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

9 Bond Prices and Yields
10 Managing Bond Investments

Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition



> 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.

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/
The above sites provide information on bond ratings.
These sites give general price information.
This site has extended information on various interest
rates. These rates can be downloaded into a
http://www.investinginbonds.com/ spreadsheet format for analysis.
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.
A bond is a security that is issued in connection with a borrowing arrangement. The borrower
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
interest payments until then: The bond has a coupon rate of zero. These bonds are issued at
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

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

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
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


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