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Chapter 11
Bond
Valuation
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Bond Valuation and Analysis
• Learning Goals
1. Explain the behavior of market interest
rates, and identify the forces that cause
interest rates to change.
2. Describe the term structure of interest
rates, and note how yield curves can be
used by investors.
3. Understand how bonds are valued in the
marketplace.
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11-2
Bond Valuation and Analysis
• Learning Goals (cont’d)
4. Describe the various measures of yield and
return, and explain how these standards of
performance are used in bond valuation.
5. Understand the basic concept of duration, how it
can be measured, and its use in the
management of bond portfolios.
6. Discuss the various bond investment strategies
and the different ways these securities can be
used by investors.
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11-3
Measuring Return
• Required Return: the rate of return an
investor must earn on an investment to be
fully compensated for its risk
Required Return
Real Rate
Expected Inflation
Risk Premium



On Investment
of Return
Premium
for Investment
For bonds, the risk premium depends upon:
• the default, or credit, risk of the issuer
• the term-to-maturity
• any call risk, if applicable
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11-4
Major Bond Sectors
• Bond market is comprised of a series of
different market sectors:
– U.S. Treasury issues
– Municipal bond issues
– Corporate bond issues
• Differences in interest rates between the
various market sectors are called
yield spreads
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11-5
Factors Affecting Yield Spreads
• Municipal bond rates are usually 20-30% lower
than corporate bonds due to tax-exempt feature
• Treasury bonds have lower rates than corporate
bonds due to no default risk
• The lower the credit rating (and higher the risk),
the higher the interest rate
• Discount (low-coupon) bonds yield less than
premium (high-coupon) bonds
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11-6
Factors Affecting Yield Spreads
(cont’d)
• Revenue muni bonds yield more than general
obligation muni bonds due to
higher risk
• Freely callable bonds yield higher than
noncallable bonds
• Bonds with longer maturities generally yield more
than shorter maturities
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11-7
What is the single biggest factor
that influences the price of bonds?
• Interest Rates
Interest rates go
G,
bond prices go
H
Interest rates go
H,
bond prices go
G
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11-8
What is the single biggest factor that
influences the direction of interest rates?
• Inflation
Inflation goes
G,
interest rates go
G
Inflation goes
H,
interest rates go
H
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11-9
Figure 11.1 The Impact of Inflation on
the Behavior of Interest Rates
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Economic Variables
that Affect Interest Rates
Economic
Variable
Change in money supply
Interest
Change
Rate
Effect
Slow increase
D
C
C
D
C
D
D
C
Slow decrease
Change in money supply
Fast increase
Fast decrease
Federal Budget
Deficit
Surplus
U.S. Economic Activity
Recession
Expansion
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11-11
Economic Variables
that Affect Interest Rates (cont’d)
Economic
Variable
Interest
Change
Federal Reserve Policies Slower growth
Faster growth
Foreign Interest Rates
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Higher
Lower
Rate
Effect
D
C
C
D
11-12
Term Structure of Interest Rates
and Yield Curves
• Term Structure of Interest Rates:
relationship between the interest rate or rate
of return (yield) on a bond and its time
to maturity
• Yield Curve: a graph that represents the
relationship between a bond’s term to
maturity and its yield at a given point
in time
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11-13
Figure 11.2 Two Types of Yield
Curves
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11-14
Theories on Shape of Yield Curve
• Slope of yield curve affect by:
– Inflation expectations
– Liquidity preferences of investors
– Supply and demand
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11-15
Theories on Shape
of Yield Curve (cont’d)
• Expectations Hypothesis
– Shape of yield curve is based upon investor expectations of future
behavior of interest rates
– If expecting higher inflation, investors demand higher interest rates
on longer maturities to compensate
for risk
– Increasing inflation expectations will result in upward-sloping yield
curve
– Decreasing inflation expectations will result in downward-sloping
yield curve
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11-16
Theories on Shape
of Yield Curve (cont’d)
• Liquidity Preference Theory
– Shape of yield curve is based upon the length of term, or maturity,
of bonds
– If investors’ money is tied up for longer periods of time, they have
