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Chapter 07 – The Risk and Term Structure of Interest Rates

Chapter 7

The Risk and Term Structure of Interest Rates

Chapter Overview

In this chapter students are introduced to the three factors that affect bond yields: default

risk, taxes, and maturity. The chapter begins with a discussion of the ratings companies

that work to assess default risk, and moves to considering the relationship between

ratings and yields. This moves into a history of junk bonds, told largely as the story of

Michael Milken (and Drexel). Tax status is explored next, followed by an analysis of the

term structure of interest rates. Students are introduced to the two theories of the term

structure and the chapter concludes with an analysis of the information contained in the

risk structure and term structure of interest rates.

Learning objectives: Establish an understanding of:

Credit risk and bond ratings

Yield curve relating bond maturities to yields

How yields anticipate and signal the future

Important Points of the Chapter

It is important to understand the differences among the many types of bonds that are sold

and traded in financial markets. Interest rate spreads, which reflect movement in the

prices of different bonds, provide important information about the workings of financial

markets. Indeed, in the example cited in this chapter (the Russian default of 1998), there

was a significant “flight to quality” (everyone wanted to hold safe U.S. Treasuries) and

markets ceased to function properly.

Application of Core Principles

Principle #2: Risk. The lower a bond’s rating, the lower its price and the higher its yield.

The yield on any bond is the sum of the yield on the benchmark U.S. Treasury bond (the

closest to being risk free) plus a default risk premium that increases with the probability

of default. High yield is the compensation for high risk.

Principle #1: Time. Longer term bonds tend to have higher yields because of the

additional time involved. Their yields depend on what people expect to happen in years

to come.

Principle #2: Risk. Uncertainty about inflation creates uncertainty about a bond’s real

return, making bonds a risky investment. A bond’s inflation risk increases with its time to

maturity.

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Teaching Tips/Student Stumbling Blocks

You may wish to review the material in Chapter 6 that introduced students to the

idea that changes in risks can be seen as shifts in the demand for bonds. This

concept is illustrated in Figure 7.1, which shows that increased risk results in a

decreased demand for bonds, a lower bond price, and a higher yield.

While the discussion of the tax implication for bonds (starts on page 159) is fairly

straightforward, some students may have difficulty with the calculations. To

reinforce the concept, have students compare a tax-free bond with a taxable bond

and see if they can derive the implied tax rate. For example, as noted on page

160, the rule is:

Tax-Exempt Bond Yield = Taxable Bond Yield x (1 – Tax Rate)

Suppose that a tax-exempt bond yields 5 percent and a taxable bond yields 7

percent. What is the implied tax rate? Plugging in theses values results in an

implied tax rate of about .29. As a follow up, have students visit the website of

Bloomberg.com (given below in the Virtual Tools section) for current data on

taxable and tax-exempt bonds.

Students are likely to have difficulty with the model of the Expectations

Hypothesis. Use the numerical example on page 162 to illustrate the concept.

Have students try the calculations with current data. A point for discussion: when

purchasing a 30 year bond, do you have to be forecasting interest rates for the

next 30 years?

Features in this Chapter

Lessons from the Crisis: Subprime Mortgages

The financial crisis of 2007–2009 initially was known as the subprime crisis because of

the mortgage-backed securities that helped trigger the crisis in the United States. A

residential mortgage is called subprime when it does not meet key standards of

creditworthiness that apply to a conventional prime mortgage. Conventional prime

mortgages are those that satisfy the rules for inclusion in a collection or pool of

mortgages to be guaranteed by a U.S. government agency. For this reason, conventional

prime mortgages also are called qualifying or conforming mortgages. Typically, a loan is

subprime if it is made to someone with a low credit score or whose income may be low

relative to the price of the home; or if the LTV is high; or if the borrower does not

provide sufficient documentation of their ability to pay. Both conventional mortgages and

subprime mortgages comes in two forms: fixed-rate and adjustable-rate mortgages (the

latter are called ARMs—Chapter 6). During the housing bubble, starting in 2002, the

volume of subprime loans surged as mortgage lenders relaxed their lending standards.

