Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
What is it?
• Yield measures the annual (or semi-annual, or some
other time period) rate of return on an investment in
fixed income securities
• In evaluating fixed income investments, the investor is
faced with a variety of measures of investment return
or yield; these include current yield, yield-to-maturity,
yield-to-call, after-tax yield, taxable equivalent yield,
and realized compound yield
Copyright 2007, The National Underwriter Company
1
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Fixed income terminology
• Bonds represent debt
– The issuer of the bond is borrowing funds
• The original purchaser of the bond is effectively making a loan to
the issuer
– The principal of the bond is the amount the issuer borrows
and promises to repay
• Also referred to as face value or par value
– The maturity date is the date on which the issuer promises to
repay the principal
– The coupon rate is the interest rate the issuer promises to
pay each period on the borrowed funds
• Also known as stated rate
• Usually paid semi-annually
• Zero coupon bonds
Copyright 2007, The National Underwriter Company
2
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Example
• Palmetto Enterprises, Inc. issues bonds with a total
face value of $10,000,000 on July 1, 2006. The bonds
pay a coupon rate of 3.5% semi-annually and mature
in 5 years on June 30, 2011. Purchasers of each
$1,000 bond will receive cash interest payments of $35
every six months, on December 31 and June 30. The
company will pay each $1,000 bondholder $35 in
interest on each of these dates and promises to repay
the $1,000 at maturity.
Copyright 2007, The National Underwriter Company
3
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
• If the coupon rate is equal to required rate of return,
then there will be no discount or premium on the bond
• If the risk level of the investment requires a rate of
return that differs from the coupon rate, the investor
must calculate the present value of the future cash
flows of the bond using the appropriate discount rate to
determine the price
• Equation 34-1
V0 
C3
Cn
C1
C2



...

(1  r )1 (1  r ) 2 (1  r ) 3
(1  r ) n
– Where V0 is the current value, C is the cash flow for each
period (1, 2, 3...), r is the required rate of return and n is the
number of periods
Copyright 2007, The National Underwriter Company
4
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
• In the case of a bond, the cash flows include interest to
be received each semi-annual period and the face
value to be received at maturity. This can be
expressed as:
• Equation 34-2
C3
Cn
Facen
C1
C2
V0 


 ... 

