Module 7
Valuation & Analysis of
Fixed-income
Investments
by
Jason G. Hovde, CIMA®, CFP®, APMA®
7353
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
This publication may not be duplicated in any way without the express written consent of the publisher. The
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The College for Financial Planning does not certify individuals to use the CFP, CERTIFIED FINANCIAL
PLANNER™, and CFP (with flame logo)® marks. CFP® certification is granted solely by Certified Financial
Planner Board of Standards Inc. to individuals who, in addition to completing an educational requirement
such as this CFP Board-Registered Program, have met its ethics, experience, and examination requirements.
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FINANCIAL PLANNER™, and federally registered CFP (with flame logo)®, which it awards to individuals who
successfully complete initial and ongoing certification requirements.
At the College’s discretion, news, updates, and information regarding changes/updates to courses or
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Center at 1-800-237-9990.
Table of Contents
Study Plan/Syllabus ................................................................ 1
Learning Activities ............................................................. 3
Exam Formula Sheet ........................................................... 4
Chapter 1: Valuation of Bonds ............................................... 5
Prices and Yields ................................................................ 5
Bond Calculations ............................................................... 8
Calculating the Price of a Zero-Coupon Bond ................... 14
Chapter 2: Duration ............................................................. 21
Duration Computations ..................................................... 27
Change in Bond Price Using Duration ............................... 31
Convexity ......................................................................... 36
Chapter 3: Bond Volatility & Constructing Portfolios ........ 40
Risk & Volatility .............................................................. 41
Immunization .................................................................... 42
Bond Swaps ...................................................................... 44
Chapter 4: Convertible Bonds .............................................. 50
Conversion Value ............................................................. 51
Bond Investment Value ..................................................... 52
Investment Premium and Conversion Premium ................. 53
Forced Conversion ............................................................ 54
Convertible Sample Calculations ...................................... 55
Convertible Preferred Stock .............................................. 56
Summary of Convertible Bond Relationships .................... 57
Summary ................................................................................ 59
Module Review ...................................................................... 61
Questions .......................................................................... 61
Answers ............................................................................ 81
References ............................................................................ 121
About the Author ................................................................. 122
Index .................................................................................... 123
Study Plan/Syllabus
U
nderstanding how bonds are valued is a key to understanding how bond
prices change as economic conditions and interest rates change. This
module helps you learn how to value bonds, how to determine the
expected price volatility of bonds, and how to use the computations to make
decisions about buying and selling bonds.
The chapters in this module are:
Valuation of Bonds
Duration
Bond Volatility & Constructing Portfolios
Convertible Bonds
The material in this module provides focus on bond valuation and volatility and
explains how to use the valuation tools to make fixed-income investment decisions.
Upon completion of this module, you should be able to use bond valuation
and duration formulas, calculate bond yields, interpret bond yield curves,
and make bond portfolio decisions for clients.
The module begins with bond yield calculations. You must know how to define
and calculate bond intrinsic values and various types of yields. Yield-to-maturity,
yield-to-call, current yield, and taxable equivalent yield are all calculations you
should master.
Duration is a very important concept, as it is a measure of a bond’s volatility.
You will most likely not need to calculate duration, but you must know how it is
used and its importance when constructing bond portfolios. Calculating change in
price using duration is a calculation you should know, as it has been regularly
tested on the CFP Certification Examination. Even more important than the
calculations themselves is that you know how to interpret the information
contained in each calculation, how to assess the effect when one or more of the
Study Plan/Syllabus

1
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
assumptions changes, and how to compare bonds to help clients make decisions
about which bonds to purchase. You should expand on the exercises given in the
Module Review Questions to practice more “what if” scenarios until you are
confident that you can intuitively understand how intrinsic value, yield-tomaturity, duration, and so forth are affected by changes in inputs.
Convertible bonds are especially complex. You must know how to use the
conversion value formula and—more importantly—know the relationships
among conversion value, investment value, conversion premium, conversion
ratio, and other convertible bond and convertible preferred stock factors.
Knowing how to calculate these values is important, but knowing what the
computations mean is even more important.
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Learning Activities
Learning Activities
Learning Objective
Readings
Module
Review
Questions
7–1
Explain factors that affect the price
and yield of fixed-income securities.
Module 7,
Chapter 1:
Valuation of
Bonds
1–7
7–2
Calculate the price, compound return,
yield-to-maturity, yield-to-call, and
taxable-equivalent yield, of fixedincome securities.
Module 7,
Chapter 1:
Valuation of
Bonds
8–16
7–3
Understand the concept of duration,
and calculate change in price using
duration.
Module 7,
Chapter 2:
Duration
17–23
7–4
Analyze the relationships among bond
ratings, yields, maturities, and
durations to determine comparative
price volatility.
24–28
7–5
Assess how changes in variables affect
bond risk and price volatility.
Module 7,
Chapter 3:
Bond Volatility
& Constructing
Portfolios
7–6
Evaluate investor profiles to
recommend appropriate fixed-income
securities for purchase.
7–7
Calculate the conversion value,
investment value, investment
premium, conversion premium, and
downside risk of convertible securities.
7–8
Analyze the relationships among
conversion value, investment value,
and market value of convertible
securities.
29–34
35–39
Module 7,
Chapter 4:
Convertible
Bonds
40–47
48
Look for the boxed objectives throughout this module to guide your studies.
Study Plan/Syllabus

3
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Exam Formula Sheet
D1
r−g
V=
r=
Dur =
 Δy 
ΔP = −D 

1 + y 
D1
+g
P
ri = rf + (rm − rf )βi
σ =
CV =
(
Σ rn − r
−
xi
β=
)
CV =
or
HPR =
Si
meani
Si
× Rim or
Sm
σp =
V=
βi =
Wi2 σi2 + W 2 σ
j
2
j
ρim σi
σm
+ 2W W COV
ij
i
j
Tp =
COVij
S + I − Pc
Pc
NOI
Capitalization Rate
rp − rf
Sp =
COVij = ρijσiσj
Rij =
Par
× Ps
CP
2
n − 1
σi
1 + y (1 + y) + t(c − y)
−
y
c[(1 + y)t − 1] + y
βp
rp − rf
σp
a = rp −  rf + (rm − rf )βp 


σi × σ j
IR =
RP − RB
σA
PLEASE NOTE: You do not need to memorize these formulas for the exam. An exact copy of this
formula sheet will be provided to you when you log on to take your IP exam. Also, the formula sheet
for the CFP Certification Examination will be different from this exam formula sheet. Prior to taking
the exam, please check with the CFP Board regarding their current exam formula sheet.
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Chapter 1: Valuation of Bonds
Reading the first part of this chapter will enable you to:
7–1
Explain factors that affect the price and yield of fixed-income
securities.
Prices and Yields
T
he current price of a bond is the discounted present value of the bond’s
future cash flow stream. A financial calculator can be used to compute a
bond’s current price (its present value) because the four inputs needed—
(1) semiannual payment, (2) par value (future value), (3) number of periods until
maturity, and (4) current market interest rate for comparable bonds—are readily
available. For bond problems in this course, assume that all bonds pay interest
semiannually (or accrue interest semiannually in the case of zero coupon bonds)
unless you are told otherwise.
Since the coupon and par value are fixed at the time a bond is issued and are not
changed during the life of the bond, a bond’s present value changes as current
market interest rates change. Current market interest rates are the discount rates
used to compute the present value of a bond.
As the discount rate rises, the present value of a bond decreases. As the discount
rate declines, the present value of a bond increases. When a bond sells above its
par value (par value is generally $1,000), it is said to be selling at a premium;
when it sells below its par value, it is said to be selling at a discount. The inverse
relationship between market interest rates and bond prices can be represented by
the following seesaw illustrations.
Chapter 1: Valuation of Bonds
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5
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
A bond at par might look like this.
$1,000
7%
If interest rates increase, the seesaw might look like this.
If interest rates decrease, the seesaw might look like this.
The current yield of a bond is the annual coupon rate divided by the current price
of the bond. When a bond is originally issued, the current yield and the coupon
rate are the same. If the price of a bond declines because market interest rates
have risen, the coupon is divided by a lower price; therefore, the current yield is
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
greater than the coupon yield. If the price of a bond rises, then the coupon is
divided by a higher price and the current yield is less than the coupon yield.
For example, assume that a new bond is issued with a 6% coupon; it pays $60 of
interest per year, in semiannual payments of $30. Assume market rates have risen
and the bond now sells for $900; the current yield is $60 divided by $900, or
6.67%. In bond market terminology, the bond yield is now 67 basis points higher.
Assume market rates have declined, and the bond now sells for $1,100; the
current yield is $60 divided by $1,100, or 5.45%. In bond market terminology,
the bond yield is now 55 basis points lower.
A bond’s yield-to-maturity (YTM) is the sum of the current yield and the
appreciation or depreciation the bond will experience between the current date
and its maturity date. In the first example in the previous paragraph, assume that
the bond has 20 years until its maturity date (40 semiannual periods). The YTM
is 6.93%, consisting of a current yield of 6.67% and a compound semiannual
return over the 20 years of 0.26% ($100 of appreciation compounded over 40
periods). (After you learn the keystrokes for computing YTM in the next section
on bond calculations, confirm this calculation and the YTC calculation below.)
Note that the YTM is greater than the current yield because the YTM includes
appreciation; in the second case in the previous paragraph, in which the YTM
includes depreciation of the value of the asset from $1,100 to $1,000, the YTM
will be less than the current yield.
A bond’s yield-to-call (YTC) is similar to the YTM, except that the number of
periods until the call date is always less than the number of periods until the
maturity date. The YTC on a bond selling at a discount will always be higher
than the YTM because the dollar amount of appreciation will be returned faster.
However, discount bonds are seldom called because the issuing corporation
could buy the bond on the market at a lower price than it would have to pay if it
called the bond. The YTC on a bond selling at a premium will always be lower
than its YTM because the dollar amount of depreciation will be incurred faster.
Chapter 1: Valuation of Bonds

7
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Reading the next part of this chapter will enable you to:
7–2
Calculate the price, compound return, yield-to-maturity, yield-to-call,
and taxable-equivalent yield, of fixed-income securities.
Bond Calculations
Taxable-Equivalent Yield
We will start with the simplest calculation you need to know. When investors
compare a taxable bond investment with a tax-free investment, it is important to
compare apples to apples. This can be done either by converting the tax-free
yield into a taxable-equivalent yield, or by converting the taxable yield into a taxfree equivalent yield.
Investors in higher tax brackets (25% is often considered the lower threshold; in
2013 the highest marginal tax bracket was 39.6%) generally are advised to buy
municipal bonds when bonds are recommended for their portfolios. A key
determinant of that decision is the taxable-equivalent yield of the tax-free bonds.
There are two situations in which to calculate a taxable equivalent yield: (1)
when a municipal bond is free from federal income tax but subject to state
income tax, and (2) when a municipal bond is free from both federal income tax
and state income tax.
Situation 1. If a municipal bond is free from federal income tax only and has
a yield of 5.5%, for an investor in the 25% tax bracket this bond would have
a taxable-equivalent yield of 7.33%. If the investor can find a taxable bond
with an equivalent credit rating and characteristics (but with a yield greater
than 7.33%), then the taxable bond will yield more, after tax, than the taxfree bond; the taxable bond should probably be purchased.
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
The taxable-equivalent yield (TEY) is computed as follows:
TEY =
Tax-free yield
1 − Marginal tax bracket
Problem. Brad Feathers is in the 33% marginal tax bracket and is considering
investing in a municipal bond with a yield of 4.2%. He is also considering
Treasury bonds with the same maturity that have a yield of 5.5%. Which
should he purchase?
To answer this we need to know the TEY of the municipal bond.
TEY =
Tax-free yield
1 − Marginal tax bracket
TEY =
4.2%
= 6.27%
1 − .33
Answer. The tax-free bond has a TEY of 6.27%, which is higher than the
5.5% yield of the Treasury bonds. Based just on yield, Brad would choose
the municipal bond.
Now if instead you knew the taxable yield was 6.27%, and wanted to know
what the tax-free equivalent was, you simply multiply the 6.27% by 1 minus
the marginal tax bracket:
6.27% × (1 – .33) = 4.2%

Situation 2. If a municipal bond is free from both federal and state income
taxation (a “double tax-exempt bond”), and the taxpayer itemizes deductions,
then the formulas are as follows:
Taxable equivalent yield =
Tax-free equivalent yield
1 − FMTB + SMTB (1 − FMTB ) 
Chapter 1: Valuation of Bonds

9
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
The reason why this is done is to take into account that a lower state taxable
income amount (and thus lower state taxes) will then result in less of a
deduction that the individual can take on Schedule A (itemized deductions)
for state income taxes. A lower deduction for state income taxes will increase
taxable income slightly. This can be condensed to:
Taxable equivalent yield =
Tax-free equivalent yield
(1 − SMTB )(1 − FMTB )
and
Tax-free equivalent yield = TEY × (1 – FMTB)(1 – SMTB)
where
TEY
TFEY
FMTB
SMTB
=
=
=
=
Taxable equivalent yield
Tax-free equivalent yield
Federal marginal tax bracket
State marginal tax bracket
Problem. Brad Feathers, who itemizes deductions, is in the 33% marginal tax
bracket, the 10% state marginal tax bracket, and is considering investing in a
municipal bond issued by his state of residence with a yield of 4.2%. He is
also considering corporate bonds with the same maturity that have a yield of
5.5%. Which should he purchase based only on yield?
To answer this we need to know the TEY of the municipal bond.
Taxable equivalent yield =
TEY =
Tax-free equivalent yield
(1 − SMTB )(1 − FMTB )
4.2%
= 6.97%
(1 − .10) (1 − .33)
Note: The denominator is .9 × .67 = .603.
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Answer. The tax-free bond has a TEY of 6.97%, which is higher than the
5.5% yield of the corporate bonds. Based just on yield, Brad would choose
the municipal bond. Note how the savings on state income taxes increases the
taxable equivalent yield from the previous problem.
Now if instead you knew the taxable yield was 6.97%, and wanted to know
what the tax-free equivalent was, you simply multiply the 6.97% by (1 –
SMTB) (1 – FMTB):
6.97% × (1 – .10) (1 – .33) = 6.97% × .603 = 4.2%
You could have several situations on the CFP exam where this calculation
will be necessary, so make sure you are comfortable with this calculation.
Note: If a taxpayer does not itemize deductions then you can simply add
together the two tax marginal brackets, so if it is 33% federal and 10% state:
TEY =
4.2
= 7.37%
(1 − .43)
Bond Yield and Valuation Calculations
The keystrokes for computing the price, yield-to-maturity, and yield-to- call for
bonds are the same as those used for single sums combined with annuities. The
single sums are the present value of the bond (the purchase price or current
market price of the bond) and the future value of the bond (generally $1,000).
The annuities are the semiannual coupon payments. On the HP-10BII+ financial
calculator, use the top row of keys for bond problems. The top row contains five
variables (N, I/YR, PV, PMT, and FV). Input four of the variables and solve for
the unknown fifth variable.
When performing these types of bond calculations, make the following
assumptions unless the problem specifically states otherwise.
1. The face value is $1,000. This is input as a positive number in FV since it is
money that is paid to the client when the bond matures.
Chapter 1: Valuation of Bonds

11
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
2. Coupon interest is given as an annual percentage rate based on the face value
($1,000 unless stated otherwise). Coupon interest is paid twice a year, so a
payment is received every six months by the investor. Coupon payments are
a positive input into the calculator. The amount of each payment is found by
dividing the annual coupon interest earned by two.
Semiannual coupon payment (PMT) =
$1,000 × Annual coupon rate
2
3. Since payments are received twice a year, the number of compounding
periods (n) is twice the number of years left to maturity.
4. If a return on “comparable bonds of the same maturity and grade” (i) is given
as an input for a bond problem, it will be given as an average annual yieldto-maturity. If you are calculating the price of a bond, this annual rate is a
necessary input.
5. There are six months until the next semiannual coupon interest payment will
be paid to the investor. This means that bond problems should be calculated
as if each payment occurs at the end of each period of n. This is an ordinary
annuity type of problem.
6. The present value of the bond, PV, is entered as a negative number because
this is considered to be a cash outflow. Any time an investor spends money,
or purchases an investment, the amount is entered as a negative number.
One caveat when doing bond yield calculations: Any rate of return (also called
internal rate of return, or IRR) assumes any interest payments are being
reinvested at the same rate. With zero-coupon bonds this is the case, since there
are no actual interest payments to reinvest, and thus no reinvestment risk.
However, with coupon bonds any YTM and YTC calculations are generally
going to be close, but will not necessarily reflect the true overall return the
investor achieves. In high-interest-rate environments the investor may not be able
to reinvest any interest payments at as high a rate as the bond is paying. For
example, owning a 10% bond and receiving interest payments when current rates
are at 7%. The opposite happens in low-interest-rate environments when interest
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
payments may be reinvested at higher rates than the bond is paying—for
example, reinvesting interest from a 5% bond when interest rates are at 7%. Just
realize that this is a potential drawback of any IRR calculations, including the
IRR calculations we did involving unequal cash flows in Module 5.
Calculating the Price of a Bond
Calculating the price of a bond—its intrinsic value—is primarily a function of
interest rates. As interest rates change, so will the intrinsic value of a bond. It is
important to remember that the “I” function on the calculator is reserved for
current interest rates (current YTM). The coupon rate of the bond is converted
into a semiannual coupon and entered as a payment.
Scenario 1. For example, what is the price (intrinsic value) of a bond with a
$1,000 face value, a 10% coupon, and three years to maturity, if comparable
bonds of the same maturity and grade are yielding 11.5%?
The 10% coupon ($100) will be converted into a $50 payment ($100/2 to reflect
the semiannual payment).
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
3, SHIFT,
xP/YR
11.5
?
50
1,000
Answer: $962.83
HP-12C:
N
I/YR
PV
PMT
FV
6
5.75
?
50
1,000
Answer: $962.83
Chapter 1: Valuation of Bonds

