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Here is another way to think about the difference between yield to maturity and holding-
period return. Yield to maturity depends only on the bond™s coupon, current price, and par
value at maturity. All of these values are observable today, so yield to maturity can be easily
calculated. Yield to maturity can be interpreted as a measure of the average rate of return if the
investment in the bond is held until the bond matures. In contrast, holding-period return is the
rate of return over a particular investment period and depends on the market price of the bond
at the end of that holding period; of course this price is not known today. Since bond prices
over the holding period will respond to unanticipated changes in interest rates, holding-period
return can at most be forecast.

Zero-Coupon Bonds
Original issue discount bonds are less common than coupon bonds issued at par. These are
bonds that are issued intentionally with low coupon rates that cause the bond to sell at a dis-
count from par value. An extreme example of this type of bond is the zero-coupon bond,
which carries no coupons and must provide all its return in the form of price appreciation.
Zeros provide only one cash flow to their owners, and that is on the maturity date of the bond.
U.S. Treasury bills are examples of short-term zero-coupon instruments. The Treasury
issues or sells a bill for some amount less than $10,000, agreeing to repay $10,000 at the bill™s
maturity. All of the investor™s return comes in the form of price appreciation over time.
Longer term zero-coupon bonds are commonly created from coupon-bearing notes and
bonds with the help of the U.S. Treasury. A broker that purchases a Treasury coupon bond may
ask the Treasury to break down the cash flows to be paid by the bond into a series of inde-
pendent securities, where each security is a claim to one of the payments of the original bond.
For example, a 10-year coupon bond would be “stripped” of its 20 semiannual coupons and
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 9.7
900 The price of a 30-year
800 zero-coupon bond
700 over time at a yield
Price ($)

600 to maturity of 10%.
Price equals
where T is time
until maturity.










Today Maturity

each coupon payment would be treated as a stand-alone zero-coupon bond. The maturities of
these bonds would thus range from six months to 10 years. The final payment of principal
would be treated as another stand-alone zero-coupon security. Each of the payments would
then be treated as an independent security and assigned its own CUSIP number, the security
identifier that allows for electronic trading over the Fedwire system. The payments are still
considered obligations of the U.S. Treasury. The Treasury program under which coupon strip-
ping is performed is called STRIPS (Separate Trading of Registered Interest and Principal of
Securities), and these zero-coupon securities are called Treasury strips. Turn back to Figure
9.1 for a listing of these bonds appearing in The Wall Street Journal.
What should happen to prices of zeros as time passes? On their maturity dates, zeros must
sell for par value. Before maturity, however, they should sell at discounts from par, because of
the time value of money. As time passes, price should approach par value. In fact, if the inter-
est rate is constant, a zero™s price will increase at exactly the rate of interest.
To illustrate this property, consider a zero with 30 years until maturity, and suppose the
market interest rate is 10% per year. The price of the bond today will be $1,000/(1.10)30
$57.31. Next year, with only 29 years until maturity, if the yield to maturity is still 10%, the
price will be $1,000/(1.10)29 $63.04, a 10% increase over its previous-year value. Because
the par value of the bond is now discounted for one fewer year, its price has increased by the
one-year discount factor.
Figure 9.7 presents the price path of a 30-year zero-coupon bond until its maturity date for
an annual market interest rate of 10%. The bond™s price rises exponentially, not linearly, until
its maturity.

After-Tax Returns
The tax authorities recognize that the “built-in” price appreciation on original-issue discount
(OID) bonds such as zero-coupon bonds represents an implicit interest payment to the holder
of the security. The Internal Revenue Service (IRS), therefore, calculates a price appreciation
schedule to impute taxable interest income for the built-in appreciation during a tax year, even
if the asset is not sold or does not mature until a future year. Any additional gains or losses that
arise from changes in market interest rates are treated as capital gains or losses if the OID
bond is sold during the tax year.
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition

316 Part THREE Debt Securities

If the interest rate originally is 10%, the 30-year zero would be issued at a price of
$1,000/(1.10)30 $57.31. The following year, the IRS calculates what the bond price would
9.8 EXAMPLE be if the yield remains at 10%. This is $1,000/(1.10)29 $63.04. Therefore, the IRS imputes
interest income of $63.04 $57.31 $5.73. This amount is subject to tax. Notice that the
Taxation of
imputed interest income is based on a “constant yield method” that ignores any changes in
OID Bonds
market interest rates.
If interest rates actually fall, let™s say to 9.9%, the bond price actually will be $1,000/
(1.099)29 $64.72. If the bond is sold, then the difference between $64.72 and $63.04 will
be treated as capital gains income and taxed at the capital gains tax rate. If the bond is not
sold, then the price difference is an unrealized capital gain and does not result in taxes in that
year. In either case, the investor must pay taxes on the $5.73 of imputed interest at the ordi-
nary income tax rate.

