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Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

Chapter 6

Bonds, Bond Prices, and the Determination of Interest

Rates

Chapter Overview

If we want to understand the financial system, particularly the bond market, we must

understand the relationship between bond prices and interest rates, the determination of

bond prices in the market (by supply and demand), and also why bonds are risky. These

issues will be covered in this chapter.

Learning Objectives: Establish an understanding of:

Present value and bond pricing

Relationship of prices, yields, and returns

Key drivers of bond prices

Risks of default, inflation risk, and interest-rate changes

Important Points of the Chapter

Any financial arrangement involving the current transfer of resources from a lender to a

borrower, with a transfer back at some time in the future, is a form of a bond. The ease

with which individuals, corporations, and governments borrow is essential to the

functioning of our economic system. While the depth and complexity of bond markets

has increased in modern times, many of their original features (dating back to the 16th and

17th centuries) remain.

Application of Core Principles

Principle #1: Time. The price of a Treasury bill is the present value of the future

payments it will make. The shorter the time period until the payments are made, the

higher the price of the bond.

Principle #4: Markets. Equilibrium in the bond market occurs when supply and demand

are equal. At a higher price there would be an excess supply of bonds, which would push

the price down. At a lower price there would be an excess demand for bonds, which

would push the price up. Only when supply and demand are equal can there be

equilibrium.

Principle #2: Risk. Risk arises from the fact that an investment has many possible payoffs

during the time horizon for which it is held. Certain risks affect the premium that

investors require over the risk-free return. Risk requires compensation.

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Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

Teaching Tips/Student Stumbling Blocks

This chapter continues the use of present value analysis to analyze how bond

prices are determined. You may wish to begin with a review of the tools from

Chapter 5.

Spend time going carefully through the examples from the text and reinforce

concepts by assigning end-of-chapter problems.

Features in this Chapter

Your Financial World: Know Your Mortgage

A large number of people with adjustable rate mortgages (ARMs) underestimate how

much the interest rate can change. Important things to know are what interest-rate index

the mortgage rate is based; how big is the mortgage rate margin above the interest-rate

index on which it is based; how frequently the rate is adjusted; does it have an initial

discount rate that will rise, and by how much; whether there is a cap on how much the

rate can rise both at one adjustment and over the life of the loan; whether there is a

payment cap, and, if the payment cap is reached, will the principal amount of the loan

then increase (this is negative amortization); and finally, whether it can be converted to a

fixed-rate mortgage.

Tools of the Trade: Reading the Bond Page

This section illustrates and explains how to read a bond table. The U.S. Treasury alone

had nearly 300 coupon-bearing instruments outstanding. The table shows that the yields

on government bonds vary significantly over time and substantially across countries.

Your Financial World: Understanding the Ads in the Newspaper

Suppose you see an ad for an investment company stating that their bond mutual funds

returned 13.5% over the last year. How is this possible if interest rates have been pretty

low? The answer is that the ad is about last year’s holding period return, when interest

rates were falling. The resulting rise in bond prices (due to the falling rates) meant the

return was more than just the interest paid by the bonds; it also included capital gains. In

a rising interest rate environment the holding period return will be negatively affected by

decreases in bond prices. That’s one reason why past performance is indeed not an

indicator of future returns.

Applying the Concept: When Russia Defaulted

On numerous occasions, investors’ concerns about increased risk in certain areas of the

globe have led to a significant shift in the demand for U.S. Treasury bonds. The default

by the Russian government in the fall of 1998 was such an occasion. As a result of the

default no one wanted to hold Russian debt or, for that matter, the debt of any emerging

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Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

market country, and so the demand for safe U.S. Treasury bonds increased. The prices of

U.S. Treasuries rose and their yields fell as their perceived riskiness declined.

Applying the Concept: Securitization

Securitization is the process by which financial institutions pool various assets that

generate a stream of payments and transform them into a bond that gives the bondholder

a claim on those payments. Mortgage-backed securities are just one form of

securitization. Any stream of payments can be used to create a bond. Securitization uses

the effiency of markets to lower the cost of borrowing by facilitating diversification of

risk, making assets liquid, allowing greater specialization in the business of finance,

broadening markets, and fostering innovation.

Your Financial World: Bonds Indexed to Inflation

There is a type of U.S. Treasury bond that compensates investors for inflation. The bond

promises to pay a fixed interest rate plus the change in the consumer price index. The

U.S. Treasury sells two types of such bonds, Series I savings bonds and Treasury

Inflation Protection Securities (or TIPS). The difference between the two is the amount

that can be purchased (savings bonds can be bought for as little as $50, while TIPS

require a $1000 investment).