13
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Calculating the Price of a Zero-Coupon Bond
Scenario 2. What is the intrinsic value (or price) of a zero-coupon bond with a
$1,000 face value, a YTM of 8.20%, and nine years to maturity?
Remember that you assume semiannual compounding for all bond calculations,
unless specifically told otherwise. This is important with zeroes so that you are
comparing apples to apples. Since we are using semiannual compounding on
coupon bonds, we need to use semiannual compounding on zero-coupon bonds.
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
9, SHIFT,
xP/YR
8.20
?
0*
1,000
Answer: $485.16
HP-12C:
N
I/YR
PV
PMT
FV
18
4.10
?
0*
1,000
Answer: $485.16
Note: Since there is no payment, you do not need to enter any payment amount
in order to solve for this problem; however, you can enter “0” if you wish.
Calculating Current Yield
Scenario 3. What is the current yield of a bond trading at $965, with a 6%
coupon, and 20 years until maturity?
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Remember that current yield is simply the annual coupon divided by the current
price. In this case we have a $60 annual coupon amount with a current price of $965.
$60/$965 = .0622 = 6.22%
The problem with the current yield is that it does not take into account any price
movement that will take place from the current price back to either the call price
(typically a slight premium over par), or the maturity price (par). In the case of
our discount bond in Scenario 3, the current yield is understating the total return
that the investor will achieve because it does not take into account the fact that
the bond will move from $965 back to $1,000 at maturity. The opposite happens
with premium bonds (bonds selling for over $1,000). The current yield on a
premium bond will overstate the total return that the investor will achieve
because it does not take into account the fact that the bond will decline from the
premium price (let’s say $1,030, for example) back to $1,000 at maturity. It is
important that an investor consider both the current yield and the yield-tomaturity (as well at the yield-to-call if there is a call feature) prior to making an
investment decision.
Figure 1 shows a way to visualize which yield generally is going to be the
highest, and which the lowest when dealing with bonds. Note that YTM is in the
middle for both premium and discount bonds.
Figure 1: Bond Trading at a Premium
CY = current yield
YTM = yield to maturity
YTC = yield to call
Chapter 1: Valuation of Bonds

15
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Figure 1 shows a bond trading at a premium (the left side of the seesaw is now
higher). Note that the current yield will now be the highest, the yield-to-maturity
next, and the yield-to-call the lowest. This is because YTM and YTC will take
into account the accretion down from the premium price back to par. Yield-tocall will be the lowest yield since if the bond is called it will be before the bond
matures, meaning the accretion back to par (or a number close to it) will be that
much faster. An investor should be aware of all three yields, and under the worstcase scenario would have the bond called, which would result in the lowest yield.
Figure 2: Bond Trading at a Discount
CY = current yield
YTM = yield to maturity
YTC = yield to call
Figure 2 shows a bond trading at a discount (the left side of the seesaw is now
lower). Note that the current yield will now be the lowest, the yield-to-maturity
next, and the yield-to-call the highest. This is because YTM and YTC take into
account the accretion up from the discount price back up to par.
Note that the seesaw would be level if the bond is trading at par. Assuming there is
no call premium, the current yield, the YTC, and the YTM would all be the same.
Normally it is premium bonds that stand the highest likelihood of being called.
This is because bonds trade at a premium when interest rates go down, and the
issuing party of the bond often may call the bond and then turn around and
borrow money at the lower current rate. For example, if a company has a 7%
bond outstanding and current rates are at 6%, the company could call the 7%
bond and then borrow at 6%, thereby saving 1% in interest charges. Discount
bonds, on the other hand, will normally not be called, since bonds trade at a
discount when interest rates go up, and the issuer of the bond will not call a bond
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
because then if they borrow it will be at a higher rate. For example, let’s say a
company has this same 7% bond, and current rates are now at 8%. There is no
incentive to call this bond based on interest rates, since borrowing costs have
now gone up. The bond may be called for other reasons, but it would not be
called based just on interest rates.
Calculating the Yield-to-Maturity for a Bond Investment
Note: Most questions to be solved with a financial function calculator give three
values ask to solve for a fourth. The exceptions to this involve calculating a
bond’s price (intrinsic value), its yield-to-maturity, and its yield-to-call. For these
problems, four values are given and the fifth value is calculated, as seen in the
subsequent examples.
Scenario 4. What is the YTM (IRR) on an investment in a bond with a $1,000 face
value, a current market price of $966, a 10% coupon, and three years to maturity?
Set the calculator to “end.”
Remember that for bond calculations you will always be converting the coupon
rate into a payment—in this case, 10% of $1,000 is $100, divided by 2 for
semiannual payments gives you a payment of $50.
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
3, SHIFT,
xP/YR
?
(966)
50
1,000
Answer: i = 11.37%
HP-12C:
N
I/YR
PV
PMT
FV
6
?
(966)
50
1,000
Answer: i = 5.6846, 2, x, = 11.37%
Chapter 1: Valuation of Bonds
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17
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Notice that for these problems the PMT and FV are positive values and the PV is
a negative value. This can be remembered by thinking of buying a bond (PV) as a
cash outflow and the PMT and FV as positive cash inflows, as interest and
principal are paid to the investor. Inputting all three of the values as positives will
result in a no solution to the problem.
When doing bond calculations, a good double-check is just to make sure the
answer makes sense. For example, the calculation we just did involved a discount
bond, which means our YTM should come out higher than our coupon rate; and
it did (11.37% vs. 10.0%).
Scenario 5. What is the yield-to-maturity of (IRR) of a zero-coupon bond with a
current market price of $360, and 22 years until maturity?
Remember to use semiannual compounding with zeroes.
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
22, SHIFT,
xP/YR
?
(360)
0*
1,000
Answer: i = 4.70%
HP-12C:
N
I/YR
PV
PMT
FV
44
?
(360)
0*
1,000
Answer: i = 2.3491, 2, x, = 4.70%
Note: Since there is no payment, you do not need to enter any payment amount
in order to solve for this problem; however, you can enter “0” if you wish.
Calculating the Yield-to-Call for a Bond Investment
Calculating yield-to-call (YTC) for a bond involves using the same keys on the
calculator as yield-to-maturity (YTM). The call date will be before the maturity
date, meaning the number of compounding periods will be less. The other
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Valuation & Analysis of Fixed-income Investments
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difference is that there is often a call premium paid to the investor if the bond is
called prior to maturity. This call premium usually is not much, perhaps $10 or
$20 on a $1,000 bond (1% to 2% premium), but it does provide some extra return
to the investor to help compensate for the bond being called before maturity.
Scenario 6. What is the YTC on an investment in a bond with a call price of
$1,020, a current market price of $1,040, a 7% coupon, and eight years until call?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
8, SHIFT,
xP/YR
?
(1,040)
35
1,020
Answer: 6.54%
HP-12C:
N
I/YR
PV
PMT
FV
16
?
(1,040)
35
1,020
Answer: 3.272, 2, x, = 6.54%
Putting It All Together—Yield Calculations
Scenario 7. Natasha purchases a 6.0% coupon bond for $985.00. The bond
matures in 20 years, and is callable in 10 years at $1,010. What is the current
yield, yield-to-maturity, and yield-to-call for this bond?
Current yield: $60/$985 = .0609 = 6.09%
YTC
YTM
30 pmt
30 pmt
(985) PV
(985) PV
1,010 FV
1,000 FV
20 N
40 N
(10, SHIFT, N on
HP-10BII+)
(20, SHIFT, N on
HP-10BII+)
I = 6.28%
I = 6.13%
Chapter 1: Valuation of Bonds
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19
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This is a discount bond, so if we refer to the previous yield seesaw this means
that YTC should be the highest, then YTM, and current yield the lowest; and this
is the case.
Scenario 8. Boris has also purchased a bond, and he has paid $1,035. It has an
8% coupon and matures in 25 years. There is a call provision in 12 years at
$1,005. What is the current yield, yield-to-maturity, and yield-to-call?
Current yield: $80/$1,035 = .0773 = 7.73%
YTC
YTM
40 pmt
40 pmt
(1,035) PV
(1,035) PV
1,005 FV
1,000 FV
24 N
50 N
12, SHIFT, N on
HP-10BII+
25, SHIFT, N on
HP-10BII+
I = 7.58%
I = 7.68%
This is a premium bond, so if we refer to the previous yield seesaw this means
that YTC should be the lowest, then YTM, and current yield the highest, and this
is the case.
Financial planners who provide guidance on individual bonds need to understand
the various yields that can be calculated, and their ramifications for the investor.
This becomes especially important when bonds are near or past a call date. A
high YTM is of little consequence if a bond ends up being called well before
maturity. In addition to yields, credit quality is important, and this was touched
on in Module 6 and will be covered in more detail later in this module.
Generally, the lower the credit rating, the higher the cost of capital. And finally,
volatility is important, and this is measured by duration, which will be covered
next.
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Chapter 2: Duration
Reading this chapter will enable you to:
7–3
Understand the concept of duration, and calculate change in price
using duration.
D
uration gives us a measure of the approximate price volatility for bonds
given a change in interest rates. As such, it is a measure of interest rate
risk. So if a bond (or a bond mutual fund) has a duration of 4, and
interest rates were to rise 1%, the bond would then decline in price about 4%. If a
bond has a duration of 9, and interest rates were to fall 1%, the bond would rise
in price about 9%. Duration enables us to look at bonds (and bond portfolios and
bond mutual funds) beyond just the yield and also to compare the interest rate
risk of bonds with different coupon rates and maturities. Morningstar provides
the durations of funds it follows. Consider the following Vanguard funds:
Fund
SEC Yield
Duration
Vanguard Short-Term Bond Index
0.51%
2.7
Vanguard Intermediate-Bond Index
1.69%
6.4
Vanguard Long-Term Bond Index
3.38%
14.8
Source: Vanguard.com, December 7, 2012
In a declining interest rate environment, the higher the duration, the greater the
returns. However, in a rising interest rate environment, high durations will result
in the greatest losses. The Vanguard Long-Term Bond Index fund has a duration
of 14.8, so if interest rates were to fall 1% the fund would be up approximately
14.8%. However, if interest rates were to rise 1%, the fund would decline
approximately 14.8%.
Duration enables advisers and investors to assess interest rate risk when
purchasing bonds (and bond mutual funds). For example, looking at the previous
table, the Vanguard Long-Term Bond Index has the highest yield, at 3.38%, and
the Vanguard Short-Term Bond Index has the lowest yield, at 0.51%. If that were
Chapter 2: Duration
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all we were looking at, then the higher yield looks more attractive. But the
pertinent question is “How much more risk am I taking for that additional 2.87%
in yield?” And duration provides that answer. If interest rates were to suddenly
move 1% in the wrong direction (meaning higher), then the Vanguard ShortTerm Bond Index fund would only move down about 2.7%, whereas the
Vanguard Long-Term Bond Index fund would move down about 14.8%, which is
a big difference. So advisers and investors have to ask themselves whether taking
on that additional risk is worth it for the additional yield.
Duration is helpful in purchasing bonds and bond mutual funds based on
expectations for interest rates. If expectations were for declining interest rates,
then you would increase the durations. However, if expectations were for interest
rates to rise, you would lower the durations. Duration can also help in matching
bond funds to a client’s risk tolerance. For example, if you have a client who is
extremely risk averse, you would keep durations lower.
We discussed the flaw in calculating yield-to-maturity (internal rate of return) for
bonds earlier. The problem with this calculation is that it assumes any interest
payments are reinvested at the same rate: the yield-to-maturity (internal rate of
return). In other words, if your YTM (IRR) is 7%, then any interest payments are
assumed to be reinvested at 7%. This is obviously not the case, as interest rates
move, you have two forces working against each other. If interest rates rise, bond
prices will fall, but you will be able, then, to reinvest any interest payments at a
higher rate. And if interest rates fall, the bond price will rise, but any interest
payments will then be reinvested at lower rates. These forces (reinvestment risk
and interest rate risk) will exactly offset each other at some point in time, and that
point in time will be a bond’s duration.
Now that you have a basic understanding of how duration is used and what it is,
let’s take a look at how it is calculated.
Duration is the weighted-average amount of time (measured in years) that it takes
to collect a bond’s principal and interest payments. This is why you often see
duration expressed in years. For example, the Vanguard Long-Term fund above
may be expressed as a duration of “14.8 years.” Don’t let this confuse you, as
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you will see the calculation is essentially a weighted average in years, but
duration’s value for the financial planner is as a measure of interest rate risk, as
discussed above. Duration is used by the planner to calculate the expected change
in bond price when interest rates change. As we saw, interest rate sensitivity and
interest rate risk are directly related to duration. Duration for a bond is similar to
beta for a stock, in that both duration and beta are volatility measures that are
multiplied by the expected change in interest rates (bonds) or the expected
market risk premium (stocks) to arrive at an expected change in the market value
of the subject bond or the expected risk premium of the subject stock. High
durations, like high betas, indicate high risk and high volatility; low durations
indicate low risk and low volatility. Treasury bills have low durations and 30year zero-coupon bonds have high durations.
Bonds have different characteristics and features. One bond may have a 20-year
maturity, a 7% coupon, and an AAA rating. A second bond may have a 12-year
maturity, an 8% coupon, and a BB rating. The market interest rate for the AAA
bond may be 6%, and the market rate for the BB bond may be 7.5%. Investors
may have a difficult time applying this information to analyze which of the two
bonds will be the most volatile when interest rates change. Duration is a relative
measure of the data that allows investors to determine which of the two bonds is
likely to be the most volatile.
Formulas are used to compute duration. The best way to understand how the
formulas work is to recognize that duration is a computation of the time-weighted
average term-to-maturity of a bond’s cash flow. The time weighting means that
cash flows that are received later receive a proportionately higher weight than
cash flows that are received sooner. Therefore, the large $1,000 payment of
principal at a bond’s maturity tilts the scale to the right.
A simple way to think of duration is viewing it as a seesaw. The fulcrum point of
the seesaw is at the duration point. In other words, the time-weighted average of
the bond’s cash flows is at the point where the seesaw balances. Consider Figure
3, which follows:
Chapter 2: Duration
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Figure 3: A Graphical Representation of Duration
Fulcrum
Point
Each column on top of the seesaw in Figure 3 represents the present value of the
cash flows to the investor. The small columns are the present values of the
semiannual interest payments, and the larger column at the right end is the
present value of the $1,000 par value of the bond plus the final semiannual
coupon payment.
Note that the present values of the semiannual interest payments decrease over
time (the columns are not drawn to scale). Thus, the present value of a coupon
payment received 10 years from today is less valuable than the present value of a
coupon payment received one year from today. The declining present values are
offset by the weighting, which becomes heavier with each succeeding cash flow.
The present value of the large $1,000 payment received when the bond matures is
weighted heavily because it is a much larger dollar amount than the interest
payments being received semiannually. This means that proportionally more weight
is on the right side of the seesaw, even though the present value of the $1,000 is not
very large. Because of the weighting of the present values of cash flows, the fulcrum
will be closer to the right end of the seesaw than to the left end.
To see how duration might change as coupon rates, market interest rates, and time to
maturity change, consider how the fulcrum point moves as these factors change.
If we have several bonds that are equal in all respects except that their coupon
rates are different, then the price of each bond will also be different because of
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
the inverse relationship between interest rates and bond prices. Bonds with higher
coupons (and, therefore, greater cash flows), discounted at the current market
interest rate, will have higher present values for each coupon payment than bonds
with lower coupons (and cash flows). Thus, the seesaw tilts downward on the left
side, and the center of gravity moves to the left. (The weighted present value of
the $1,000 principal payment is the same for all bonds of the same maturity.) In
other words, bonds with higher coupon rates have lower durations and are less
volatile to interest rate changes than bonds with lower coupon rates. Note that the
duration of a zero-coupon bond is equal to its maturity, since the only cash flow
from a zero-coupon bond is the $1,000 principal payment at maturity. The
duration of a zero-coupon bond will always be greater than the duration of
coupon bond of the same maturity.
If market interest rates are higher, but the coupon rate and maturity of a bond stay
constant, then the present value of each coupon payment and of the par value will
decrease. The fact that the cash flows are time weighted means that the present
value of the $1,000 par value payment decreases proportionately more.
Therefore, the right side of the seesaw will rise, and the center of gravity will
shift to the left. So, an increase in market interest rates decreases duration,
assuming that all other factors are equal.
If the maturity of a bond increases, but the coupon and market interest rates stay
constant, then the right side of the seesaw becomes longer, and the center of
gravity shifts to the right. Therefore, an increase in maturity increases duration,
assuming that all other factors are equal.
These principles can be summarized as follows: Duration is inversely related to
changes in market and coupon interest rates, and it is directly related to changes
in maturity. The following matrix may help.
Coupon
Current Market
Interest Rates
Maturity
Increases Duration
Decreases
Decreases
Increases
Decreases Duration
Increases
Increases
Decreases
Chapter 2: Duration
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Note that there is an inverse relationship between duration and both coupon rates
and current market interest rates—as interest rates increase duration decreases (or
as interest rates decrease then duration increases). However, with maturity there
is a tandem relationship, so as maturity increases so does duration (or as maturity
decreases so does duration). Consider the following bonds, and determine which
has the highest duration of the two:
Scenario
Bond Alpha
Bond Omega
A
5% coupon with 10-year
maturity
5% coupon with 15-year
maturity
B
6% coupon with 8-year maturity
7% coupon with 8-year maturity
C
7% coupon with 15-year
maturity
0% coupon with 15-year
maturity
Answers. Scenario A: Bond Omega; Scenario B: Bond Alpha; Scenario C: Bond
Omega.
In Scenario A, both bonds have the same coupon rate; however, Bond Omega has
a 15-year maturity compared to Bond Alpha’s 10-year maturity. The longer the
maturity, the higher (longer if expressed as years) the duration, so Bond Omega
has the higher duration.
In Scenario B, both bonds have the same maturity; however, Bond Alpha has a
6% coupon compared with a 7% coupon for Bond Omega. The lower the coupon
rate, the higher (longer) the duration. As the coupon rate declines, duration
increases, so Bond Alpha will have the higher duration.
In Scenario C, both bonds have the same maturity; however, Bond Omega is a
zero-coupon bond compared with a 7% coupon for Bond Alpha. Once again, the
lower the coupon rate, the higher (longer) the duration. Since the entire payment
is received at maturity for zero-coupon bonds, a zero-coupon bond’s maturity and
duration are the same. So Bond Omega’s duration is 15.
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Valuation & Analysis of Fixed-income Investments
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Duration Computations
Calculating duration for bonds is not as simple as computing the price or YTM.
A rather complex-looking formula is provided on the CFP Board exam formula
sheet, but fortunately there are only three inputs. The formula for computing a
bond’s duration is as follows:
Dur =
1 + y (1 + y) + t(c − y)
−
y
c[(1 + y)t − 1] + y
where
y
=
Yield-to-maturity per period
c
=
Coupon rate per period
t
=
Number of periods until maturity (think “t” for time)
If the compounding period is annual, then all numbers reflect annual rates; if the
compounding period is semiannual, then the number of periods is twice the
number of years, and the coupon rate and YTM are one-half of the annual rates.
Annual compounding. What is the duration of a bond that has 20 years to
maturity and a coupon of 8% when the current market interest rate is 6%?
Assume annual compounding.
Dur =
1 + y (1 + y ) + t(c − y )
−
y
c[(1 + y ) t − 1] + y
1 + .06 (1 + .06) + 20(.08 − .06)
−
=
.06
.08[(1 + .06) 20 − 1] + .06
Chapter 2: Duration
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27
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
1.06
1.06 + .4
−
=
.06 .08[2.21] + .06
1.46
17.67 −
=
.24
11.59 periods
Answer: 11.59 years
Since the compounding period is annual, the 11.59 periods is also the number of
years.
Note: In the brackets in the denominator you need to take “1 + .06” to the 20th
power, and then subtract 1:
HP-10BII+
HP-12C
1.06
1.06
SHIFT
ENTER
Yx
20
(on the “x” key)
20
Yx
=
=
3.2071
3.2071
(3.21 rounded)
(3.21 rounded)
Semiannual compounding. What is the duration of a bond that has 20 years to
maturity and a coupon of 8% when the current market interest rate is 6%?
Assume semiannual compounding.
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Valuation & Analysis of Fixed-income Investments
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20 × 2 (semiannual) =
40 for “t”
.08 /2 =
.04 for “c”
.06/2 =
.03 for “y”
Dur =
1 + y (1 + y ) + t(c − y )
−
y
c[(1 + y ) t − 1] + y
1 + .03 (1 + .03) + 40(.04 − .03)
−
.03
.04[(1 + .03) 40 − 1] + .03
1 + .03
1.03 + .40
−
=
.03
.04[2.26] + .03
34.33 −
1.43
= 22.41 periods ÷ 2 = 11.21 years
.12
Answer: 11.21 years
Since the compounding period is semiannual, the duration in periods must be
divided by two to get the duration in years. The semiannual computation should
result in a lower duration because compounding takes place more frequently than
with annual compounding.
This formula is found on the CFP Board Certification Examination formula
sheet, and the calculation is being tested more frequently now than it has been in
the past.
Alternative calculation. Here is an easier way to get at an approximation of
duration just using the bond calculations you have already learned. The formula
(which you will need to memorize, it is not provided for you) is:
Duration =
Priceif yields decline − Priceif yieldsrise
2(current price)(.01)
Chapter 2: Duration

