CHAPTER
5
The Risk Structure and Term
Structure of Interest Rates
WHY INVEST IN TREASURY BILLS IF THEIR INTEREST RATES ARE SO
LOW?
•In February 2010, Moody’s Investors Service hinted that large budget deficits
could affect the Aaa rating of government bonds.
•Also in 2010, Treasure bills offered very low interest rates, yet investors
bought them even though Treasury bonds offered much higher rates.
•In the corporate bond market, investors were also buying bonds with very low
yields.
•In this lesson, we study why these unusual situations occur.
Key Issue and Question
Issue: During the financial crisis, the bond rating agencies were
criticized for having given high ratings to securities that proved to be
very risky.
Question: Should the government more closely regulate the credit
rating agencies?
5.1 Learning Objective
Explain why bonds with the same maturity can have different interest rates.
Why might bonds that have the same maturities—for example, all the bonds that will
mature in 30 years—have different interest rates, or yields to maturity?
Four factors account for these differences:
•Risk
•Liquidity
•Information costs
•Taxation
Risk structure of interest rates The relationship among interest rates on bonds that
have different characteristics but the same maturity.
Default Risk
Bonds differ with respect to default risk (sometimes called credit risk), which is the
risk that the bond issuer will fail to make payments of interest or principal.
The Risk Structure of Interest Rates
Default Risk
Bonds differ with respect to default risk (sometimes called credit risk), which is the
risk that the bond issuer will fail to make payments of interest or principal.
Measuring Default Risk
• The default risk premium on a bond is the difference between the interest rate on
the bond and the interest rate on a Treasury bond that has the same maturity.
• Many investors rely on credit rating agencies to provide them with information on
the creditworthiness of corporations and governments that issue bonds.
Bond rating A single statistic that summarizes a rating agency’s view of the issuer’s
likely ability to make the required payments on its bonds.
The Risk Structure of Interest Rates
The Risk Structure of Interest Rates
Changes in Default Risk and in the Default Risk Premium
Determining Default Risk Premium in Yields
The initial default risk premium can be seen by comparing yields associated
with the prices P1T and P1C.
Because the price of the safer U.S. Treasury bond is greater than that of the
riskier corporate bond, we know that the yield on the corporate bond must be
greater than the yield on the Treasury bond to compensate investors for
bearing risk.
Figure 5.1 (1 of 2)
The Risk Structure of Interest Rates
Changes in Default Risk and in the Default Risk Premium
Determining Default Risk Premium in Yields
As the default risk on corporate bonds increases, in panel (a), the demand for
corporate bonds shifts to the left.
In panel (b), the demand for Treasury bonds shifts to the right.
The price of corporate bonds falls to P2C, and the price of Treasury bonds rises
to P2T, so the yield on Treasury bonds falls relative to the yield on corporate
bonds. Therefore, the default risk premium has increased.•
Figure 5.1 (2 of 2)
The Risk Structure of Interest Rates
Changes in Default Risk and in the Default Risk Premium
Rising Default Premiums during Recessions
The default premium typically rises during a recession.
For the 2001 recession, the figure shows a fairly typical pattern, with the
spread between the interest rate on corporate bonds and the interest rate on
Treasury bonds rising from about 2 percentage points before the recession to
more than 3 percentage points during the recession.
Figure 5.2 (1 of 2)
The Risk Structure of Interest Rates
Changes in Default Risk and in the Default Risk Premium
Rising Default Premiums during Recessions
For the 2007–2009 recession, the figure shows that the increase in the default
risk premium was much larger. It rose from less than 2 percentage points
before the recession began to more than 6 percentage points at the height of
the financial crises in the fall of 2008.•
Figure 5.2 (2 of 2)
The Risk Structure of Interest Rates
Making the Connection
Do Credit Rating Agencies Have a Conflict of Interest?
• John Moody began the modern bond rating business by publishing Moody’s
Analyses of Railroad Investments in 1909.
• By the 1920s, the work of rating agencies expanded to cover an increasing number
of industries.
• In the post-World War II period, prosperity diminished the role of rating agencies,
but by the late 1970s, recession, inflation, and government regulations once again
expanded the work of rating agencies.
• When the rating agencies began charging firms and governments—rather than
investors—for their services, a conflict of interest emerged.
