
to slope upward when short-term interest rates are low and to be inverted when
short-term interest rates are high (fact 2).
Because each of our two theories explains empirical facts that the other cannot, a
logical step is to combine the theories, which leads us to the liquidity premium theory.
The liquidity premium theory of the term structure states that the interest rate on a
long-term bond will equal an average of short-term interest rates expected to occur
over the life of the long-term bond plus a liquidity premium (also referred to as a term
premium) that responds to supply and demand conditions for that bond.
The liquidity premium theory’s key assumption is that bonds of different maturi-
ties are substitutes, which means that the expected return on one bond does influence
the expected return on a bond of a different maturity, but it allows investors to prefer
one bond maturity over another. In other words, bonds of different maturities are
assumed to be substitutes but not perfect substitutes. Investors tend to prefer shorter-
term bonds because these bonds bear less interest-rate risk. For these reasons,
investors must be offered a positive liquidity premium to induce them to hold longer-
term bonds. Such an outcome would modify the expectations theory by adding a pos-
itive liquidity premium to the equation that describes the relationship between long-
and short-term interest rates. The liquidity premium theory is thus written as:
(3)i
nt
ϭ
i
t
ϩ i

e
tϩ1
ϩ i
e
tϩ2
ϩ
. . .
ϩ i
e
tϩ(nϪ1
)

n
ϩ l
nt
Liquidity
Premium and
Preferred Habitat
Theories
CHAPTER 6
The Risk and Term Structure of Interest Rates
133
5
The statement that there is no uncertainty about the return if the term to maturity equals the holding period is
literally true only for a discount bond. For a coupon bond with a long holding period, there is some risk because
coupon payments must be reinvested before the bond matures. Our analysis here is thus being conducted for
discount bonds. However, the gist of the analysis remains the same for coupon bonds because the amount of this
risk from reinvestment is small when coupon bonds have the same term to maturity as the holding period.
where l
nt

ϭ the liquidity (term) premium for the n-period bond at time t, which is
always positive and rises with the term to maturity of the bond, n.
Closely related to the liquidity premium theory is the preferred habitat theory,
which takes a somewhat less direct approach to modifying the expectations hypothe-
sis but comes up with a similar conclusion. It assumes that investors have a prefer-
ence for bonds of one maturity over another, a particular bond maturity (preferred
habitat) in which they prefer to invest. Because they prefer bonds of one maturity over
another they will be willing to buy bonds that do not have the preferred maturity only
if they earn a somewhat higher expected return. Because investors are likely to prefer
the habitat of short-term bonds over that of longer-term bonds, they are willing to
hold long-term bonds only if they have higher expected returns. This reasoning leads
to the same Equation 3 implied by the liquidity premium theory with a term premium
that typically rises with maturity.
The relationship between the expectations theory and the liquidity premiums and
preferred habitat theories is shown in Figure 5. There we see that because the liquid-
ity premium is always positive and typically grows as the term to maturity increases,
the yield curve implied by the liquidity premium theory is always above the yield
curve implied by the expectations theory and generally has a steeper slope.
A simple numerical example similar to the one we used for the expectations
hypothesis further clarifies what the liquidity premium and preferred habitat theories
in Equation 3 are saying. Again suppose that the one-year interest rate over the next
five years is expected to be 5, 6, 7, 8, and 9%, while investors’ preferences for hold-
ing short-term bonds means that the liquidity premiums for one- to five-year bonds
are 0, 0.25, 0.5, 0.75, and 1.0%, respectively. Equation 3 then indicates that the inter-
est rate on the two-year bond would be:
5% ϩ 6%
2
ϩ 0.25% ϭ 5.75%
134 PART II
Financial Markets

/>/YieldCurve.html
This site lets you look at the
dynamic yield curve at any
point in time since 1995.
FIGURE 5 The Relationship
Between the Liquidity Premium
(Preferred Habitat) and Expectations
Theory
Because the liquidity premium is
always positive and grows as the
term to maturity increases, the
yield curve implied by the liquid-
ity premium and preferred habitat
theories is always above the yield
curve implied by the expectations
theory and has a steeper slope.
Note that the yield curve implied
by the expectations theory is
drawn under the scenario of
unchanging future one-year inter-
est rates.
302520151050
Years to Maturity,
n
Interest
Rate,
i
nt
Expectations Theory
Yield Curve