29
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
First we need to calculate the current price of the bond. Remember our scenario:
What is the duration of a bond that has 20 years to maturity and a coupon of 8%
when the current market interest rate is 6%? Assume semiannual compounding.
Current Bond Price
40 pmt
1,000 FV
40 N (20, SHIFT, n, on HP-10BII+)
6 I (3 I on HP-12C)
PV = 1,231.15
Now, don’t clear the calculator and find out what the price would be if interest
rates were to increase by 1%, and decrease by 1%:
Interest rates increase
by 1%
Interest rates decrease
by 1%
6 I (3 I on HP-12C)
7 I (3.5 I on HP-12C)
5 I (2.5 I on HP-12C)
PV = 1231.15
PV = 1106.78
PV = 1376.54
Current Bond Price
40 pmt
1,000 FV
40 N (20, SHIFT, n, on
HP-10BII+)
So now let’s plug in the numbers to the formula, and for simplicity’s sake the
bond prices are rounded up to the nearest dollar amount:
1,377 − 1,107
270
=
= 10.97
2(1,231)(.01) 24.62
This number calculated this way will come out slightly lower than the longer
calculation using the formula found on the formula sheet. In this case we came
up with 10.97, and with the other formula we came up with 11.21. This is a much
faster way for many to come up with an approximation of duration. If you use
this method, count on coming up with a number that is approximately 0.20 to
0.25 lower than the figure you will arrive at using the provided formula.
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Even if you do not have to do the calculation on the CFP Board exam it is very
important that you understand what duration is and how it is used. You can
expect at least several conceptual questions dealing with duration, and you need
to understand how it can be used to measure the risk and volatility of bonds.
Change in bond price using duration has been tested more frequently, and that
will be covered next.
Change in Bond Price Using Duration
Duration is a useful tool to help investors determine the expected change in the
price of a bond for a given change in interest rates. A rule-of-thumb approach is
to multiply the duration by the expected change in rates. Using the data from the
examples above, we could say that if interest rates are expected to change 1%,
the approximate percentage change in the price of the bond is 11.21% (when
semiannual compounding is used). If rates are expected to change one-half of
1%, then the expected percentage change in bond price is 5.61% (11.21% × .50).
For a more precise answer, the following general formula is used.
 Δy 
Δ P = −D 

1 + y 
where
ΔP
= Change in price
–D = Duration of the bond (expressed as a negative)
Δy = Expected change in interest rates
y = Current yield-to-maturity (current interest rate)
Note that “y” is the current yield-to-maturity (current interest rate), not the
coupon rate. You do not need the coupon rate when using this formula; the
coupon rate has already been taken into account when calculating duration.
Chapter 2: Duration
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Example. Assume there is a bond with a 10% coupon with a current market price
of $1,030, a duration of 3.5 (using annual compounding), and interest rates are
currently at 8%. What is the approximate price change in this bond if interest
rates rise 1%? (Note that this would be 100 basis points, which is .0100.)
ΔP
= Change in price
-D = –3.5
Δy = +.0100
y = .08
 Δy 
Δ P = −D 

1 + y 
ΔP = −3.5 ×
.0100
1.08
–3.5 × .0093 = –0.0324
Note that the –.0324 means a 3.24% decline in the bond price. So if we multiply
this by the current price of the bond ($1,030 in this case) we can obtain the
approximate price movement:
–.0324 × $1,030 = –33.38
$1,030 – $33.38 = $996.62
Using this formula, we can see that the bond that is currently at $1,030 and
would decline to approximately $997 if interest rates were to increase by 1%.
Note that there is a negative sign in front of the duration number in the formula.
This is done because if interest rates go up it would be a negative duration
number times a positive interest rate number, meaning a negative answer (the
bond going down in price, as in our example). Whereas if interest rates go down
there would be a negative duration number times a negative change in interest
rates, meaning a positive answer (the bond going up in price),
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Let’s look at the above example, but this time have the interest rate falling 0.5%.
(Note that this would be 50 basis points, which is .0050.)
ΔP = −3.5 ×
−0.0050
1.08
–3.5 × –.0046 = +0.0162*
+.0162 × $1,030 = +$16.69
Note that the +.0162 means a 1.62% increase in the bond price.
$1,030 + $16.69 = $1,046.69
We see that the bond, which is currently trading at $1,030, would rise to
approximately $1,047 if interest rates were to decline 0.5%.
The above two examples assumed annual compounding—we used the 8% current
yield-to-maturity. We can also do this calculation using semiannual
compounding by simply dividing the 8% by 2: .08/2 = .04. Everything else
remains the same (although to be more accurate we should recalculate duration
using semiannual compounding rather than annual compounding, which would
result in a slightly lower duration than 3.5; however, for simplicity’s sake we will
continue to use 3.5). Here is how the two examples above would look using
semiannual compounding:
ΔP = −3.5 ×
.0100
1.04
–3.5 × .0096 = –0.0337*
–0.0337 × $1,030 = –$34.66
Note that the –0.0337 means a 3.37% decline in the bond price.
$1,030 – $34.66 = $995.34
Chapter 2: Duration

33
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Note that the change in price is now –$34.66 (down 3.37%), compared with –
$33.38 (down 3.24%) with annual compounding. Semiannual compounding will
result in a larger number (loss in this case) due to the additional compounding.
Here is how our second example would look with interest rates falling 0.5% and
using semiannual compounding:
ΔP = −3.5 ×
−0.0050
1.04
–3.5 × –.0048 = +0.0168*
+0.0168 × $1,030 = +17.33
Note that the +0.0168 means a 1.68% increase in the bond price.
$1,030 + $17.33 = $1,047.33
Note that the change in price is now +$17.33 (up 1.68%), compared with
+$16.69 (up 1.62%) with annual compounding. The additional compounding has
resulted in a slightly larger number.
This is the extent to which you need to know the calculation for change in price
using duration. The concept of “modified duration,” which adjusts for comparing
annual and semiannual compounding, is covered next.
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Modified Duration
Refer back to the calculations that were done for duration, and we came up with
11.59 years for annual compounding, and 11.21 years for semiannual
compounding. The problem is that the durations for the bonds were computed
using different assumptions (annual versus semiannual compounding). Therefore,
the bonds’ durations must be adjusted to account for this difference so that we are
comparing apples to apples when using duration to determine the price sensitivity
of two or more bonds. The method used to do this is called modified duration.
Modified duration is calculated for each bond by using part of the preceding
formula. Modified duration is then multiplied by the expected annual percentage
change in market yield to obtain the percentage change in price. If the formula
above were rewritten in this manner, it would look like the following formula.
ΔP =
−D
× Δy × PB (for annual compounding)
1+ y
ΔP =
−D
× Δy × PB (for semiannual compounding)
1+ y
2
The first element of the equation, after the equal sign and before the first
multiplication sign, is the computation for modified duration. The computation of
modified duration for the two bonds in the preceding duration computations is as
follows:
−11.59
= − 10.93 (for annual compounding)
1.06
−11.21
= − 10.88 (for semiannual compounding)
1.03
Chapter 2: Duration
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Modified duration adjusts for the fact that different assumptions were used, and it
standardizes both so that you are comparing apples to apples. The durations now
are virtually equivalent, with only a 5 basis point difference (between 10.93 and
10.88), compared to the 38 basis point difference (11.59 compared with 11.21) if
the raw figures (called the Macaulay duration) were used. Also note that these
durations of 10.93 and 10.88 are much closer to the 10.97 duration we came up
with using an alternative approach (rather than using the provided formula) for
calculating duration:
Duration =
Priceif yields decline − Priceif yieldsrise
2(current price)(.01)
Computing modified duration is similar to computing risk-adjusted returns for
stocks. If two stocks have different standard deviations and different returns,
computing each stock’s risk-adjusted return standardizes both stocks so that they
can be compared with each other. Computing modified duration accomplishes
the same result for bonds. Once the modified durations are computed, they can be
multiplied by the expected change in interest rates to compute the expected
percentage changes in the prices of the bonds. As stated before, you will not need
to calculate modified duration. This brief description was provided to show how
duration can be adjusted (modified) for a more accurate representation of price
changes.
Convexity
Using duration to compute the expected price change given an expected change
in YTM assumes that a linear relationship applies to the change in YTM and
change in price. The linear relationship is considered valid for relatively small
changes in YTM, generally less than 1%. When the expected change in YTM is
greater, then the linear relationship does not apply. In other words, duration may
give us a good idea of price volatility given a 1% change in interest rate, but as
the price change increases it becomes less accurate. For example, given a
duration of 8, a 1% change in rate equates to approximately a 8% change in
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price, but a 2% change in rates does not equate to a 16% change in price, or a 3%
change in rates to a 24% change in price, etc. Convexity is a measurement that helps
to measure the impact of interest rate changes greater than 1%. With convexity, a
curvilinear (rather than a linear) relationship exists, as shown in Figure 4.
Figure 4: Convexity
In the figure, the straight line represents the linear relationship defined by
duration. Generally, straight bonds exhibit positive convexity, represented by the
upward-sloping line. As the curve shows, when market interest rates decline, the
actual price increase of the bond is greater than would be computed using only
duration; when market interest rates increase, the actual price decrease of the
bond is less than would be computed using only duration. So, the general rule is
that duration understates the price increase when rates fall and duration
overstates the price decrease when rates rise. Positive convexity is a desirable
characteristic to have in bonds, especially during periods when interest rates
exhibit high volatility.
Below is an example of what happens when interest rates decrease and a bond
has a positive convexity:
Chapter 2: Duration
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Duration
% Change in
Interest
Rates
Approximate Price
Change Without
Convexity
Approximate
Price Change
With Positive
Convexity
3
–1%
+3%
+3%
3
–2%
+6%
+6.5%
3
–3%
+9%
+10%
Note that this table is just for illustration purposes as different bonds have
varying degrees of convexity. But you can see that as the percentage change in
interest rates increases, the price change in the bond is more than duration alone
would explain.
Let’s take a look at what happens when interest rates increase:
Duration
% Change in
Interest Rates
Approximate
Price Change
Without
Convexity
Approximate
Price Change
With Positive
Convexity
3
+1%
–3%
–3%
3
+2%
–6%
–5.5%
3
+3%
–9%
–8%
Notice now with interest rates increasing, the price change in the bond is less
than duration alone would explain; in other words, the bond does not go down in
value as much.
Negative convexity is the opposite, with a bond declining more in value than
duration alone would explain in a rising interest rate environment. Also with
negative convexity, a bond will not rise as much in value as duration alone would
indicate in a declining interest rate environment. Callable bonds and mortgagebacked bonds are typical examples of bonds with negative convexity. The
previous graph visually shows how mortgage-backed bonds and callable bonds
do not increase much in price when interest rates fall, and go down in price more
when interest rates rise.
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Convexity can be calculated; its calculation gives the mathematical difference
between the actual price-YTM curve and the zero-convexity straight line that
represents the price change expected solely due to duration (the difference
between the curved line and the straight line in the graph). The sum of the price
change expected due to duration and the price change expected due to convexity
equals the total expected price change of the bond. You are not expected to make
this calculation on the CFP exam, however. Simply knowing the impact that
convexity has on the true expected price change due to a change in interest rates
is sufficient.
Chapter 2: Duration
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Chapter 3: Bond Volatility &
Constructing Portfolios
Reading the first part of this chapter will enable you to:
7–4
Analyze the relationships among bond ratings, yields, maturities, and
durations to determine comparative price volatility.
T
he reasons for a bond’s volatility are similar to the reasons for a stock’s
volatility. Bonds have both systematic and unsystematic risk.
Unsystematic risk is a function of the underlying company itself. A
bond’s unsystematic risk is reflected in the bond’s credit rating. The top four
credit ratings (AAA, AA, A, and BBB) generally indicate a company with strong
credit and, therefore, one with low unsystematic risk. Credit ratings below BBB
reflect companies with higher unsystematic risk. In general, the bonds of
companies with high credit ratings have less business risk than the bonds of
companies with lower credit ratings.
The financial uncertainty of companies with lower credit ratings makes the
repayment of principal for their bonds more unpredictable. In general, when
interest rates rise, the spread between high-quality and low-quality debt widens;
when interest rates fall, the spread narrows. Investors assume that risk increases
as rates rise and decreases as rates fall.
Yields are also an indication of the credit risk of a company. To compensate
investors for a higher level of unsystematic risk, bonds with lower credit ratings
generally have higher coupons than bonds with higher credit ratings. As
discussed earlier, higher coupons help to lower duration, thereby helping to lower
the systematic risk of the bond. The amount by which duration is lowered in
high-coupon bonds is not significant, however.
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A direct relationship exists between a bond’s maturity and duration and the bond’s
volatility. Longer maturities and durations reflect higher volatility. For a portfolio of
bonds, the unsystematic risk associated with credit ratings and yields becomes less
important than the systematic risk associated with maturity and duration.
Therefore, investors should pay the most attention to a bond’s (or a bond fund’s)
maturity and duration when judging the relative potential volatility of a single
bond and of a portfolio of bonds. Investors who have a low capacity for volatility
should invest in short- to intermediate-term bonds; investors with a higher
capacity for volatility may invest in long-term bonds, zero-coupon bonds, and
high-yield bonds when they are confident about lower interest rates in the near
future. When they are less confident or when they expect higher interest rates in
the near future, they may sell their long-maturity, high-duration bonds and
reinvest in short-maturity, low-duration bonds.
Risk & Volatility
Reading the next part of this chapter will enable you to:
7–5
Assess how changes in variables affect bond risk and price volatility.
Bond default risk is primarily a function of credit rating. Bonds with lower credit
ratings have a higher degree of risk of loss of principal. Loss of principal is not
an issue otherwise, since a bond will return its $1,000 principal at its stated
maturity date.
Changes, or anticipated changes, in credit ratings can have an impact on a bond’s
price volatility. The prices of bonds for companies in financial difficulty may
decline sharply in anticipation of a possible downgrade in a bond’s credit rating.
Bonds that may be upgraded, especially from, say, BB to BBB, might see a large
increase in price. The reason for this is that BBB is the lowest rating included in
the larger category of investment-grade bonds—meaning that the bonds are of
sufficient quality to be available for investment by many institutions, such as
pension plans, endowments, etc. Therefore, an upgrade to this level may result in
Chapter 3: Bond Volatility & Constructing Portfolios
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a large increase in demand for the bonds from these institutions. Professional
high-yield bond investors attempt to limit their credit risk by buying seasoned
issues with intermediate maturities instead of new issues with long maturities.
The greatest changes in volatility are the result of changes in creditworthiness
and market interest rates. Therefore, bonds with high durations are subject to the
greatest degree of price volatility. Bond fund managers constantly readjust the
durations of their portfolios to minimize volatility risk if they anticipate higher
interest rates. Likewise, if they anticipate lower interest rates, they will extend
the durations in their portfolios to the extent allowed in their charters.
Individual investors can take similar actions with mutual funds, although such
actions can be offset by income taxes that flow from the transaction. Investors
can sell high-duration bond funds and buy low-duration funds when they
anticipate interest rate increases. They can move back into high-duration funds
when they anticipate interest rate decreases. In IRAs and 401(k) plans, the tax
consequences are not relevant, and such switching may be profitable.
Immunization
When investors have a specific goal to fund at the end of a known time horizon,
they can take specific steps to “immunize” the goal against interest rate and
reinvestment risk. Immunization is practiced primarily by institutional investors
managing pension plans and endowments (insurance companies), where future
funding needs are targeted by year over a long time horizon. Individual investors
also can immunize, but on a more limited basis, such as for ensuring that dollars
are available to fund a college education.
Immunization is the process of matching the duration (not maturity) of a bond or
a bond portfolio to the time horizon of a cash need. A single zero-coupon bond
with a duration (and maturity in the case of a zero) equal to the time until a child
starts college immunizes against the cost of a college education. A portfolio of
bonds with a duration equal to the year pension payments are required to be made
to retirees immunizes the pension plan against the liability due at that time.
Technically, immunization offsets interest rate risk and reinvestment risk. If
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interest rates rise after a portfolio is immunized, the falling bond value is offset
by the bond coupon cash flows, which are assumed to be reinvested at
increasingly higher rates, thereby offsetting the bond’s price decline, and
ensuring that the cash needed to fund the goal is available. If interest rates fall
after immunization, the decline in interest earned on reinvested coupon income is
assumed to offset by the increase in the value of the bond.
Institutional investors can use coupon bonds to immunize the multiple liabilities
typical of a pension or endowment plan, but individual investors must rely on
zero-coupon bonds. If individuals were to use coupon bonds, they would have to
sell one bond and purchase another bond several times over the time horizon,
since durations change as market interest rates change. The trading costs on the
odd lots typically purchased by individual investors would quickly neutralize the
benefits of immunization.
Another approach investors use to offset the impact of interest rate risk when
interest rates increase and reinvestment risk when interest rates decrease is to
construct laddered or barbell portfolios. Bond ladders and barbells allow an
investor with no opinion on the future direction of interest rates to be hedged for
either rising or falling rates.
In a ladder portfolio, bonds with maturities spread out over the time horizon are
used (e.g., buy 2-, 4-, 6-, 8-, and 10-year bonds). If interest rates increase over the
next two years, the 2-year bond is reinvested into a 10-year bond (since the
original 10-year bond now has an 8-year maturity) at a coupon higher than the
original 10-year bond. Although all bond prices have declined, the reduction in
time until maturity softens the impact. Because all the bonds will be held until
their maturity, the price decline will be offset by future price increases until the
par value is received at maturity.
In a barbell portfolio, the amount to be invested in bonds is divided between
short-term issues and long-term issues (e.g., 1-, 2-, 3-, 4-, and 5-year bonds and
21-, 22-, 23-, 24-, and 25-year bonds). If rates increase, the large price decline of
long bonds is softened by the small price decline of the short bonds; if rates
decrease, the large price increase of the 25-year bond is accompanied by a small
price increase of the 5-year bond.
Chapter 3: Bond Volatility & Constructing Portfolios
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In both ladders and barbells, the short-term bonds minimize losses if rates rise,
whereas the long-term bonds give the opportunity for significant price
appreciation if rates fall. Both allow investors to minimize the regret that
accompanies declines in bond values when interest rates rise, and to experience
the euphoria that accompanies increases in bond values when interest rates fall.
There is a third approach, called a bullet portfolio. With a bullet portfolio
maturities are concentrated in the intermediate-term maturity relative to shorter
and longer maturities. For example, you may have small amounts invested in 2-,
3-, 5-, and 7-year maturities, a substantial amount invested at 10 years, and then
small amounts invested again at 15, 20, 25, and 30 years.
All three approaches may have a similar weighted average portfolio duration. It’s
just that each is constructed in a different way.
Bond Swaps
The objective of a bond swap is to sell a position while simultaneously entering
into another position with the goal of achieving a better return or improving the
portfolio in some way. Swaps may be done to increase current yield or yield-tomaturity, or may be done to take advantage of yield spreads, to improve the
quality (rating) of the portfolio, or for tax purposes. Listed below are the most
common bond swaps.
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44
Pure yield pick-up swap. This involves swapping out of a lower-yield bond
into a higher-yielding bond, thus improving both current yield and yield-tomaturity. An example of when this can be done is when the yield curve is
upward sloping, providing greater returns in the longer-term maturities. An
investor would then sell a shorter-term maturity and move into a longer-term
maturity. A risk with this strategy is that it will increase duration, so if the
entire yield curve moves higher (interest rates increase), then the loss will be
greater with the longer-term bond.
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Valuation & Analysis of Fixed-income Investments
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
Substitution swap. A substitution swap takes advantage of when bonds are
temporarily mispriced. The bond that is substituted should be essentially the
same as far as maturity, quality, call features, and coupon. For example, there
may be two corporations that have the same A credit rating, and both have
7% coupon, noncallable, 15-year maturity bonds outstanding. One is priced
at a YTM of 7.5%, and the other 7.2%. So selling the bond with the YTM of
7.2% and purchasing the one with a 7.5% YTM would be an example of a
substitution swap. The risk here would be that there may be some other
reason why the one bond is yielding more than the other, such as the
company with the 7.5% YTM is about to be downgraded. If the one bond is
riskier than the other, then the substitution swap is not a wise move.

