8 Key excerpts on "Coupon Bond"

• 

  eBook - ePub

  Accounting for Investments, Volume 2

  A Practitioner's Handbook

  • R. Venkata Subramani(Author)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  Various governments issue government bonds in their own currency and sovereign bonds in foreign currencies. Local governments issue municipal bonds to finance their projects. Corporate entities also issue bonds or borrow money from a bank or from the public.

  The term “fixed income security” is also applied to an investment in a bond that generates a fixed income on such investment. Fixed income securities can be distinguished from variable return securities such as stocks where there is no assurance about any fixed income from such investments. For any corporate entity to grow as a business, it must often raise money to finance the project, fund an acquisition, buy equipment or land or invest in new product development. Investors will invest in a corporate entity only if they have the confidence that they will be given something in return commensurate with the risk profile of the company.

  Bond coupon

  The coupon or coupon rate of a bond is the amount of interest paid per year expressed as a percentage of the face value of the bond. It is the stated interest rate that a bond issuer will pay to a bond holder.

  For example, if an investor holds $100,000 nominal of a 5 percent bond then the investor will receive $5,000 in interest each year, or the same amount in two installments of $2,500 each if interest is payable on a half-yearly basis.

  The word “coupon” indicates that bonds were historically issued as bearer certificates, and that the possession of the certificate was conclusive proof of ownership. Also, there used to be printed on the certificate several coupons, one for each scheduled interest payment covering a number of years. At the due date the holder (investor) would physically detach the coupon and present it for payment of the interest.

  Bond maturity

  The bond’s maturity date refers to a future date on which the issuer pays the principal to the investor. Bond maturities usually range from one year up to 30 years or even more. But this maturity date must be seen as the last future date (except if the borrower is in default) on which the investor will receive the principal amount from the issuer. Depending on redemption features, the real reimbursement date can be very different (much shorter). These redemption features usually give the right to the investors and/or the issuer to advance the maturity date of the bond.

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  eBook - ePub

  Investing in Fixed Income Securities

  Understanding the Bond Market

  • Gary Strumeyer(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  A debt instrument, regardless of its maturity and issuer, is a contract between the issuer and holder. The contract obligates the issuer to pay you, the holder, a stated interest payment on the dates specified. Usually the stated annual interest payment, or coupon, is paid in two installments (i.e., every six months). The annual payment date typically falls on the same day of the year designated for the ultimate redemption or maturity of the debt instrument. For example, if the specific day the issuer has promised to pay off the debt, its maturity date, is April 1, 2035, the semiannual interest payments will typically be made on April 1 and six months later, October 1, each and every year until the maturity date of the bond. If the annual coupon rate is specified as 6 percent, then 3 percent will be paid each April 1 and 3 percent each October 1. While semiannual payments are the most common, other payment intervals are utilized as well. Some fixed income instruments pay monthly (i.e., Ginnie Maes) while others may pay annually. Some securities, like savings bonds, T-bills, and zero coupon Treasuries, are issued without a coupon, paying interest at maturity.

  The coupon rate is the contractual interest rate paid for the life of the instrument. It does not change, except in variable rate securities and, in rare instances, when a change was specified in the original offering agreement (commonly referred to as a step-up security). Thus, a 6.25 percent coupon rate pays 6.25 percent per annum until the obligation matures.

  The market interest rate or market yield (yield to maturity) is a different concept. Market rates can change minute by minute and are influenced by all the forces that affect the marketplace, including fundamental or economics-related events, supply and demand and technical factors.