1
2
3
n
(1  r ) (1  r )
(1  r )
(1  r )
(1  r ) n
– In this version of the discounted cash flow equation, C
represents each periodic coupon payment and Face
represents the face or par value of the bond to be received at
maturity (n).
Copyright 2007, The National Underwriter Company
5
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
Semiannual
Period
1
2
3
4
5
6
7
8
9
10
Total
Cash
Flow
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
• Cash Flows for
Palmetto Enterprises
– 5 years
• Ten semi-annual periods
– Face value of bond
received in period 10
along with final coupon
payment.
1,035.00
1,350.00
Copyright 2007, The National Underwriter Company
6
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
Semiannual
Period
1
2
3
4
5
6
7
8
9
10
Total
Cash
Flow
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
1,035.00
1,350.00
Present
Value
33.65
32.36
31.11
29.92
28.77
27.66
26.60
25.57
24.59
699.21
959.45
• Cash Flows for
Palmetto Enterprises
discounted at
investor’s rate of
return (4%)
Copyright 2007, The National Underwriter Company
– Worth only 959.45 in
today’s dollars given a
desired return of 4%
– Fair price of bond to
satisfy investor’s
7
required rate of return
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
Semiannual
Period
1
2
3
4
5
6
7
8
9
10
Total
Cash
Flow
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
35.00
1,035.00
1,350.00
Present
Value
33.98
32.99
32.03
31.10
30.19
29.31
28.46
27.63
26.82
770.14
1,042.65
• Cash Flows for
Palmetto Enterprises
discounted at
investor’s rate of
return (3%)
Copyright 2007, The National Underwriter Company
– Worth 1042.65 in
today’s dollars given a
desired return of 3%
– Fair price of bond to
satisfy investor’s
8
required rate of return
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
• Summary
Desired Semi-annual
Rate of Return
4.0%
3.5%
3.0%
Copyright 2007, The National Underwriter Company
Present Value
of Bond
_
$ 959.45
$1,000.00
$1,042.65
9
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
• Required Rate of Return
– Market rate of interest
• Rate of return that market participants require in order to
purchase a particular bond or other offerings that are functionally
equivalent
– Yield to maturity
• The yield expected if the bond is held to its maturity date
• Rate of return that will make the net present value of investing in
the bond zero, assuming:
– the bond is held to maturity
– all promised interest and principal payments are received when due
– coupon payments can be reinvested at the same rate of interest
Copyright 2007, The National Underwriter Company
10
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Pricing
Equation 34-3
Present Value of Future Cash Flows
Less:
Initial Investment_
Equals: Net Present Value
Copyright 2007, The National Underwriter Company
11
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Market Interest Rates
• There are two primary components to the required
rate of return: the risk free rate and a risk premium
• A risk-free asset is one whose future return can be
predicted with near certainty
– Ex. 3 month treasury bill
– A risk-free rate of return is a return that would be expected if
an investment had virtually no risk
• Inflation is a major factor
Copyright 2007, The National Underwriter Company
12
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Market Interest Rates
• Risk premium
– The additional return that must be paid to compensate
investors for additional risk
• Yield Spread
– The difference between the bond’s yield to maturity and that
of a risk-free bond (e.g., a government bond) with otherwise
similar underlying characteristics (such as maturity)
• Bond’s credit rating
– Often correlates with the additional rate of return required by
risky corporate debt in excess of that required for a U.S.
government bond of the same maturity
Copyright 2007, The National Underwriter Company
13
Reuters Corporate Spreads for Industrials as of 06/30/04
Rating
1 yr
2 yr
3 yr
5 yr
7 yr
10 yr
30 yr
Aaa/AAA
5
10
15
22
27
30
55
Aa1/AA+
10
15
20
32
37
40
60
Aa2/AA
15
25
30
37
44
50
65
Aa3/AA-
20
30
35
45
53
55
70
A1/A+
30
40
45
58
62
65
79
A2/A
40
50
57
65
71
75
90
A3/A-
50
65
79
85
82
88
108
Baa1/BBB+
60
75
90
97
100
107
127
Baa2/BBB
65
80
88
95
126
149
175
Baa3/BBB-
75
90
105
112
116
121
146
Ba1/BB+
85
100
115
124
130
133
168
Ba2/BB
290
290
265
240
265
210
235
Ba3/BB-
320
395
420
370
320
290
300
B1/B+
500
525
600
425
425
375
450
B2/B
525
550
600
500
450
450
725
B3/B-
725
800
775
800
750
775
850
1500
1600
1550
1400
1300
1375
1500
Caa/CCC
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• The coupon rate of interest determines the periodic
cash interest payment that will be made by the issuer to
the bondholders
• The yield-to-maturity is the effective rate that the
bondholder expects to receive based upon the actual
selling price of the bond
– Not necessarily the same rate the issuer pays in interest and
principal repayments
• Only if the bond is sold at par value will the coupon rate
equal the yield to maturity
Copyright 2007, The National Underwriter Company
15
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• If the bond is callable (redeemable by the issuer prior to
maturity at a pre-determined price), it is also useful for
the bondholder to compute the expected yield-to-call.
• Equation 34-4
V0 
C3
Cn
Call Pr ice n
C1
C2



...