Intermarket spread swap. The intermarket spread swap is similar to the
substitution swap in that it is taking advantage of mispricing in the market.
However, in this case the swap is entered into because of perceived
mispricing between two sectors of the market, such as corporate bonds and
government bonds. For example, if the spread between corporate bonds and
government bonds is considered too wide, then the investor would sell the
government bonds and buy the corporate bonds. If the spread then narrows,
the corporate bonds will outperform the government bonds. Typically, the
spread between government and corporate bonds widens when the
economy slows or is in a recession. The reason for this is twofold. First,
there is the “flight to safety” into government bonds, which drives down
the yields of government securities. At the same time, the increased
business risk and bankruptcy risk for corporations will drive up the yields
on corporate bonds. This spread typically narrows again during times of
economic prosperity.

Rate anticipation swap. This is a play based on an investor’s opinion on the
direction of interest rates. If an investor believes interest rates are going to
fall, then shorter duration bonds will be sold and longer durations purchased.
Conversely, if an investor believes interest rates are going to rise, then longer
duration bonds will be sold, and shorter durations purchased.
Chapter 3: Bond Volatility & Constructing Portfolios
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Tax swap. A tax swap occurs when an investor sells a bond for a capital loss,
and then purchases a bond with similar characteristics from another issuer.
This enables the investor to recognize a capital loss for tax purposes while
still maintaining a similar bond position.

Reading the next part of this chapter will enable you to:
7–6
Evaluate investor profiles to recommend appropriate fixed-income
securities for purchase.
The two basic elements of a diversified investment portfolio are allocations to
financial assets (equities and fixed-income securities) and real (or hard) assets
(commodities, real estate, and natural resources). Within the financial assets
class, some proportion is allocated to equities and, generally, a smaller proportion
is allocated to fixed-income investments.
After making a decision to allocate some percentage of assets to fixed-income
investments, investors must decide which specific types of fixed-income
investments to make. Investors who are more concerned with stability of
principal and income will focus on some types of bonds or bond funds, such as
Treasury bills, money market funds, and funds with AAA-rated issues. Investors
who want to focus on capital gains will select other types of bonds or bond funds,
such as zero-coupon bonds, high-yield bond funds, or funds with long durations.
If an investor is in a 25% or higher marginal tax bracket, then tax-free bonds may
make more economic sense than taxable bonds. An investor in a higher marginal
tax bracket should always compute the taxable-equivalent yield to determine if
more after-tax income is possible in tax-free bonds than is possible in taxable
bonds. General obligation (GO) municipal bonds have traditionally been
considered safe because the municipalities can increase taxes to pay the bonds.
However, the financial strength of certain municipalities has been weakened
since the credit crisis of 2008, even to the point of bankruptcy in the 2012 cases
of Stockton, CA and San Bernardino, CA. In many cases, the biggest trouble spot
is the high pension obligations that both local and state municipalities have.
Therefore, the general assurance that municipalities can raise taxes to cover their
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obligations now comes into question so that each municipal bond, whether
general obligation or revenue, needs to be analyzed for the specific financial
strength backing them. This is best left to professional analysts, so most investors
should use such a professional or buy municipal bond mutual funds or ETFs.
Investors who buy taxable bonds and who are concerned about default risk
should consider Treasury securities. If they live in a state that has a state income
tax, the income from Treasury securities is excluded from the income reported on
state tax returns. In states with high state and local income taxes, the savings
could be substantial.
U.S. agency bonds might be appropriate for investors who want a current yield
that is higher than those available on Treasury bills, notes, or bonds. With the
exception of GNMA securities, agency issues are not guaranteed by the U.S.
government. Some agencies are callable; the degree of call protection should be
determined prior to purchase.
Investors who want a specific amount of money in the future, such as seven
years, should consider 7-year Treasury zero-coupon bonds. These bonds are free
from default risk and will provide the face value of the bonds in seven years. If
held in a regular account, income taxes need to be paid annually on the accrued
interest. However, this situation is no different from owning a mutual fund where
annual distributions are reinvested in additional shares so that the taxes on these
distributions will be paid with other funds, a common practice often encouraged
by investment advisers. Paying taxes each year on the accrued interest might be
worth doing so in exchange for the assurance of the lump sum needed in seven
years. For diversification, investors might consider bonds issued by other
countries for a portion of the fixed income investments in the portfolio.
Domestic bonds are issued locally by a domestic borrower and are usually
denominated in the local currency. For example, U.S. government bonds would
be considered a domestic bond. The same would apply for Germany or France
issuing government bonds—these would be considered domestic bonds. This also
applies for a corporation issuing debt in their respective country—these would
also be considered domestic bonds since these are bonds issued locally by a
domestic borrower and are usually denominated in the local currency. The United
States makes up approximately 41% of the world’s domestic bond market.
Chapter 3: Bond Volatility & Constructing Portfolios
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The international (foreign) debt market, on the other hand, consists of bonds
issued in a local market by a foreign borrower, and usually denominated in the
local currency. Yankee bonds, which are issued by foreign corporations or
governments, but are sold in the United States and denominated in U.S. dollars,
fall into this category. This allows a U.S. investor to buy the bond of a foreign
firm without having to deal with exchange rate risk. Each country has their own
name for foreign bonds issued in their country in their own currency. For
example, in the UK they are called Bulldog bonds, and in Japan they are called
Samurai bonds. Eurobonds are also another type of international bond, and these
are bonds underwritten by international bond syndicates and sold in several
national markets. The term “Eurobond” can be confusing in that it sounds like the
bond has to be denominated in euros, but it can be in any currency, such as yen
or pounds. A better term perhaps would be “international bond” rather than
“Eurobond.” International bonds are available from developed countries (such as
Germany or Japan) or emerging markets (such as India or Vietnam).
Duration is important for all bond investors. Risk-averse investors should
consider bonds with low durations. Aggressive investors should consider bonds
with high durations when they anticipate that interest rates will decline, and they
should consider bonds with low durations when they anticipate that interest rates
will rise.
An investor’s time horizon is more important than his or her age when one is
considering the duration and maturities of bonds in a portfolio. Many investors
decide that they should invest for the short term when in retirement. However,
these investors may have a 20-year life expectancy at age 60 or 65. The joint life
expectancy of a retired couple could exceed 20 years. If a bond investor’s time
horizon could exceed 10 years, such an investor would still need to invest in
something other than just Treasury bills.
One strategy for retirees is to set up a ladder of TIP bonds. For example, a retiree
could buy, say, $30,000 of TIPS maturing in 2013, 2014, 2015, and so on for as
many years as their life expectancy. Each year she would receive cash flow from
the maturity TIPs, adjusted for inflation. This would be best set up in a traditional
IRA account so that no current taxes would need to be paid on the inflation-
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adjusted principal of the non-maturing bonds. TIPS do not have default risk, call
risk, interest rate risk (if held to maturity), and little, if any, purchasing power
risk—all risks to avoid, if possible, during retirement.
Convertible bonds are an option for investors who like the higher income stream
that bonds provide and who want the opportunity for capital gains from the same
investment. When stock yields dropped to record lows in the 1990s, convertibles
were a more attractive option than stocks for income-oriented investors. We will
learn about convertibles next.
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Chapter 4: Convertible Bonds
Reading the first part of this chapter will enable you to:
7–7
Calculate the conversion value, investment value, investment
premium, conversion premium, and downside risk of convertible
securities.
A
convertible bond is a debt instrument that can be converted into the
issuer’s common stock. As such, it is a hybrid security that has a
valuation tied to both the stock and the bond value, which will be
subsequently explained. Typically it is younger, less-established companies that
issue convertible bonds in order to entice investors to purchase their bonds. In
addition, the interest rate on the convertible will be less than that of a straight
bond, thereby saving the company money on its interest payments. Later, if the
company is successful and the stock goes up, the bonds can be converted into stock,
at which time the bond interest payments will end, again saving the company money.
Since young, growth companies pay little, if any, cash dividends, this conversion
saves the company money it can use to grow the company.
Once companies become more established, typically they can borrow in the
marketplace and not have to offer a conversion feature. Note that companies will
not want to offer convertible debt if they have better options—this is because
upon conversion dilution will occur, and the number of outstanding shares will
increase and thus impact current shareholders. The cardinal rule when buying a
convertible bond is to buy the bond only if the investor likes the prospects of
owning the underlying stock.
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Conversion Value
The formula for computing the conversion value of a convertible bond is:
CV =
Par
× Ps
CP
where
CV
=
Conversion value
Par
=
Face value of bond (generally $1,000)
=
=
Conversion price
Current market price of underlying stock
CP
Ps
The face value of the bond divided by the conversion price is known as the
conversion ratio. The conversion ratio is the number of shares of stock into
which the bond can be converted. The conversion value is how much the bond is
worth if it were to be converted into stock, and then valued based on the current
market price of the stock.
If the conversion price is $40 per share, then the conversion ratio is 25 shares,
which is computed as follows:
$1,000
= 25
$40
This means that when the common stock is $40 per share, the investor who
converts a convertible bond into shares of stock will hold 25 shares of stock with
a market value that is equal to the face value of the bond. When the stock sells
below the conversion price of $40, the value of the bond as stock is less than the
face value of the bond. An investor generally will not convert the bond if the stock is
selling for less than $40 per share because he or she could hold the bond until its
maturity (or call date) and be assured of receiving $1,000 (or the call price) while
also receiving interest income until the bond either matures or is called.
Chapter 4: Convertible Bonds
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Be careful with when to use the conversion ratio, and when not to. You only use
the conversion ratio if a conversion price is given to you. If the number of shares
is given to you there is no need to do the ratio. For example, in the scenario
above we were given a conversion price, which we then used in the conversion
ratio to determine the number of shares ($1,000/$40 = 25 shares) we are entitled
to. But if we were given the number of shares (25 shares), then there would be no
need to use the conversion ratio, since it has already been calculated for us and
we know the number of shares that the bond can be converted into.
Bond Investment Value
A bond’s investment value is the same as its intrinsic value as a straight bond.
This can also be referred to as its value as debt. It can be calculated with a
financial calculator, and you have already learned the keystrokes. You will
simply be calculating the present value of cash flows from receipts of semiannual
interest payments and from the $1,000 face value received at maturity.
Assume that a convertible bond has a coupon rate of 6%, has 20 years to
maturity, and has a $1,000 face value, when current market interest rates are 5%.
The investment value (intrinsic value) of the bond is computed with a financial
calculator as follows:
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
20, SHIFT,
xP/YR
5
?
30
1,000
Answer: $1,125.51
HP-12C:
N
I/YR
PV
PMT
FV
40
2.5
?
30
1,000
Answer: $1,125.51
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If this is the same bond as one that is convertible into 25 shares of stock, then an
investor will not convert the bond into stock if the stock is selling at $30 per
share. To do so, the investor would be giving $1,125 worth of bond value to
acquire $750 (25 shares × $30) worth of value in the stock.
Investment Premium and Conversion
Premium
Because a convertible bond is like a straight bond combined with an option
contract, an investor pays a premium whenever he or she buys a convertible
bond. Take the preceding bond with a current investment value of $1,125. If this
bond were not a convertible bond, the investor would be willing to pay only
$1,125 to purchase the bond. Because it is a convertible bond and because the
investor has a call option to acquire 25 shares of the company’s stock, the
investor will be willing to pay more, and have to pay more than the bond’s
investment value for this option.
Let’s say the current market price of the convertible bond is $1,250. The investor,
then, is paying an investment premium of $125 over the investment value of the
bond for the option.
The investor is also paying a conversion premium, the difference between the
market price of the convertible bond and the conversion value. If the market price
of the stock is currently $30 per share, then the conversion premium is $500,
which is the current market price of the convertible bond ($1,250) minus the
conversion value of the bond ($30 × 25 shares = $750).
Both of these premiums can be shown as percentages. The investment premium
is 11.1%, which is computed as follows:
$125
= 11.1%
$1,125
Chapter 4: Convertible Bonds
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53
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
The conversion premium is 66.7%, which is computed as follows:
$500
= 66.7%
$750
In other words, the investor currently holds a convertible bond for which he or
she paid a premium that is 11.1% greater than the investment value of the bond
and 66.7% greater than the value of the bond as stock (if the bond were converted
to stock).
Downside Risk
Because a convertible bond is purchased at a premium over its value as a bond,
the market value of the convertible bond could fall substantially if the market
price of the underlying stock falls greatly. The point at which that fall is
cushioned is the investment value of the bond.
The downside risk of a convertible bond is the dollar or percentage decline from
the current market price of the convertible bond (in our example, $1,250) to the
investment value of the bond. In other words, the investment premium is the
measure of a bond’s downside risk. As computed previously, the downside risk
for the bond in the example is $125 ($1,250 market value minus $1,125 intrinsic
value). However, the percentage downside risk is not 11.1%; it is 10.0%, which
is computed as follows:
$125
= 10.0%
$1,250
Forced Conversion
Usually the conversion of a bond into stock is at the option of the bondholder.
However, there are circumstances under which conversion can be forced by the
company. For example, assume a bond is selling near its conversion value of
$1,225. If the bond has a call provision that allows the company to call the bond
at, say, $1,100, the bondholder has two choices: (1) have the bond called at
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Valuation & Analysis of Fixed-income Investments
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$1,100, or (2) convert the bond into stock worth $1,225. Obviously, the
bondholder will convert the bond into stock since doing that gives him the greater
value. He can then keep the stock or sell the stock and reinvest in another bond if he
wants interest income. In these circumstances the company has forced the
bondholder to convert the bond to stock and ends the interest payments on the bond.
Convertible Sample Calculations
Kathleen Sullivan purchased a convertible bond of GetGo Corporation a few
years ago. The bond has an 8.5% coupon rate, interest is paid semiannually, and
the bond matures in six years. Comparable debt yields 9.5% currently. Kathleen’s
bond is convertible at $29 a share. The current price of GetGo common stock is
$32, and the current price of the convertible bond is $1,226.00.
A. What is the conversion value of the convertible bond?
1,000
= 34.483 shares × $32 = $1,103.45
29
B. What is the investment value of the convertible bond?
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
6, SHIFT,
xP/YR
9.5
?
42.50
1,000
Answer: $955.05
HP-12C:
N
I/YR
PV
PMT
FV
12
4.75
?
42.50
1,000
Answer: $955.05
Chapter 4: Convertible Bonds