Liquidity
Premium,
l
nt
Liquidity Premium (Preferred Habitat) Theory
Yield Curve
while for the five-year bond it would be:
Doing a similar calculation for the one-, three-, and four-year interest rates, you
should be able to verify that the one- to five-year interest rates are 5.0, 5.75, 6.5, 7.25,
and 8.0%, respectively. Comparing these findings with those for the expectations the-
ory, we see that the liquidity premium and preferred habitat theories produce yield
curves that slope more steeply upward because of investors’ preferences for short-
term bonds.
Let’s see if the liquidity premium and preferred habitat theories are consistent
with all three empirical facts we have discussed. They explain fact 1 that interest rates
on different-maturity bonds move together over time: A rise in short-term interest
rates indicates that short-term interest rates will, on average, be higher in the future,
and the first term in Equation 3 then implies that long-term interest rates will rise
along with them.
They also explain why yield curves tend to have an especially steep upward
slope when short-term interest rates are low and to be inverted when short-term
rates are high (fact 2). Because investors generally expect short-term interest rates
to rise to some normal level when they are low, the average of future expected short-
term rates will be high relative to the current short-term rate. With the additional
boost of a positive liquidity premium, long-term interest rates will be substantially
above current short-term rates, and the yield curve would then have a steep upward
slope. Conversely, if short-term rates are high, people usually expect them to come
back down. Long-term rates would then drop below short-term rates because the
average of expected future short-term rates would be so far below current short-
term rates that despite positive liquidity premiums, the yield curve would slope

downward.
The liquidity premium and preferred habitat theories explain fact 3 that yield
curves typically slope upward by recognizing that the liquidity premium rises with a
bond’s maturity because of investors’ preferences for short-term bonds. Even if short-
term interest rates are expected to stay the same on average in the future, long-term
interest rates will be above short-term interest rates, and yield curves will typically
slope upward.
How can the liquidity premium and preferred habitat theories explain the occa-
sional appearance of inverted yield curves if the liquidity premium is positive? It must
be that at times short-term interest rates are expected to fall so much in the future that
the average of the expected short-term rates is well below the current short-term rate.
Even when the positive liquidity premium is added to this average, the resulting long-
term rate will still be below the current short-term interest rate.
As our discussion indicates, a particularly attractive feature of the liquidity pre-
mium and preferred habitat theories is that they tell you what the market is predict-
ing about future short-term interest rates just from the slope of the yield curve. A
steeply rising yield curve, as in panel (a) of Figure 6, indicates that short-term inter-
est rates are expected to rise in the future. A moderately steep yield curve, as in panel
(b), indicates that short-term interest rates are not expected to rise or fall much in the
future. A flat yield curve, as in panel (c), indicates that short-term rates are expected
to fall moderately in the future. Finally, an inverted yield curve, as in panel (d), indi-
cates that short-term interest rates are expected to fall sharply in the future.
5% ϩ 6% ϩ 7% ϩ 8% ϩ 9%
5
ϩ 1% ϭ 8%
CHAPTER 6
The Risk and Term Structure of Interest Rates
135
In the 1980s, researchers examining the term structure of interest rates questioned
whether the slope of the yield curve provides information about movements of future

short-term interest rates.
6
They found that the spread between long- and short-term
interest rates does not always help predict future short-term interest rates, a finding
that may stem from substantial fluctuations in the liquidity (term) premium for long-
term bonds. More recent research using more discriminating tests now favors a dif-
ferent view. It shows that the term structure contains quite a bit of information for the
very short run (over the next several months) and the long run (over several years)
Evidence on the
Term Structure
136 PART II
Financial Markets
6
Robert J. Shiller, John Y. Campbell, and Kermit L. Schoenholtz, “Forward Rates and Future Policy: Interpreting
the Term Structure of Interest Rates,” Brookings Papers on Economic Activity 1 (1983): 173–217; N. Gregory
Mankiw and Lawrence H. Summers, “Do Long-Term Interest Rates Overreact to Short-Term Interest Rates?”
Brookings Papers on Economic Activity 1 (1984): 223–242.
FIGURE 6 Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium Theory
Term to Maturity
Term to Maturity
Term to Maturity
Term to Maturity
(a
)
F
u
t
u
r
e

s
h
o
rt-t
e
rm int
e
r
es
t r
a
t
es
expected to rise
(b) Future short-term interest rates
expected to stay the same
(c) Future short-term interest rates
expected to fall moderately
(d) Future short-term interest rates
expected to fall sharply
Yield to
Maturity
Yield to
Maturity
Yield to
Maturity
Yield to
Maturity
but is unreliable at predicting movements in interest rates over the intermediate term

