Download The Term Structure of Interest Rates

R. GLENN
HUBBARD
ANTHONY PATRICK
O’BRIEN
Money,
Banking, and
the Financial
System
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
CHAPTER
5
The Risk Structure and Term
Structure of Interest Rates
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
5.1
Explain why bonds with the same maturity can have different interest rates
5.2
Explain why bonds with different maturities can have different interest rates
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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 chapter, we study why these unusual situations occur.
• An Inside Look at Policy on page 148 describes the testimony before
Congress of rating agencies about the ratings of mortgage-backed securities.
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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?
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5.1 Learning Objective
Explain why bonds with the same maturity can have different interest rates.
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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.
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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.
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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)
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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)
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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)
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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)
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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.
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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 mortgagebacked bonds.
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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.
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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.
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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
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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.
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Solved Problem
5.1
How Would a VAT Affect Interest Rates?
Solving the Problem
Step 1 Review the chapter material.
Step 2 Analyze the effect of the tax policy change on the interest rate on
municipal bonds.
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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.
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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.
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5.2 Learning Objective
Explain why bonds with different maturities can have different interest rates.
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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 upwardsloping yield curve.
• Infrequently, there are times when short-term interest rates are higher than
long-term interest rates, resulting in a downward-sloping yield curve.
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Figure 5.4
The Treasury Yield Curve
This figure shows the
Treasury yield curves for
June 22, 2009, and June
22, 2010.•
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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.•
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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.
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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
short-term 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.
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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.
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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.
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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:
𝑒
$1,000 1 + 𝑖2𝑡 1 + 𝑖2𝑡 = $1,000 1 + 𝑖1𝑡 1 + 𝑖1𝑡+1
.
This equality can be reduced to:
𝑖2𝑡
𝑒
𝑖1𝑡 + 𝑖1𝑡+1
=
.
2
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 one-year 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:
𝑒
𝑒
𝑒
𝑒
𝑖1𝑡 + 𝑖1𝑡+1
+ 𝑖1𝑡+2
+ 𝑖1𝑡+3
+ . . . +𝑖1𝑡+(𝑛−1
𝑖𝑛𝑡 =
.
𝑛
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Interpreting the Term Structure Using the Expectations Theory
• The term structure provides us with information on what bond investors must
expect to happen to short-term rates in the future.
𝑒
For example, if i1t = 2% and i2t = 3%, then 𝑖1𝑡+1
= 2(3%) – 2% = 4%.
3% =
2% + Expected one−year rate one year from now
= 4%
2
• Similarly, we can calculate the expected one-year rate two years from now,
using the expected one-year rate one year from now that we just calculated:
2% + 4% + Expected one−year rate one year from now
4% =
= 6%
3
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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.
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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.•
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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 short-term rate.
• But if the yield curve is typically upward sloping, investors must be expecting
short-term 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.
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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 long-term 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.
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Solved Problem
5.2a
Is There Easy Money to Be Made from the Term Structure?
Solving the Problem
Step 1 Review the chapter 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 shortterm 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.
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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.
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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.
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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 long-term 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.
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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.
𝑖2𝑡
𝑒
𝑖1𝑡 + 𝑖1𝑡+1
𝑇𝑃
=
+ 𝑖2𝑡
,
2
𝑇𝑃
where 𝑖2𝑡
is the term premium on a two-year bond.
Or, more generally, the interest rate on an n-period bond is equal to:
𝑖𝑛𝑡 =
𝑒
𝑒
𝑒
𝑒
𝑖1𝑡 + 𝑖1𝑡+1
+ 𝑖1𝑡+2
+ 𝑖1𝑡+3
+ . . . +𝑖1𝑡+(𝑛−1
𝑛
𝑇𝑃
+ 𝑖2𝑡
.
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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 two-year Treasury note was 0.05% and the term premium on a threeyear Treasury note was 0.10%?
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Solved Problem
5.2b
Using the Liquidity Premium Theory to Calculate Expected Interest Rates?
Solving the Problem
Step 1 Review the chapter 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.
𝑖2𝑡
𝑒
0.39% + 𝑖1𝑡+1
𝑒
= 0.95% =
+ 0.05%, or, 𝑖1𝑡+1
= 1.41%
2
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.
𝑖3𝑡
𝑒
0.39% + 1.41% + 𝑖1𝑡+2
𝑒
= 1.51% =
+ 0.10%, or, 𝑖1𝑡+2
= 2.43%
2
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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.
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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.•
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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.
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Answering the Key Question
At the beginning of this chapter, 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.
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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.
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AN INSIDE LOOK AT POLICY
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