55
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
C. What is the downside risk for this GetGo convertible bond?
$1,226.00 current market price – $955.05 investment value = $270.95 downside risk.
Remember that for downside risk we take the difference between the current
market price of the convertible bond and its investment value ($955.05), even
though the conversion value ($1,103.45) is higher in this case. The downside risk
of a convertible bond will always be the difference between the current market
value of the bond and its investment value, regardless of what the conversion
value may be.
Note that as interest rates change so will the investment value of the bond, which
then means the downside risk will also change. For this reason “downside risk” is
a bit misleading—it is not set in stone!
Convertible Preferred Stock
Sometimes a company issues preferred stock that can be converted into its
common stock. Doing this allows the company to pay a lower dividend on the
preferred stock than as straight preferred because the conversion feature has
value. The concepts for convertible preferred stock are similar to those for
convertible bonds. The conversion price is the number of shares of common
stock that will be received in exchange for the preferred stock times the current
market price of the common stock. The investment value (intrinsic value) of the
preferred stock is the annual dividend of the preferred stock divided by the
current market interest rate on comparable convertible preferred stock. Note that
this is the same formula that was presented in Module 4 for the zero growth
version of the dividend growth model. Investment value is computed as follows:
P=
Do
r
where
56
P
=
Investment value
Do
=
Annual preferred stock dividend (zero growth)
r
=
Comparable yield (think “r” for required yield)

Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Reading the next part of this chapter will enable you to:
7–8
Analyze the relationships among conversion value, investment value,
and market value of convertible securities.
Summary of Convertible Bond Relationships
Figure 5 summarizes the relationships among the values found in convertible bonds.
Figure 5: Convertible Bond Relationships
Bond
Price
($)
Market price
Conversion
value line
A
Investment
value of bond
Stock Price ($)
The conversion value is directly related to the price of the underlying stock. As
long as the conversion value is less than the investment value of the bond, the
holder would be foolish to convert. He or she would exchange a bond for stock
that is worth less than what the bond would be worth if it was a straight bond and
not a convertible bond.
Chapter 4: Convertible Bonds

57
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
After the conversion value of the stock has reached the investment value of the
bond, then conversion might make sense. At that intersection point (point A in
Figure 5) and above, the investor would exchange a bond for stock that is worth
more than what the bond would be worth if it were a straight bond and not a
convertible bond.
If the price of the underlying stock falls drastically, the convertible feature is, in
effect, worthless at that time so the bond will trade as a straight bond. This is
called a “busted convertible bond.” However, if the conversion value of the bond
is slightly below the investment value of the bond, the actual market price of the
bond will most likely exceed the investment value. This is because, in effect, the
investor holds both a straight bond and an option to convert the bond into stock,
which has value to the bondholder. In this situation, the bond’s market value
might not fall below the investment value of the bond, and, in fact, sell for a
small premium over the investment value. This premium, which is paid by the
investor, is shown by the shaded area in Figure 5.
On the other hand, a benefit of convertible bonds occurs when the conversion
value is greater than the investment value of the bond (due to strong upward
movement in the stock price). Should the convertible bond not be converted and
the stock begin to fall in price, the market value of the bond will not fall
proportionally with the stock after the price of the convertible nears the
investment value. In effect, the investment value of the bond acts as a floor; the
option to convert becomes nearly worthless, but the investment value of the bond
remains intact.
Sometimes, when the market value of the underlying stock falls, the company’s
financial ratios deteriorate to the point that the company’s ability to repay debt
principal becomes impaired. In that case, the investment value of the bond may
fall, causing further losses in the convertible bond, as the convertible price drops
alongside the stock. Investors should be made aware of this possibility, especially
since the companies that issue convertible bonds frequently are those with less
stable financial positions.
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Summary
K
nowing how to calculate bond yields and prices, and understanding
their implications in putting together bond portfolios, is very important.
You should know how to calculate taxable equivalent yield, current
yield, yield-to-call, yield-to-maturity, and the intrinsic value of a bond.
Duration is another extremely important concept since it measures the volatility
of individual bonds or bond portfolios. You should understand the uses of
duration, and understand what increases and decreases duration, and how to use
this knowledge to select the appropriate bond investment for a given scenario.
You should also know how to calculate duration and the change in a bond price
using duration. Immunization and convexity are two terms that you should know
and understand.
Convertible bonds are a type of hybrid security that many investors find difficult
to understand. A convertible bond is a combination of a straight bond and an
option contract (called an “embedded option”) on the underlying stock. Investors
who buy convertibles must pay a premium for this option that exceeds the
investment value of the bond, and this fact causes many investors to shun
convertibles. However, if an investor understands convertible bonds, they can be
a valuable addition to his or her investment portfolio.
Having read the material in this module, you should be able to:
7–1
Explain factors that affect the price and yield of fixed-income
securities.
7–2
Calculate the price, compound return, yield-to-maturity, yield-tocall, and taxable-equivalent yield, of fixed-income securities.
7–3
Understand the concept of duration, and calculate change in price
using duration.
Summary

59
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
7–4
Analyze the relationships among bond ratings, yields, maturities, and
durations to determine comparative price volatility.
7–5
Assess how changes in variables affect bond risk and price volatility.
7–6
Evaluate investor profiles to recommend appropriate fixed-income
securities for purchase.
7–7
Calculate the conversion value, investment value, investment
premium, conversion premium, and downside risk of convertible
securities.
7–8
Analyze the relationships among conversion value, investment value,
and market value of convertible securities.
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Module Review
Questions
7–1
Explain factors that affect the price and yield of fixed-income
securities.
1. On what four factors does the calculation of a bond’s price depend?
Go to answer.
2. How is the price of each of the following determined?
a. a perpetual debt instrument
Go to answer.
b. a bond with a maturity date
Go to answer.
3. Which contribute more to the present value of a bond, interest payments
received in the near future or those received in the distant future? Explain
your answer.
Go to answer.
4. Explain why bond prices and interest rates are inversely related.
Go to answer.
5. What do the terms “discount” and “premium” mean in relation to the pricing
of a bond?
Go to answer.
6. Describe what each of the following bond yields represents and explain how
each is determined.
a. current yield
Go to answer.
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
b. yield-to-maturity
Go to answer.
c. yield-to-call
Go to answer.
7. Describe the general circumstances under which each of the following
relationships exists.
a. The YTC is higher than the YTM.
Go to answer.
b. The YTC is lower than the YTM.
Go to answer.
c. The current yield is higher than the YTM.
Go to answer.
d. The current yield is lower than the YTM.
Go to answer.
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7–2
Calculate the price, compound return, yield-to-maturity, yield-tocall, and taxable-equivalent yield, of fixed-income securities.
8. What are the taxable-equivalent yields of municipal bonds with the following
tax-free yields for investors in the following marginal tax brackets?
Tax-Free
Yield
TEY
25%
Bracket
TEY
28%
Bracket
TEY
33%
Bracket
TEY
35%
Bracket
4%
4.5%
5%
Go to answer.
9. Jane Roberts owns a public purpose municipal bond that pays 6%.
a. Assuming she is in the 35% marginal tax bracket, what yield on
corporate bonds would be comparable to the yield on Jane’s current
investment?
Go to answer.
b. What if Jane itemizes deductions and is also in an 8% state marginal tax
bracket. What yield on corporate bonds would then be comparable to
Jane’s current investment?
Go to answer.
Module Review
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10. Paulette Doyle’s marginal tax bracket is 35%. She is considering either a
corporate bond that pays 8% annually or a tax-exempt municipal bond. What
yield on the municipal bond would be comparable to the yield on the taxable
corporate bond?
Go to answer.
11. Your client asks what the market price of a particular bond should be. The
bond pays 12% coupon interest semiannually. The bond will mature in seven
years and will pay a face value of $1,000. Comparable bonds (bonds with
similar maturities and of the same investment grade) are yielding 14.9%.
What should be the price of this bond?
Go to answer.
12. Your client asks what the market price of a particular zero-coupon bond
should be. The bond will mature in seven years and will pay a face value of
$1,000. Comparable bonds (bonds with similar maturities and of the same
investment grade) are yielding 14.9%. What should be the price of this bond?
Go to answer.
13. Calculate the following bond values.
a. What is the intrinsic value (price) of a newly issued bond with a 12%
coupon rate, 30 years to maturity, and a $1,000 maturity value when
current market rates for comparable bonds are at 12%?
Go to answer.
b. What will be the bond’s price one year after issue if market rates drop to
9%?
Go to answer.
c. What will be the bond’s price one year after issue if market rates rise to
15%?
Go to answer.
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14. A bond has a market price of $875. The bond pays 12% coupon interest
semiannually. The bond will mature in seven years and will pay a face value
of $1,000.
a. What is the YTM (IRR) for this bond?
Go to answer.
b. What is the YTM if the bond currently has a market price of $1,200?
Go to answer.
15. Your client recently purchased a zero-coupon bond for $630. It has a $1,000
face value and matures in six years. What is the YTM for this bond?
Go to answer.
16. Your client purchased a bond for $950. The bond has a coupon rate of 11%,
it matures in 17 years, and it is callable in five years at $1,110. What is the
YTC for this bond?
Go to answer.
7–3
Understand the concept of duration, and calculate change in price
using duration.
17. What factors determine the amount of price fluctuation in a bond?
Go to answer.
18. Compare the price volatility of the following types of bonds.
a. bonds with long maturities compared to bonds with short maturities,
assuming both have the same coupon rate
Go to answer.
b. bonds with low coupon rates compared to bonds with high coupon rates,
assuming both have the same maturity
Go to answer.
Module Review
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
19. How can an investor minimize the uncertainty surrounding the realized
compound yield of a bond?
Go to answer.
20. What is duration, and how is it used?
Go to answer.
21. Calculate the duration and expected price change for each of the following
bonds.
a. Market rate greater than coupon rate. Assume that the coupon is 6%,
that the market interest rate is 7%, that there are 16 years until maturity,
and that compounding is annual. Also assume that interest rates are
subsequently expected to fall by 50 basis points.
Go to answer.
b. Coupon rate greater than market rate. Assume that the coupon is 8%,
that the market interest rate is 6%, that there are 22 years until maturity,
and that compounding is semiannual. Also assume that interest rates are
subsequently expected to rise by 60 basis points.
Go to answer.
c. Zero-coupon bond. Assume that the current market interest rate is 7%,
that there are 18 years until maturity, and that compounding is
semiannual. Also assume that interest rates are subsequently expected to
fall by 30 basis points.
Go to answer.
22. Calculate the approximate duration for the bond example found in question
21b. Assume that the coupon is 8%, interest rates change by 1%, that the
market interest rate is 6%, that there are 22 years until maturity, and that
compounding is semiannual.
Go to answer.
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23. IBM has a bond with a 7% coupon; the bond matures in 2035 for $1,000. In
2010, the current price of the bond was 107 5/8 (107.625% of par, or 1.07625 ×
$1,000 = $1,076.25). Assume that the bond had 26 years until maturity at that
time.
a. What is the YTM of the IBM bond?
Go to answer.
b. Using the YTM computed in part a. of this question (rounded to the
nearest tenth), what is the duration of the IBM bond using semiannual
compounding?
Go to answer.
c. If the YTM is expected to fall 40 basis points in the next year, by how
much would the price of the IBM bond change?
Go to answer.
7–4
Analyze the relationships among bond ratings, yields, maturities, and
durations to determine comparative price volatility.
24. Consider the following three bonds and determine which bond is most
susceptible to price fluctuations.

Bond 1: A-rated, pays a coupon of 11%, matures in 12 years

Bond 2: AA-rated, pays a coupon of 12%, matures in 7 years

Bond 3: BBB-rated, pays a coupon of 9%, matures in 15 years
Go to answer.
Module Review

67
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
25. Consider the following bonds.

Bond 1: BBB-rated, pays a coupon of 9%, matures in 6 years

Bond 2: BBB-rated, pays a coupon of 9%, matures in 11 years

Bond 3: BBB-rated, pays a coupon of 7%, matures in 11 years

Bond 4: BBB-rated, pays a coupon of 7%, matures in 6 years
a. Determine whether Bond 1 or Bond 2 has more potential for price
fluctuation and give a reason why.
Go to answer.
b. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Go to answer.
c. Determine whether Bond 3 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
d. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
26. Consider the following bonds.

Bond 1: AA-rated, pays a coupon of 9%, matures in 7 years

Bond 2: BB-rated, pays a coupon of 9%, matures in 12 years

Bond 3: BB-rated, pays a coupon of 9%, matures in 7 years

Bond 4: AA-rated, pays a coupon of 9%, matures in 12 years
a. Determine whether Bond 1 or Bond 3 has more potential for price
fluctuation and give a reason why.
Go to answer.
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Valuation & Analysis of Fixed-income Investments
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b. Determine whether Bond 2 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
c. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
d. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Go to answer.
27. Consider the following bonds.

Bond 1: BBB-rated, pays a coupon of 8%, matures in 5 years

Bond 2: AA-rated, pays a coupon of 12%, matures in 5 years

Bond 3: BBB-rated, pays a coupon of 12%, matures in 5 years

Bond 4: AA-rated, pays a coupon of 8%, matures in 5 years
a. Determine whether Bond 1 or Bond 3 has more potential for price
fluctuation and give a reason why.
Go to answer.
b. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
c. Determine whether Bond 2 or Bond 4 has more potential for price
fluctuation and give a reason why.
Go to answer.
d. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Go to answer.
Module Review
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
28. Review the Morningstar reports for the American Century Diversified Bond
fund and the AllianceBernstein Bond Corporate Bond fund.
American Century Diversified Bond Inv ADFIX
Key Stats
Morningstar
Category
Morningstar Rating
Intermediate-Term
Bond
NAV (01-07-05)
Day Change
$10.20
$0.00
Total Assets($mil)
Expense Ratio %
Front Load %
Deferred Load %
516
0.64
None
None
Yield % (TTM)
Min Investment
Manager
Start Date
3.21
$2,500
Jeffrey L. Houston
01-01-94
Morningstar Style Box
Average Eff Duration
3.79 Yrs
Average Eff Maturity
5.38 Yrs
Average Credit Quality
AAA
Data through 09-30-04
Volatility
Measurements
Trailing 3-Yr through 1231-04
*Trailing 5-Yr through 1231-04
Standard Deviation
4.20 Sharpe Ration
0.90
Mean
5.12 Bear Market Decile
Rank*
Modern Portfolio Theory
Statistics
Standard Index
LB Agg
R-Squared
Trailing 3- Yr through 12-31-04
Best Fit Index
Lehman Bros. U.S. Universal Bond
98
99
Beta
0.93
0.96
Alpha
-0.69
-1.45
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
AllianceBernstein Bond Corp Bd A CBFAX
Key Stats
Morningstar
Category
NAV
Morningstar Rating (01-07-05)
Day Change
Long-Term Bond
$12.33
$0.00
Total Assets($mil) Expense Ratio %
Front Load %
Deferred Load
%
875
1.16
4.25
1.00
Yield % (TTM)
Min Investment
Manager
Start Date
5.79
$1,000
Lawrence Shaw
08-05-02
Michael A. Snyder
08-05-02
Morningstar Style Box
Average Eff Duration
6.60 Yrs
Average Eff Maturity
20.40 Yrs
Average Credit Quality
BBB
Data through 03-31-04
Volatility
Measurements
Trailing 3-Yr through
12-31-04
Standard Deviation
8.57 Sharpe Ration
Mean
7.30 Bear Market Decile
Rank*
Modern Portfolio Theory Statistics
Standard Index
LB Agg
R-Squared
*Trailing 5-Yr through 1231-04
0.70
7
Trailing 3- Yr through 12-31-04
Best Fit Index CSFB High Yield
28
55
Beta
0.99
0.95
Alpha
1.34
–5.19
Module Review