In the News: Gross’s Burning Bond Market Fails to Frighten Investors

Investors who lost a significant amount of retirement savings in the financial crisis

shifted to bonds to reduce risk. While investors who hold bonds until they mature don’t

lose money unless the issuer defaults, those who trade can suffer losses if the interest

rates rise. Further, long-term Treasuries had as many losing years as stocks did n the last

85 years.

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Lessons of the Article: Some investors view long‐term bonds as much safer

than stocks, but losses on such bonds are similarly frequent, and their

inflation‐adjusted returns are lower on average. With bond yields near record

lows in 2012 and the Federal Reserve pursuing an accommodative monetary

policy, worries about bonds encouraged some professional investors to favor

equities or to purchase TIPS despite their subzero inflation‐adjusted yields.

Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

Additional Teaching Tools

In an article from Business Week (“Bonds: Sorting Through the Confusion”, January 6,

2010), David Bogoslaw writes, “Getting your investment portfolio’s bond allocation right

will not be easy in 2010 amid conflicting views on inflation from investment strategists

and policymakers.” Many experts are watching inflation on the fear that the Fed will not

withdraw the massive amounts of money in the economy as it begins to heat up.

However, these experts are not convinced that January was the time to enter the TIPS

market, as the payoff was not yet worth moving.

Virtual Tools

Use the withholding calculator on the IRS website to adjust the amount taken from your

paycheck. It is located at www.irs.gov.

Visit the web site of the Treasury to see how Series I and TIPS can be purchased; it is

located at http://www.fiscal.treasury.gov/.

For More Discussion

Joan Robinson once stated that anyone who bought an infinite-maturity consol would

have “to think he knows exactly what the rates of interest will be every day from now to

Kingdom Come.” Relate this to the discussion of interest rate risk in this chapter.

(Source: Robinson, Joan, “The Rate of Interest,” Econometrica 19 (1951): 92-111; she

was objecting to the version of the Expectations Hypothesis that relates forward interest

rates to expectations of future short term interest rates. This will be covered in more

detail in Chapter 7.)

Chapter Outline

I. Bond Prices

There are four basic types of bonds: zero-coupon bonds, which promise a single

future payment (like a U.S. Treasury Bill); fixed payment loans (like conventional

mortgages); coupon bonds, which make periodic interest payments and repay the

principal at maturity (like U.S. Treasury Bonds and most corporate bonds); and

consols, which make periodic interest payments but never repay the principal that was

borrowed. In this section we will see how each of these is priced.

A. Zero-Coupon Bonds

1. These are pure discount bonds (also called discount bonds) since they sell at a

price below their face value.

2. The difference between the selling price and the face value represents the

interest on the bond.

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3. The price of such a bond, like a Treasury bill (called “T-bill”), is the present

value of the future payment.

4. The most common maturity of a T-bill is 6 months; the Treasury does not

issue them with a maturity greater than 1 year.

5. The shorter the time until the payment is made the higher the price of the

bond, so 6 month T-bills have a higher price that a one-year T-bill.

6. The interest rate and the price for the T-bill move inversely. If we know the

face value and the price then we can solve for the interest rate.

B. Fixed Payment Loans

1. Conventional home mortgages and car loans are examples of fixed payment

loans; they promise a fixed number of equal payments at regular intervals.

2. These loans are amortized, meaning that the borrower pays off the principal

along with the interest over the life of the loan. Each payment includes both

interest and some portion of the principal.

3. The price of the loan is the present value of all the payments.

C. Coupon Bonds

1. The value of a coupon bond is the present value of the periodic interest

payments plus the present value of the principal repayment at maturity.

2. The latter part, the repayment of the principal, is just like a zero-coupon bond.

D. Consols

1. A consol offers only periodic interest payments; the borrower never repays the

principal.

2. There are no privately issued consols because only governments can credibly

promise to make payments forever.

3. The price of a consol is the present value of all the future interest payments,

which is a bit complicated because there are an infinite number of payments.

II. Bond Yields

A. Yield to Maturity

1. The most useful measure of the return on holding a bond is called the yield to

maturity. This is the yield bondholders receive if they hold the bond to its

maturity when the final principal payment is made.

