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Chapter 11
Bond Valuation
1
Bond Valuation and Analysis
 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.
3.
Understand how bonds are valued in the
marketplace.
2
Bond Valuation and Analysis
 Goals
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.
6.
Discuss the various bond investment strategies.
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, or risk of the issuer
• the term-to-maturity
• any call risk, if applicable
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.
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
6
Factors Affecting Yield Spreads
 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
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
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
9
The Impact of Inflation on the Behavior of
Interest Rates
10
Economic Variables
that Affect Interest Rates
Economic
Variable
Interest
Change
Rate
Effect
Change in money supply
Slow increase
Slow decrease
Change in money supply
Fast increase
Fast decrease
D
C
C
D
C
D
D
C
Federal Budget
U.S. Economic Activity
Deficit
Surplus
Recession
Expansion
11
Economic Variables
that Affect Interest Rates
Economic
Variable
Interest
Change
Rate
Effect
Federal Reserve Policies
Slower growth
D
C
C
D
Faster growth
Foreign Interest Rates
Higher
Lower
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
13
Two Types of Yield Curves
14
Theories on Shape of Yield Curve
 Slope of yield curve affect by:

Inflation expectations

Liquidity preferences of investors

Supply and demand
15
Theories on Shape of Yield Curve
 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 upwardsloping yield curve

Decreasing inflation expectations will result in downwardsloping yield curve
16
Theories on Shape of Yield Curve
 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
17
Theories on Shape of Yield Curve
 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
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
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
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
21
The Pricing of Bonds
 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
22
The Pricing of Bonds
 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
23
The Pricing of Bonds
 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%?
24
Ways to Measure Bond Yield
 Current yield
 Yield-to-Maturity
 Yield-to-Call
 Expected Return
25
Current Yield
 Simplest yield calculation
 Only looks at current income
Annual interest
Current yield 
Current market price of the bond
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
27
Yield-to-Maturity
 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?
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
29
Yield-to-Call
 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?
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
31
Expected Return
 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?
32
Bond Duration
 Bond Duration: A measure of bond price
fluctuation, which captures both price and
reinvestment risk and which is used to
indicate how a bond will react in different
interest rate environments
33
Bond Duration
 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
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
35
The Concept of Duration
 Bond duration is a better indicator than bond
maturity of the impact of interest rates on
bond price (price fluctuation) (Remember
Reinvestment…)

If interest rates are going up, hold bonds
with short durations

If interest rates are going down, hold
bonds with long durations
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
37
Duration Calculation for a 7.5%, 15-Year
Bond Priced to Yield 8%
38
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.
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
40
Bond Investment Strategies
 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
dollar-cost averaging benefits
41
Bond Investment Strategies
 Bond Swaps
 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)
42
Bond Investment Strategies
 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
43
Review
 Goals
1.
Explained the behavior of market interest rates, and
identify the forces that cause interest rates to change.
2.
Described the term structure of interest rates, and
note how yield curves can be used by investors.
3.
Understood how bonds are valued in the
marketplace.
44
Review
 Goals
4.
Described the various measures of yield and return,
and explain how these standards of performance are
used in bond valuation.
5.
Understood the basic concept of duration, how it
can be measured, and its use in the management of
bond portfolios.
6.
Discussed the various bond investment strategies
and the different ways these securities can be used
by investors.
45
The End!
46
Chapter 11
Additional Chapter Art
47
Yield Curves on U.S. Treasury Issues
48
Yield Curves on U.S. Treasury Issues
49
Bond Immunization
50