71
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
a. Which of the two funds would you expect to be more volatile, and why?
Go to answer.
b. What evidence is there in the Morningstar report of the greater volatility
of the fund you chose?
Go to answer.
7–5
Assess how changes in variables affect bond risk and price volatility.
29. In Question 21, you computed the duration and expected price change for
several types of bonds. The characteristics and the estimated percentage price
changes of those bonds are summarized in the following table (BP stands for
basis points).
Bond
Coupon
Market
Rate
Maturity
Duration
Δy
A
6
7
16
10.42
50 BP
4.9%
B
8
6
22
11.80
60 BP
6.9%
C
0
7
18
18.00
30 BP
5.2%
ΔP (%)
What conclusions can you reach about bond risk and volatility relative to
different characteristics of these bonds and changes in some of their
variables?
Go to answer.
30. The following table shows characteristics of four bond funds. The funds are
listed in order of ascending credit quality. Fund A is a high-yield bond fund.
The last three bonds are also ranked by decreasing average maturity.
Review the data in the table and explain how each fund’s risk and volatility
is affected by the differences in variables.
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Fund
Average
Credit
Quality
Average
Weighted
Coupon
Average
Maturity
Standard
Deviation
Average
Effective
Duration
Fund A
B
7.8
NA
3.74
3.8
Fund B
BBB
8.1
23.1
7.84
9.3
Fund C
A
7.3
12.5
3.92
5.9
Fund D
AA
7.9
4.4
2.1
3.3
Go to answer.
31. If you want to ensure that $40,000 is available in 13 years when your child is
about to enter college, would you select a zero-coupon bond that matures in
13 years or a coupon bond that matures in 13 years? Why did you select the
one you did?
Go to answer.
32. If you have a risk-averse client who is concerned about fluctuating bond
prices, but who wants to have relatively high income from a bond portfolio,
how would you construct a bond portfolio so that you can help the client
resolve both of these apparently conflicting concerns?
Go to answer.
33. Summarize all the relationships between price, coupon, maturity, interest
rates, and duration that you have discovered in this module.
Go to answer.
34. Explain the following bond portfolio management strategies.
a. tax swap
Go to answer.
b. substitution swap
Go to answer.
Module Review
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c. intermarket spread swap
Go to answer.
d. pure yield pickup swap
Go to answer.
e. rate anticipation swap
Go to answer.
f.
laddered portfolio
Go to answer.
g. barbell portfolio
Go to answer.
h. immunization
Go to answer.
7–6
Evaluate investor profiles to recommend appropriate fixed-income
securities for purchase.
35. Robert Berens, age 65, is retiring and has $150,000 to invest. He is interested
in purchasing fixed-income securities to provide for his income needs during
retirement. Robert will not have any other substantial income, and he will be
in the 15% marginal income tax bracket. He has invested in bonds in the
past, and he plans to be actively involved in this investment.
What kind of fixed-income security is appropriate for Robert, and why?
(Consider type, risk rating, marginal tax bracket, term, and other relevant
factors.)
Go to answer.
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36. John Bloom, age 49, wants to take early retirement next year when he turns
50. He wants to invest $200,000 in a fixed-income security to provide him
with additional income. He estimates that he will be in the 33% marginal tax
bracket. He has invested previously, and he is willing to be aggressive with
this investment to increase his return.
What kind of fixed-income security is appropriate for John, and why?
(Consider type, risk rating, marginal tax bracket, term, and other relevant
factors.)
Go to answer.
37. Kent Walters, age 32, has $40,000 to invest in a fixed-income security. He
has invested in various types of bonds for 10 years, he considers himself to
be an aggressive investor, and he is in the 28% marginal income tax bracket.
His primary goal is capital appreciation; income is a secondary consideration.
Kent’s financial planner has presented the following securities and their
before-tax yields.
a. 15-year, BB-rated, noncallable corporate bonds trading near par with a
yield of 6.8%
b. 20-year, A-rated, discount, public purpose, callable general obligation
municipal bonds with a taxable-equivalent yield of 7.2%
c. 10-year, A-rated, premium, callable, sinking fund, corporate bonds with
a yield of 4.5%
d. Treasury bills with a yield of 2.5%
Which one of these fixed-income securities would be an appropriate choice
for Kent, and why?
Go to answer.
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38. Kathy Connelly, age 20, is just starting college and needs to invest $25,000
in fixed-income securities. She is in the 15% tax bracket and plans to use the
interest income and principal as needed to pay her college expenses for the
next four years. She is looking for a low-risk investment, and she knows she
must receive principal periodically from these securities. The following
securities are available to Kathy at the before-tax yields indicated.

Investment A: BB-rated, public purpose, municipal revenue bonds with
an after-tax yield of 7.0%

Investment B: 12-year, B-rated, discount, callable corporate bonds with a
before-tax yield of 8.8%

Investment C: eight-year Treasury notes with a before-tax yield of 6.8%

Investment D: AA-rated, noncallable, five-year corporate bonds with a
before-tax yield of 8.5%
Which one of these securities would be an appropriate choice for Kathy, and
why?
Go to answer.
39. Answer the following questions about selecting bonds for client portfolios.
a. What sort of characteristics would you look for in a bond chosen for a
client with a high risk tolerance?
Go to answer.
b. What sort of characteristics would you look for in a bond chosen for a
client with a moderate risk tolerance?
Go to answer.
c. What sort of characteristics would you look for in a bond chosen for a
client with a low risk tolerance?
Go to answer.
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d. If you believe that interest rates will decline sharply in the future, what
bond characteristics would you search for?
Go to answer.
e. If you believe that interest rates will rise sharply in the future, what bond
characteristics would you search for?
Go to answer.
7–7
Calculate the conversion value, investment value, investment
premium, conversion premium, and downside risk of convertible
securities.
40. Janice Carlysle owns a ZZT Corporation convertible bond. The bond has a
9.5% coupon rate that is paid semiannually; the bond matures in 8 years.
Comparable debt (with the same rating and maturity date) is yielding 11%.
Janice’s bond is convertible at $27 a share, the current market price of ZZT
common stock is $35, and the bond sells for $1,400.
a. What is the conversion value of the bond?
Go to answer.
b. What is the investment value of the bond?
Go to answer.
c. What is the bond’s investment premium?
Go to answer.
d. What is the bond’s conversion premium?
Go to answer.
e. What is the downside risk percentage of the bond?
Go to answer.
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41. James Perry owns a QV Inc. convertible bond. The bond has a coupon rate of
10% that is paid semiannually; the bond matures in 12 years. Comparable
debt yields 8% currently. His bond is convertible into 24 shares of stock. The
current market price of QV common stock is $34, and the bond sells for
$1,200.
a. What is the conversion value of the bond?
Go to answer.
b. What is the investment value of the bond?
Go to answer.
c. What is the bond’s investment premium?
Go to answer.
d. What is the bond’s conversion premium?
Go to answer.
e. What is the downside risk percentage of the bond?
Go to answer.
42. Assume that a convertible bond has a face value of $1,000 and that it is
selling in the market for $890. Its conversion price is $50 per share. The
underlying common stock is selling for $38 per share. The bond pays $40
semiannually in interest and matures in 20 years. The market interest rate on
comparable bonds is 12%.
a. What is the bond’s conversion ratio?
Go to answer.
b. What is the conversion value?
Go to answer.
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c. What is the investment value of the convertible bond?
Go to answer.
d. Express the downside risk as a percentage.
Go to answer.
43. An investor can obtain 1.5 shares of common stock through conversion of 1
share of preferred stock. The price of the common stock is $35. The
convertible preferred stock has no maturity date and pays an annual dividend
of $3. The yield on comparable nonconvertible preferred stock is 12%.
a. What is the conversion value of this convertible preferred stock?
Go to answer.
b. What is the investment value of this convertible preferred stock?
Go to answer.
44. If preferred stock does not have a required sinking fund or call feature, it may
be viewed as a perpetual debt instrument. How is the intrinsic value of this
type of preferred stock calculated?
Go to answer.
45. Explain how to determine the intrinsic value of preferred stock that has a
finite life.
Go to answer.
46. If a preferred stock pays an annual dividend of $5 and investors can earn
12% on alternative, comparable investments, what is the price that should be
paid for this stock?
Go to answer.
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47. If the preferred stock in the previous question had a call feature, and if
investors expected the stock to be called for $100 after 12 years, what price
would be paid for this stock?
Go to answer.
7–8
Analyze the relationships among conversion value, investment value,
and market value of convertible securities.
48. In the following figure, what does the shaded area represent?
Bond
Price
($)
Market price
Conversion
value line
A
Investment
value of bond
Stock Price ($)
Go to answer.
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Answers
7–1
Explain factors that affect the price and yield of fixed-income
securities.
1. On what four factors does the calculation of a bond’s price depend?
The price of a bond is related to (1) the interest paid by the bond,
(2) the interest rate available on comparable bonds of the same
maturity and grade (market interest rate), (3) the maturity date of the
bond, and (4) the bond’s principal or call amount.
Return to question.
2. How is the price of each of the following determined?
a. a perpetual debt instrument
The price of a perpetual debt instrument is equal to the present
value of an infinite stream of payments, which is determined as
follows: annual interest payment divided by the current market
interest rate.
Return to question.
b. a bond with a maturity date
The price of a bond with a maturity date is equal to the present
value of the interest payments plus the present value of the
principal to be received at maturity. (The present value of a bond,
also known as its intrinsic value, can be determined with a
financial function calculator.)
Return to question.
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3. Which contribute more to the present value of a bond, interest payments
received in the near future or those received in the distant future? Explain
your answer.
The interest payments received in the near future contribute more to
the present value of a bond because dollars received in the distant
future have less value today. The present value of $100 received in 3
years is greater than the present value of $100 received in 20 years.
Return to question.
4. Explain why bond prices and interest rates are inversely related.
Because the dollar amount of interest paid by a bond is constant (i.e.,
there is a fixed flow of income), the price (or intrinsic value) of the
bond changes in the opposite direction of a change in interest rates,
which would encourage investors to purchase it. For example, if the
market interest rates of comparable bonds increase, the value (price)
of the bond declines, which makes its flow of income attractive to
investors (who could otherwise receive a larger flow of income from
other newly issued, higher-coupon bonds). When market rates
decrease, the price of the bond increases because its flow of income
is more valuable to investors (who would otherwise have to accept a
smaller flow of income from other newly issued, lower-coupon bonds).
Return to question.
5. What do the terms “discount” and “premium” mean in relation to the pricing
of a bond?
In relation to bonds, the discount is the amount by which a bond sells
below its maturity value to be competitive with bonds of comparable
quality. The premium is the amount by which a bond’s price exceeds
its maturity value. If the coupon rate of a bond is less than the market
yield, the bond’s price is below its maturity value (i.e., it is a discount
bond). If the bond’s coupon rate is greater than the market yield, the
bond’s price exceeds its maturity value (it is a premium bond).
Return to question.
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6. Describe what each of the following bond yields represents and explain how
each is determined.
a. current yield
The current yield of a bond is a measure of the return on the bond
based on the stated cash interest per year and the bond’s current
market price. Current yield is calculated by dividing the annual
interest payment by the market price. Current yield does not take
into account the difference between a bond’s purchase price and
its redemption value.
Return to question.
b. yield-to-maturity
YTM is the compound yield earned on a bond from the time it is
purchased until its maturity date. (It includes both the periodic
cash income received and any capital gains or losses that arise
because the principal amount is greater or smaller than the
current market price.) YTM is the market rate of return, the interest
rate that equates the stream of interest payments and the par
value at maturity to the bond’s current price.
Return to question.
c. yield-to-call
YTC is a measure of the yield for bonds that are likely to be called.
In calculating YTC, the number of periods until the call date is
used instead of the number of periods until maturity, and the call
price is used instead of the face value.
Return to question.
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7. Describe the general circumstances under which each of the following
relationships exists.
a. The YTC is higher than the YTM.
For a discount bond, the YTC is higher than the YTM if the bond is
called and the principal is redeemed early.
Return to question.
b. The YTC is lower than the YTM.
If a bond is selling at a premium and it is called by the issuing firm
at par, then the YTC would be lower than the YTM.
Return to question.
c. The current yield is higher than the YTM.
If a bond sells at a premium, the current yield is higher than the
YTM.
Return to question.
d. The current yield is lower than the YTM.
If a bond sells at a discount, the current yield is lower than the
YTM.
Return to question.
7–2
Calculate the price, compound return, yield-to-maturity, yield-tocall, and taxable-equivalent yield, of fixed-income securities.
8. What are the taxable-equivalent yields of municipal bonds with the following
tax-free yields for investors in the following marginal tax brackets?
Tax-Free
Yield
TEY
25%
Bracket
TEY
28%
Bracket
TEY
33%
Bracket
TEY
35%
Bracket
4%
5.33%
5.56%
5.97%
6.15%
4.5%
6.00%
6.25%
6.72%
6.92%
5%
6.67%
6.94%
7.46%
7.69%
Return to question.
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9. Jane Roberts owns a public purpose municipal bond that pays 6%.
a.
Assuming she is in the 35% marginal tax bracket, what yield on
corporate bonds would be comparable to the yield on Jane’s current
investment?
TEY =
.06
= 9.23%
1 − .35
Return to question.
b. What if Jane itemizes deductions and is also in an 8% state marginal
income tax bracket. What yield on corporate bonds would then be
comparable to Jane’s current investment?
Taxable equivalent yield =
TEY =
Tax-free equivalent yield
(1 − SMTB )(1 − FMTB )
.06
= 10.03%
(1 − .08 )(1 − .35 )
Return to question.
10. Paulette Doyle’s marginal tax bracket is 35%. She is considering either a
corporate bond that pays 8% annually or a tax-exempt municipal bond. What
yield on the municipal bond would be comparable to the yield on the taxable
corporate bond?
.08 =
Tax-free yield
1 − .35
Tax-free yield = .08 × (.65) = 5.20%
Return to question.
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11. Your client asks what the market price of a particular bond should be. The
bond pays 12% coupon interest semiannually. The bond will mature in seven
years and will pay a face value of $1,000. Comparable bonds (bonds with
similar maturities and of the same investment grade) are yielding 14.9%.
What should be the price of this bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
2
7,
SHIFT,
xP/YR
I/YR
PV
PMT
FV
14.9
?
60
1,000
HP-12C:
N
I
14
7.45
PV
PMT
FV
?
60
1,000
Answer: $876.54
Return to question.
12. Your client asks what the market price of a particular zero-coupon bond
should be. The bond will mature in seven years and will pay a face value of
$1,000. Comparable bonds (bonds with similar maturities and of the same
investment grade) are yielding 14.9%. What should be the price of this bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
2
7,
SHIFT,
xP/YR
I/YR
PV
PMT
FV
14.9
?
0
1,000
HP-12C:
N
14
I
7.45
PV
PMT
FV
?
0
1,000
Answer: $365.69
Return to question.
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13. Calculate the following bond values.
a. What is the intrinsic value (price) of a newly issued bond with a 12%
coupon rate, 30 years to maturity, and a $1,000 maturity value when
current market rates for comparable bonds are at 12%?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
I/YR
PV
PMT
FV
30,
SHIFT,
xP/YR
12
?
60
1,000
HP-12C:
N
I
PV
PMT
FV
60
6
?
60
1,000
Answer: $1,000
Return to question.
b. What will be the bond’s price one year after issue if market rates drop to
9%?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
I/YR
PV
PMT
FV
29,
SHIFT,
xP/YR
9
?
60
1,000
HP-12C:
N
I
PV
PMT
FV
58
4.5
?
60
1,000
Answer: $1,307.38
Return to question.
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c. What will be the bond’s price one year after issue if market rates rise to
15%?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
2
29,
SHIFT,
xP/YR
I/YR
PV
PMT
FV
15
?
60
1,000
HP-12C:
N
I
PV
PMT
FV
58
7.5
?
60
1,000
Answer: $803.02
Return to question.
14. A bond has a market price of $875. The bond pays 12% coupon interest
semiannually. The bond will mature in seven years and will pay a face value
of $1,000.
a. What is the YTM (IRR) for this bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
7,
SHIFT,
xP/YR
I/YR
?
PV
(875)
Answer: 14.94%
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PMT
60
FV
1,000
HP-12C:
N
I
PV
PMT
FV
14
?
(875)
60
1,000
Answer: 7.47, 2, x = 14.94%
Return to question.
b. What is the YTM if the bond currently has a market price of $1,200?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
2
I/YR
7,
SHIFT,
xP/YR
?
PV
PMT
(1,20
0)
60
FV
1,000
Answer: 8.19%
HP-12C:
N
I
PV
PMT
FV
14
?
(1,200)
60
1,000
Answer: 4.0948, 2, x = 8.19%
Return to question.
15. Your client recently purchased a zero-coupon bond for $630. It has a $1,000
face value and matures in six years. What is the YTM for this bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
6, SHIFT,
xP/YR
?
(630)
0
1,000
Answer: 7.85%
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HP-12C:
N
I
PV
PMT
FV
12
?
(630)
0
1,000
Answer: 3.9254, 2, x = 7.85%
Return to question.
16. Your client purchased a bond for $950. The bond has a coupon rate of 11%,
it matures in 17 years, and it is callable in five years at $1,110. What is the
YTC for this bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
N
I/YR
PV
PMT
FV
2
5,
SHIFT,
xP/YR
?
(950)
55
1,110
Answer: 14.02%
HP-12C:
N
I
PV
PMT
FV
10
?
(950)
55
1,110
Answer: 7.0080, 2, x = 14.02%
Return to question.
7–3
Understand the concept of duration, and calculate change in price
using duration.
17. What factors determine the amount of price fluctuation in a bond?
Price fluctuations are affected by a bond’s grade (credit/default risk),
its coupon rate, its length of time to maturity, its duration, and any
changes in market interest rates.
Return to question.
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18. Compare the price volatility of the following types of bonds.
a. bonds with long maturities compared to bonds with short maturities,
assuming both have the same coupon rate
Bonds with long maturities are more volatile than bonds with short
maturities. The principal payment and coupon payments for
longer-term bonds occur further into the future, which raises the
duration.
Return to question.
b. bonds with low coupon rates compared to bonds with high coupon rates,
assuming both have the same maturity
Bonds with low coupon rates are more volatile than bonds with
high coupon rates. Assuming everything else is equal, low-coupon
bonds have higher durations than high-coupon bonds because the
present value of their time-weighted cash flows is lower. If an
investor thought that interest rates were going to decline, then he
would choose the low coupon bonds with the higher durations.
Return to question.
19. How can an investor minimize the uncertainty surrounding the realized
compound yield of a bond?
An investor can reduce one source of risk by purchasing only
noncallable bonds, which are bonds that cannot be retired prior to
maturity. (Noncallable bonds tend to sell for lower yields, however.)
The uncertainty associated with changes in interest rates remains. A
zero-coupon bond eliminates the uncertainty about the reinvestment
rate because there are no coupons to reinvest. Longer-term zerocoupon bonds have very volatile prices, however, due to their 0%
interest coupon. Duration and time until maturity are the same with
zero coupon bonds since there are no cash flows until the bond
matures. For example, a 20-year zero coupon bond would have a
duration of 20.
Return to question.
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20. What is duration, and how is it used?
Duration tells an investor what the approximate price movement of a
bond (or a bond mutual fund) would be given a 1% change in interest
rates. Duration is the weighted-average amount of time it takes to
collect a bond’s interest and principal payments. Duration is used to
compare the interest rate risk of bonds that have different coupons
and different maturities (i.e., to relate bond price sensitivity to interest
rate changes). Investors can reduce interest rate risk by selecting
bonds with shorter durations. They also can match the duration of
their portfolios with the timing of their cash flow needs. By matching
duration to the term of a goal, they optimize the trade-off between
interest rate risk and reinvestment risk.
Return to question.
21. Calculate the duration and expected price change for each of the following
bonds.
a. Market rate greater than coupon rate. Assume that the coupon is 6%,
that the market interest rate is 7%, that there are 16 years until maturity,
and that compounding is annual. Also assume that interest rates are
subsequently expected to fall by 50 basis points.
Dur =
1 + y (1 + y) + t(c − y)
−
y
c[(1 + y)t − 1] + y
y = .07
t = 16
c = .06
1 + .07 (1 + .07) + 16(.06 − .07)
−
=
.07
.06[(1 + .07)16 − 1] + .07
1.07 − .16
= 15.29 − 4.87 = 10.42
15.29 −
.06[(2.95) − 1] + .07
Duration =
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Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Using a financial calculator and assuming annual compounding,
the market price of the bond at current market rates is computed
to be $905.53 (1000 FV, 60 PMT, 16 N, I = 7, PV = 905.53).
ΔP = −D ×
ΔP = −10.42 ×
Δy
1+ y
−.0050
= + 0.0487
1 + .07
+0.0487 × $905.53 = $44.10
The bond’s price will increase by approximately $44 if interest
rates fall by 50 basis points.
Return to question.
b. Coupon rate greater than market rate. Assume that the coupon is 8%,
that the market interest rate is 6%, that there are 22 years until maturity,
and that compounding is semiannual. Also assume that interest rates are
subsequently expected to rise by 60 basis points.
Dur =
1 + y (1 + y) + t(c − y)
−
y
c[(1 + y)t − 1] + y
y = .06/2 = .03
t = 22 × 2 = 44
c = .08/2 = .04
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Duration =
34.33 −
1 + .03 (1 + .03 ) + 44 (.04 − .03 )
−
=
44
.03
.04[(1 + .03 ) − 1] + .03
1.03 + .44
= 34.33 − 10.75 = 23.58 periods = 11.79
.04[(3.67) − 1] + .03
Using a financial calculator and assuming semiannual
compounding, the market price of the bond at current market rates
is computed to be $1,242.54 (HP-10BII+: set for 2 P/YR, 1000 FV,
40 PMT, 22 SHIFT N, 6 I, PV = 1242.54)(HP12C: 1000 FV, 40
PMT, 44 N, 3 I, PV =1242.54).
ΔP = −D ×
ΔP = −11.79 ×
Δy
1+ y
.0060
= −0.0687
1 + .03
–0.0687 × 1,242.54 = –$85.34
The bond’s price will decrease by approximately $85 if interest
rates rise by 60 basis points.
Return to question.
c. Zero-coupon bond. Assume that the current market interest rate is 7%,
that there are 18 years until maturity, and that compounding is
semiannual. Also assume that interest rates are subsequently expected to
fall by 30 basis points.
Dur =
94