Borrowers could obtain loans with lower down payments (high LTVs) and ever-poorer

documentation. A complacent belief that the rise in nationwide house prices that had

continued since the 1930s would persist indefinitely encouraged lending to borrowers

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Chapter 07 – The Risk and Term Structure of Interest Rates

with progressively lower ability to pay. When house prices started to fall in 2006, home

values fell to less than the amount of the mortgage—and lenders became unwilling to

refinance many subprime loans. A wave of defaults followed resulting in problems with

MBSs.

Lessons from the Crisis: Rating Agencies

Ratings mistakes contributed significantly to the financial crisis of 2007-2009. Ratings

that agencies had awarded to mortgage backed securities (MBS) were higher than they

should have been. When US housing prices started to decline, MBS ratings were

downgraded sharply, which reinforced the decline in MBS prices. Several things

contributed to the rating errors, including the fact that issuers consulted (and paid for the

consultation) with rating agencies to see which bond structure would yield the highest

rating. When the agency actually rated the structure, there was a conflict of interest in

rating what they had been consulted on. Further, agencies evaluating the mortgage debt

estimated the risk of default using mathematical models, but these models did not have

any period of time in which housing prices fell nationwide. Bond issuers also paid rating

agencies, and the rating system had only one scale for every kind of default probability.

Your Financial World: Your Credit Rating

In this section students will find a brief discussion of credit scores, what influences them,

and why they matter.

Lessons from the Crisis: Asset-Backed Commercial Paper

Asset-backed commercial paper (ABCP) is a short-term liability with a maturity of up to

270 days. The ABCP is collateralized assets in a special portfolio. In the housing boom

that preceded the financial crisis of 2007-2009, some large banks created shadow banks

to lower their costs and limit their own asset holding. These shadow banks issued ABCP

and used the money to buy mortgages and other loans. The off-balance-sheet financing

allowed the banks to boost leverage and take more risk. The long-term maturity of the

assets and the short-term maturity of the liabilities (the ABCP) posed a roll-over risk to

the ABCP issuers. That is, that issuers would be unable to borrow or sell the asset to be

able to return the principle to the ABCP holders. When the value of some mortgages

became highly uncertain in 2007, purchasers of ABCP grew anxious that their

commercial paper might plunge in value. Firms that issued the ABCP faced an

immediate threat to their survival. Some banks failed while other banks absorbed the loss

on the commercial paper after they were unable to sell the mortgages.

Tools of the Trade: Reading Charts

Using a Treasury yield curve chart from The Wall Street Journal, this section gives a

step-by-step illustration of how to read charts. It provides a very good illustration of how

changes in the vertical scale of a graph can be misleading for its interpretation.

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Applying the Concept: The Flight to Quality

Russia’s 1998 default on its bonds is used as an example of how dramatic changes in

financial markets can occur as investors react to changing circumstances. The shock set

off an “almost unprecedented flight to quality” which resulted in a more than doubling of

the spread between U.S. Treasury bill and commercial paper rates. William McDonough,

then President of the New York Federal Reserve Bank, called it “the most serious

financial crisis since World War II” and worried that the problems in financial markets

would spread to the wider economy.

In the News: Banks Decline Yield Curve Invitation to Party On

This article from Business Week, January 7, 2007, discusses how the occurrence of an

“inverted” yield curve typically precedes a recession. The yield curve is considered to

have predictive power because long-term interest rates represent the market’s

expectations for future short-term rates. Prior to 2007, some predicted that the inverted

yield curve was going to defy history this time. The article points out that the yield curve

was right, it just took longer to get to recession this time.

Lessons of the article:

The slope of the yield curve can help predict the direction and speed of

economic growth. At the beginning of 2010, the yield curve was unusually

steep, pointing to a strong economic expansion (see Figure 7.9B, where the

steep slope in 2010 is shown as a high value for the term spread). However, in

the aftermath of the financial crisis of 2007-2009, lenders were especially

cautious about extending credit to risky borrowers, even though risk spreads

had narrowed sharply from crisis peaks (see Figure 7.8B). The author argues

that it is only a matter of time until the steep yield curve encourages lenders to

start lending again. However, the willingness to lend depends on how quickly

intermediaries gain confidence that borrowers will repay. Even years later,

many potential borrowers are still repairing their balance sheets that were

damaged by the record plunge of U.S. housing prices.

