>

dramatic examples of both in recent years. A rate risk.

9 Bond Prices and Yields

10 Managing Bond Investments

www.mhhe.com/bkm

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

9

BOND PRICES

AND YIELDS

AFTER STUDYING THIS CHAPTER

YOU SHOULD BE ABLE TO:

> Compute a bond™s price given its yield to maturity, and

compute its yield to maturity given its price.

> Calculate how bond prices will change over time for a given

interest rate projection.

> Identify the determinants of bond safety and rating.

> Analyze how call, convertibility, and sinking fund provisions

will affect a bond™s equilibrium yield to maturity.

> Analyze the factors likely to affect the shape of the yield

curve at any time.

294

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

Related Websites http://www.standardandpoors.com/ratings/

corporates/index.htm

http://www.bankrate.com/brm/default.asp

http://www.moodys.com

http://www.bloomberg.com/markets

http://www.fitchinv.com

http://cnnfn.cnn.com/markets/bondcenter/

The above sites provide information on bond ratings.

rates.html

http://www.stls.frb.org/fred

These sites give general price information.

This site has extended information on various interest

http://www.bondresources.com

rates. These rates can be downloaded into a

http://www.investinginbonds.com/ spreadsheet format for analysis.

http://www.bondsonline.com/docs/

bondprofessor-glossary.html

These sites contain detailed information on bonds. They

are comprehensive and have many related links.

n the previous chapters on risk and return relationships, we have treated securities

I at a high level of abstraction. We have assumed implicitly that a prior, detailed

analysis of each security already has been performed, and that its risk and return

features have been assessed.

We turn now to specific analyses of particular security markets. We examine val-

uation principles, determinants of risk and return, and portfolio strategies commonly

used within and across the various markets.

We begin by analyzing debt securities. A debt security is a claim on a specified

periodic stream of income. Debt securities are often called fixed-income securities,

because they promise either a fixed stream of income or a stream of income that is

determined according to a specified formula. These securities have the advantage of

being relatively easy to understand because the payment formulas are specified in

advance. Uncertainty surrounding cash flows paid to the security holder is minimal as

long as the issuer of the security is sufficiently creditworthy. That makes these secu-

rities a convenient starting point for our analysis of the universe of potential invest-

ment vehicles.

The bond is the basic debt security, and this chapter starts with an overview of

bond markets, including Treasury, corporate, and international bonds. We turn next to

bond pricing, showing how bond prices are set in accordance with market interest

rates and why bond prices change with those rates. Given this background, we can

compare the myriad measures of bond returns such as yield to maturity, yield to call,

holding-period return, or realized compound yield to maturity. We show how bond

prices evolve over time, discuss certain tax rules that apply to debt securities, and

show how to calculate after-tax returns. Next, we consider the impact of default or

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

296 Part THREE Debt Securities

debt security credit risk on bond pricing and look at the determinants of credit risk and the

default premium built into bond yields. Finally, we turn to the term structure of

A security such as a

bond that pays a interest rates, the relationship between yield to maturity and time to maturity.

specified cash flow

over a specific period.

9.1 BOND CHARACTERISTICS

A bond is a security that is issued in connection with a borrowing arrangement. The borrower

bond

issues (i.e., sells) a bond to the lender for some amount of cash; the bond is in essence the

A security that

“IOU” of the borrower. The arrangement obligates the issuer to make specified payments to

obligates the issuer

the bondholder on specified dates. A typical coupon bond obligates the issuer to make semi-

to make specified

payments to the annual payments of interest, called coupon payments, to the bondholder for the life of the

holder over a period bond. These are called coupon payments because, in precomputer days, most bonds had

of time.

coupons that investors would clip off and mail to the issuer of the bond to claim the interest

payment. When the bond matures, the issuer repays the debt by paying the bondholder the

bond™s par value (or equivalently, its face value). The coupon rate of the bond serves to de-

face value,

termine the interest payment: The annual payment equals the coupon rate times the bond™s par

par value

value. The coupon rate, maturity date, and par value of the bond are part of the bond inden-

The payment to the

ture, which is the contract between the issuer and the bondholder.

bondholder at the

To illustrate, a bond with a par value of $1,000 and a coupon rate of 8% might be sold to a

maturity of the bond.

buyer for $1,000. The issuer then pays the bondholder 8% of $1,000, or $80 per year, for the

stated life of the bond, say 30 years. The $80 payment typically comes in two semiannual in-

coupon rate

stallments of $40 each. At the end of the 30-year life of the bond, the issuer also pays the

A bond™s annual

$1,000 par value to the bondholder.

interest payment per

Bonds usually are issued with coupon rates set high enough to induce investors to pay par

dollar of par value.

value to buy the bond. Sometimes, however, zero-coupon bonds are issued that make no

coupon payments. In this case, investors receive par value at the maturity date, but receive no

zero-coupon

interest payments until then: The bond has a coupon rate of zero. These bonds are issued at

bond

prices considerably below par value, and the investor™s return comes solely from the differ-

A bond paying no

ence between issue price and the payment of par value at maturity. We will return to these

coupons that sells at a

bonds below.

discount and provides

only a payment of par

value at maturity.