(the time in between).
7
The liquidity premium and preferred habitat theories are the most widely accepted
theories of the term structure of interest rates because they explain the major empir-
ical facts about the term structure so well. They combine the features of both the
expectations theory and the segmented markets theory by asserting that a long-term
interest rate will be the sum of a liquidity (term) premium and the average of the
short-term interest rates that are expected to occur over the life of the bond.
The liquidity premium and preferred habitat theories explain the following facts:
(1) Interest rates on bonds of different maturities tend to move together over time, (2)
yield curves usually slope upward, and (3) when short-term interest rates are low,
yield curves are more likely to have a steep upward slope, whereas when short-term
interest rates are high, yield curves are more likely to be inverted.
The theories also help us predict the movement of short-term interest rates in the
future. A steep upward slope of the yield curve means that short-term rates are expected
to rise, a mild upward slope means that short-term rates are expected to remain the
same, a flat slope means that short-term rates are expected to fall moderately, and an
inverted yield curve means that short-term rates are expected to fall sharply.
Summary
CHAPTER 6
The Risk and Term Structure of Interest Rates
137
7
Eugene Fama, “The Information in the Term Structure,” Journal of Financial Economics 13 (1984): 509–528;
Eugene Fama and Robert Bliss, “The Information in Long-Maturity Forward Rates,” American Economic Review 77
(1987): 680–692; John Y. Campbell and Robert J. Shiller, “Cointegration and Tests of the Present Value Models,”
Journal of Political Economy 95 (1987): 1062–1088; John Y. Campbell and Robert J. Shiller, “Yield Spreads and
Interest Rate Movements: A Bird’s Eye View,” Review of Economic Studies 58 (1991): 495–514.
Interpreting Yield Curves, 1980–2003
Application

Figure 7 illustrates several yield curves that have appeared for U.S. govern-
ment bonds in recent years. What do these yield curves tell us about the pub-
lic’s expectations of future movements of short-term interest rates?
Study Guide Try to answer the preceding question before reading further in the text. If you
have trouble answering it with the liquidity premium and preferred habitat
theories, first try answering it with the expectations theory (which is simpler
because you don’t have to worry about the liquidity premium). When you
understand what the expectations of future interest rates are in this case,
modify your analysis by taking the liquidity premium into account.
The steep inverted yield curve that occurred on January 15, 1981, indi-
cated that short-term interest rates were expected to decline sharply in the
future. In order for longer-term interest rates with their positive liquidity
premium to be well below the short-term interest rate, short-term interest
rates must be expected to decline so sharply that their average is far below
the current short-term rate. Indeed, the public’s expectations of sharply lower
short-term interest rates evident in the yield curve were realized soon after
January 15; by March, three-month Treasury bill rates had declined from the
16% level to 13%.
138 PART II
Financial Markets
The steep upward-sloping yield curves on March 28, 1985, and January
23, 2003, indicated that short-term interest rates would climb in the future.
The long-term interest rate is above the short-term interest rate when short-
term interest rates are expected to rise because their average plus the liquid-
ity premium will be above the current short-term rate. The moderately
upward-sloping yield curves on May 16, 1980, and March 3, 1997, indicated
that short-term interest rates were expected neither to rise nor to fall in the
near future. In this case, their average remains the same as the current short-
term rate, and the positive liquidity premium for longer-term bonds explains
the moderate upward slope of the yield curve.

FIGURE 7 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.
12345 5 101520
6
8
10
12
14
16
Terms to Maturity (Years)
Interest Rate (%)
May 16, 1980
March 28, 1985
January 15, 1981
March 3, 1997
0
4
2
January 23, 2003
Summary
1. Bonds with the same maturity will have different
interest rates because of three factors: default risk,
liquidity, and tax considerations. The greater a bond’s
default risk, the higher its interest rate relative to other
bonds; the greater a bond’s liquidity, the lower its
interest rate; and bonds with tax-exempt status will
have lower interest rates than they otherwise would.
The relationship among interest rates on bonds with the
same maturity that arise because of these three factors is
known as the risk structure of interest rates.