2. The yield to maturity can be calculated from the present value formula.

3. If the yield to maturity equals the coupon rate, the price of the bond is the

same as its face value. If the yield is greater than the coupon rate, the price is

lower; if the yield is below the coupon rate, the price is greater.

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4. If you buy a bond at a price less than its face value you will receive its interest

and a capital gain, which is the difference between the price and the face

value. As a result you have a higher return than the coupon rate.

5. When the price is above the face value, the bondholder incurs a capital loss

and the bond’s yield to maturity falls below its coupon rate.

B. Current Yield

1. Current yield is a commonly used, easy-to-compute measure of the proceeds

the bondholder receives for making a loan.

2. It is the yearly coupon payment divided by the price.

3. The current yield measures that part of the return from buying the bond that

arises solely from the coupon payments; it ignores the capital gain or loss that

arises when the bond’s price differs from its face value.

4. The current yield moves inversely to the price; if the price is above the face

value, the current yield falls below the coupon rate. When the price falls

below the face value, the current yield rises above the coupon rate. If the

price and the face value are equal the current yield and the coupon rate are

equal.

5. Since the yield to maturity takes account of capital gains (and losses), when

the bond price is less than its face value the yield to maturity is higher than the

current yield, and if the price is greater than face value, the yield to maturity is

lower than the current yield, which is lower than the coupon rate.

C. Holding Period Returns

1. The investor’s return from holding a bond need not be the coupon rate.

2. Most holders of long-term bonds plan to sell them well before they mature,

and because the price of the bond may change in the time since its purchase,

the return can differ from the yield to maturity.

3. The greater the price change the more important the capital gain or loss

becomes as part of the holding period return.

4. The longer the term of the bond, the greater the price movements and

associated risk can be.

III. The Bond Market and the Determination of Interest Rates

To find out how bond prices are determined and why they change we need to look

at the supply and demand in the bond market. Let’s discuss the quantity of bonds

outstanding (the stock of bonds) and consider bonds prices rather than interest rates.

The analysis will consider the one-year zero-coupon bond.

A. Bond Supply, Bond Demand, and Equilibrium in the Bond Market

1. The bond supply curve is the relationship between the price and quantity of

bonds people are willing to sell, all other things being equal.

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2. The bond supply curve is upward sloping; the higher the price of a bond, the

larger the quantity supplied will be because investors will be tempted to sell

bond that they hold and companies will find it advantageous to issue new

bonds.

3. The bond demand curve is the relationship between the price and quantity of

bonds that investors demand, all other things being equal.

4. The bond demand curve slopes down; as the price falls, the reward for

holding the bond rises so there is a greater quantity demanded.

5. Equilibrium in the market is the price at which the quantity demanded

equals the quantity supplied of bonds.

6. If the price is too high (above equilibrium) the excess supply of bonds will

push the price back down. If the price is too low (below equilibrium) the

excess demand for bonds will push it up.

7. Over time the supply and demand curves can shift, leading to changes in the

equilibrium price.

B. Factors that Shift Bond Supply

1. We can identify the factors that shift the supply curve for bonds:

a. Changes in government borrowing: the more governments borrow the

greater the quantity of bonds supplied, shifting the curve to the right.

b. Changes in business conditions: business-cycle expansions mean more

investment opportunities, prompting firms to increase their borrowing

and increasing the quantity of bonds supplied. By the same logic, weak

economic growth can lead to rising bond prices and lower interest rates.

c. Changes in expected inflation: bond issuers care about the real cost of

borrowing, so if inflation is expected to increase then the real cost falls

and the desire to borrow rises, resulting in the bond supply curve shifting

to the right.

d. Changes in corporate taxation: changes in the tax code are infrequent,

but when they occur they affect the quantity of bonds supplied. Tax

incentives that make investment less costly increase the quantity of

bonds supplied.

C. Factors that Shift Bond Demand

1. Six factors shift the demand for bonds:

a. Wealth: increases in wealth shift the demand for bonds to the right as

wealthier people invest more.

b. Expected inflation: a fall in expected inflation will shift the demand for

bonds to the right.

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c. The expected return on stocks and other assets: if the return on bonds

rises relative to the return on alternative investments, the demand for

bonds will shift to the right.

d. Expected interest rates: changes in expected interest rates affect bond

prices; if interest rates are expected to fall, then bond prices are expected

to rise, and the demand for bonds shifts to the right.

e. Risk relative to alternatives: if a bond is less risky then the demand will

shift to the right.

f. The liquidity of bonds relative to alternatives: the more liquid an asset

the higher its demand, shifting the demand curve to the right.

