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Part - IX
Fundamentals of Debt Securities
1
Basics

What is debt?


It is a financial claim.
Who issues is?

The borrower of funds

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For whom it is a liability
Who holds it?

The lender of funds
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For whom it is an asset
2
Basics (Cont…)

What is the difference between debt
and equity?


Debt does not confer ownership rights on
the holder.
It is merely an IOU

A promise to pay interest at periodic intervals
and to repay the principal itself at a
prespecified maturity date.
3
Basics (Cont…)

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It has a finite life span
The interest payments are contractual
obligations

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Borrowers are required to make payments
irrespective of their financial performance
Interest payments have to be made before any
dividends can be paid to equity holders.
In the event of liquidation


The claims of debt holders must be settled first
Only then can equity holders be paid.
4
Nomenclature

Debt securities are referred to by a variety of
names.

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Bills
Notes
Bonds
Debentures
In the U.S. a debenture is an unsecured
bond.
In India the terms are used interchangeably.
5
U.S. Treasury Securities


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They are fully backed by the federal
government.
Consequently they are devoid of credit
risk or the risk of default.
The interest rate on such securities is
used as a benchmark for setting rates
on other kinds of debt.
6
U.S. Treasury Securities (Cont…)


The Treasury issues three categories of
marketable securities.
T-bills are discount securities


They are issued at a discount from their
face values and do not pay interest.
T-notes and T-bonds are sold at face
value and pay interest periodically.
7
U.S. Treasury Securities (Cont…)

T-bills are issued with a original time to
maturity of one year or less.


Consequently they are Money Market
instruments.
T-notes and T-bonds have a time to
maturity exceeding one year at the time
of issue.

They are therefore Capital Market
instruments.
8
Plain Vanilla & Bells and
Whistles

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The most basic form of a bond is called
the Plain Vanilla version.
This is true for all securities, not just for
bonds.
More complicated versions are said to
have
`Bells and Whistles’ attached.
9
Face Value


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It is the principal value underlying the
bond.
It is the amount payable by the
borrower to the lender at maturity.
It is the amount on which the periodic
interest payments are calculated.
10
Term to Maturity



It is the time remaining in the life of the
bond.
It represents the length of time for
which interest has to be paid as
promised.
It is represents the length of time after
which the face value will be repaid.
11
Coupon



The coupon payment is the periodic
interest payment that has to be made
by the borrower.
The coupon rate when multiplied by the
face value gives the dollar value of the
coupon.
Most bonds pays coupons on a semiannual basis.
12
Example of Coupon
Calculation

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Consider a bond with a face value of
$1000.
The coupon rate is 8% per annum paid
semi-annually.
So the bond holder will receive
1000 x 0.08
___ = $40 every six months.
2
13
Yield to Maturity (YTM)
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Yield to maturity is the rate of return that an
investor will get if he buys the bond at the
prevailing market price and holds it till
maturity.
In order to get the YTM, two conditions must
be satisfied.
The bond must be held till maturity.
All coupon payments received before maturity
must be reinvested at the YTM.
14
Value of a Bond

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A bond holder gets a stream of contractually
promised payments.
The value of the bond is the value of this
stream of cash flows.
However you cannot simply add up cash
flows which are arising at different points in
time.
Such cash flows have to be discounted before
being added.
15
Price versus Yield

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Price versus yield is a chicken and egg
story, that is, we cannot say which
comes first.
If we know the yield that is required by
us, we can quote a price accordingly.
Similarly, once we acquire the asset at a
certain price, we can work out the
corresponding yield.
16
Bond Valuation
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A bond is an instrument that will pay identical
coupon payments every period, usually every
six months, for a number of years, and will
then repay the face value at maturity.
The periodic cash flows obviously constitute
an annuity.
The terminal face value is a lump sum
payment.
17
Bond Valuation (Cont…)
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Consider a bond that pays a semi-annual
coupon of $C/2, and which has a face value
of $M.
Assume that there are N coupons left, and
that we are standing on a coupon payment
date.
That is, we are assuming that the next
coupon is exactly six months away.
The required annual yield is y, which implies
that the semi-annual yield is y/2.
18
Bond Valuation (Cont…)

The present value of the coupon stream
is:
19
Bond Valuation (Cont…)

The present value of the face value is:
20
Bond Valuation (Cont…)

So the price of the bond is:
21
Illustration
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IBM has issued a bond with a face value
of $1,000.
The coupon is 8% per year to be paid
on a semi-annual basis, on July 15 and
January 15 every year.
Assume that today is 15 July 2002 and
that the bond matures on 15 January
2022.
The required yield is 10% per annum.
22
Illustration (Cont…)
23
Par, Discount & Premium
Bonds