Additional Teaching Tools

Credit scores are important for getting a loan and affect the cost of a loan in terms of the

interest rate assessed (as pointed out in this chapter). However, paying attention to your

credit report can also give you an edge in avoiding identity theft. In an article entitled

“Safeguard Identity with Regular Checks of Credit Reports” (by Kim Komando with

reporting by Ted Rybka, The Journal News, May 10, 2004) the author points out that

credit reporting services “watch for early warning signs of identity theft. They let you

know if a merchant has checked your address or if someone has submitted a change of

address for you.” The credit reporting services may also be able to provide, for a fee,

access to an identity theft specialist and insurance against losses incurred due to identity

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theft. The author points out that to really be safe a consumer would need to subscribe to

all three credit-reporting services because a credit check could go to any one of them.

Virtual Tools

Students may find it of interest to visit the web sites of the three credit-reporting

services; they are TransUnion (www.transunion.com), Experian

(www.experian.com), and Equifax (www.equifax.com).

To find out more about identity theft and what to do if it happens to you. Visit the

website of the Federal Trade Commission at

http://www.ftc.gov/bcp/edu/microsites/idtheft/

Bond market data is available on websites such as Bloomberg.com at

http://www.bloomberg.com/markets/rates/

The SmartMoney.com web site has current information about the bond market

and the yield curve, and a number of interesting tools including a bond calculator

and a “Living Yield Curve.” The “Living Yield Curve” section provides an

excellent illustration of how the yield curve can be used to predict economic

activity; it includes examples of a normal yield curve (from December 1984), a

steep curve (April 1992), an inverted curve (August 1981) and a flat or humped

curve (April 1989).

For More Discussion

In his “Economic Scene” column for The New York Times (Thursday, May 27, 2004),

Alan B. Krueger reports that “James Carville once mused that instead of coming back as

the president or the pope or a .400 baseball hitter if there were reincarnation, he would

rather come back as the bond market because ‘you can intimidate everybody.’”

Chapter Outline

I. Ratings and the Risk Structure of Interest Rates

The risk of default (i.e., that a bond issuer will fail to make a bond’s promised

payments) is one of the most important risks a bondholder faces, and it varies among

issuers. Credit rating agencies have come into existence to assess the default risk of

different issuers.

A. Bond Ratings

1. The best-known rating services are Moody’s and Standard & Poor’s.

2. Companies with good credit earn high ratings, suggesting that they will have

little difficulty meeting the bond’s payment obligations.

3. The two companies have similar letter-based ratings systems; these are

illustrated in Table 7.1.

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4. “Investment Grade” comprises the top four ratings; the next group is the

non-investment speculative grades, which are often referred to as “junk

bonds”.

5. There are two types of junk bonds: “fallen angels” which were once

investment grade but the companies’ situations have changed, and “original

issue” junk bonds which are bonds for which little is known about the risk of

the issuer.

6. The ratings companies continually monitor the situations of firms and

announce rating changes; a lowering of the rating is a “downgrade” and an

improvement is an “upgrade”.

B. Commercial Paper Ratings

1. Commercial paper is a short-term version of a bond, issued both by

corporations and governments.

2. This is unsecured debt because the borrower offers no collateral.

3. Commercial paper is issued on a discount basis, and most of it has a maturity

of between 5 to 45 days.

4. Moody’s and Standard & Poor’s provide rations of commercial paper issuers

in the same way they do bonds. The lowest default risk issues are now termed

“prime” grade or investment grade.

C. The Impact of Ratings on Yields

1. The lower a bond’s rating the lower its price and the higher its yield.

2. A bond yield can be thought of as the sum of two parts: the yield on the U.S.

Treasury bond (called “benchmark bonds” because they are close to being

risk-free) and a risk spread or default risk premium.

