Chapter 2 Securities Markets and Transactions 15
Chapter 11
Bond Valuation
Outline
Learning Goals
I. The Behavior of Market Interest Rates
A. Keeping Tabs on Market Interest Rates
B. What Causes Interest Rates to Move?
C. The Term Structure of Interest Rates and Yield Curves
1. Types of Yield Curves
2. Plotting Your Own Curves
3. Explanations of the Term Structure of Interest Rates
a. Expectations Hypothesis
b. Liquidity Preference Theory
c. Market Segmentation Theory
d. Which Theory Is Right?
4. Using the Yield Curve in Investment Decisions
Concepts in Review
II. The Pricing of Bonds
A. The Basic Bond Valuation Model
B. Annual Compounding
C. Semiannual Compounding
D. Accrued Interest
Concepts in Review
III. Measures of Yield and Return
A. Current Yield
B. YieldtoMaturity
1. Using Annual Compounding
2. Using Semiannual Compounding
2. Yield Properties
3. Finding the Yield on a Zero
C. YieldtoCall
D. Expected Return
E. Valuing a Bond
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16 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Concepts in Review
IV. Duration and Immunization
A. The Concept of Duration
B. Measuring Duration
1. Duration for a Single Bond
2. Duration for a Portfolio of Bonds
C. Bond Duration and Price Volatility
D. Effective Duration
E. Uses of Bond Duration Measures
1. Bond Immunization
Concepts in Review
V. Bond Investment Strategies
A. Passive Strategies
B. Trading on Forecasted Interest Rate Behavior
C. Bond Swaps
Concepts in Review
Summary
Key Terms
Discussion Questions
Problems
Case Problems
11.1 The Bond Investment Decisions of Dave and Marlene Carter
11.2 Grace Decides to Immunize Her Portfolio
Excel@Investing
Key Concepts
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Chapter 2 Securities Markets and Transactions 17
1. The important role that interest rates play in the bond investment process and the basic
determinants of market rates
2. The term structure of interest rates and yield curves
3. Fundamentals of bond valuation, including basic measures of yield and return
4. The concept of duration, including effective duration, and its measurement; how duration is
applied in immunizing bond portfolios
5. Various types of bond investment programs and the ways debt securities can be used by investors;
employment of bond ladders is a passive strategy, whereas buying high duration bonds prior to
interest rate drops would be a more active and risky strategy
Overview
1. Interest rates are an integral component of the bond valuation process. Some class time should be
spent discussing the economics of interest rates. The various forces that drive interest rates should be
covered next. In this context, the instructor can introduce the term structure of interest rates.
Inevitably students will ask how the risk-free rate could remain below the inflation rate for extended
periods. This question can be used to open a discussion of the Federal Reserve, the measures it has
available to stimulate the economy, and the consequences, good and bad, for bond investors.
2. The text then presents three different explanations of the term structure of interest rates: the
Expectations hypothesis, the liquidity preference theory, and the market segmentation theory. The
discussion of this important topic should include yield curves, how they are plotted, and their use in
making investment decisions.
3. The next section discusses the bond valuation process. It shows how, given the market rate of
interest and other details regarding the bond (such as the maturity, coupon, and face value), it is
possible to compute the “correct” price of the bond. An example showing this computation should be
worked out in class, including how fluctuations in the market interest rates induce changes in the
price of the bond. The magnitude of price changes depends on the amount of change in the market
interest rate, as well as on the maturity and coupon of the bond.
4. The concepts of bond yields and returns, along with the computation and use of current
yield,promised yield, yield-to-call, and expected yield, are discussed next. The instructor may wish to
demonstrate financial calculator and spreadsheet techniques for calculating the yield-to-maturity
using tables. It is also important to emphasize that what matters to investors is the return from the
bond, not its yield.
5. Bond duration is one of the most important concepts in bond valuation and investing. After
demonstrating the shortcomings of yield-to-maturity, the concept and measurement of duration can be
illustrated. In this regard, the instructor can work out an example to illustrate how duration and
modified duration aid investors in gauging a bond’s price volatility. Instead of being used to forecast
price changes, price changes are calculated and employed in the process of calculating effective
duration.
6. Bond immunization is presented next. This technique preserves the value of a bond portfolio. Bond
immunization involves constructing a bond portfolio with a weighted average duration that matches
the investor’s investment horizon.
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7. Bond investment strategies can be either active or passive. Passive investment strategies include
buy-and-hold and bond ladders. Trading on interest rate swings and bond swaps are considered active
strategies. The instructor might point out the advantages and disadvantages (risks) of each technique.
8. One interesting teaching strategy is to start out with a bond priced at par and show the decline/rise
from an interest rate decrease/increase of the same magnitude. Due to convexity, bond prices will rise
faster than they decline!