CHAPTER 6
The Risk and Term Structure of Interest Rates
139
2. Four theories of the term structure provide
explanations of how interest rates on bonds with
different terms to maturity are related. The expectations
theory views long-term interest rates as equaling the
average of future short-term interest rates expected to
occur over the life of the bond; by contrast, the
segmented markets theory treats the determination of
interest rates for each bond’s maturity as the outcome of
supply and demand in that market only. Neither of
these theories by itself can explain the fact that interest
rates on bonds of different maturities move together
over time and that yield curves usually slope upward.
3. The liquidity premium and preferred habitat theories
combine the features of the other two theories, and by
so doing are able to explain the facts just mentioned.
They view long-term interest rates as equaling the
average of future short-term interest rates expected to
occur over the life of the bond plus a liquidity
premium. These theories allow us to infer the market’s
expectations about the movement of future short-term
interest rates from the yield curve. A steeply upward-
sloping curve indicates that future short-term rates are
expected to rise, a mildly upward-sloping curve
indicates that short-term rates are expected to stay the
same, a flat curve indicates that short-term rates are
expected to decline slightly, and an inverted yield curve
indicates that a substantial decline in short-term rates is

expected in the future.
Key Terms
default, p. 120
default-free bonds, p. 121
expectations theory, p. 129
inverted yield curve, p. 127
junk bonds, p. 124
liquidity premium theory, p. 133
preferred habitat theory, p. 134
risk premium, p. 121
risk structure of interest rates, p. 120
segmented markets theory, p. 132
term structure of interest rates, p. 120
yield curve, p. 127
Questions and Problems
Questions marked with an asterisk are answered at the end
of the book in an appendix, “Answers to Selected Questions
and Problems.”
1. Which should have the higher risk premium on its
interest rates, a corporate bond with a Moody’s Baa
rating or a corporate bond with a C rating? Why?
*2. Why do U.S. Treasury bills have lower interest rates
than large-denomination negotiable bank CDs?
3. Risk premiums on corporate bonds are usually anticycli-
cal; that is, they decrease during business cycle expan-
sions and increase during recessions. Why is this so?
*4. “If bonds of different maturities are close substitutes, their
interest rates are more likely to move together.” Is this
statement true, false, or uncertain? Explain your answer.
5. If yield curves, on average, were flat, what would this

say about the liquidity (term) premiums in the term
structure? Would you be more or less willing to accept
the expectations theory?
*6. Assuming that the expectations theory is the correct
theory of the term structure, calculate the interest
rates in the term structure for maturities of one to five
years, and plot the resulting yield curves for the fol-
lowing series of one-year interest rates over the next
five years:
(a) 5%, 7%, 7%, 7%, 7%
(b) 5%, 4%, 4%, 4%, 4%
How would your yield curves change if people pre-
ferred shorter-term bonds over longer-term bonds?
7. Assuming that the expectations theory is the correct
theory of the term structure, calculate the interest rates
in the term structure for maturities of one to five years,
and plot the resulting yield curves for the following
path of one-year interest rates over the next five years:
(a) 5%, 6%, 7%, 6%, 5%
(b) 5%, 4%, 3%, 4%, 5%
How would your yield curves change if people pre-
ferred shorter-term bonds over longer-term bonds?
QUIZ
*8. If a yield curve looks like the one shown in figure (a)
in this section, what is the market predicting about
the movement of future short-term interest rates?
What might the yield curve indicate about the mar-
ket’s predictions about the inflation rate in the future?
9. If a yield curve looks like the one shown in (b), what
is the market predicting about the movement of future