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In the above example, the price of the bond
is less than the face value of $1,000.
Such a bond is called a Discount Bond, since
it is trading at a discount from the face value.
The reason why it is trading for less than the
face value is because the required yield of
10% is greater than the rate of 8% that the
bond is paying by way of interest.
24
Par, Discount & Premium
Bonds
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If the required yield were to equal the coupon
rate, the bond would sell for $1,000.
Such bonds are said to be trading at Par.
If the required yield were to be less than the
coupon rate the price will exceed the face
value.
Such bonds are called Premium Bonds, since
they are trading at a premium over the face
value.
25
Zero Coupon Bonds
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A Plain Vanilla bond pays coupon interest
every period, typically every six months, and
repays the face value at maturity.
A Zero Coupon Bond on the other hand does
not pay any coupon interest.
It is issued at a discount from the face value
and repays the principal at maturity.
The difference between the price and the
face value constitutes the interest for the
buyer.
26
Illustration

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Microsoft is issuing zero coupon bonds
with 5 years to maturity and a face
value of $10,000.
If you want a yield of 10% per annum,
what price will you pay?
The price of the bond is obviously the
present value of a single cash flow of
$10,000, discounted at 10%.
27
Illustration (Cont…)


In practice, we usually discount the face
value using a semi-annual rate of y/2,
where y in this case is 10%.
This is to facilitate comparisons with
conventional bonds which pay coupon
interest every six months.
28
Zero Coupon Bonds

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
Zero coupon bonds are called zeroes by
traders.
They are also referred to as Deep
Discount Bonds.
They should not be confused with
Discount Bonds, which are Plain Vanilla
bonds which are trading at a discount
from the face value.
29
Valuation in between
Coupon Dates

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While valuing a bond we assumed that
we were standing on a coupon payment
date.
This is a significant assumption because
it implies that the next coupon is
exactly one period away.
What should be the procedure if the
valuation date is in between two
coupon payment dates?
30
The Procedure
for Treasury Bonds
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Calculate the actual number of days
between the date of valuation and the
next coupon date.
Include the next coupon date.
But do not include the starting date.
Let us call this interval N1.
31
Treasury Bonds (Cont…)
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Calculate the actual number of days
between the coupon date preceding the
valuation date and the following coupon
date.
Once again include the ending date but
exclude the starting date.
Let us call this time interval as N2.
32
Treasury Bonds (Cont…)

The next coupon is then k periods away
where
33
Illustration
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There is a Treasury bond with a face
value of $1,000.
The coupon rate is 8% per annum, paid
on a semi-annual basis.
The coupon dates are 15 July and 15
January.
The maturity date is 15 January 2022.
Today is 15 September 2002.
34
No. of Days Till the
Next Coupon Date
Month
No. of Days
September
15
October
31
November
30
December
31
January
15
TOTAL
122
35
No. of Days between
Coupon Dates
Month
July
August
September
October
November
December
January
TOTAL
No. of Days
16
31
30
31
30
31
15
184
36
Treasury Bonds (Cont…)
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K = 122/184 = .6630
This method is called the Actual/Actual
method and is often pronounced as the
Ack/Ack method.
It is the method used for Treasury
bonds in the U.S.
37
The Valuation Equation

Wall Street professionals will then price
the bond using the following equation.
38
Valuation

In our example
39
The 30/360 Approach
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The Actual/Actual method is applicable for
Treasury bonds in the U.S.
For corporate bonds in the U.S. we use what
is called the 30/360 method.
In this method the number of days between
successive coupon dates is always taken to
be 180.
That is each month is considered to be of 30
days.
40
The 30/360 Approach (Cont…)
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The number of days from the date of
valuation till the next coupon date is
calculated as follows.
The start date is defined as
D1 = (month1, day1,year1)
The ending date is defined as
D2 = (month2,day2,year2)
41
The 30/360 Approach (Cont…)
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The number of days is then calculated
as
360(year2 – year1) + 30(month2 –
month1) + (day2 – day1)
42
Additional Rules
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If day1 = 31 then set day1 = 30
If day1 = 30 or has been set equal to
30, then if day2 = 31, set day2 = 30
If day1 is the last day of February, then
set day1 = 30
43
Examples of Calculations
Start Date
End Date
Feb-01-86
Actual
Days
31
Days Based
on 30/360
30
Jan-01-86
Jan-15-86
Feb-15-86
Jul-15-86
Nov-01-86
Dec-15-86
Dec-31-86
Feb-01-88
Feb-01-86
Apr-01-86
Sep-15-86
Mar-01-87
Dec-31-86
Feb-01-87
Mar-01-88
17
45
62
120
16
31
29
16
46
60
120
16
31
30
44
Pricing of A Corporate Bond