• During the financial crisis, rating agencies came under increased scrutiny. In July
2010, Congress passed the Dodd-Frank Wall Street Reform and Consumer
Protection Act, and a new Office of Credit Ratings was created within the Securities
and Exchange Commission (SEC) to oversee the work of credit rating agencies.
The Risk Structure of Interest Rates
Liquidity and Information Costs
• Investors care about liquidity, so they are willing to accept a lower interest rate
on more liquid investments than on less liquid—or illiquid—investments, all
other things being equal.
• Similarly, investors care about the costs of acquiring information on a bond.
• An increase in a bond’s liquidity or a decrease in the cost of acquiring
information about the bond will increase the demand for the bond.
• During the financial crisis of 2007–2009, homeowners were defaulting on
many of the mortgages contained in the bonds. To make matters worse,
investors came to realize that they did not fully understand these bonds and
had difficulty finding information contained in the mortgage-backed bonds.
The Risk Structure of Interest Rates
Tax Treatment
• Investors care about the after-tax return on their investments—that is, the return
the investors have left after paying their taxes.
How the Tax Treatment of Bonds Differs
Municipal bonds Bonds issued by state and local governments.
The Risk Structure of Interest Rates
How the Tax Treatment of Bonds Differs
• The coupons on corporate bonds can be subject to federal, state, and local
taxes. The coupons on Treasury bonds are subject to federal tax but not to
state or local taxes. The coupons on municipal bonds are typically not subject
to federal, state, or local taxes.
• It is important to recall that bond investors can receive two types of income
from owning bonds:
(1) interest income from coupons and
(2) capital gains (or losses) from price changes on the bonds.
• Interest income is taxed at the same rates as wage and salary income. Capital
gains are taxed at a lower rate than interest income. Capital gains are also
taxed only if they are realized, which means that the investor sells the bond
for a higher price than he or she paid for it. Unrealized capital gains are not
taxed.
The Risk Structure of Interest Rates
The Effect of Tax Changes on Interest Rates
The Effect of Changes in Taxes on Bond Prices
If the federal income tax rate increases, tax-exempt municipal bonds will be more
attractive to investors, and Treasury bonds will be less attractive.
In panel (a), the demand curve for municipal bonds shifts to the right, from DMuni1
to DMuni2, increasing the price from PM1 to PM2 and lowering the interest rate.
In panel (b), the demand curve for Treasury bonds shifts to the left, from DTreas1 to
DTreas2, lowering the price from PT1 to PT2 and raising the interest rate.•
Figure 5.3
Solved Problem
5.1
How Would a VAT Affect Interest Rates?
Suppose the federal government eliminates the federal income tax and
replaces it with a VAT. Explain the effect of this policy change on the
interest rates on municipal bonds, corporate bonds, and Treasury bonds.
Draw three graphs, one for each market, to illustrate your answer.
The Risk Structure of Interest Rates
Solved Problem
5.1
How Would a VAT Affect Interest Rates?
Solving the Problem
Step 1 Review the lesson material.
Step 2 Analyze the effect of the tax policy change on the interest rate on
municipal bonds.
The Risk Structure of Interest Rates
Solved Problem
5.1
How Would a VAT Affect Interest Rates?
Solving the Problem (continued)
Step 3 Analyze the effect of the tax
Step 4 Analyze the effect of the tax
policy change on the interest
policy change on the interest
rate on corporate bonds.
rate on Treasury bonds.
Step 5 Summarize your findings.
Replacing the federal income tax with a VAT would increase the interest rate on municipal
bonds and lower the interest rates on corporate bonds and Treasury bonds.
The Risk Structure of Interest Rates
The Risk Structure of Interest Rates
Making the Connection
Is the U.S. Treasury Likely to Default on Its Bonds?
• Bonds issued by governments are called sovereign debt. Recent examples of
sovereign debt defaults include Russia and Argentina. In the nineteenth century,
many U.S. states also defaulted on their bonds. Circa 2010, investors feared that
several European countries might default on their debt.
• Investors typically consider U.S. Treasury bonds to be default-risk free, but rating
agencies worry that very large projected budget deficits will increase the volume of
Treasury bonds issued and that the resulting interest payments will take an ever
increasing fraction of the federal budget.
• Governments can raise taxes or create money to make the interest payments, but
these two alternatives can be painful.
