10
Chapter
Bond Prices and Yields
Fundamentals
of Investments
Valuation & Management
second edition
Charles J. Corrado Bradford D.Jordan
McGraw Hill / Irwin
Slides by Yee-Tien (Ted) Fu
10 - 2
Bond Prices and Yields
Goal
McGraw Hill / Irwin
Our goal in this chapter is to
understand the relationship between
bond prices and yields, and to
examine some of the fundamental
tools of bond risk analysis used by
fixed-income portfolio managers.
 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
10 - 3
Bond Basics
 A bond essentially is a security that offers the investor a
series of fixed interest payments during its life, along
with a fixed payment of principal when it matures.
 So long as the bond issuer does not default, the
schedule of payments does not change.
 When originally issued, bonds normally have maturities
ranging from 2 years to 30 years, but bonds with
maturities of 50 or 100 years also exist.
 Bonds issued with maturities of less than 10 years are
usually called notes.
 A very small number of bond issues have no stated
maturity, and these are referred to as perpetuities or
consols.
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10 - 4
Bond Basics
Straight bond
An IOU that obligates the issuer to pay to the
bondholder a fixed sum of money (called the
principal, par value, stated value or face value) at
the bond’s maturity, along with constant, periodic
interest payments (called coupons) during the life
of the bond.
 U.S. Treasury bonds are straight bonds.
 Special features may be attached, creating convertible
bonds, “putable” bonds, “putable” bonds have a put
feature that grants bondholders the right to sell their
bonds back to the issuer at a special put price.
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10 - 5
Bond Basics
 Two basic yield measures for a bond are its
coupon rate and current yield.
Annual coupon
Coupon rate 
Par value
Annual coupon
Current yield 
Bond price
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Bond Basics
 example1, suppose a $1,000 par value bond
pays semiannual coupons of $40. The annual
coupon is then $80, and stated as a percentage
of par value the bond's coupon rate is
 $80 / $1,000 = 8%.
 example2, suppose a $1,000 par value bond
paying an $80 annual coupon has a price of
$1,032.25.
 The current yield is $80 / $1,032.25 = 7.75%.
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Straight Bond Prices and Yield to Maturity
Yield to maturity (YTM)
The discount rate that equates a bond’s price
with the present value of its future cash
flows.
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10 - 8
Straight Bond Prices and Yield to Maturity
Bond price = present value of all the coupon payments
+ present value of the principal payment

C 
1
Bond price 
1
2M

YTM
YTM
1


2



FV

 1  YTM 2 M

2


where C = annual coupon, the sum of 2 semiannual
coupons
FV = face value
M = maturity in years
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10 - 9
Straight Bond Prices and Yield to Maturity
 Suppose a bond has a $1,000 face value, 20
years to maturity, an 8 percent coupon rate,
and a yield of 9 percent. What’s the price?
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 At simple interest:
 P = A/(1 + nr)
 At interest compounded annually:
 P = A/(1 + r)n
 At interest compounded q times a year:
 P = A/(1 + r/q)nq
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Straight Bond Prices and Yield to Maturity
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Premium and Discount Bonds
 Bonds are commonly distinguished according
to the relative relationship between their
selling price and their par value.
 Premium bonds: price > par value
YTM < coupon rate
 Discount bonds: price < par value
YTM > coupon rate
 Par bonds:
price = par value
YTM = coupon rate
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Premium and Discount Bonds
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Premium and Discount Bonds
 In general, when the coupon rate and YTM are
held constant …
for discount bonds: the longer the term to
maturity, the greater the discount from par
value, and
for premium bonds: the longer the term to
maturity, the greater the premium over par
value.
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10 - 15
Premium and Discount Bonds
 Example 10.2: Premium and Discount Bonds.
Suppose a bond has a $1,000 face value, with
eight years to maturity and a 7 percent coupon
rate. If its yield to maturity is 9 percent, does
this bond sell at a premium or discount? Verify
your answer by calculating the bond’s price.
 Since the coupon rate is smaller than the yield,
this is a discount bond.
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10 - 16
Premium and Discount Bonds
 Example 10.3: Premium Bonds Consider two bonds,
both with a 9 percent coupon rate and the same yield
to maturity of 7 percent, but with different maturities
of 5 and 10 years. Which has the higher price? Verify
your answer by calculating the prices.
 First, since both bonds have a 9 percent coupon and a
7 percent yield, both bonds sell at a premium. Based
on what we know, the one with the longer maturity
will have a higher price.
 We can check these conclusions by calculating the
prices as follows:
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10 - 17
Premium and Discount Bonds
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10 - 18
Premium and Discount Bonds
 Example 10.4: Discount Bonds Now consider two
bonds, both with a 9 percent coupon rate and the
same yield to maturity of 11 percent, but with
different maturities of 5 and 10 years. Which has the
 higher price? Verify your answer by calculating
prices.
 These are both discount bonds. (Why?) The one with
the shorter maturity will have a higher price. To
check, the prices can be calculated as follows:
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10 - 19
Premium and Discount Bonds
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10 - 20
Relationships among Yield Measures
 Since the current yield is always between the
coupon rate and the yield to maturity (unless
the bond is selling at par) …
for premium bonds:
coupon rate > current yield > YTM
for discount bonds:
coupon rate < current yield < YTM
for par value bonds:
coupon rate = current yield = YTM
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10 - 21
A note on bond price quotes
 Clean price : the price of a bond net of accrued
interest , this the price that is typically quoted .
 Dirty price : the price of a bond including
accrued interest , also known as the full or
invoice price , this is the price the buyer
actually pays .
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10 - 22
Calculating Yields
 To calculate a bond’s yield given its price, we
use the straight bond formula and then try
different yields until we come across the one
that produces the given price.

