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Part - IXFundamentals of Debt

Securities

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Basics

What is debt? It is a financial claim.

Who issues is? The borrower of funds

For whom it is a liability

Who holds it? The lender of funds

For whom it is an asset

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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.

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Basics (Cont…) It has a finite life span The interest payments are contractual

obligations 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.

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Nomenclature Debt securities are referred to by a variety

of names. Bills Notes Bonds Debentures

In the U.S. a debenture is an unsecured bond.

In India the terms are used interchangeably.

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U.S. Treasury Securities

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.

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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.

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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.

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Plain Vanilla & Bells and Whistles

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.

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Face Value

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.

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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.

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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 semi-annual basis.

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Example of Coupon Calculation

Consider a bond with a face value of $1000.

The coupon rate is 8% per annum paid semi-annually.

So the bond holder will receive1000 x 0.08

___ = $40 every six months.2

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Yield to Maturity (YTM) 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.

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Value of a Bond 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.

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Price versus Yield 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.

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Bond Valuation 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.

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Bond Valuation (Cont…) 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.

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Bond Valuation (Cont…)

The present value of the coupon stream is:

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Bond Valuation (Cont…)

The present value of the face value is:

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Bond Valuation (Cont…)

So the price of the bond is:

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Illustration 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.

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Illustration (Cont…)

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Par, Discount & Premium Bonds 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.

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Par, Discount & Premium Bonds 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.

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Zero Coupon Bonds 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.

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Illustration 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%.

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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.

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Zero Coupon Bonds 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.

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Valuation in between Coupon Dates 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?

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The Procedure for Treasury Bonds

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.

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Treasury Bonds (Cont…)

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.

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Treasury Bonds (Cont…)

The next coupon is then k periods away where

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Illustration 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.

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No. of Days Till the Next Coupon Date

Month No. of Days

September 15

October 31

November 30

December 31

January 15

TOTAL 122

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No. of Days between Coupon Dates

Month No. of Days

July 16

August 31

September 30

October 31

November 30

December 31

January 15

TOTAL 184

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Treasury Bonds (Cont…)

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.

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The Valuation Equation

Wall Street professionals will then price the bond using the following equation.

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Valuation

In our example

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The 30/360 Approach 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.

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The 30/360 Approach (Cont…)

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)

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The 30/360 Approach (Cont…)

The number of days is then calculated as

360(year2 – year1) + 30(month2 – month1) + (day2 – day1)

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Additional Rules

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

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Examples of Calculations

Start Date

End Date Actual Days

Days Based on 30/360

Jan-01-86 Feb-01-86 31 30

Jan-15-86 Feb-01-86 17 16

Feb-15-86 Apr-01-86 45 46

Jul-15-86 Sep-15-86 62 60

Nov-01-86 Mar-01-87 120 120

Dec-15-86 Dec-31-86 16 16

Dec-31-86 Feb-01-87 31 31

Feb-01-88 Mar-01-88 29 30

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Pricing of A Corporate Bond

Let us assume that the bond considered earlier was a corporate bond rather than a Treasury bond.

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Pricing (Cont…)

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30/360 European Convention

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

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Examples of Calculations

Start Date

End Date Actual Days

Days Based on 30/360E

Mar-31-86

Dec-31-86

275 270

Dec-15-86

Dec-31-86

16 15

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Other Conventions 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.

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Accrued Interest 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.

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Accrued Interest (Cont…)

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

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Accrued Interest (Cont…)

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.

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Why Accrued Interest?

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.

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Why Accrued Interest? (Cont…) 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.

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Why Accrued Interest (Cont…)

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

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Why Accrued Interest? (Cont…) 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.

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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.

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Clean versus Dirty Prices

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.

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Treasury Bills (T-Bills) 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.

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T-Bills 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

Off-The-Run securities. They tend to be less liquid.

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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.

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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

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Price Calculation

Dollar Discount is given by:

D = d x V x 360mT

Price = P = V - D

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Example

A bill with a face value of $1,000,000 has 80 days to maturity.

The quoted yield is 8%. D = 1,000,000x.08x

360

80

= 177,77.78

P = 1,000,000 – 177,77.78 =$982,222.22

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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 =

.

22.222,982

22.222,982000,000,1 80

360x

= 8.1448%