Chapter 10 – Bond Prices and Yields
CHAPTER TEN
BOND PRICES AND YIELDS
CHAPTER OVERVIEW
1. Bond Characteristics
PPT 10-2 through PPT 10-13
Data from 2008 on the size of the bond markets is provided at the beginning. Notice that the bond markets
in total are much larger than the equity markets. Basic characteristics of bonds follow in the PPT. Stress
that the most common denomination is $1,000 for corporate bonds and Treasury bonds. Individual
investor buys a bond issued by an entity in their home state the interest income is exempt from state taxes
as well. Capital gains taxes will still apply. Many municipal bonds are insured by a bond insurer such as
MBIA. This is done to improve marketability.
U.S. bonds are registered, but most bonds issued outside the U.S. are bearer bonds. With bearer bonds you
must clip off the coupon and mail it in to get your interest as you are not a registered owner, although a
callable bond gives the issuing corporation the right to call the bond back from the bond holders. The call
provision is in the favor of the bond issuer, the issuer is likely to call in the bond when interest rates have
fallen. The bond will be redeemed at a price over par, but the investor will reinvest in a lower interest-rate
environment. The firm is not going to call the bond unless its market value is been above the call price.
Most bonds are callable after an initial call protection period of 3 to 5 years. The quid pro quo is that bond
Chapter 10 – Bond Prices and Yields
Foreign bonds are bonds issued by a borrower from a country other than the one in which the bond is sold.
The bonds are denominated in the currency of the country in which it is sold. They are often given colorful
names. For instance, Yankee bonds are bonds issued in the U.S. by foreign borrowers; they are
outside of Japan. These offerings allow banks and corporate treasurers to borrow money in different
currencies and at different interest rates.
A list of many of the key innovations in the bond market is provided. Developments in the asset-backed
markets are changing traditional methods of finance for many corporations. One of the innovative types of
bonds, inverse floaters, was a type of security held by Orange County Municipality when they went
2. Bond Pricing
PPT 10-14 through PPT 10-19
The bond pricing equation is presented in the PPT.
Prices that are quoted in the financial pages do not contain accrued interest. Most pricing examples that
are used in finance also do not include accrued interest. Actual invoice prices to buy a bond will include
any interest that has accrued since the last coupon payment. The flat price or quoted price assumes the
bond is purchased on a coupon payment date. If the bond buyer purchases a bond between payment dates
the buyer’s invoice price = flat price + accrued interest. Accrued interest can be calculated with the
following formula:
The key provisions for a bond are outlined in the indenture (or contract) of the bond. Note that the
indenture will specify a trustee to enforce the covenants in the bond contract. Covenants are specific
provisions within the bond contract that specify things like payment terms, financial constraints on the bond
issuers such as a maximum debt-to-equity ratio, minimum liquidity ratios, maximum dividend payment,
etc.
3. Bond Yields
PPT 10-20 through PPT 10-25
The relationship between bond prices and yields along with a graph of the relationship is presented. The
concept of yield to maturity can be related to prior work the students have done by equating it to the IRR.
payments coupon between Days
payment coupon last since Days
2
Coupon$ Annual
Interest Accrued
discussion of discount and premium bonds through examples. The discount bond increases in price to
compensate the bondholder for a lower current yield while the opposite occurs with a premium bond.
The PPT also displays how the call option affects value when comparing a callable and non-callable bond.
The call provision caps the upside potential when rates decline. The impact that reinvesting has on future
4. Bond Prices over Time
PPT 10-26 through PPT 10-30
The behavior of discount and premium bonds over time is presented. Class discussion of the reasoning
behind the premium and discount, as it relates to current yields, helps students to understand pricing. A
premium bond is priced above par because the coupon rate is too high relative to what the bond is supposed
to be yielding. The only way to get the expected yield down to the ytm is to have the bond priced above
par. In this case, the current yield on the bond will be above the promised yield. Hence there must be a
capital loss on the premium bond over the year to get the overall yield down to the promised ytm. All
bonds with a finite maturity experience these price movements over time, which are called the “Pull to
Par”. STRIPS are Treasury securities where the coupon payments and the final principal payment are
‘stripped’ out and sold separately. These can be useful for cash matching when a payment is due at a set
time period in the future.
The IRS rules that the built-in price increase, due to approaching maturity on all original issue discount
(OID) bonds, is taxable as interest income and is taxed at the investor’s ordinary income tax rate. Any
other gains or losses on the OID bond are treated as capital gains or losses. This is true for all OIDs, not
just zeros. 5. Default Risk and Bond Pricing
PPT 10-31 through PPT 10-41
The rating systems contain major and sub-categories that allow for differentiation in the major categories.