Treasury Bonds and Notes

Figure 9.1 is an excerpt from the listing of Treasury issues in The Wall Street Journal. Trea-

sury note maturities range up to 10 years, while Treasury bonds with maturities ranging from

10 to 30 years appear in the figure. In 2001, the Treasury suspended new issues of 30-year

bonds, making the 10-year note the longest currently issued Treasury. As of 2002, there have

been no announcements of any plans to resume issuing the 30-year bond. Both bonds and

notes are issued in denominations of $1,000 or more. Both make semiannual coupon pay-

ments. Aside from their differing maturities at issue date, the only major distinction between

T-notes and T-bonds is that in the past, some T-bonds were callable for a given period, usually

callable bonds

during the last five years of the bond™s life. The call provision gives the Treasury the right to

Bonds that may be

repurchase the bond at par value during the call period.

repurchased by the

The highlighted bond in Figure 9.1 matures in October 2006. Its coupon rate is 61„2%. Par

issuer at a specified

call price during the value is $1,000; thus, the bond pays interest of $65 per year in two semiannual payments of

call period. $32.50. Payments are made in April and October of each year. The bid and ask prices1 are quoted

1

Recall that the bid price is the price at which you can sell the bond to a dealer. The ask price, which is slightly higher,

is the price at which you can buy the bond from a dealer.

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

297

9 Bond Prices and Yields

F I G U R E 9.1

Listing of Treasury issues

Source: The Wall Street Journal, November 29, 2001. Reprinted by permission of Dow Jones & Company, Inc. via Copyright Clearance Center, Inc. © 2001

Dow Jones & Company. All Rights Reserved Worldwide.

in points plus fractions of 1„32 of a point (the numbers after the colons are the fractions of a point).

Although bonds are sold in denominations of $1,000 par value, the prices are quoted as a per-

centage of par value. Therefore, the bid price of the bond is 109:08 1098„32 109.25% of par

value or $1,092.50, while the ask price is 10911„32 percent of par, or $1,093.44.

The last column, labeled Ask Yld, is the bond™s yield to maturity based on the ask price.

The yield to maturity is often interpreted as a measure of the average rate of return to an in-

vestor who purchases the bond for the ask price and holds it until its maturity date. We will

have much to say about yield to maturity below.

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill

Essentials of Investments, Companies, 2003

Fifth Edition

298 Part THREE Debt Securities

Accrued interest and quoted bond prices The bond prices that you see quoted

in the financial pages are not actually the prices that investors pay for the bond. This is be-

cause the quoted price does not include the interest that accrues between coupon payment

dates.

If a bond is purchased between coupon payments, the buyer must pay the seller for accrued

interest, the prorated share of the upcoming semiannual coupon. For example, if 40 days have

passed since the last coupon payment, and there are 182 days in the semiannual coupon pe-

riod, the seller is entitled to a payment of accrued interest of 40/182 of the semiannual coupon.

The sale, or invoice price of the bond, which is the amount the buyer actually pays, would

equal the stated price plus the accrued interest.

In general, the formula for the amount of accrued interest between two dates is

Annual coupon payment Days since last coupon payment

Accrued interest

2 Days separating coupon payments

Suppose that the coupon rate is 8%. Then the semiannual coupon payment is $40. Because

40 days have passed since the last coupon payment, the accrued interest on the bond is $40

9.1 EXAMPLE (40/182) $8.79. If the quoted price of the bond is $990, then the invoice price will be

$990 $8.79 $998.79.

Accrued Interest

The practice of quoting bond prices net of accrued interest explains why the price of a ma-

turing bond is listed at $1,000 rather than $1,000 plus one coupon payment. A purchaser of an

8% coupon bond one day before the bond™s maturity would receive $1,040 on the following

day and so should be willing to pay a total price of $1,040 for the bond. In fact, $40 of that to-

tal payment constitutes the accrued interest for the preceding half-year period. The bond price

is quoted net of accrued interest in the financial pages and thus appears as $1,000.

Corporate Bonds

Like the government, corporations borrow money by issuing bonds. Figure 9.2 is a sample of

corporate bond listings in The Wall Street Journal. The data presented here differ only slightly

from U.S. Treasury bond listings. For example, the highlighted AT&T bond pays a coupon rate

of 81„8% and matures in 2022. Like Treasury bonds, corporate bonds trade in increments of 1„32

point. AT&T™s current yield is 8.1%, which is simply the annual coupon payment divided by

the bond price ($81.25/$997.50). Note that current yield measures only the annual interest in-

come the bondholder receives as a percentage of the price paid for the bond. It ignores the fact

that an investor who buys the bond for $997.50 will be able to redeem it for $1,000 on the ma-

turity date. Prospective price appreciation or depreciation does not enter the computation of