1 + y (1 + y) + t(c − y)
−
y
c[(1 + y)t − 1] + y
Valuation & Analysis of Fixed-income Investments
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
Duration =
29.57 −
1 + .035 (1 + .035 ) + 36 (.00 − .035 )
−
=
36
.035
.00[(1 + .035 ) − 1] + .035
1.035 − 1.26
= 29.57 − ( −6.43) = 36.00 periods = 18.00 years
0 + .035
Note that no calculation is necessary for a zero-coupon bond
since the duration of a zero-coupon bond is the remaining term
(18 years in this problem).
Using a financial calculator and assuming semiannual
compounding, the market price of the bond at current market rates
is computed to be $289.83 (HP-10BII+: set for 2 P/YR, 1000 FV,
18 SHIFT N, 7 I, PV = 289.83)(HP-12C: 1000 FV, 36 N, 3.5 I, PV =
289.83).
ΔP = −D ×
ΔP = −18.00 ×
Δy
1+ y
−.0030
= .0522
1 + .035
.0522 × 289.83 = $15.12
The bond’s price will increase by approximately $15 if interest
rates fall by 30 basis points. Note that, due to positive convexity,
the actual price increase will be greater than the amount
computed based on duration alone.
Return to question.
22. Calculate the approximate duration for the bond example found in question
21b. Assume that the coupon is 8%, interest rates change by 1%, that the
market interest rate is 6%, that there are 22 years until maturity, and that
compounding is semiannual.
Module Review
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95
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Duration =
Price if yields decline - Price if yields rise
2(current price)(.01)
Current Bond
Price
Interest rates
increase by 1%
Interest rates
decrease by 1%
6 I (3 I on
HP-12C)
7 I (3.5 I on
HP-12C)
5 I (2.5 I on
HP-12C)
PV = 1242.54
PV = 1111.41
PV = 1397.56
40 pmt
1,000 FV
44 N (22, SHIFT, n,
on HP-10BII+)
Duration =
1,398 – 1,111
287
=
= 11.54
2(1,243)(.01) 24.86
Return to question.
23. IBM has a bond with a 7% coupon; the bond matures in 2035 for $1,000. In
2010, the current price of the bond was 107 5/8 (107.625% of par, or 1.07625 ×
$1,000 = $1,076.25). Assume that the bond had 26 years until maturity at that
time.
a. What is the YTM of the IBM bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
26,
SHIFT,
xP/YR
I/YR
?
PV
(1,076.25)
Answer: 6.39%
HP-12C:
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Valuation & Analysis of Fixed-income Investments
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PMT
35
FV
1,000
N
I
PV
PMT
FV
52
?
(1076.25)
35
1,000
Answer: 3.1973, 2, x = 6.39%
Return to question.
b. Using the YTM computed in part a. of this question (rounded to the
nearest tenth), what is the duration of the IBM bond using semiannual
compounding?
y = .064/2 = .032
t = 26 x 2 = 52
c = .07/2 = .035
Dur =
Duration =
32.25 −
1 + y (1 + y) + t(c − y)
−
y
c[(1 + y) t − 1] + y
1 + .032 (1 + .032 ) + 52(.035 − .032 )
−
=
52
.032
.035[ (1 + .032 ) − 1] + .032
1.032 + .156
= 32.25 − 6.71 = 25.54 periods = 12.77 years
.145 + .032
Return to question.
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c. If the YTM is expected to fall 40 basis points in the next year, by how
much would the price of the IBM bond change?
ΔP = −D ×
ΔP = −12.77 ×
Δy
1+ y
−.0040
= + 0.0495
1 + .032
+0.0495 × 1,076.25 = $53.27
The bond’s price will increase by approximately $53 if interest
rates fall by 40 basis points.
Return to question.
7–4
Analyze the relationships among bond ratings, yields, maturities, and
durations to determine comparative price volatility.
24. Consider the following three bonds and determine which bond is most
susceptible to price fluctuations.

Bond 1: A-rated, pays a coupon of 11%, matures in 12 years

Bond 2: AA-rated, pays a coupon of 12%, matures in 7 years

Bond 3: BBB-rated, pays a coupon of 9%, matures in 15 years
Bond 3 is most susceptible because it has the lowest rating, longest
maturity, and lowest coupon rate. (Bonds with lower coupon rates are
subject to greater price fluctuations than higher coupon bonds. If
interest rates rise, for example, the cash flows are discounted at the
higher rate, and the present value falls more than it would in a higher
coupon bond, in which more cash is provided in the form of interest
payments.)
Return to question.
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Valuation & Analysis of Fixed-income Investments
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25. Consider the following bonds.

Bond 1: BBB-rated, pays a coupon of 9%, matures in 6 years

Bond 2: BBB-rated, pays a coupon of 9%, matures in 11 years

Bond 3: BBB-rated, pays a coupon of 7%, matures in 11 years

Bond 4: BBB-rated, pays a coupon of 7%, matures in 6 years
a. Determine whether Bond 1 or Bond 2 has more potential for price
fluctuation and give a reason why.
Bond 2 has more potential for price fluctuation because it has a
longer maturity.
Return to question.
b. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Bond 3 has more potential for price fluctuation because it has a
lower coupon rate.
Return to question.
c. Determine whether Bond 3 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 3 has more potential for price fluctuation because it has a
longer maturity.
Return to question.
d. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 4 has more potential for price fluctuation because it has a
lower coupon rate.
Return to question.
Module Review
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99
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26. Consider the following bonds.

Bond 1: AA-rated, pays a coupon of 9%, matures in 7 years

Bond 2: BB-rated, pays a coupon of 9%, matures in 12 years

Bond 3: BB-rated, pays a coupon of 9%, matures in 7 years

Bond 4: AA-rated, pays a coupon of 9%, matures in 12 years
a. Determine whether Bond 1 or Bond 3 has more potential for price
fluctuation and give a reason why.
Bond 3 has more potential for price fluctuation because it has a
lower rating.
Return to question.
b. Determine whether Bond 2 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 2 has more potential for price fluctuation because it has a
lower rating.
Return to question.
c. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 4 has more potential for price fluctuation because it has a
longer maturity.
Return to question.
d. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Bond 2 has more potential for price fluctuation because it has a
longer maturity.
Return to question.
100
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Valuation & Analysis of Fixed-income Investments
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27. Consider the following bonds.

Bond 1: BBB-rated, pays a coupon of 8%, matures in 5 years

Bond 2: AA-rated, pays a coupon of 12%, matures in 5 years

Bond 3: BBB-rated, pays a coupon of 12%, matures in 5 years

Bond 4: AA-rated, pays a coupon of 8%, matures in 5 years
a. Determine whether Bond 1 or Bond 3 has more potential for price
fluctuation and give a reason why.
Bond 1 has more potential for price fluctuation because it has a
lower coupon rate.
Return to question.
b. Determine whether Bond 1 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 1 has more potential for price fluctuation because it has a
lower rating.
Return to question.
c. Determine whether Bond 2 or Bond 4 has more potential for price
fluctuation and give a reason why.
Bond 4 has more potential for price fluctuation because it has a
lower coupon rate.
Return to question.
d. Determine whether Bond 2 or Bond 3 has more potential for price
fluctuation and give a reason why.
Bond 3 has more potential for price fluctuation because it has a
lower rating.
Return to question.
Module Review
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101
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28. Review the Morningstar reports for the American Century Diversified Bond
fund and the AllianceBernstein Bond Corporate Bond fund.
American Century Diversified Bond Inv ADFIX
Key Stats
Morningstar
Category
Morningstar Rating
Intermediate-Term
Bond
NAV (01-07-05)
Day Change
$10.20
$0.00
Total Assets($mil)
Expense Ratio %
Front Load %
Deferred Load %
516
0.64
None
None
Yield % (TTM)
Min Investment
Manager
Start Date
3.21
$2,500
Jeffrey L. Houston
01-01-94
Morningstar Style Box
Average Eff Duration
3.79 Yrs
Average Eff Maturity
5.38 Yrs
Average Credit Quality
AAA
Data through 09-30-04
Volatility
Measurements
Trailing 3-Yr through 1231-04
*Trailing 5-Yr through 1231-04
Standard Deviation
4.20 Sharpe Ration
0.90
Mean
5.12 Bear Market Decile
Rank*
Modern Portfolio Theory
Statistics
Standard Index
LB Agg
R-Squared
Trailing 3- Yr through 12-31-04
Best Fit Index
Lehman Bros. U.S. Universal Bond
98
99
Beta
0.93
0.96
Alpha
-0.69
-1.45
102
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Valuation & Analysis of Fixed-income Investments
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AllianceBernstein Bond Corp Bd A CBFAX
Key Stats
Morningstar
Category
NAV
Morningstar Rating (01-07-05)
Day Change
Long-Term Bond
$12.33
$0.00
Total Assets($mil) Expense Ratio %
Front Load %
Deferred Load
%
875
1.16
4.25
1.00
Yield % (TTM)
Min Investment
Manager
Start Date
5.79
$1,000
Lawrence Shaw
08-05-02
Michael A. Snyder
08-05-02
Morningstar Style Box
Average Eff Duration
6.60 Yrs
Average Eff Maturity
20.40 Yrs
Average Credit Quality
BBB
Data through 03-31-04
Volatility
Measurements
Trailing 3-Yr through
12-31-04
Standard Deviation
8.57 Sharpe Ration
Mean
7.30 Bear Market Decile
Rank*
Modern Portfolio Theory Statistics
Standard Index
LB Agg
R-Squared
*Trailing 5-Yr through 1231-04
0.70
7
Trailing 3- Yr through 12-31-04
Best Fit Index CSFB High Yield
28
55
Beta
0.99
0.95
Alpha
1.34
–5.19
Module Review
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103
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
a. Which of the two funds would you expect to be more volatile, and why?
The AllianceBernstein bond fund should be more volatile because
its duration is 6.60 years, compared to a duration of 3.79 years for
the American Century bond fund. Also, the Alliance fund has
bonds with an average credit quality of BBB, compared to an
average quality of AAA for the American Century fund.
Return to question.
b. What evidence is there in the Morningstar report of the greater volatility
of the fund you chose?
The standard deviation and beta of the AllianceBernstein fund are
higher than those of the American Century fund.
Return to question.
7–5
Assess how changes in variables affect bond risk and price volatility.
29. In Question 21, you computed the duration and expected price change for
several types of bonds. The characteristics and the estimated percentage price
changes of those bonds are summarized in the following table (BP stands for
basis points).
Bond
Coupon
Market
Rate
Maturity
Duration
A
6
7
16
10.42
50 BP
4.9%
B
8
6
22
11.80
60 BP
6.9%
C
0
7
18
18.00
30 BP
5.2%
Δy
ΔP (%)
What conclusions can you reach about bond risk and volatility relative to
different characteristics of these bonds and changes in some of their
variables?
Bond C, the zero-coupon bond, has a maturity that is between the two
coupon bonds, yet the bond has a relatively large price change,
considering the relatively small change in the market interest rate.
Zero-coupon bonds have a large degree of price volatility because
they have no coupon payments to reduce duration.
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Bond B has a maturity that is six years longer than that of Bond A,
which should result in Bond B having a larger duration than Bond A.
Although this is the case, this effect is somewhat muted because
Bond B also has a larger coupon than Bond A. Larger coupons
reduce duration, while longer maturities increase duration. The
decrease in Bond B’s duration due to its higher coupon does not
totally offset its longer maturity, so Bond B’s duration is, in fact, higher
than Bond A’s duration. The higher duration of Bond B increases the
bond’s price volatility over that of Bond A. Bond A’s duration is also
helped somewhat by the bond’s higher market interest rate. The
higher market rate could be due to the fact that Bond A may have a
lower credit rating than Bond B, making it even more risky than its
duration alone indicates.
Return to question.
30. The following table shows characteristics of four bond funds. The funds are
listed in order of ascending credit quality. Fund A is a high-yield bond fund.
The last three bonds are also ranked by decreasing average maturity.
Review the data in the table and explain how each fund’s risk and volatility
is affected by the differences in variables.
Fund
Average
Credit
Quality
Average
Weighted
Coupon
Average
Maturity
Standard
Deviation
Average
Effective
Duration
Fund A
B
7.8
NA
3.74
3.8
Fund B
BBB
8.1
23.1
7.84
9.3
Fund C
A
7.3
12.5
3.92
5.9
Fund D
AA
7.9
4.4
2.1
3.3
The difference in credit quality seems to have little effect on the
bonds’ coupons. All are within one percentage point of one another.
The difference in coupon rates does not appear to have any
measurable effect on risk.
Module Review
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105
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As the average maturity of the non-high-yield bond funds decreases,
standard deviation and duration also decrease. Therefore, both risk
and volatility decrease as average maturity decreases. Although the
credit rating of the high-yield bond fund (Fund A with an average
credit quality of B) is low, the standard deviation and duration of the
fund is relatively low—in the same range as the A (Fund C) and AA
(Fund D) bond funds. Therefore, although this fund has some
potential unsystematic risk, its volatility risk is not significant.
Assuming sufficient diversification of bonds within the fund, the
unsystematic risk may also be minimal.
Return to question.
31. If you want to ensure that $40,000 is available in 13 years when your child is
about to enter college, would you select a zero-coupon bond that matures in
13 years or a coupon bond that matures in 13 years? Why did you select the
one you did?
The appropriate bond is the one with duration close to the duration of
the goal. The goal’s duration is 13 years. The appropriate bond is the
zero-coupon bond, since a zero’s duration is equal to its maturity. The
duration of a coupon bond is less than its maturity. The coupon bond’s
duration must be less than 13 years, since its maturity is 13 years.
Return to question.
32. If you have a risk-averse client who is concerned about fluctuating bond
prices, but who wants to have relatively high income from a bond portfolio,
how would you construct a bond portfolio so that you can help the client
resolve both of these apparently conflicting concerns?
You would construct a laddered bond portfolio. Although the exact
structure could take on any number of formats, one structure might be
to purchase bonds with 3-, 6-, 9-, 12-, 15-, and 18-year maturities.
The longer maturities would have higher coupons providing a high
income, but they would have significant interest-rate risk. The shorter
maturities would not provide much income, but their price fluctuations
would be small compared to the fluctuations of the 15- and 18-year
bonds. The overall portfolio would have an above-average income
and a below-average price volatility.
Return to question.
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33. Summarize all the relationships between price, coupon, maturity, interest
rates, and duration that you have discovered in this module.
 Bond prices and interest rate changes are inversely related.