  THE BASICS OF PRICE

  While the coupon on a fixed rate bond or note is constant (set for the life of the bond), the market yield varies for that security, depending on numerous market forces. Thus, for most of the life of the debt instrument, the market yield will be higher or lower than the coupon yield. That difference between coupon and market yield, if any, determines a bond’s price. When the coupon and market yield are identical, for example both 5.5 percent, the price of the bond will be par, or $1,000 per $1,000 bond. But if the coupon yield is 5.5 percent while the market yield has declined to 5.25 percent, the stream of interest payments represented by the 5.5 percent coupon yield cannot be replaced by buying a new comparable or virtually identical debt security. That makes the existing 5.5 percent coupon-bearing bond more valuable as it will pay $55 per year for each $1,000 bond, whereas a new bond priced at par would pay only $52.50 per year. To compensate for its added value, the price of the existing bond will have to rise sufficiently, depending on its maturity, to recalculate the yield from 5.5 percent to the 5.25 percent market yield, thus raising the price of the bond.

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  eBook - ePub

  Fixed Income Securities

  Concepts and Applications

  • Sunil Kumar Parameswaran(Author)
  • 2019(Publication Date)
  • De Gruyter

    (Publisher)

  coupon payment. The name came about because in earlier days bonds were issued with a booklet of post-dated coupons. On an interest payment date, the holder was expected to detach the relevant coupon and claim his payment. Even today, bearer bonds come with a booklet of coupons. These are bonds where no record of ownership is maintained, unlike in the case of conventional or registered bonds. Thus the holder of a bearer bond needs to produce the coupon to claim the interest that is due.

  The coupon may be denoted as a rate or as a dollar value. We will denote the coupon rate by c. The dollar value, C, is therefore given by

  c × M

  . Most bonds pay interest on a semiannual basis, and consequently the semiannual cash flow is

  c × M / 2

  . Semiannual coupons are the norm in the UK, US, Japan, and Australia. However, in certain regions like the European Union, bonds typically pay annual coupons.

  Consider a bond with a face value of $1,000 that pays a coupon of 8% per annum on a semiannual basis. The annual coupon rate is 0.08. The semiannual coupon payment is

  0.08 × 1 , 000 / 2 = $ 40

  .

  Yield to Maturity

  The yield to maturity, like the coupon rate, is also an interest rate. The difference is that whereas the coupon rate is the rate of interest paid by the issuer, the yield to maturity, commonly referred to as the YTM, is the rate of return required by the market. At a given point in time, the yield may be greater than, equal to, or less than the coupon rate. The YTM is denoted by y and is the rate of return that a buyer gets when acquiring the bond at the prevailing price and holding it to maturity.

  Valuation of a Bond

  To value a bond, we first assume that we are standing on a coupon payment date. That is, we assume that a coupon has just been received, and consequently the next coupon is exactly six months or one period away. If T is the term to maturity in years, we have N coupons remaining where

  N = 2 T

  . We receive N coupon payments during the life of the bond, where each payment or cash flow is equal to

  C / 2

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  eBook - ePub

  Investment Theory and Risk Management

  • Steven Peterson(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  They do this through their agent, the U.S. Treasury). Treasuries (U.S. government securities), come in two basic types: those that mature in one year or less and pay only the face value (but no coupon), and those that mature in more than one year that pay face value at maturity in addition to periodic coupon payments. The former are referred to as Treasury bills while the latter are either Treasury notes (10 years maturity or less) or Treasury bonds. Only bills pay no coupons. These are therefore referred to as zero Coupon Bonds, or, for short, just zeros. They are sold at discount (through Treasury auctions) and perhaps later through secondary bond markets. Let's do these first, since they are easiest. First, a word on notation: Let P be the price, C the cash flow to the holder, and r, the interest rate—the bond's yield to maturity. Consider then the simple case in which the government desires to borrow $100 for one year. That is, suppose the Treasury prints up a bond certificate with a face value of $100 to be paid to the holder in one year at maturity. This is the principal. Suppose that the outcome of a sealed bid auction is that someone will agree to purchase this paper for $90 now and in one year, will redeem it for its face value at maturity ($100). Then that person has bought this zero at discount for 90 and earns: Thus, the return on this bond, if held to maturity, is 11 percent. This is also called the yield on the bond. If the market price were $95 instead, then this would generate a yield of about 5.26 percent. Notice that the bond's price and return are inversely related. This means that, in general, if the Treasury borrows more, the supply of bonds rises, driving down their market prices, which increases their yields. Looked at differently, Here, we see that the market price of the bond is the discounted present value of C ; P represents the price bid to receive $100 one year from now

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  eBook - ePub

  Treasury Finance and Development Banking

  A Guide to Credit, Debt, and Risk

  • Biagio Mazzi(Author)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Y , we also know that the bond trades above par.