The highest four major categories are labeled as investment grade. Bonds that have ratings in lower major
categories are referred to as speculative grade or junk bonds. The major factors that determine a bond’s
rating are provided The highest rated firms have high levels of profitability, high levels of cash flow to
debt, high levels of coverage and liquidity ratios and lower levels of financial leverage.
Some bond contracts have covenants that provide protection against default. Sinking funds can prevent a
cash crisis at maturity since they require the firm to systematically repay part of the principal. The larger
cash flow requirements of a sinking fund can substantially reduce coverage and cash flow ratios prior to
calling bonds can hurt the bondholder. Serial bonds are not callable and this is a plus, but the staggered
maturities can reduce the liquidity of the bonds and make them more expensive.
Subordination of future debt and dividend restrictions serve to protect existing creditors. Collateral
provides the protection of asset value in case of default. Students should be aware that a bond without any
collateral is termed a debenture.
Chapter 10 – Bond Prices and Yields
During the credit crisis of 2008 the spread between Treasury bonds and junk-bond yields widened from 3%
in 2007 to 15% at the start of 2009! Many blame the crisis on excessive use of exotic derivatives such as
CDSs. They are partly correct, but the large number of factors led to the crisis. These include excess
leverage, lax regulation, excessively cheap credit, congressional interference in the mortgage markets.
Currency manipulation by export driven countries, unethical mortgage originators and misaligned executive
pay incentives all played a significant role as well, along with major failures of the ratings agencies to
identify the level of risk involved in mortgage securities.
Ratings agencies are paid by the firms issuing the securities. This creates a large conflict of interest
between the issuer and the bond rater. The government has granted a monopoly to the top three rating
agencies, although others exist. Even now, participation in TALF funding requires the securities be rated
by one of the big three (Moody’s, S&P and Fitches). We have known for a long time that bond prices move
ahead of announced downgrades in ratings. This is probably not due to information leakage ahead of the
announced change, but rather due to the slowness of the agency to respond and the unwillingness to
downgrade. Extrapolation bias also exists in the current agency-based paradigm as explained below.
A credit default swap (CDS) is an insurance policy on the default risk of a bond or loan. The seller of the
swap collects an annual premium (and sometimes an upfront fee) from the swap buyer. The buyer of the
Obviously if the economy experiences greater than expected defaults, these contracts magnify the losses
many times over resulting in a series of defaults. More detail can help students to understand this problem.
With a CDS there was no principal investment required; a low capital requirement (important if regulated);
and with a strong seller credit rating, little collateral was required. The result was excessive risk taking on
both sides. Buyers took on more risk because they were insured, even though insurer’s collateral was
As the text points out, the lack of transparency in this market helped cause the credit freeze after the
subprime mortgage crisis began. No one could tell the obligations and exposure of counterparties so it was
too risky to make a loan. AIG had over $400 billion in CDS contracts on subprime mortgages and other
loans and was going bankrupt. The failure of AIG might have trigged defaults at other institutions that
were counting on payments from AIG to protect their own investments. Ultimately the government decided
6. The Yield Curve
PPT 10-42 through PPT 10-47
The term structure of interest rates depicts the relationship between term to maturity and maturity for a
group of bonds that are identical in all aspects except maturity. In practice, identical means the same
rating, preferably the same coupon so that you don’t get into tax differences.
10–4
future short-term rates but also include added compensation, a liquidity premium, for greater risk.
The Pure Expectations Theory of the Term Structure
Long-term rates are a function of expected future short-term rates. This is the case with some restrictive
assumptions. First, if transaction costs are zero, securities are perfectly divisible, and most importantly,
future interest rates can be perfectly predicted. With these assumptions, a simple arbitrage argument will
this case an upward-sloping term structure unambiguously implies that the market is expecting higher
future short-term rates and a downward slope means that the market is expecting lower future short-term
rates. Liquidity Preference
The liquidity preference idea deals with the reality that future interest rates cannot be forecast perfectly so
that the arbitrage argument used above is a risky arbitrage. More importantly it is riskier to invest for n
The formula for calculation of forward rates is presented. Depending on the scope of coverage in your
class, it can be useful to extend the discussion to a multi-year context. Sample yield curves and volatility
of term spreads are also provided.
Excel Applications
Two excel spreadsheets for this chapter are available on the website. The first spreadsheet provides a