The procedure illustrated in Example 9.8 is applied to the taxation of other original issue
discount bonds, even if they are not zero-coupon bonds. Consider, as another example, a
30-year maturity bond that is issued with a coupon rate of 4% and a yield to maturity of 8%.
For simplicity, we will assume that the bond pays coupons once annually. Because of the low
coupon rate, the bond will be issued at a price far below par value, specifically at a price of
$549.69. (Confirm this for yourself.) If the bond™s yield to maturity remains at 8%, then its
price in one year will rise to $553.66. (Confirm this also.) This provides a pretax holding-
period return of exactly 8%:
$40 ($553.66 $549.69)
HPR 0.08
The increase in the bond price based on a constant yield, however, is treated as interest
income, so the investor is required to pay taxes on imputed interest income of $553.66
$549.69 $3.97, as well as on the explicit coupon income of $40. If the bond™s yield actually
changes during the year, the difference between the bond™s price and the “constant yield
value” of $553.66 would be treated as capital gains income if the bond were sold at year-end.

7. Suppose that the yield to maturity of the 4% coupon, 30-year maturity bond actu-
ally falls to 7% by the end of the first year, and that the investor sells the bond after
CHECK the first year. If the investor™s tax rate on interest income is 36% and the tax rate
on capital gains is 28%, what is the investor™s after-tax rate of return?

Although bonds generally promise a fixed flow of income, that income stream is not riskless
unless the investor can be sure the issuer will not default on the obligation. While U.S. gov-
ernment bonds may be treated as free of default risk, this is not true of corporate bonds. If the
grade bond
company goes bankrupt, the bondholders will not receive all the payments they have been
A bond rated BBB and promised. Therefore, the actual payments on these bonds are uncertain, for they depend to
above by Standard & some degree on the ultimate financial status of the firm.
Poor™s, or Baa and
Bond default risk is measured by Moody™s Investor Services, Standard & Poor™s Corpora-
above by Moody™s.
tion, Duff and Phelps, and Fitch Investors Service, all of which provide financial information
on firms as well as quality ratings of large corporate and municipal bond issues. Each firm as-
speculative grade
signs letter grades to the bonds of corporations and municipalities to reflect their assessment
or junk bond
of the safety of the bond issue. The top rating is AAA or Aaa. Moody™s modifies each rating
A bond rated BB or class with a 1, 2, or 3 suffix (e.g., Aaa1, Aaa2, Aaa3) to provide a finer gradation of ratings.
lower by Standard &
The other agencies use a or modification.
Poor™s, Ba or lower
Those rated BBB or above (S&P, Duff and Phelps, Fitch) or Baa and above (Moody™s) are
by Moody™s, or an
considered investment grade bonds, while lower-rated bonds are classified as speculative
unrated bond.
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 9.8
Bond Ratings
Definitions of each
Very High High Very bond rating class
Quality Quality Speculative Poor
Sources: From Stephen A.
Ross, Randolph W.
Standard & Poor™s AAA AA A BBB BB B CCC D
Westerfield, and Jeffrey A.
Moody™s Aaa Aa A Baa Ba B Caa C Jaffe, Corporate Finance,
McGraw-Hill Publishing.
At times both Moody™s and Standard & Poor™s use adjustments to these ratings. S&P Data from various editions
uses plus and minus signs: A is the strongest A rating and A the weakest. Moody™s of Standard & Poor™s
uses a 1, 2, or 3 designation”with 1 indicating the strongest. Bond Guide and
Moody™s Bond Guide.

Moody™s S&P

Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay
interest and principal is extremely strong.
Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and
repay principal. Together with the highest rating, this group comprises
the high-grade bond class.
A A Debt rated A has a strong capacity to pay interest and repay principal,
although it is somewhat more susceptible to the adverse effects of
changes in circumstances and economic conditions than debt in higher-
rated categories.
Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to
pay interest and repay principal. Whereas it normally exhibits adequate
protection parameters, adverse economic conditions or changing
circumstances are more likely to lead to a weakened capacity to pay
interest and repay principal for debt in this category than in higher-rated
categories. These bonds are medium grade obligations.
Ba BB Debt rated in these categories is regarded, on balance, as predomi-
B B antly speculative with respect to capacity to pay interest and repay
Caa CCC principal in accordance with the terms of the obligation. BB and Ba
Ca CC indicate the lowest degree of speculation, and CC and Ca the highest
degree of speculation. Although such debt will likely have some quality
and protective characteristics, these are outweighed by large
uncertainties or major risk exposures to adverse conditions. Some issues
may be in default.
C C This rating is reserved for income bonds on which no interest is being
D D Debt rated D is in default, and payment of interest and/or repayment of
principal is in arrears.

grade or junk bonds. Certain regulated institutional investors such as insurance companies
have not always been allowed to invest in speculative grade bonds.
Figure 9.8 provides the definitions of each bond rating classification.

Junk Bonds
Junk bonds, also known as high-yield bonds, are nothing more than speculative grade (low-
rated or unrated) bonds. Before 1977, almost all junk bonds were “fallen angels,” that is,
bonds issued by firms that originally had investment grade ratings but that had since been
downgraded. In 1977, however, firms began to issue “original-issue junk.”
Bodie’Kane’Marcus: III. Debt Securities 9. Bond Prices and Yields © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition


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