  Let us stress the importance of the concept of yield by looking at the word itself. A bond can be roughly considered to be made of two parts, the principal and the coupon. The principal is the amount of money the investor lends to the borrower and is the main component of the deal, the coupon payments can be seen as the compensation the investor requires for delaying the consumption of the principal.3

  We have seen that the borrower sets the coupon by making sure that, once the bond is discounted and taking into account the market’s perception of the borrower’s own credit risk, the price is more or less par. This means that the coupon is the element taking care of the borrower’s credit. Bonds, however, can be very long dated instruments and between the time the coupon is set and a subsequent time, the credit standing of the borrower might change, making the coupon value irrelevant as a credit signal. Moreover, irrespective of the price paid for the bond, at maturity the investor receives the full principal amount, the unit of measure being the principal amount. Here is where the yield plays a crucial role in telling how much the investment is really yielding. If an investor pays 95 for a bond with a 5% (of 100, of course) annual coupon, then the investment yields more than simply 5%.

  For the most liquid bonds the yield plays such an important role that it can be traded alongside the bond price (not separately, of course, as the trader chooses to quote one or the other). 5.2.3 Duration

  We have not mentioned up to now in any context the concept of sensitivity, that is, the impact of the price of a financial instrument due to a small movement in one of the variables leading to its value. This, of course, is very important in finance as it constitutes the foundation of replication, hedging, and risk-neutral pricing. In the interest rate world the most important of these sensitivities is the PV01

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  eBook - ePub

  Bond Duration and Immunization

  Early Developments and Recent Contributions

  • Gabriel Hawawini, Gabriel Hawawini(Authors)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  3 Maturity provides information only about the date of final payment. However, nonzero Coupon Bonds generate regularly scheduled payments before maturity. Thus, maturity provides an incomplete description of the time pattern of all the payments of a bond. The longer the term to maturity, the higher the coupon rate, or the higher the market yield, the more important are the coupon payments relative to the maturity payment. Duration views a conventional nonzero Coupon Bond as a zero coupon serial bond with consecutive maturity payments equal to the coupon payments plus a larger payment at final maturity. It thus considers all payments generated by a bond. Duration is defined as:

  where

  D = Duration

  C = Dollar value of coupon payment

  A = Dollar value of maturity payment

  t = Period in which payment is made

  r = Interest rate applicable for period t

  n = Maturity period

  This formulation is seen to be an ordinary weighted average of the time periods in which payments are to be made. Each period is weighted by the present value of the corresponding payment or price of the maturing serial bond. That is, duration identifies the length of time from the present at which the bond generates the average present value dollar. This period may be considered the average life of the bond. It is equal to the maturity of a single payment zero Coupon Bond selling at the same market price as the Coupon Bond, generating the same yield, and having a par value equal to the sum of the total payments generated by the bond when all coupons are reinvested to maturity.

  For zero Coupon Bonds, duration is equal to maturity. For all other bonds, duration is shorter than maturity. However, the relationship between duration and maturity is non-linear and complex. For bonds priced at or above par, duration increases monotonically with maturity but at a decreasing rate. This explains both the much publicized direct relation between price volatility and term to maturity cited earlier and Malkiel’s Theorem 3. For discount bonds, the relationship is more complex. Duration increases with maturity to a point before perpetuity, peaks at that point, and subsequently declines.4 For all bonds, differences between duration and maturity are small for short maturities but increase as maturity increases. Lawrence Fisher and Roman Weil note that for all bonds duration is bounded at perpetuity by (r+p)/rp, where r is the yield to maturity and p

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  eBook - ePub

  Encyclopedia of Financial Models

  • Frank J. Fabozzi, Frank J. Fabozzi(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Finally, let's suppose that the discount rate is equal to the coupon rate. That is, suppose that the discount rate is 6%. It can be shown that the present value of the coupon payments is $21.0591 and the present value of the maturity value is $78.9409. Thus, the bond's value in this case is $100 or par value. Thus, when a bond's coupon rate is equal to the discount rate, the bond will trade at par value. Note that the preceding statement is strictly true only when a bond is valued on its coupon payment dates.