less liquidity and demand higher interest rates to compensate for
real or perceived risks
– Investors won’t tie their money up for longer periods unless paid
more to do so
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11-17
Theories on Shape
of Yield Curve (cont’d)
• Market Segmentation Theory
– Shape of yield curve is based upon the supply and demand
for funds
– The supply and demand changes based upon the maturity levels:
short-term vs. long-term
– If more borrowers (demand) want to borrow long-term than
investors want to invest (supply) long-term, then the interest rates
(price) for long-term funds will go up
– If fewer borrowers (demand) want to borrow long-term than
investors want to invest (supply) long-term, then the interest rates
(price) for long-term funds will go down
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11-18
Interpreting Shape of Yield
Curve
• Upward-sloping yield curves result from:
– Higher inflation expectations
– Lender preference for shorter-maturity loans
– Greater supply of shorter-term loans
• Flat or downward-sloping yield curves result from:
– Lower inflation expectations
– Lender preference for longer-maturity loans
– Greater supply of longer-term loans
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11-19
Basic Bond Investing Strategy
• If you expect interest rates to increase, buy
short-term bonds
• If you expect interest rates to decrease, buy
long-term non-callable bonds
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11-20
The Pricing of Bonds
• Bonds are priced according to the present
value of their future cash flow streams
Bond price 
Present value of the annuity
Present value of the

of annual interest income
bond's par value
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11-21
The Pricing of Bonds (cont’d)
• Bond prices are driven by market yields
• Appropriate yield at which the bond should sell is
determined before price of the bond
– Required rate of return is determined by market,
economic and issuer characteristics
– Required rate of return becomes the bond’s
market yield
– Market yield becomes the discount rate that is used to
value the bond
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11-22
The Pricing of Bonds (cont’d)
• Bond prices are comprised of two components:
– Present value of the annuity of coupon payments, plus
– Present value of the single cash flow from repayment of
the principal at maturity
• Compounding refers to frequency coupons
are paid
– Annual compounding: coupons paid once per year
– Semi-annual compounding: coupons paid every
six months
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11-23
The Pricing of Bonds (cont’d)
• Bond Pricing Example:
– What is the market price of a
$1,000 par value 20 year bond that
pays 9 ½ % compounded annually
when the market rate is 10%?
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11-24
Ways to Measure Bond Yield
• Current yield
• Yield-to-Maturity
• Yield-to-Call
• Expected Return
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11-25
Current Yield
• Simplest yield calculation
• Only looks at current income
Annual interest
Current yield 
Current market price of the bond
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11-26
Yield-to-Maturity
• Most important and widely used yield calculation
• True yield received if the bond is held to maturity
• Assumes all interest income is reinvested at rate
equal to market rate at time of YTM calculation—
no reinvestment risk
• Calculates value based upon PV of interest
received and the appreciation of the bond if held
until maturity
• Difficult to calculate without a financial calculator
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11-27
Yield-to-Maturity (cont’d)
• Yield-to-Maturity Example:
– Find the yield-to-maturity on a
7 ½ % ($1,000 par value) bond
that has 15 years remaining to
maturity and is currently trading
in the market at $809.50?
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11-28
Yield-to-Call
• Similar to yield-to-maturity
• Assumes bond will be called on the first
call date
• Uses bonds call price (premium) instead of
the par value
• True yield received if the bond is held
to call
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11-29
Yield-to-Call (cont’d)
• Yield-to-Call Example:
– Find the yield-to-call of a 20-year,
10 ½ % bond that is currently
trading at $1,204, but can be
called in 5 years at a call price
of $1,085?
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11-30
Expected Return
• Used by investors who expect to actively
trade in and out of bonds rather than hold
until maturity date
• Similar to yield-to-maturity
• Uses estimated market price of bond at
expected sale date instead of the par value
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11-31
Expected Return (cont’d)
• Expected Return Example:
– Find the expected return on a 7
½% bond that is currently priced in
the market at $810 but is expected
to rise to $960 within a 3-year
holding period?