short-term interest rates? What might the yield curve
indicate about the market’s predictions about the infla-
tion rate in the future?
*10. What effect would reducing income tax rates have on
the interest rates of municipal bonds? Would interest
rates of Treasury securities be affected, and if so, how?
Using Economic Analysis
to Predict the Future
11. Predict what will happen to interest rates on a
corporation’s bonds if the federal government guaran-
tees today that it will pay creditors if the corporation
goes bankrupt in the future. What will happen to the
interest rates on Treasury securities?
*12. Predict what would happen to the risk premiums on
corporate bonds if brokerage commissions were low-
ered in the corporate bond market.
13. If the income tax exemption on municipal bonds were
abolished, what would happen to the interest rates on
these bonds? What effect would the change have on
interest rates on U.S. Treasury securities?
*14. If the yield curve suddenly becomes steeper, how
would you revise your predictions of interest rates in
the future?
15. If expectations of future short-term interest rates sud-
denly fall, what would happen to the slope of the
yield curve?
140 PART II
Financial Markets
Web Exercises
1. The amount of additional interest investors receive

due to the various premiums changes over time.
Sometimes the risk premiums are much larger than at
other times. For example, the default risk premium
was very small in the late 1990s when the economy
was so healthy business failures were rare. This risk
premium increases during recessions.
Go to www
.federalreserve.gov/releases/releases/h15
(historical data) and find the interest rate listings for
AAA and Baa rated bonds at three points in time, the
most recent, June 1, 1995, and June 1, 1992. Prepare
a graph that shows these three time periods (see
Figure 1 for an example). Are the risk premiums sta-
ble or do they change over time?
2. Figure 7 shows a number of yield curves at various
points in time. Go to www
.bloomberg.com, and click
on “Markets” at the top of the page. Find the Treasury
yield curve. Does the current yield curve fall above or
below the most recent one listed in Figure 7? Is the
current yield curve flatter or steeper than the most
recent one reported in Figure 7?
3. Investment companies attempt to explain to investors
the nature of the risk the investor incurs when buying
shares in their mutual funds. For example, Vanguard
carefully explains interest rate risk and offers alterna-
tive funds with different interest rate risks. Go to
guar
d.com/VGApp/hnw
/FundsStocksOverview.

a. Select the bond fund you would recommend to an
investor who has very low tolerance for risk and a
short investment horizon. Justify your answer.
b. Select the bond fund you would recommend to an
investor who has very high tolerance for risk and a
long investment horizon. Justify your answer.
Yield to
Maturity
Term to Maturity
(a)
Yield to
Maturity
Term to Maturity
(b)
PREVIEW
Rarely does a day go by that the stock market isn’t a major news item. We have wit-
nessed huge swings in the stock market in recent years. The 1990s were an extraor-
dinary decade for stocks: the Dow Jones and S&P 500 indexes increased more than
400%, while the tech-laden NASDAQ index rose more than 1,000%. By early 2000,
both indexes had reached record highs. Unfortunately, the good times did not last,
and many investors lost their shirts. Starting in early 2000, the stock market began to
decline: the NASDAQ crashed, falling by over 50%, while the Dow Jones and S&P
500 indexes fell by 30% through January 2003.
Because so many people invest in the stock market and the price of stocks affects
the ability of people to retire comfortably, the market for stocks is undoubtedly the
financial market that receives the most attention and scrutiny. In this chapter, we look
at how this important market works.
We begin by discussing the fundamental theories that underlie the valuation of
stocks. These theories are critical to understanding the forces that cause the value of
stocks to rise and fall minute by minute and day by day. Once we have learned the

methods for stock valuation, we need to explore how expectations about the market
affect its behavior. We do so by examining the theory of rational expectations. When
this theory is applied to financial markets, the outcome is the efficient market hypoth-
esis. The theory of rational expectations is also central to debates about the conduct
of monetary policy, to be discussed in Chapter 28.
Theoretically, the theory of rational expectations should be a powerful tool for
analyzing behavior. But to establish that it is in reality a useful tool, we must compare
the outcomes predicted by the theory with empirical evidence. Although the evidence
is mixed and controversial, it indicates that for many purposes, the theory of rational
expectations is a good starting point for analyzing expectations.
Computing the Price of Common Stock
Common stock is the principal way that corporations raise equity capital. Holders of
common stock own an interest in the corporation consistent with the percentage of
outstanding shares owned. This ownership interest gives stockholders—those who
hold stock in a corporation—a bundle of rights. The most important are the right to
vote and to be the residual claimant of all funds flowing into the firm (known as
cash flows), meaning that the stockholder receives whatever remains after all other
141
Chapter
The Stock Market, the Theory of
Rational Expectations, and the
Efficient Market Hypothesis
7
claims against the firm’s assets have been satisfied. Stockholders are paid dividends
from the net earnings of the corporation. Dividends are payments made periodically,
usually every quarter, to stockholders. The board of directors of the firm sets the level
of the dividend, usually upon the recommendation of management. In addition, the
stockholder has the right to sell the stock.
One basic principle of finance is that the value of any investment is found by
computing the value today of all cash flows the investment will generate over its life.