  Valuing a Zero-Coupon Bond

  For a zero-Coupon Bond, there is only one cash flow—the repayment of principal at maturity. The value of a zero-Coupon Bond that matures N years from now is:

  where i is the semiannual discount rate.

  The expression presented above states that the price of a zero-Coupon Bond is simply the present value of the maturity value. In the present value computation, why is the number of periods used for discounting rather than the number of years to the bond's maturity when there are no semiannual coupon payments? We do this in order to make the valuation of a zero-Coupon Bond consistent with the valuation of a Coupon Bond. In other words, both coupon and zero-Coupon Bonds are valued using semiannual discounting rates.

  To illustrate, the value of a 10-year zero-Coupon Bond with a maturity value of $100 discounted at a 6.4% interest rate is $53.2606, as presented below: Valuing a Bond between Coupon Payments

  In our discussion of bond valuation to this point, we have assumed that the bonds are valued on their coupon payment dates (that is, the next coupon payment is one full period away). For bonds with semiannual coupon payments, this occurs only twice a year. Our task now is to describe how bonds are valued on the other 363 days (or 364 days) of the year.

  In order to value a bond with a settlement date between coupon payments, we must answer three questions. First, how many days are there until the next coupon payment date? The answer depends on the day count convention for the bond being valued. Second, how should we compute the present value of the cash flows received over the fractional period? Third, how much must the buyer compensate the seller for the coupon earned over the fractional period? This amount is accrued interest. We will answer these three questions in order to determine the full price and the clean price of a Coupon Bond. For a more detailed discussion of these issues for not only U.S. bonds but bonds traded in other countries, see Krgin (2002).

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  eBook - ePub

  Introduction to Fixed Income Analytics

  Relative Value Analysis, Risk Measures and Valuation

  • Frank J. Fabozzi, Steven V. Mann(Authors)
  • 2010(Publication Date)
  • Wiley

    (Publisher)

  i) = 3% (6%/2) Number of years to maturity = 4

  To determine the present value of the coupon payments, we compute the following expression:

  Simply put, this number tells us how much the coupon payments contribute to the bond’s value. In addition, the bondholder receives the maturity value when the bond matures so the present value of the maturity value must be added to the present value of the coupon payments. The present value of the maturity value is

  This number ($78.9409) tells us how much the bond’s maturity value contributes to the bond’s value. The bond’s value is the sum of these two present values, which in this case is $100 ($21.0591 + $78.9409).

  When an option-free bond is issued, the coupon rate and the term to maturity are fixed. Consequently, as yields change in the market, bond prices will move in the opposite direction, as we will see in the next two scenarios. Generally, a bond’s coupon rate at the time of issuance is set at approximately the required yield demanded by the market for comparable bonds. By comparable, we mean bonds that have the same maturity and the same risk exposure. The price of an option-free Coupon Bond at issuance will then be approximately equal to its par value. In the example presented above, when the required yield is equal to the coupon rate, the bond’s price is its par value ($100).

  Valuing a Bond When the Discount Rate is Greater Than the Coupon Rate

  We now take up the case when the discount rate is greater than the coupon rate. Suppose now that the relevant discount rate for our 4-year, 6% Coupon Bond is 7%. The data are summarized below:

  Semiannual coupon payment = $3 (per $100 of par value) Semiannual discount rate (i) = 3.5% (7%/2) Number of years to maturity = 4

  Note that the only number that has changed from the previous scenario is the semiannual discount rate, which has increased from 3% to 3.5%. We compute the present value of the coupon payments in the same manner as before:

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