Let us assume that the bond considered
earlier was a corporate bond rather
than a Treasury bond.
45
Pricing (Cont…)
46
30/360 European Convention
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In this convention, if day2 = 31, then it
is always set equal to 30.
So the additional rules are:
If day1 = 31 then set day1 = 30
If day2 = 31 then set day2 = 30
If day1 is the last day of February, then
set day1 = 30
47
Examples of Calculations
Start Date End Date
Actual
Days
Mar-31-86 Dec-31-86 275
Days
Based on
30/360E
270
Dec-15-86 Dec-31-86 16
15
48
Other Conventions
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Actual/365 Convention
In this case the year is considered to have 365 days,
while calculating the denominator, even in leap years.
Actual/365 Japanese
This is used for Japanese Government Bonds (JGBs)
It is similar to the Actual/365 method.
The only difference is that in this case, the extra day
in February is ignored in leap years, while calculating
both the numerator and the denominator.
49
Accrued Interest

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The price of a bond is the present value of all
the cash flows that the buyer will receive
when he buys the bond.
Thus the seller is compensated for all the
cash flows that he is parting with.
This compensation includes the amount due
for the fact that the seller is parting with the
entire next coupon, although he has held it
for a part of the current coupon period.
50
Accrued Interest (Cont…)
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This compensation is called Accrued
Interest.
Let us denote the sale date by t; the
previous coupon date by t1; and the
following coupon date by t2
The accrued interest is given by
51
Accrued Interest (Cont…)

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Both the numerator and the
denominator are calculated according to
the conventions discussed above.
That is for U.S. Treasury bonds the
Actual/Actual method is used, whereas
for U.S. corporate bonds the 30/360
method is used.
52
Why Accrued Interest?
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Why should we calculate the accrued
interest if it is already included in the
price calculation?
The answer is that the quoted bond
price does not include accrued interest.
That is, quoted prices are net of
accrued interest.
53
Why Accrued Interest?
(Cont…)
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The rationale is as follows.
On July 15 the price of the Treasury
bond using a YTM of 10% was $829.83.
On September 15 the price using a yield
of 10% is $843.5906.
Since the required yield on both the
days is the same, the increase in price
is entirely due to the accrued interest.
54
Why Accrued Interest (Cont…)
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On July 15 the accrued interest is zero.
This is true because on a coupon
payment date, the accrued interest has
to be zero.
On September 15 the accrued interest
is
55
Why Accrued Interest?
(Cont…)
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The price net of accrued interest is
$843.5906 - $13.4783 = $830.1123$, which
is very close to the price of $829.83 that was
observed on July 15.
We know that as the required yield changes,
so will the price.
If the accrued interest is not subtracted from
the price before being quoted, then we would
be unsure as to whether the observed price
change is due to a change in the market yield
or is entirely due to accrued interest.
56
Why Accrued Interest?
(Cont…)


However if prices are reported net of
accrued interest, then in the short run,
observed price changes will be entirely
due to changes in the market yield.
Consequently bond prices are always
reported after subtracting the accrued
interest.
57
Clean versus Dirty Prices

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Quoted bond prices are called clean or
add-interest prices.
When a bond is purchased in addition
to the quoted price, the accrued
interest has also to be paid.
The total price that is paid is called the
dirty price or the flat price.
58
Treasury Bills (T-Bills)

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They are short term debt instruments
issued by the U.S. Treasury.
They are devoid of credit risk.
They are highly liquid.
Bills with original terms to maturity of 13
weeks, 26 weeks, and 52 weeks are
regularly issued.
59
T-Bills

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13 week and 26 week bills are issued every
week.
One year bills are issued once a month.
The most recently issued securities are
called On-The-Run securities.
These are highly liquid.
Instruments issued earlier are called OffThe-Run securities.
They tend to be less liquid.
60
T-Bills

These are zero coupon securities.


That is, they are issued at a discount from the
face value.
The yield that is quoted for bills is a
discount yield.

Such yields are used to calculate the difference
between the face value and the price to be
paid.
61
Calculation of The Discount


For all calculations involving money
market instruments the year is assumed
to have 360 days.
Let us use the following symbols:



V = Face Value
Tm = Days to Maturity
d = Quoted Yield
62
Price Calculation

Dollar Discount is given by:
Tm
D=dxVx
360
Price = P = V - D
63
Example



A bill with a face value of $1,000,000
has 80 days to maturity.
The quoted yield is 8%.
80
D = 1,000,000x.08x
360
= 177,77.78
P = 1,000,000 – 177,77.78
=$982,222.22
64
Rate of Return


The rate of return if the bill is
purchased at this price will be greater
than the quoted yield.
R.O.R =
1,000,000  982,222.22 360
x
80
982,222.22
= 8.1448%
.
65