For example, a commercial building will sell for a price that reflects the net cash flows
(rents – expenses) it is projected to have over its useful life. Similarly, we value com-
mon stock as the value in today’s dollars of all future cash flows. The cash flows a
stockholder might earn from stock are dividends, the sales price, or both.
To develop the theory of stock valuation, we begin with the simplest possible sce-
nario: You buy the stock, hold it for one period to get a dividend, then sell the stock.
We call this the one-period valuation model.
Suppose that you have some extra money to invest for one year. After a year, you will
need to sell your investment to pay tuition. After watching CNBC or Wall Street Week
on TV, you decide that you want to buy Intel Corp. stock. You call your broker and
find that Intel is currently selling for $50 per share and pays $0.16 per year in divi-
dends. The analyst on Wall Street Week predicts that the stock will be selling for $60
in one year. Should you buy this stock?
To answer this question, you need to determine whether the current price accu-
rately reflects the analyst’s forecast. To value the stock today, you need to find the pres-
ent discounted value of the expected cash flows (future payments) using the formula
in Equation 1 of Chapter 4. Note that in this equation, the discount factor used to dis-
count the cash flows is the required return on investments in equity rather than the
interest rate. The cash flows consist of one dividend payment plus a final sales price.
When these cash flows are discounted back to the present, the following equation
computes the current price of the stock:
(1)
where P
0
=the current price of the stock. The zero subscript refers to
time period zero, or the present.
Div
1
=the dividend paid at the end of year 1.
k

e
=the required return on investments in equity.
P
1
=the price at the end of the first period; the assumed sales
price of the stock.
To see how Equation 1 works, let’s compute the price of the Intel stock if, after
careful consideration, you decide that you would be satisfied to earn a 12% return on
the investment. If you have decided that k
e
= 0.12, are told that Intel pays $0.16 per
year in dividends (Div
1
= 0.16), and forecast the share price of $60 for next year (P
1
= $60), you get the following from Equation 1:
P
0
ϭ
0.16
1 ϩ 0.12
ϩ
$60
1 ϩ 0.12
ϭ $0.14 ϩ $53.57 ϭ $53.71
P
0
ϭ
Div
1

(1 ϩ k
e
)
ϩ
P
1
(1 ϩ k
e
)
The One-Period
Valuation Model
142 PART II
Financial Markets

Access detailed stock quotes,
charts, and historical stock data.
Based on your analysis, you find that the present value of all cash flows from the
stock is $53.71. Because the stock is currently priced at $50 per share, you would
choose to buy it. However, you should be aware that the stock may be selling for less
than $53.71, because other investors place a different risk on the cash flows or esti-
mate the cash flows to be less than you do.
Using the same concept, the one-period dividend valuation model can be extended to
any number of periods: The value of stock is the present value of all future cash flows.
The only cash flows that an investor will receive are dividends and a final sales price
when the stock is ultimately sold in period n. The generalized multi-period formula
for stock valuation can be written as:
(2)
If you tried to use Equation 2 to find the value of a share of stock, you would
soon realize that you must first estimate the value the stock will have at some point
in the future before you can estimate its value today. In other words, you must find

P
n
in order to find P
0
. However, if P
n
is far in the future, it will not affect P
0
. For exam-
ple, the present value of a share of stock that sells for $50 seventy-five years from now
using a 12% discount rate is just one cent [$50/(1.12
75
)=$0.01]. This reasoning
implies that the current value of a share of stock can be calculated as simply the pres-
ent value of the future dividend stream. The generalized dividend model is rewrit-
ten in Equation 3 without the final sales price:
(3)
Consider the implications of Equation 3 for a moment. The generalized dividend
model says that the price of stock is determined only by the present value of the div-
idends and that nothing else matters. Many stocks do not pay dividends, so how is it
that these stocks have value? Buyers of the stock expect that the firm will pay dividends
someday. Most of the time a firm institutes dividends as soon as it has completed the
rapid growth phase of its life cycle.
The generalized dividend valuation model requires that we compute the present
value of an infinite stream of dividends, a process that could be difficult, to say the
least. Therefore, simplified models have been developed to make the calculations eas-
ier. One such model is the Gordon growth model, which assumes constant dividend
growth.
Many firms strive to increase their dividends at a constant rate each year. Equation 4
rewrites Equation 3 to reflect this constant growth in dividends:

(4)
where D
0
=the most recent dividend paid
g =the expected constant growth rate in dividends
k
e
=the required return on an investment in equity
P
0
ϭ
D
0
ϫ (1 ϩ g
)
1
(1 ϩ k
e
)
1
ϩ
D
0
ϫ (1 ϩ g
)
2
(1 ϩ k
e
)
2

ϩ
…
ϩ
D
0
ϫ (1 ϩ g
)
ϱ
(1 ϩ k
e
)
ϱ
The Gordon
Growth Model
P
0
ϭ
͚
∞
tϭ1

D
t
(1 ϩ k
e
)
t
P
0
ϭ

D
1
(1 ϩ k
e
)
1
ϩ
D
2
(1 ϩ k
e
)
2
ϩ ϩ
D
n
(1 ϩ k
e
)
n
ϩ
P
n
(1 ϩ k
e
)
n
The Generalized
Dividend
Valuation Model

CHAPTER 7
The Stock Market, the Theory of Rational Expectations, and the Efficient Market Hypothesis
143
Equation 4 has been simplified using algebra to obtain Equation 5.
1
(5)
This model is useful for finding the value of stock, given a few assumptions:
1. Dividends are assumed to continue growing at a constant rate forever. Actually, as long
as they are expected to grow at a constant rate for an extended period of time, the
model should yield reasonable results. This is because errors about distant cash
flows become small when discounted to the present.
2. The growth rate is assumed to be less than the required return on equity, k
e
. Myron
Gordon, in his development of the model, demonstrated that this is a reasonable
assumption. In theory, if the growth rate were faster than the rate demanded by
holders of the firm’s equity, in the long run the firm would grow impossibly large.
How the Market Sets Security Prices
Suppose you went to an auto auction. The cars are available for inspection before the
auction begins, and you find a little Mazda Miata that you like. You test-drive it in the
parking lot and notice that it makes a few strange noises, but you decide that you
would still like the car. You decide $5,000 would be a fair price that would allow you
to pay some repair bills should the noises turn out to be serious. You see that the auc-
tion is ready to begin, so you go in and wait for the Miata to enter.
Suppose there is another buyer who also spots the Miata. He test-drives the car
and recognizes that the noises are simply the result of worn brake pads that he can
fix himself at a nominal cost. He decides that the car is worth $7,000. He also goes in
and waits for the Miata to enter.
Who will buy the car and for how much? Suppose only the two of you are inter-
ested in the Miata. You begin the bidding at $4,000. He ups your bid to $4,500. You

P
0
ϭ
D
0
ϫ (1 ϩ g
)
(k
e
Ϫ g
)
ϭ
D
1
(k
e
Ϫ g
)
144 PART II
Financial Markets
1
To generate Equation 5 from Equation 4, first multiply both sides of Equation 4 by (1 ϩ k
e
)/(1 ϩ g) and sub-
tract Equation 4 from the result. This yields:
Assuming that k
e
is greater than g, the term on the far right will approach zero and can be dropped. Thus, after
factoring P
0

out of the left-hand side:
Next, simplify by combining terms to:
P
0
ϭ
D
0
ϫ (1 ϩ g
)
k
e
Ϫ g
ϭ
D
1
k
e
Ϫ g
P
0
ϫ
(1 ϩ k
e
)
Ϫ (1 ϩ g
)
1 ϩ g
ϭ D
0
P

0
ϫ c
1 ϩ k
e
1 ϩ g
Ϫ 1d ϭ D
0
P
0
ϫ (1 ϩ k
e
)
(1 ϩ g
)
Ϫ P
0
ϭ D
0
Ϫ
D
0
ϫ (1 ϩ g
)
∞
(1 ϩ k
e
)
∞