C 
1
Bond price 
1
2M
YTM 
YTM
1


2



FV

 1  YTM 2 M

2


 To speed up the calculation, financial
calculators and spreadsheets may be used.
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10 - 23
Yield to Call
 A callable bond allows the issuer to buy back
the bond at a specified call price anytime after
an initial call protection period, until the bond
matures.
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10 - 24
Yield to Call
 Yield to call (YTC) is a yield measure that
assumes a bond issue will be called at its
earliest possible call date.

1
Callable  C 1 
bond price YTC 
YTC
1


2

where C =
CP =
T =
YTC =
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
CP

2T
 1  YTC

2



2T
constant annual coupon
call price of the bond
time in years to earliest possible call date
yield to call assuming semiannual coupons
 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
10 - 25
Interest Rate Risk
Interest rate risk
The possibility that changes in interest rates
will result in losses in a bond’s value.
 The yield actually earned or “realized” on a
bond is called the realized yield, and this is
almost never exactly equal to the yield to
maturity, or promised yield.
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10 - 26
Interest Rate Risk and Maturity
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10 - 27
Reinvestment Risk
Reinvestment rate risk
The uncertainty about future or target date
portfolio value that results from the need to
reinvest bond coupons at yields not known
in advance.

A simple solution is to purchase zero coupon bonds.
In practice however, U.S. Treasury STRIPS are the
only zero coupon bonds issued in sufficiently large
quantities, and they have lower yields than even the
highest quality corporate bonds.
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10 - 28
Price Risk versus Reinvestment Rate Risk
Price risk
The risk that bond prices will decrease.
Arises in dedicated portfolios when the
target date value of a bond or bond portfolio
is not known with certainty.
 Interest rate increases act to decrease bond
prices (price risk) but increase the future value
of reinvested coupons (reinvestment rate risk),
and vice versa.
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10 - 29
Immunization
Immunization
Constructing a portfolio to minimize the
uncertainty surrounding its target date value.
 It is possible to engineer a portfolio such that
price risk and reinvestment rate risk offset
each other more or less precisely.
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10 - 30
Chapter Review
 Bond Basics
Straight Bonds
 Coupon Rate and Current Yield

 Straight Bond Prices and Yield to Maturity
Straight Bond Prices
 Premium and Discount Bonds
 Relationships among Yield Measures

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10 - 31
Chapter Review
 More on Yields
Calculating Yields
 Yield to Call

 Interest Rate Risk and Malkiel’s Theorems
Promised Yield and Realized Yield
 Interest Rate Risk and Maturity
 Malkiel’s Theorems

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10 - 32
Chapter Review
 Duration
Macaulay Duration
 Modified Duration
 Calculating Macaulay’s Duration
 Properties of Duration

 Dedicated Portfolios and Reinvestment Risk
Dedicated Portfolios
 Reinvestment Risk

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10 - 33
Chapter Review
 Immunization
Price Risk versus Reinvestment Rate Risk
 Immunization by Duration Matching
 Dynamic Immunization

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