• In 2010, investors in the United States and elsewhere didn’t seem to think that the
U.S. Treasury would default on its bonds because they were willing to buy them at
interest rates that were too low to include a default premium.
The Risk Structure of Interest Rates
5.2 Learning Objective
Explain why bonds with different maturities can have different interest rates.
Term structure of interest rates The relationship among the interest rates on bonds
that are otherwise similar but that have different maturities.
• The Treasury yield curve shows the relationship on a particular day among the
interest rates on Treasury bonds with different maturities.
• When short-term rates are lower than long-term rates, we have an upward-sloping
yield curve.
• Infrequently, there are times when short-term interest rates are higher than longterm interest rates, resulting in a downward-sloping yield curve.
The Term Structure of Interest Rates
Figure 5.4
The Treasury Yield Curve
This figure shows the
Treasury yield curves for
June 22, 2009, and June
22, 2010.•
The Term Structure of Interest Rates
Figure 5.5
The Interest Rates on 3-Month Treasury Bills and 10-Year Treasury Notes, January
1970–May 2010
The figure shows that most of the time since 1970, the interest rates on 3-month Treasury
bills (indicated by the red line) have been lower than the interest rates on 10-year Treasury
notes (indicated by the blue line). During a few periods, though, the interest rate on the 3month Treasury bill has been higher than the interest rate on the 10-year Treasury note.•
The Term Structure of Interest Rates
Making the Connection
Negative Interest Rates on Treasury Bills?
• Can the nominal interest rate ever be negative?
• A negative nominal interest rate means that the lender is actually paying the
borrower interest in return for borrowing the lender’s money. What lender would
ever do that?
• In fact, at times during the Great Depression of the 1930s and again during the
financial crisis of 2007–2009, investors were willing to accept negative interest
rates on the Treasury bills by paying prices that were higher than the bills’ face
values.
• Because interest rates on other short-term investments, such as bank certificates
of deposit or money market mutual fund shares, were also very low, investors were
giving up relatively little to temporarily park their funds in default-risk free
Treasury bills.
The Term Structure of Interest Rates
Explaining the Term Structure
Any explanation of the term structure should be able to account for three important
facts:
1. Interest rates on long-term bonds are usually higher than interest rates on shortterm bonds.
2. Interest rates on short-term bonds are occasionally higher than interest rates on
long-term bonds.
3. Interest rates on bonds of all maturities tend to rise and fall together.
Economists have advanced three theories to explain these facts: the expectations
theory, the segmented markets theory, and the liquidity premium theory or preferred
habitat theory. We examine these theories next.
The Term Structure of Interest Rates
The Expectations Theory of the Term Structure
Expectations theory A theory of the term structure of interest rates that holds that
the interest rate on a long-term bond is an average of the interest rates investors
expect on short-term bonds over the lifetime of the long-term bond.
The two key assumptions of the expectations theory are:
1. Investors have the same investment objectives.
2. For a given holding period, investors view bonds of different maturities as being
perfect substitutes for one another. That is, holding a 10-year bond for 10 years is the
same to investors as holding a five-year bond for five years and another five-year bond
for a second five years.
The Term Structure of Interest Rates
The Expectations Theory Applied in a Simple Example
Suppose that you intend to invest $1,000 for two years and are considering one of two
strategies:
1.The buy-and-hold strategy.
With this strategy, you buy a two-year bond and hold it until maturity.
After two years, the $1,000 investment will have grown to
$1,000(1 + i2t)(1 + i2t).
2.The rollover strategy.
With this strategy, you buy a one-year bond today and hold it until it matures in one
year. At that time, you buy a second one-year bond, and you hold it until it matures at
the end of the second year.
After two years, you will expect your $1,000 investment to have grown to
$1,000(1 + i1t) (1 + ie it+1).
With the rollover strategy, you must form an expectation of what the interest rate on
the one-year bond will be.
The Term Structure of Interest Rates
The Expectations Theory Applied in a Simple Example
A key point to understand is that under the assumptions of the expectations theory,
the returns from the two strategies must be the same.
Arbitrage should result in the returns from the two strategies being the same.
Therefore, we can write:
This equality can be reduced to:
This equation tells us that the interest rate on the two-year bond is an average of the
interest rate on the one-year bond today and the expected interest rate on the oneyear bond one year from now.