(1  r )1 (1  r ) 2 (1  r ) 3
(1  r ) n
(1  r ) n
– As before, V0 is the selling price of the bond. Now n is the
number of periods to the call date and Call Price is the price to
be received by the bond holder if the bond is called
– The call price usually includes a small “call premium”
Copyright 2007, The National Underwriter Company
16
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• Using our example, the bond is initially offered at par
value of $1,000.00 and is callable at the end of six
periods (three years) at 102. V0 is $1,000, Call Price
is $1,020, each coupon payment is $35 and n is 6.
Solving for r results in a value of 3.803% semiannually. This is the bond’s yield-to-call at issue.
Copyright 2007, The National Underwriter Company
17
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• It was noted earlier that the rate of return actually realized
on a bond investment held to maturity could differ from
the expected yield-to-maturity (or yield-to-call)
• This is due to reinvestment risk
– Consider the $1,000 bond from Example 34-1. If it is sold at par
value, then our expected yield to maturity is 3.5% semi-annually
– If interest rates subsequently fall to 3% before any coupon
payments are received, the investor must reinvest those amounts
at only 3%
• The bondholder’s wealth at the end of the period is $1,401.24
• This is comprised of the accumulated coupon payments reinvested at
3% semi-annually and the principal which is received at maturity
Copyright 2007, The National Underwriter Company
18
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• This is due to reinvestment risk
– The realized compound yield can be found by solving an
internal rate of return problem
• $1,000 is the initial investment (Present Value), $1,401.24 as the
wealth at the end of 10 periods (Future Value), and 10 is the
number of periods.
• Solving for the rate of return results in a realized compound yield of
3.43%
• Lower than our expected yield to maturity of 3.5% since our interest
payments were reinvested at a lower rate.
Copyright 2007, The National Underwriter Company
19
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• Other than municipal bonds, most bonds are subject to
income tax. Expression of the after-tax yield becomes
important.
• Equation 34-5
After Tax Yield  Before Tax Yield  (1  Tax Rate)
– If the expected semi-annual yield-to-maturity is 3.5% and our
tax rate is 25%, our after-tax yield would be 2.625% on a semiannual basis.
Copyright 2007, The National Underwriter Company
20
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• In the case of a non-taxable bond (municipal bond), you
can reverse the process to determine the taxable
equivalent yield of a tax-free bond
• Equation 34-6
Tax Free Yield
Taxable EquivalentYield 
(1  Tax Rate)
– If a municipal bond has a tax-free yield-to-maturity of 3% and
our tax rate is 25%, then the taxable equivalent yield would be
4.0%.
Copyright 2007, The National Underwriter Company
21
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• Annualized yields
– Interest rates must be compounded
• Interest earned on interest received during the year
• Equation 34-7
Annualized Yield  ((1 NonAnnualizedYield )n  1)*100
– Where n is the number of compounding periods and Non
Annualized Yield is expressed in decimal format
– 3.5% (0.035) semi-annual yield to maturity converts to an
annualized yield of 7.1225%
Copyright 2007, The National Underwriter Company
22
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• The current yield is an approximation as to how much
the bondholder is earning from his investment on a
current or short-term basis
– Measured as the annual coupon interest payment divided by the
price of the bond
• If our $1,000 bond is sold at par, the current yield would be ($35 X
2)/$1000 or 7.0%
• When a bond is sold at par, the annual coupon rate, expected yield
to maturity, and current yield are all equal
• For a bond sold at a premium ($1,042.65 in our example), the
current yield (6.71%) is less than the coupon rate (7%) and more
than the expected yield to maturity (6.1%)
• For a discount bond ($959.45 in our example), the current yield
(7.3%) is more than the coupon rate (7%) but less than the
expected yield to maturity (8.16%).
Copyright 2007, The National Underwriter Company
23
Selected Wall Street Journal Corporate Bond Data as of
Thursday July 13, 2006
Maturity
Last
Price
Last
Yield
EST
Spread
US
T
EST $
Vol
(000’s)
6.450
May 01,
2036
96.413
6.729
155
10
57,055
7.500
Apr. 15,
2032
110.13
0
6.670
150
30
50,000
Company (ticker)
Coupo
n
Goldman Sachs
Group (GS)
Valero Energy
Corp (VLO)
Last Yield is the yield-to-maturity of the bond based upon its last price. EST
Spread is estimated spread in basis points over U.S. Treasury Security with
maturity listed under UST. EST $ Vol is the total dollar volume of activity in that
bond.
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Bond Yields
• The Goldman Sachs bond is selling at a discount
(96.413%) to par value.
– The yield-to-maturity is higher than the promised coupon
payment
– This bond matures in 30 years and offers a spread or premium
over ten-year U.S. Government bonds of 155 basis points
• The Valero Energy bond on the other hand is offering a
higher coupon rate than is required given its risk and it
is therefore selling at a premium
– The yield-to-maturity is 6.670% versus a coupon rate of 7.50%
Copyright 2007, The National Underwriter Company
25
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Inverse relationship between interest rates (required
returns) and bond prices
– When interest rates rise, bond market prices decline
• Some bonds are more sensitive to changes in interest
rates than others
Copyright 2007, The National Underwriter Company
26
Price
Price Versus Yield to Maturity
$1,400.00
$1,300.00
$1,200.00
$1,100.00
$1,000.00
$900.00
$800.00
$700.00
$600.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.0
%
%
%
%
%
%
%
%
%
% 0%
YTM
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Nonlinear relationship between bond yields and bond
prices
– 1% (relative) change in interest rates does not necessarily
result in a 1% (relative) change in the price of the bond
• From our previous example and the above graph, we
know that if the required market rate of interest is 3.5%
semi-annually, the bond price should be $1,000.00
Copyright 2007, The National Underwriter Company
28
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• If interest rates decline to 3% semi-annually, then the
bond price will rise to $1,042.65
– The price of the bond rose by $42.65, which is 4.265% of the
original price
• A 100 basis point (or 1% absolute) decline in annual interest rates,
which equates to a 50 basis point (or 0.5%) semi-annual move in
rates, caused the price of the bond to change by 4.265% and in
the opposite direction
• This is a measure of the bond’s volatility
• A more volatile bond will show a greater change in price
for a given change in interest rates.
Copyright 2007, The National Underwriter Company
29
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
Semiannual
Period
Cash
Flow
Present
Value
PV
times
Period
1
35.00
33.82
33.82
2
35.00
32.67
65.35
3
35.00
31.57
94.70
4
35.00
30.50
122.00
5
35.00
29.47
147.35
6
35.00
28.47
170.84
7
35.00
27.51
192.57
8
35.00
26.58
212.64
9
35.00
25.68
231.13
10
1,035.00
733.73
7337.31
Total
1,350.00
1,000.00
8,607.69
• Duration
•
– The weighted average time until
receipt of all of a bond’s cash flows.
n
Ct (t )
Equation 34-8