Long-term bonds are more affected by interest rate changes than
are short-term bonds (i.e., they have longer durations and
therefore more price volatility).

Lower-coupon bonds are more affected by interest rate changes
than are higher-coupon bonds (i.e., they have more price
volatility).

Lower-rated bonds have more price volatility than higher-rated
bonds.

Bonds with longer durations are more volatile than bonds with
shorter durations.

There is a positive relationship between maturity and duration.

There is an inverse relationship between the market interest rate
(YTM) and duration.

There is an inverse relationship between coupon rate and
duration.
Return to question.
34. Explain the following bond portfolio management strategies.
a. tax swap
A tax swap occurs when an investor sells a bond for a capital loss
and immediately reinvests the proceeds in a bond of similar
characteristics (yield, maturity, credit rating, etc.), but one that is
from another issuer. The investor does this to recognize the
capital loss for tax purposes, and still maintain his or her bond
portfolio position.
Return to question.
Module Review
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b. substitution swap
A substitution swap occurs when an investor sells one bond and
purchases another bond with similar characteristics, but chooses
one with a higher yield-to-maturity.
Return to question.
c. intermarket spread swap
An intermarket spread swap is a variation of the substitution swap
in which the difference in yields (the spread) between two types of
bonds (e.g., corporate and government bonds) seems excessively
high.
Return to question.
d. pure yield pickup swap
A pure yield pickup swap occurs when an investor sells short-term
bonds and purchases long-term bonds to increase the yield on the
bond portfolio.
Return to question.
e. rate anticipation swap
A rate anticipation swap occurs when an investor believes that
interest rates will change dramatically and adjusts the maturity of
his or her portfolio accordingly. The investor who anticipates that
rates will rise will shorten the average maturity and duration of his
or her portfolio; the investor who anticipates that rates will fall will
lengthen the average maturity and duration of his or her portfolio.
Return to question.
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Valuation & Analysis of Fixed-income Investments
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f.
laddered portfolio
An investor uses a laddered strategy to minimize interest rate risk.
Instead of trying to anticipate which way interest rates will change,
the investor spreads out money invested in bonds over some
period of time (e.g., 1 to 10 years, every 5 years from 5 through 30
years, etc.). Regardless of which way interest rates move, the
investor will have some bonds that benefit and some that suffer.
Return to question.
g. barbell portfolio
A barbell approach is a more dramatic variation of the laddering
strategy. Very short-term and very long-term bonds are purchased
so that the bond portfolio is heavily weighted in both long- and
short-maturity issues, with no bonds in the middle. The purpose is
similar to that of the laddering approach.
Return to question.
h. immunization
Immunization is an approach that attempts to match the duration
of a bond portfolio with the duration of cash needs. It is used
frequently by financial institutions and retirement plans that have
cash obligations that can be calculated with some degree of
precision as to their time requirements.
Return to question.
Module Review

109
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7–6
Evaluate investor profiles to recommend appropriate fixed-income
securities for purchase.
35. Robert Berens, age 65, is retiring and has $150,000 to invest. He is interested
in purchasing fixed-income securities to provide for his income needs during
retirement. Robert will not have any other substantial income, and he will be
in the 15% marginal income tax bracket. He has invested in bonds in the
past, and he plans to be actively involved in this investment.
What kind of fixed-income security is appropriate for Robert, and why?
(Consider type, risk rating, marginal tax bracket, term, and other relevant
factors.)
A high-grade corporate bond (AA or AAA), a Treasury note or bond,
or a federal agency security like a Ginnie Mae would be appropriate.
All of these can be bought at par, pay periodic income, and have good
marketability. Because he is in a low marginal tax bracket, taxable
securities would most likely provide more after-tax income than
municipal bonds. An intermediate term of 7 to 15 years would give
adequate yield with only moderate interest rate risk.
Return to question.
36. John Bloom, age 49, wants to take early retirement next year when he turns
50. He wants to invest $200,000 in a fixed-income security to provide him
with additional income. He estimates that he will be in the 33% marginal tax
bracket. He has invested previously, and he is willing to be aggressive with
this investment to increase his return.
What kind of fixed-income security is appropriate for John, and why?
(Consider type, risk rating, marginal tax bracket, term, and other relevant
factors.)
Because of his high tax bracket, municipal revenue bonds are
appropriate, assuming their equivalent yield exceeds the yield of
corporate bonds. Purchasing bonds with lower ratings (BB or BBB)
would be consistent with his aggressive attitude of attempting to
increase his return while realizing additional income from this
investment. If rates fall, longer maturities may be appropriate to
provide capital gain potential.
Return to question.
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Valuation & Analysis of Fixed-income Investments
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37. Kent Walters, age 32, has $40,000 to invest in a fixed-income security. He
has invested in various types of bonds for 10 years, he considers himself to
be an aggressive investor, and he is in the 28% marginal income tax bracket.
His primary goal is capital appreciation; income is a secondary consideration.
Kent’s financial planner has presented the following securities and their
before-tax yields.
a. 15-year, BB-rated, noncallable corporate bonds trading near par with a
yield of 6.8%
b. 20-year, A-rated, discount, public purpose, callable general obligation
municipal bonds with a taxable-equivalent yield of 7.2%
c. 10-year, A-rated, premium, callable, sinking fund, corporate bonds with
a yield of 4.5%
d. Treasury bills with a yield of 2.5%
Which one of these fixed-income securities would be an appropriate choice
for Kent, and why?
Investment “b.” is an appropriate choice. On an after-tax basis, it has
the highest return (5.18%), and when compared to the BB-rated
bonds with a 4.90% after-tax return, the municipal bonds have a
higher after-tax yield with a better risk rating. Compared to the A-rated
corporate bonds, the municipal bonds are less likely to be called since
they are trading at a discount. There is no reason for the investor to
seek the security of Treasuries (with a 1.80% after-tax return), given
his aggressive risk profile. Also, since his primary goal is capital
appreciation, the discounted, 20-year bond is most likely to provide
capital gains if interest rates decrease.
Return to question.
Module Review

111
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
38. Kathy Connelly, age 20, is just starting college and needs to invest $25,000
in fixed-income securities. She is in the 15% tax bracket and plans to use the
interest income and principal as needed to pay her college expenses for the
next four years. She is looking for a low-risk investment, and she knows she
must receive principal periodically from these securities. The following
securities are available to Kathy at the before-tax yields indicated.

Investment A: BB-rated, public purpose, municipal revenue bonds with
an after-tax yield of 7.0%

Investment B: 12-year, B-rated, discount, callable corporate bonds with a
before-tax yield of 8.8%

Investment C: eight-year Treasury notes with a before-tax yield of 6.8%

Investment D: AA-rated, noncallable, five-year corporate bonds with a
before-tax yield of 8.5%
Which one of these securities would be an appropriate choice for Kathy, and
why?
Investment D is most appropriate. Because Kathy is in a marginal tax
bracket of 15%, the municipal bonds, which have a poor risk rating,
result in a taxable equivalent return of only 8.2%. The Treasury notes
are too long term, and they subject her to too much interest rate risk.
The B-rated bonds are too speculative, and they also have too long of
a time frame.
Return to question.
39. Answer the following questions about selecting bonds for client portfolios.
a. What sort of characteristics would you look for in a bond chosen for a
client with a high risk tolerance?
a bond with a high duration, a low or zero coupon, a long maturity,
and a relatively low credit rating
Return to question.
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b. What sort of characteristics would you look for in a bond chosen for a
client with a moderate risk tolerance?
a bond with a moderate duration (5 to 10 years) and an
intermediate maturity (7 to 15 years), a coupon that is near current
market rates, and a low investment grade credit rating, such as A
or BBB
Return to question.
c. What sort of characteristics would you look for in a bond chosen for a
client with a low risk tolerance?
a bond with a low duration and a short maturity, a coupon that is
at current market rates, and a high investment-quality rating
Return to question.
d. If you believe that interest rates will decline sharply in the future, what
bond characteristics would you search for?
bonds that have long maturities and high durations and that have
low (or zero) coupons
Return to question.
e. If you believe that interest rates will rise sharply in the future, what bond
characteristics would you search for?
bonds that have short maturities and low durations and that have
(if available) high coupon rates
Return to question.
Module Review

113
© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
7–7
Calculate the conversion value, investment value, investment
premium, conversion premium, and downside risk of convertible
securities.
40. Janice Carlysle owns a ZZT Corporation convertible bond. The bond has a
9.5% coupon rate that is paid semiannually; the bond matures in 8 years.
Comparable debt (with the same rating and maturity date) is yielding 11%.
Janice’s bond is convertible at $27 a share, the current market price of ZZT
common stock is $35, and the bond sells for $1,400.
a. What is the conversion value of the bond?
The conversion value is $1,296.30, which is computed as follows:
CV =
Par
1,000
× Ps =
× 35 = $1,296.30
CP
27
Return to question.
b. What is the investment value of the bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
8, SHIFT,
xP/YR
I/YR
PV
PMT
11
?
47.50
1,000
HP-12C:
N
I
PV
PMT
FV
16
5.5
?
47.50
1,000
Answer: $921.53
Return to question.
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FV
c. What is the bond’s investment premium?
The investment premium is $478.47, the difference between the
bond’s market price of $1,400 and the bond’s investment value of
$921.53.
Return to question.
d. What is the bond’s conversion premium?
The conversion premium is $103.70, the difference between the
bond’s market price of $1,400 and the bond’s conversion value of
$1,296.30.
Return to question.
e. What is the downside risk percentage of the bond?
The downside risk is 34.2%, which is computed as follows:
1, 400 − 921.53
= 34.2%
1, 400
If the price of the underlying stock falls substantially, the maximum
that the price of the bond can fall is about 34%. You always use
the difference between the market value and the investment value
(not conversion value, even if higher) to determine downside risk.
Return to question.
41. James Perry owns a QV Inc. convertible bond. The bond has a coupon rate of
10% that is paid semiannually; the bond matures in 12 years. Comparable
debt yields 8% currently. His bond is convertible into 24 shares of stock. The
current market price of QV common stock is $34, and the bond sells for
$1,200.
a. What is the conversion value of the bond?
The conversion value is $816.00, which is computed as follows:
(Note that the conversion ratio is given and does not have to be
computed.)
CV =
Par
× P s = 24 × 34 = $816.00
CP
Return to question.
b. What is the investment value of the bond?
Set the calculator to “end.”
Module Review
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HP-10BII+:
P/YR
N
2
12,
SHIFT,
xP/YR
I/YR
PV
PMT
FV
8
?
50
1,000
HP-12C:
N
I
PV
PMT
FV
24
4
?
50
1,000
Answer: $1,152.47
Return to question.
c. What is the bond’s investment premium?
The investment premium is $47.53 (the difference between the
bond’s market price of $1,200 and the bond’s investment value of
$1,152.47).
Return to question.
d. What is the bond’s conversion premium?
The conversion premium is $384.00 (the difference between the
bond’s market price of $1,200 and the bond’s conversion value of
$816.00).
Return to question.
e. What is the downside risk percentage of the bond?
The downside risk is 3.97%, which is computed as follows:
1,200 − 1,152.47
= 3.97%
1,200
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If the price of the underlying stock falls substantially, the maximum
that the price of the bond can fall is less than 4%.
Return to question.
42. Assume that a convertible bond has a face value of $1,000 and that it is
selling in the market for $890. Its conversion price is $50 per share. The
underlying common stock is selling for $38 per share. The bond pays $40
semiannually in interest and matures in 20 years. The market interest rate on
comparable bonds is 12%.
a. What is the bond’s conversion ratio?
The conversion ratio is the face value divided by the conversion
price.
CR =
1,000
= 20 shares
50
Return to question.
b. What is the conversion value?
The conversion value is the conversion ratio times the market
price of the stock.
CV = 20 × 38 = $760
Return to question.
c. What is the investment value of the convertible bond?
Set the calculator to “end.”
HP-10BII+:
P/YR
2
N
I/YR
PV
PMT
FV
20,
SHIFT,
xP/YR
12
?
40
1,000
Module Review
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HP-12C:
N
I
PV
PMT
FV
40
6
?
40
1,000
Answer: $699.07
Return to question.
d. Express the downside risk as a percentage.
The downside risk is 21.5%, which is computed as follows:
890 − 699
= 21.5%
890
Return to question.
43. An investor can obtain 1.5 shares of common stock through conversion of 1
share of preferred stock. The price of the common stock is $35. The
convertible preferred stock has no maturity date and pays an annual dividend
of $3. The yield on comparable nonconvertible preferred stock is 12%.
a. What is the conversion value of this convertible preferred stock?
The conversion value is $52.50, which is computed as follows:
1.5 × $35 = $52.50
Return to question.
b. What is the investment value of this convertible preferred stock?
The investment value is $25, which is computed as follows:
$3
= $25
.12
Return to question.
44. If preferred stock does not have a required sinking fund or call feature, it may
be viewed as a perpetual debt instrument. How is the intrinsic value of this
type of preferred stock calculated?
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The fixed annual dividend (D) of this type of preferred stock is divided
by the yield (r) being earned on comparable preferred stock of a
similar grade.
P
=
D
r
Return to question.
45. Explain how to determine the intrinsic value of preferred stock that has a
finite life.
The intrinsic value of preferred stock that has a finite life is equal to
the present value of the dividend payments plus the present value of
the amount that is returned to the stockholder when the preferred
stock is retired. The keystrokes for this are the same as those for a
bond valuation problem.
Return to question.
46. If a preferred stock pays an annual dividend of $5 and investors can earn
12% on alternative, comparable investments, what is the price that should be
paid for this stock?
The price paid should be $41.67.
P=
5
= $41.67
.12
Return to question.
47. If the preferred stock in the previous question had a call feature, and if
investors expected the stock to be called for $100 after 12 years, what price
would be paid for this stock?
Set the calculator to “end.”
HP-10BII+ & HP-12C:
P/YR
1
N
I/YR
12
12.0
PV
?
PMT
5
FV
100
Answer: $56.64
Return to question.
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7–8
Analyze the relationships among conversion value, investment value,
and market value of convertible securities.
48. In the following figure, what does the shaded area represent?
Bond
Price
($)
Market price
Conversion
value line
A
Investment
value of bond
Stock Price ($)
The shaded area represents the premium that an investor might pay
to purchase a convertible bond. Since a convertible bond is, in
essence, a straight bond plus an option contract, an investor usually
pays more for such a bond than its value as a straight bond. The
shaded area also represents the downside risk of the bond. The
premium will be small until the value of the underlying stock rises
above the intersection of the conversion value and the investment
value. Above that point, the convertible bond will act more like a stock
than a bond.
Return to question.
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References
Bank for International Settlements, <www.bis.org> (November 2009, November
2011).
Bodie, Zvi, and Marcus Kane, Investments, 5th edition. New York: McGraw Hill,
2002.
Bondsonline Group Inc., <www.bondsonline.com> (December 2006).
Dow Jones & Company Inc., The Wall Street Journal Online, <www.wsj.com>
(December 2006).
Fabozzi, Frank J., Fixed Income Analysis, 2nd edition. Hoboken, NJ: John Wiley
& Sons, 2007.
Fabozzi, Frank J., Fixed Income Analysis for the Chartered Financial Planner
Analyst® Program, 2nd edition. New Hope, PA: Frank J. Fabozzi Associates,
2004.
Gitman, Lawrence J., and Michael D. Joehnk, Fundamentals of Investing.
Boston: Pearson, Addison Valley, 2005.
Mayo, Herbert B., Investments: An Introduction, 8th edition. Mason, OH: SouthWestern, 2006.
Morningstar Inc., Morningstar Principia Pro Plus for Mutual Funds. Chicago:
Morningstar Inc., 1998, 2007, 2009.
Reilly, Frank K., and Keith C. Brown, Investment Analysis and Portfolio
Management, 8th edition, Mason, OH: South-Western, 2006.
Solnik, Bruno, and Dennis McLeavey, International Investments, 5th edition.
Pearson Addison Wesley, 2003.
Vanguard Mutual Funds, <www.vanguard.com> (December 7, 2012).
References
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.
About the Author
Jason G. Hovde, CIMA®, CFP®, APMA® is the Senior
Director of Certification and Designation Programs as well
as an Associate Professor at the College for Financial
Planning. Prior to joining the College, Jason had a financial
planning/investment advisory practice and was a branch
manager for one of the largest independent broker-dealers in
the country. Additionally, he spent several years with another
independent broker-dealer, first as a trader and options principal, and then as a
member of the senior management team. Jason holds two bachelor’s degrees, one
in accounting and the other in behavioral science from Metropolitan State
University of Denver, as well as an MBA in finance and accounting from Regis
University. You can contact Jason at jason.hovde@cffp.edu.
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Index
A master index covering all modules of this course can be found in the Self-Study
Examination book.
Bond calculations, 8
immunization, 42
current yield, 14
ladders and barbells, 43
price, 13
yield-to-call (YTC), 7
taxable-equivalent yield, 8
yield-to-maturity (YTM), 7
yield and valuation, 11
Convertible bonds, 50
yield-to-call, 18
bond investment value, 52
yield-to-maturity, 17
conversion premium, 53
zero-coupon price, 14
conversion value, 51
Bond swaps, 44
convertible preferred stock, 56
intermarket spread, 45
convertible sample calculations, 55
pure yield pickup, 44
downside risk, 54
rate anticipation, 45
investment premium, 53
substitution, 45
Convexity, 36
tax, 46
Duration, 21
Bonds
computations, 27
calculations, 8
convexity, 36
current yield, 5
modified, 35
Index
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© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.