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11-32
Bond Duration
• Bond Duration: A measure of bond price
volatility, which captures both price and
reinvestment risk and which is used to
indicate how a bond will react in different
interest rate environments
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11-33
Bond Duration (cont’d)
• Improvement over yield-to-market because factors
in reinvestment risk
• Compares the sensitivity to changes in
interest rates
• Bond Duration is the average amount of time that
it takes to receive the interest and the principal
• Calculates the weighted average of the cash flows
(interest and principal payments) of the bond,
discounted to the present time
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11-34
The Concept of Duration
• Generally speaking, bond duration
possesses the following properties:
– Bonds with higher coupon rates have shorter
durations
– Bonds with longer maturities have longer
durations
– Bonds with higher YTM lead to shorter
durations
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11-35
The Concept of Duration
(cont’d)
• Bond duration is a better indicator than
bond maturity of impact of interest rates on
bond price (price volatility)
– If interest rates are going up, hold bonds with
short durations
– If interest rates are going down, hold bonds with
long durations
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11-36
Measuring Duration
• Steps in calculating duration
– Step 1: Find present value of each coupon or
principal payment
– Step 2: Divide this present value by current market price
of bond
– Step 3: Multiple this relative value by the year in which
the cash flow is to be received
– Step 4: Repeat steps 1 through 3 for each year in the
life of the bond then add up the values computed in
Step 3
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11-37
Table 11.1 Duration Calculation for a
7.5%, 15-Year Bond Priced to Yield 8%
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Bond Immunization
• Strategy to derive a specified rate of return regardless of
what happens to market interest rates over holding period
• Seeks to offset the opposite changes in bond valuation
caused by price effect and reinvestment effect
– Price effect: change in bond value caused by interest rate changes
– Reinvestment effect: as coupon payments are received, they are
reinvested at higher or lower rates than original coupon rate
• Bond immunization occurs when the average duration of
the bond portfolio just equals the investment time horizon.
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11-39
Bond Investment Strategies
• Conservative Approach
– Main focus is high current income
– High credit quality bonds are used
– Usually longer holding periods
• Aggressive Approach
– Main focus is capital gains
– Usually shorter holding periods with frequent
bond trading
– Use forecasted interest rate strategy to time
bond trading
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11-40
Bond Investment Strategies
(cont’d)
• Buy-and-hold strategy
– Replace bonds as they mature or quality declines
• Bond ladder strategy
– Set up “ladder” by investing equal amounts into varying
maturity dates (i.e. 3-, 5-, 7- and 10 years)
– As bonds mature, purchase new bonds with 10-year
maturity to keep ladder growing
– Provides higher yields of longer-term bonds and dollarcost averaging benefits
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11-41
Bond Investment Strategies
(cont’d)
• Bond Swaps
– Occur when investor sells one bond and simultaneously
buys another bond in its place
• Yield pickup swap strategy
– Sell a lower yielding bond and replace it with a
comparable credit quality bond with higher yield
– Often done between different bond sectors (i.e.
industrial bonds vs. utility bonds)
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11-42
Bond Investment Strategies
(cont’d)
• Tax swap strategy
– Sell a bond that has declined in value, use the
capital loss to offset other capital gains, and
repurchase another bond of comparable
credit quality
– Watch out for wash sales—new bond cannot be
an identical issue to old bond
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11-43
Chapter 11 Review
• Learning Goals
1. Explain the behavior of market interest rates, and
identify the forces that cause interest rates to change.
2. Describe the term structure of interest rates, and note
how yield curves can be used by investors.
3. Understand how bonds are valued in the marketplace.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
11-44
Chapter 11 Review (cont’d)
• Learning Goals (cont’d)
4. Describe the various measures of yield and return, and
explain how these standards of performance are used
in bond valuation.
5. Understand the basic concept of duration, how it
can be measured, and its use in the management of
bond portfolios.
6. Discuss the various bond investment strategies and
the different ways these securities can be used
by investors.
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11-45
Chapter 11
Additional
Chapter Art
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Figure 11.3A Yield Curves on U.S.
Treasury Issues
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11-47
Figure 11.3B Yield Curves on U.S.
Treasury Issues
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11-48
Table 11.2 Bond Immunization
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11-49