t
t 1 (1  i )
Dur  n
Ct

t
t 1 (1  i )
• This is the weighted average
maturity of the bond’s cash flow
expressed in years
Copyright 2007, The National Underwriter Company
– changes as the price and yield to
maturity change
– Macaulay duration for Frederick
Macaulay who derived it in a paper
published in 1938
– 4.3 years for this example
30
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Macaulay duration can be approximated without the
calculation of each year’s present values
• Equation 34-9
1  y (1  y )  T (c  y )
Dur 

y
c (1  y ) T  1  y


– Where y is the yield to maturity, c is the coupon rate and T is
the time to maturity
– For our sample bond using y = .035, c =.035 and T=10 (all in
periods) yields an approximation for duration of 8.6 periods or
4.3 years.
Copyright 2007, The National Underwriter Company
31
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Modified Duration
• Equation 34-10
Macaulay Duration
D
1 y
– Where D is modified duration and y is the yield to maturity per
period (the annual yield to maturity divided by the number of
compounding periods per year). For our previous sample
bond, 4.3/1.035 equals 4.15
Copyright 2007, The National Underwriter Company
32
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Equation 34-11
P
  D ( y )
P
• Where ∆y is the change in annual yield in decimal form
• A decline in semi-annual interest rates from 3.5% to
3%. In decimal form this is 0.01 (1%)
– A decrease of 100 basis points on an annual basis should
cause the bond price to change by approximately -4.15*(-.01)
= +0.0415 or +4.15%.
• This is close to the observed price increase from $1,000.00 to
$1,042.65 or about 4.265%.
Copyright 2007, The National Underwriter Company
33
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Example 34-2: TRR Financial Enterprises is raising
debt to fund a business acquisition. In order to
preserve cash flow while integrating this new
business, TRR decides to issue zero-coupon bonds
with a total face value of $5,000,000. Each $1,000
bond matures in 5 years. Given the risk level of TRR
and current market conditions, investors desire a 4%
semi-annual rate of return on their investment.
Copyright 2007, The National Underwriter Company
34
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Only one cash flow involved
– The investor will receive $1,000 at maturity in five years
• The present value of $1,000 over 10 semi-annual periods at a
4% semi-annual rate is $675.56
• This is 67.556% of par value and a substantial discount to
$1,000.
• Duration
– In this special case, duration is equal to the remaining life of
the bond (5 yrs)
Copyright 2007, The National Underwriter Company
35
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• Across all bonds, a higher duration equates to higher
bond price volatility
– Zero-coupon bonds are more volatile than other bonds of the
same maturity, all else being equal
– Bonds with a longer maturity (hence a longer duration) are
more volatile than bonds of shorter maturity
• Curvilinear relationship between interest rates and
bond prices
– Duration measures the slope of a line tangent to the curve at
a particular point.
• One must consider convexity, which is a measure of the
curvature of the relationship between bond yields and prices
Copyright 2007, The National Underwriter Company
36
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
Semiannual
Period
Cash
Flow
Present
Value
PV
times
Period
PV times
t times
(t+1)
1
35.00
33.82
33.82
67.63
2
35.00
32.67
65.35
196.04
3
35.00
31.57
94.70
378.82
4
35.00
30.50
122.00
610.01
5
35.00
29.47
147.35
884.07
6
35.00
28.47
170.84
1,195.85
7
35.00
27.51
192.57
1,540.54
8
35.00
26.58
212.64
1,913.72
9
35.00
25.68
231.13
2,311.25
10
1,035.00
733.73
7,337.31
80,710.41
Total
1,350.00
1,000.00
8,607.69
89,808.33
Copyright 2007, The National Underwriter Company
• Convexity is determined by
taking our duration
computation one step
further and multiplying PV
times t by t+1
• Convexity = Total divided by
price of bond times number
of compounding periods
squared times one plus
yield squared.
• 89,808.33/
• ((1,000.00*4)*(1.035)2)
• = 20.9593.
37
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Price, Duration and Convexity
P
1
2
  D(y )  Convexity(y )
P
2
Copyright 2007, The National Underwriter Company
38
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Interest Rate Volatility
• The change in price for a 100 basis point decline in
interest rates can be measured as
– (-4.15(-.01) + 0.5*20.9593*(0.0001) = 0.0423 or 4.255%
– The bond actually increased in value 4.265%.
• Convexity is always a good thing for the bond investor,
regardless of whether interest rates rise or fall
– If interest rates fall, convexity augments the increase in the price of