Generally, the interest rate on an n-year bond—where n can be any number of years—
is equal to:
The Term Structure of Interest Rates
Interpreting the Term Structure Using the Expectations Theory
The Term Structure of Interest Rates
Interpreting the Term Structure Using the Expectations Theory
More generally, according to the expectations theory:
• An upward-sloping yield curve is the result of investors expecting future
short-term rates to be higher than the current short-term rate.
• A flat yield curve is the result of investors expecting future short-term rates
to be the same as the current short-term rate.
• A downward-sloping yield curve is the result of investors expecting future
short-term rates to be lower than the current short-term rate.
The Term Structure of Interest Rates
Figure 5.6
Using the Yield Curve to Predict Interest Rates: The Expectations Theory
Under the expectations theory, the slope of the yield curve shows that future
short-term interest rates are expected to
(a) rise,
(b) remain the same, or
(c) fall relative to current levels.•
The Term Structure of Interest Rates
Shortcomings of the Expectations Theory
• The expectations theory explains an upward-sloping yield curve as being the result
of investors expecting future short-term rates to be higher than the current shortterm rate.
• But if the yield curve is typically upward sloping, investors must be expecting shortterm rates to rise most of the time.
• This explanation seems unlikely because at any particular time, short-term rates
are about as likely to fall as to rise.
The Term Structure of Interest Rates
Solved Problem
5.2a
Is There Easy Money to Be Made from the Term Structure?
The term interest carry trade is sometimes used to refer to borrowing at a low
short-term interest rate and using the borrowed funds to invest at a higher longterm interest rate.
a. How would you advise an investor who is thinking of following a carry
trade strategy? What difficulties would you point out in the strategy?
b. If the yield curve was inverted, or downward sloping, would a carry
trade strategy still be possible? Briefly explain.
The Term Structure of Interest Rates
Solved Problem
5.2a
Is There Easy Money to Be Made from the Term Structure?
Solving the Problem
Step 1 Review the lesson material.
Step 2 Use the expectations theory of the term structure to answer the questions
in part (a).
If the expectations theory is correct, the average of the expected short-term
interest rates over the life of a long-term investment should be roughly equal to the
interest rate on the long-term investment, which would wipe out any potential profits from
the interest carry trade. Moreover, if interest rates rise more rapidly than expected, the
price of the long-term investment will decline, and the investor will suffer a capital loss.
Step 3 Answer part (b) by explaining whether the interest carry trade would still be
possible if the yield curve were inverted.
If the yield curve were inverted, with long-term rates lower than short-term rates, an
institutional investor could borrow long term and invest the funds at the higher short-term
rates. In this case, the investor would be subject to reinvestment risk, or the risk that after
the short-term investment has matured, the interest rate on new short-term investments
will have declined.
The Term Structure of Interest Rates
The Segmented Markets Theory of the Term Structure
Segmented markets theory A theory of the term structure of interest rates that holds
that the interest rate on a bond of a particular maturity is determined only by the
demand and supply of bonds of that maturity.
The segmented markets theory addresses the shortcomings of the expectations
theory by making two related observations:
1. Investors in the bond market do not all have the same objectives.
2. Investors do not see bonds of different maturities as being perfect substitutes for
each other.
•Markets for bonds of different maturities are separated from each other, or
segmented. Investors who participate in the market for bonds of one maturity do not
participate in markets for bonds of other maturities.
The Term Structure of Interest Rates
The Segmented Markets Theory of the Term Structure
• Relative to short-term bonds, long-term bonds have two shortcomings:
• They are subject to greater interest-rate risk, and they are often less liquid.
• The reason why the yield curve is typically upward sloping is that more investors
are in the market for short-term bonds, causing their prices to be higher and their
interest rates lower, and fewer investors are in the market for long-term bonds,
causing their prices to be lower and their interest rates higher.
• The segmented markets theory, however, cannot explain why short-term interest
rates would ever be greater than long-term interest rates (a downward-sloping
yield curve), or why interest rates of all maturities tend to rise and fall together.
The Term Structure of Interest Rates
The Liquidity Premium Theory
Liquidity premium theory (or preferred habitat theory) A theory of the term structure
of interest rates that holds that the interest rate on a long-term bond is an average of
the interest rates investors expect on short-term bonds over the lifetime of the longterm bond, plus a term premium that increases in value the longer the maturity of the
bond.