3. The default risk premium should increase as the bond rating decreases.

4. Considering yield this way also allows us to see that when U.S. Treasury bond

yields change all other yields will change in the same direction.

5. Data on the risk structure of interest rates supports these predictions; this is

illustrated in Figure 7.2 on page 155.

6. The difference of a couple of points in yield has a big affect on the cost of

debt. For instance, as noted on page 156, the difference between a 5 percent

rate and a 7 percent rate is a 40% difference.

II. Differences in Tax Status and Municipal Bonds

1. The second important factor that affects the return on a bond is taxes.

2. Bondholders must pay income tax on the interest income they receive from

privately issued bonds, but government bonds are treated differently.

3. Interest payments on bonds issued by state and local governments, called

“municipal” or “tax-exempt” bonds are specifically exempt from taxation.

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4. The general rule in the United States is that one level of government does not

tax the interest income from bonds issued by another level of government

(although the issuing government may tax it).

5. A tax exemption affects a bond’s yield because it affects how much of the

return the bondholder gets to keep.

6. The yield on a tax-exempt bond equals the taxable bond yield times one minus

the tax rate.

III.The Term Structure of Interest Rates

1. A third factor that affects a bond’s yield is its maturity.

2. The relationship among bonds with the same risk characteristics but different

maturities is called the term structure of interest rates. A plot of this, the yield

curve, is shown in Figure 7.4.

3. Three conclusions can be drawn from studying the data:

a. Interest rates of different maturities tend to move together.

b. Yields on short-term bonds are more volatile than those on long-term

bonds.

c. Long-term yields tend to be higher than short-term yields.

4. There are two explanations for these relationships, the Expectations

Hypothesis and the Liquidity Premium Theory.

A. The Expectations Hypothesis

1. The hypothesis begins with the observation that the risk-free interest rate can

be computed, assuming that there is no uncertainty about the future.

2. This means that an investor would be indifferent between holding a two-year

bond or a series of two one-year bonds because certainty means that bonds of

different maturities are perfect substitutes for each other.

3. Therefore, when interest rates are expected to rise long-term rates will be

higher than short-term rates and the yield curve will slope up (and vice versa);

if interest rates are expected to remain unchanged, the yield curve will be flat.

4. From this we can construct investment strategies that must have the same

yield. Assuming the investor has a two-year horizon, the investor can:

a. Invest in a two-year bond and hold it to maturity.

b. Invest in a one-year bond today and a second one a year from now

when the first one matures.

5. The hypothesis tells us that investors will be indifferent between the two

strategies, so the strategies must have the same return.

6. Therefore the rate on the two-year bond must be the average of the current

one-year rate and the expected future one-year rate.

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7. The implications are the three conclusions we noted above (IV, 3).

8. However, in order to explain why the yield curve normally slopes upward, we

need to extend the hypothesis to include risk.

B. The Liquidity Premium Theory

1. Risk is the key to understanding the slope of the yield curve.

2. The upward slope is due to long-term bonds being riskier than short-term

bonds.

3. The longer the term the greater the inflation and interest-rate risk.

a. Inflation risk increases over time because investors, who care about

the real return, must forecast inflation over longer periods.

b. Interest-rate risk arises when an investor’s horizon and the bond’s

maturity do not match. If holders of long-term bonds need to sell them

before maturity and interest rates have increased, the bonds will lose

value.

4. Including risk in the model means that we can think of yield as having two

parts: one that is risk-free and one that is a risk premium.

5. Again, we arrive at the same three conclusions about the term structure of

interest rates.

IV. The Information Content of Interest Rates

1. The risk and term structure of interest rates contain useful information about

overall economic conditions.

2. These indicators are helpful in evaluating both the present health of the

economy and its likely future course.

3. Risk spreads provide one type of information, the term structure another.

Information in the Risk Structure of Interest Rates

1. An impending recession raises the risk premium on privately issued bonds

because of the increasing risk that corporations cannot meet their obligations.