D. Understanding Changes in Equilibrium Bond Prices and Interest Rates

1. An increase in expected inflation shifts bond supply to the right and bond

demand to the left. The two effects reinforce each other, resulting in a lower

bond price and a higher interest rate.

2. A business-cycle downturn shifts the bond supply to the left and the bond

demand to the left. In this case the bond price can rise or fall, depending on

which shift is greater. But interest rates tend to fall in recessions, so bond

prices are likely to increase.

IV. Why Bonds Are Risky

Bondholders face three major risks:

A. Default Risk

1. There is no guarantee that a bond issue will make the promised payments.

2. Investors who are risk averse require some compensation for bearing risk;

the more risk, the more compensation they demand.

3. The higher the default risk the higher the probability that bondholders will

not receive the promised payments and thus, the higher the yield.

B. Inflation Risk

1. Bonds promise to make fixed-dollar payments, and bondholders are

concerned about the purchasing power of those payments.

2. The nominal interest rate will be equal to the real interest rate plus the

expected inflation rate plus the compensation for inflation risk.

3. The greater the inflation risk, the larger will be the compensation for it.

C. Interest-Rate Risk

1. Interest-rate risk arises from the fact that investors don’t know the holding

period yield of a long-term bond.

2. If you have a short investment horizon and buy a long-term bond you will

have to sell it before it matures, and so you must worry about what happens

if interest rates change.

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Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

3. Because the price of long-term bonds can change dramatically, this can be

an important source of risk.

Using FRED: Codes for Data in This Chapter

Data Series FRED Data Code

Three‐month Treasury bill rate TB3MS

One‐year Treasury bill rate TB1YR

Two‐year Treasury constant maturity rate GS2

10‐year Treasury constant maturity rate GS10

30‐year Treasury constant maturity rate GS30

Five‐year Treasury inflation‐indexed yield FII5

10‐year Treasury inflation‐indexed yield FII10

30‐year Treasury inflation‐indexed yield FII30

Consumer price index CPIAUCSL

Survey: expected inflation over 12 months MICH

Japan Treasury bill rates INTGSTJPM193N

Brazil Treasury bill rates INTGSTBRM193N

Terms Introduced in Chapter 6

capital gain

capital loss

consol or perpetuity

current yield

default risk

holding period return

inflation risk

inflation-indexed bonds

interest-rate risk

investment horizon

U.S. Treasury bill (T-bill)

yield to maturity

zero-coupon bond

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Chapter 06 – Bonds, Bond Prices, and the Determination of Interest Rates

Lessons of Chapter 6

1. Valuing bonds is an application of present value.

a. Pure discount or zero-coupon bonds promise to make a single payment on a

predetermined future date.

b. Fixed-payment loans promise to make a fixed number of equal payments at

regular intervals.

c. Coupon bonds promise to make periodic interest payments and repay the principal

at maturity.

d. Consols (perpetuities) promise to make periodic coupon payments forever.

2. Yields are measures of the return on holding a bond.

a. The yield to maturity is a measure of the interest rate on a bond. To compute it,

set the price of the bond equal to the present value of the payments.

b. The current yield on a bond is equal to the coupon rate divided by the price.

c. When the price of a bond is above its face value the coupon rate is greater than

the current yield, which is higher than the yield to maturity.

d. One-year holding period returns are equal to the sum of the current yield and any

capital gain or loss arising from a change in a bond’s price.

3. Bond prices (and bond yields) are determined by supply and demand in the bond

market.

a. The higher the price, the larger the quantity of bonds supplied.

b. The higher the price, the smaller the quantity of bonds demanded.

c. The supply of bonds rises when

i. Governments need to borrow more.

ii. General business conditions improve.

iii. Expected inflation rises.

d. The demand for bonds rises when

i. Wealth increases.

ii. Expected inflation falls.

iii. The expected return, relative to other investments, rises.

iv. The expected future interest rate falls.

v. Bonds become less risky, relative to other investments.

vi. Bonds become more liquid, relative to other investments.

4. Bonds are risky because of

a. Default risk: the risk that the issuer may fail to pay.

b. Inflation risk: the risk that the inflation rate may be more or less than expected,

affecting the real value of the promised nominal payments.

c. Interest Rate Risk: the risk that the interest rate might change, causing the bond’s

price to change.

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