Term premium The additional interest investors require in order to be willing to buy a
long-term bond rather than a comparable sequence of short-term bonds.
The Term Structure of Interest Rates
The Liquidity Premium Theory
• In effect, then, the liquidity premium theory adds a term premium to the
expectations theory’s equation linking the interest rate on a long-term bond
to the interest rate on short-term bonds.
where
is the term premium on a two-year bond.
Or, more generally, the interest rate on an n-period bond is equal to:
The Term Structure of Interest Rates
Solved Problem
5.2b
Using the Liquidity Premium Theory to Calculate Expected Interest Rates?
Using the table above, what did investors expect the interest rate to be on the
one-year Treasury bill two years from that time if the term premium on a twoyear Treasury note was 0.05% and the term premium on a three-year Treasury
note was 0.10%?
The Term Structure of Interest Rates
Solved Problem
5.2b
Using the Liquidity Premium Theory to Calculate Expected Interest Rates?
Solving the Problem
Step 1 Review the lesson material.
Step 2 Use the liquidity premium equation that links the interest rate on a
long-term bond to the interest rates on short-term bonds to calculate the
interest rate that investors expected on the one-year Treasury bill one year
from February 19, 2010.
Step 3 Answer the problem by using the result from step 2 to calculate the
interest rate investors expected on the one-year Treasury bill two years from
February 19, 2010.
The Term Structure of Interest Rates
The Term Structure of Interest Rates
Using the Term Structure to Forecast Economic Variables
• The slope of the yield curve shows the short-term interest rates that bond market
participants expect in the future.
• In addition, if fluctuations in expected real interest rates are small, the yield curve
contains expectations of future inflation rates.
• For example, If the real interest rate is expected to remain constant, you can
interpret an upward-sloping yield curve to mean that inflation is expected to rise,
leading investors to expect higher nominal interest rates.
• Economists and market participants also look to the slope of the yield curve to
predict the likelihood of a recession.
• Models of the term structure reveal that in every recession since 1953, the term
spread has narrowed significantly. That is, the yield on the 10-year Treasury note
has declined significantly relative to the yield on the 3-month Treasury bill.
The Term Structure of Interest Rates
Using the Term Structure to Forecast Economic Variables
Figure 5.7
Interpreting the Yield
Curve
Models of the term
structure, such as the
liquidity premium
theory, help analysts
use data on the
Treasury yield curve
to forecast the future
path of the economy.•
The Term Structure of Interest Rates
Using the Term Structure to Forecast Economic Variables
• During recessions, interest rates typically fall, and short-term rates tend to fall more
than long-term rates.
• In this situation, the liquidity premium theory of the term structure predicts that
long-term rates should fall relative to short-term rates, making the yield curve
inverted.
The Term Structure of Interest Rates
Answering the Key Question
At the beginning of this lesson, we asked the question:
“Should the government more closely regulate credit rating agencies?”
Like other policy questions we will encounter in this book, this question
has no definitive answer.
During the financial crisis of 2007–2009, many bonds had much higher
levels of default risk than the credit rating agencies had indicated.
Some observers argued that the rating agencies had a conflict of interest
in being paid by the firms whose bond issues they rate.
Other observers, though, argued that the ratings may have been accurate
when given, but the creditworthiness of the bonds declined rapidly
following the unexpected severity of the housing bust and the resulting
financial crisis.
AN INSIDE LOOK AT POLICY
Executives from Moody’s, Standard and Poor’s Describe Pressure to
Grant High Ratings
LOS ANGELES TIMES, Credit Rating Executives Say They Were Pressured to Give Good Ratings
Key Points in the Article
• In 2008, Congress investigated allegations of pressure on the rating agencies to
grant investment-grade ratings to certain financial instruments.
• The conflict of interest started back in the 1970s, when rating agencies switched
from selling ratings to investors to selling ratings to the firms whose bonds they
rated.
• Credit agencies provided the Congressional subcommittee with evidence of
extensive downgrading of mortgage-backed securities between 2004 and 2007.
• After downgrading those securities, their price fell and the yields rose. Investors
increased their demand for safer Treasury bonds, causing their prices to rise and
yields to fall.
AN INSIDE LOOK AT POLICY