Money banking and the financial system 1e by hubbard and OBrien chapter 05

The Risk Structure and Term Structure of Interest RatesC H A P T E R 5 5.1 5.2 Explain why bonds with the same maturity can have different interest rates LEARNING OBJECTIVES After studyi

System

The Risk Structure and Term Structure of Interest Rates

C H A P T E R 5

5.1 5.2

Explain why bonds with the same maturity can have different interest rates

LEARNING OBJECTIVES

After studying this chapter, you should be able to:

Explain why bonds with different maturities can have different 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

C H A P T E R 5

The Risk Structure and Term Structure of Interest Rates

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

Default Risk

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

is the risk that the bond issuer will fail to make payments of interest or principal

Default Risk

is the risk that the bond issuer will fail to make payments of interest or principal

• 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

Measuring Default Risk

The Risk Structure of Interest Rates

Changes in Default Risk and in the Default Risk Premium

Figure 5.1 (1 of 2) 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

The Risk Structure of Interest Rates

Changes in Default Risk and in the Default Risk Premium

Figure 5.1 (2 of 2) 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

Changes in Default Risk and in the Default Risk Premium

Figure 5.2 (1 of 2) 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

The Risk Structure of Interest Rates

Changes in Default Risk and in the Default Risk Premium

Figure 5.2 (2 of 2) 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

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

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 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

to D Muni2 , increasing the price from P M

1 to P M

D Treas2 , lowering the price from P T

1 to P T

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

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.

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

policy change on the interest rate on corporate bonds.

Step 4 Analyze the effect of the tax

policy change on the interest rate on Treasury bonds.

Step 5 Summarize your findings.

Replacing the federal income tax with a VAT would increase the interest rate on municipal

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

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

long-term interest rates, resulting in a downward-sloping yield curve

Figure 5.4

The Treasury Yield Curve

This figure shows the Treasury yield curves for June 22, 2009, and June

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

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.

The Expectations Theory of the Term Structure

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

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 Term Structure of Interest Rates

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 + i 2t )(1 + i 2t)

•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 + i 1t ) (1 + i e

it+1)

With the rollover strategy, you must form an expectation of what the interest

rate on the one-year bond will be

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 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:

The Expectations Theory Applied in a Simple Example

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.

Interpreting the Term Structure Using the Expectations Theory

The Term Structure of Interest Rates

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

Figure 5.6

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

The Term Structure of Interest Rates