2. An economic slowdown or recession does not affect the risk of holding

government bonds.

3. Recessions do not affect all companies equally, and the impact on those with

high ratings is likely to be small. Therefore the spread between U.S.

Treasuries and highly rated bonds is not likely to move by much.

4. For firms with lower ratings, the situation is quite different; the lower the

initial grade of the bond, the more the default risk premium rises as general

economic conditions deteriorate.

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A. Information in the Term Structure of Interest Rates

1. Information on the term structure also helps us to forecast general economic

conditions.

2. The yield curve usually slopes upward, but on rare occasions it can be

inverted and slope downward (short-term rates exceed long-term yields).

3. An inverted yield curve predicts an economic slowdown because it signals a

fall in short-term interest rates. Figure 7.8 on page 167 illustrates this.

Using FRED: Codes for Data in This Chapter

Data Series FRED Data Code

Moody’s Aaa corporate bond yield AAA

Moody’s Baa corporate bond yield BAA

BofA Merrill Lynch US corporate BBB effective

yield

BAMLC0A4CBBBEY

BofA Merrill Lynch US high‐yield BB effective

yield

BAMLH0A1HYBBEY

BofA Merrill Lynch US high‐yield B effective

yield

BAMLH0A2HYBEY

BofA Merrill Lynch US high‐yield CCC or below BAMLH0A3HYCEY

effective yield

10‐year Treasury yield GS10

3‐month Treasury bill rate TB3MS

3‐month AA nonfinancial commercial paper rate CPN3M

Consumer price index CPIAUCSL

Real GDP (chained 2005 dollars) GDPC1

Brazil Treasury bill rates INTGSTBRM193N

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Terms Introduced in Chapter 7

benchmark bond

commercial paper

expectations hypothesis of the term structure

fallen angel

flight to quality

interest-rate spread

inverted yield curve

investment-grade bond

junk bond

liquidity premium theory of the term structure

municipal bonds

prime-grade commercial paper

rating

ratings downgrade

ratings upgrade

risk spread

risk structure of interest rates

spread over Treasuries

tax-exempt bond

taxable bond

term spread

term structure of interest rates

yield curve

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Lessons of Chapter 7

1. Bond ratings summarize the likelihood that a bond issuer will meet its payment

obligations.

a. Highly rated investment-grade bonds are those with the lowest risk of default.

b. If a firm encounters financial difficulties, its bond rating may be downgraded.

c. Commercial paper is the short-term version of a privately issued bond.

d. Junk bonds are high-risk bonds with very low ratings. Firms that have a high

probability of default issue these bonds.

e. Investors demand compensation for default risk in the form of a risk premium.

The higher the risk of default, the lower a bond’s rating, the higher its risk

premium, and the higher its yield.

2. Municipal bonds are usually exempt from income taxes. Because investors care

about the after-tax returns on their investments, these bonds have lower yields than

bonds whose interest payments are taxable.

3. The term structure of interest rates is the relationship between yield to maturity and

time to maturity. A graph with the yield to maturity on the vertical axis and the time

to maturity on the horizontal axis is called the yield curve.

a. Any theory of the term structure of interest rates must explain three facts:

i. Interest rates of different maturities move together

ii. The yields on short-term bonds are more volatile than the yields on long-term

bonds

iii. Long-term yields are usually higher than short-term yields.

b. The expectations hypothesis of the term structure of interest rates states that

long-term interest rates are the average of expected future short-term interest

rates. This hypothesis explains only the first two facts about the term structure of

interest rates.

c. The liquidity premium theory of the term structure of interest rates, which is

based on the fact that long-term bonds are riskier than short-term bonds, explains

all three facts described in 3a.

4. The risk structure and the term structure of interest rates both signal financial

market’s expectations of future economic activity. Specifically, the likelihood of a

recession will be higher when

a. The risk spread, or the range the between low- and high-grade bond yields, is

wide.

b. The yield curve slopes downward, or is inverted, so that short-term interest rates

are higher than long-term interest rates.

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