Answers to Concepts in Review
11.1 There is no single market rate of interest applicable to all segments of the bond market. Instead, a
series of market yields exists for a variety of market instruments. In general, the interest rate on a
11.2 The behavior of interest rates is perhaps the single most important element in determining the level of
return from a bond investment program. Interest rates affect the level of current income earned
byconservative investors, as well as the amount of capital gains generated by aggressive bond
11.3 The term structure of interest rates is the relationship between the interest rate or yield and the time
to maturity for any class of similar risk securities. The yield curve is just a graphic representation of
Usually the yield curve has an upward slope. The upward-sloping yield curve indicates that yields
tend to increase with longer maturities. The longer a bond has to go to maturity, the greater the
potential for price volatility and the risk of loss. Thus, investors usually require higher yields on
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Chapter 2 Securities Markets and Transactions 19
11.4 Analyzing the changes in yield curves over time provides investors with information about future
interest rate movements and how they can affect price behavior and comparative returns. For
Differences in yields on different maturities at a particular point in time, or the “steepness” of the
Even among longer–term maturities, the spread between different longer-term maturities should be
11.5 Bond prices are driven by market yields. In the marketplace, the appropriate yield at which the bond
should sell is determined first, and then that yield is used to find the price of the bond. The yield is a
You cannot value a bond without knowing its market yield, which functions as the discount rate in
11.6 Bonds are usually priced using semiannual compounding because in practice, most bonds pay interest
every six months. Semiannual compounding makes discounting of semiannual coupon payments
11.7 Current yield is a measure of a bond’s current income. It is the amount of current income that a bond
provides relative to its prevailing market price. Yield-to-maturity is a more complete measure and
Promised yield is the same as yield-to-maturity. Promised yield is computed assuming the bond is
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11.8 When we are dealing with semiannual cash flows, to be technically correct, we should find the bond’s
“effective” annual yield. However, the market convention for finding the annual yield is simply to
11.9 The reinvestment of interest income is an important consideration because the rate earned on
reinvested interest income has a significant impact on an investor’s overall return over a bond’s life.
11.10 Duration is a measure that captures the timing and magnitude of a bond’s cash payments, and it is
helpful in assessing the interest rate exposure of a bond. Duration is a kind of weighted average
Modified durationis a simple calculation that makes a direct link between a bond’s duration and
the extent to which its price reacts to interest rate changes. A bond’s modified duration is simply
Percent change in bond price 1 Modified duration Change in interest rates
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Chapter 2 Securities Markets and Transactions 21
Like modified duration, effective duration calculates the approximate percentage change in a
is
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i i
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11.11 Market interest rate changes have two effects: the price effect and the reinvestment effect, which
occur in opposite directions. When a bond portfolio is immunized, these two effects exactly offset
Bond immunization allows an investor to derive a specified rate of return from bond investments
Portfolio immunization is not a passive investment strategy; it requires continual portfolio
11.12 Bond ladders are a passive investment strategy whereby an equal amount of money is invested in
a series of bonds with staggered maturities. Suppose an investor wants to confine her investing to
fixed income securities with maturities of ten years or less. She could set up the ladder by investing in
Tax swaps involve replacing a bond with a capital loss with a similar security. By selling the bond
11.13 An aggressive bond investor would employ the highly risky forecasted interest rate behavior
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11.14 The interest sensitivity of a bond determines how much the bond’s price will fluctuate for a given
change in interest rates. Obviously, when rates drop, bond traders want to capitalize on this and, as
Suggested Answers to Discussion Questions
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Chapter 2 Securities Markets and Transactions 23
11.1 Expectations hypothesis. The yield curve reflects investor expectations about future interest rates and
nothing else. When rates are expected to rise (fall), the yield curve slopes up (down).
Liquidity preference theory. According to this theory, the difference between short-term and
long-term rates reflects not only interest rate expectations, but also differences in risk between short
and long maturities. Long-term bond rates should usually be higher than shorter–term rates because of
Market segmentation theory. The debt market is segmented, with some investors (such as banks
and corporations) having strong preferences to participate in the short end of the market, while others
(such as life insurance companies and pension funds) prefer to participate in the long end.. An
equilibrium exists in the short term between suppliers and demanders of funds in each market
11.2 Answers will vary with each student and the conditions prevailing in the markets at the time the
assignment is made.
d. There is a direct relationship between duration and modified duration, so if modified duration
11.4 a. An aggressive investor would be more concerned with capital gains, that is, price
appreciation. If she believes that interest rates are headed up, then she should invest in
b. A very conservative investor might include only short-term, investment-grade corporate,
c. 1. An insurance company or pension fund that must rely on predictable income streams
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4. Zero coupon bonds typically appeal to investors who have a buy-and-hold investment strategy
11.5 Answers will vary with each student.
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