the bond.
– If interest rates rise, convexity dampens the decline in the price.
• The combination of duration and convexity allows us to predict
movements in our bond’s value for expected changes in interest
rates
Copyright 2007, The National Underwriter Company
39
Measuring Yield
Chapter 34
Tools & Techniques of
Investment Planning
Special Cases
• U.S Treasury Bills
– Short term securities issued for
13, 26 and 52 week periods
• These are issued on a discount
basis (zero coupon), in
increments of $1,000 face value
• The price quotes for Treasury
bills are somewhat unusual
compared to other fixed income
investments and warrants some
explanation
• Consider the following quote
from the U.S. Treasury web site
(www.publicdebt.treas.gov):
Copyright 2007, The National Underwriter Company
Term:
Issue Date:
Maturity Date:
Discount Rate:
Investment Rate:
Price Per $100:
CUSIP:
182-Day
09-28-2000
03-29-2001
5.985%
6.258%
96.974
912795FZ9
40
Measuring Yield
Chapter 34
Tools & Techniques of
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• Treasury bill prices are quoted in terms of the Discount Rate
– The price is derived by computing the discount based upon a
360 day year and the maturity in days of the bill:
• 100 – ((182/360) x (5.985% x 100)) = 96.974
• Examine the annualized yield-to-maturity rather than the
discount rate
– To compute the yield to maturity on a Treasury Bill, calculate
the internal rate of return for a single period with a present
value of 96.974 and a future value (par) of 100.000.
– The resulting rate is 3.1204%, which is the yield to maturity for
a 182 day period.
– The annualized rate listed by the Treasury is 3.1204%*365/182
or 6.258%.
• This is not a compounded rate.
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Special Cases
• Convertible bonds
– The conversion feature allows the investor to exchange the
bond for a pre-specified amount of another security, typically a
common stock
– Convertibles offer much of the upside potential of an equity
security and the downside protection of a bond
• The upside portion: the holder has the right to surrender the bond
in exchange for a fixed number of shares of the common stock,
which rise in value if the shares appreciate
• The downside protection:
– the bondholder need not acquire the stock if its price does not rise
– the investor can hold the bond to maturity and collect its face value at
maturity or sell it to another investor in the interim period.
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Special Cases
• Convertibles bonds pay the coupon rate of interest
semi-annually on the face amount of the security
– Convertible bond with a $1,000 face value and a coupon rate
of 5.5% will pay $27.50 (i.e., ½ X .055 X $1,000) twice each
year
– Assume this convertible bond can be converted into 16 2/3
shares of common stock
• Implies a conversion price of $60, which is simply the face value
($1,000) divided by the conversion ratio (16.667)
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Special Cases
• Evaluate both parts of hybrid security
– If the current price of the stock of the issuer is $50 and the
investor could elect to surrender the bond today in exchange for
16 2/3 shares
• Clearly, the convertible could not be priced less than $833.33 (16 2/3
shares X $50 per share) in today’s market because investors would
simply buy and convert it, thereby reaping an immediate (arbitrage)
profit
• The $833.33 is known as the convertible’s conversion value.
– Expected market price as the present value of the future stream
of interest and principal payments discounted at the appropriate
rate (3.5% in this case): $839.84
• The value of the convertible as a bond alone is called its bond value
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Special Cases
• The conclusion of the preceding two-stage analysis is
that the minimum price of a convertible is the greater of
its Bond Value and its Conversion Value
– Its conversion premium
• is defined as the percentage difference between its current
market price and its theoretical minimum value
• Assuming the bond is currently selling for $1,050, its conversion
premium would be $210.16 or 25.02% ($210.16/839.84). This is
the premium the market is willing to pay for the potential increase
in the stock price.
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Where Can I Find out More?
1. The Handbook of Fixed Income Securities, 6th
Edition, Frank J. Fabozzi, Editor, (McGraw Hill, 2000).
2. The Bond Book, 2nd Edition, Annette Thau, (McGraw
Hill, 2001)
3. The Bond Bible, Marilyn Cohen and Nick Watson,
(New York Institute of Finance, 2000).
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