Discount Bond
A discount bond is a bond that is issued for less than its face value, typically because it pays no interest or a lower interest rate than the market rate. Investors purchase discount bonds at a discount to their face value and receive the full face value when the bond matures. The difference between the purchase price and the face value represents the investor's return.
8 Key excerpts on "Discount Bond"
eBook - ePub- Frank J. Fabozzi, Frank J. Fabozzi(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
...The price is less than par value and the bond is said to be trading at a discount. This will occur when the fixed coupon rate a bond offers (6%) is less than the required yield demanded by the market (the 7% discount rate). A Discount Bond has an inferior coupon rate relative to new comparable bonds being issued at par so its price must drop so as to offer the required yield of 7%. If the Discount Bond is held to maturity, the investor will experience a capital gain that just offsets the lower current coupon rate so that it appears equally attractive to new comparable bonds issued at par. Suppose instead of a 7% discount rate, a 5% discount rate is used. This discount rate is less than the coupon rate on the bond (6%). It can be shown that the present value of the coupon payments is $21.5104 and the present value of the maturity value is $82.0747. Thus, the bond's value in this case is $103.5851. That is, the price is greater than par value and the bond is said to be trading at a premium. This will occur when the fixed coupon rate a bond offers (6%) is greater than the required yield demanded by the market (the 5% discount rate). Accordingly, a premium bond carries a higher coupon rate than new bonds (otherwise the same) being issued today at par so the price will be bid up and the required yield will fall until it equals 5%. If the premium bond is held to maturity, the investor will experience a capital loss that just offsets the benefits of the higher coupon rate so that it will appear equally attractive to new comparable bonds issued at par. 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...
eBook - ePubInvesting in Fixed Income Securities
Understanding the Bond Market
- Gary Strumeyer(Author)
- 2012(Publication Date)
- Wiley(Publisher)
...For our corporate bond, that translates into $10. Price quotes that include fractions of a point are handled similarly. A price of 95½ translates into 95.5 percent of par, or $955. U.S. corporate bonds trade in minimum price movements of one-eighth of a point. This minimum movement is called a tick and it represents $1.25 per $1,000 par amount. U.S. Treasury bonds are quoted in 32nds of a point. Premium/Par/Discount Bonds trade at different prices on any given day. The price will be a function of the bond’s coupon interest rate, the length of time until it matures, the credit rating of the issuer, the existence of any embedded options, and how the market values this combination of characteristics. That valuation will take the form of the interest rate used to discount the bond’s cash flows. If the market determines that a particular bond currently carries a level of risk that is adequately compensated by its coupon interest, it will value the bond at par, or 100 percent of its face value. If the market determines that the bond carries more or less risk than is compensated by the coupon, it will value the bond at a discount (a price less than par) or a premium (a price greater than par). Some bonds are originally issued at a discount from par. Securities such as Treasury bills, with original maturities of one year or less, are issued at a discount. These securities carry no coupons—the difference between the discount price paid when the bond is purchased and the par amount received at maturity is the return to the investor. Some coupon-bearing bonds are issued as original issue discounts (OIDs). This type of security is found in the corporate and municipal bond markets. Along with the return from the bond’s coupons, the lower price at issuance is a sweetener that will enhance the bond’s overall return...
eBook - ePubTreasury Finance and Development Banking
A Guide to Credit, Debt, and Risk
- Biagio Mazzi(Author)
- 2013(Publication Date)
- Wiley(Publisher)
...The issue price is usually reached through an auction-type sale. There is an announcement of an imminent debt issuance on the part of an entity; the bond has a certain coupon and investors subscribe to the sale. The interest (or lack thereof) drives the issue price. This means that in real life things happen in a slightly different order. The corrections to the discount factors are driven by a market feeling for the entity’s credit. The entity itself then sets, before the auction, the coupon so that, taking into account the market’s feeling, the price is going to be roughly par. Because the coupon usually takes values no more granular than a quarter of a percentage and because at the auction itself, market feeling can change, the price of the bond cannot be exactly par at issuance. This does not change the fact that an investor at maturity receives the par value. When the price is greater than par, the bond is said to be sold at a premium ; when it is lower, it is sold at a discount. From this little exercise we hope we have shown what was considered interesting as far as bond pricing was concerned: we have played with three elements, the bond price, the coupon, and the corrections and we have shown how, at different moments, some can be kept fixed and some others can be implied. It is probably time to stop calling a correction and move toward a notation more in line with the literature. In Section 2.2.1 and elsewhere where we discussed zero rates, we have shown the relationship between a discount factor and a simple rate. Using a similar approach, let us write (5.3) substituting into Equation 5.2 we obtain (5.4) where we have introduced Y, the yield of the bond, or to be more precise the yield to maturity of the bond since the calculation assumes that we intend to hold the bond up to maturity. (When pricing bonds, details are very important but some are beyond the scope of this book...
eBook - ePub- Robert Irons(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...The issuer of the bond agrees to repay the debt in full on a certain date and to make regular interest payments until that date (assuming the life of the debt is more than one year). A debtor issues a bond (a firm or a government), and a creditor buys a bond (an investor, either an individual or an institution, such as a hedge fund, or an insurance company, or a mutual fund). All bonds have most or all of the following features: An issue date (the date on which the bond was issued), a maturity date (the date on which the contract ends, and the loan amount is repaid) and an original maturity (the time between the issue date and the maturity date). Thus, a bond that is issued on March 1, 2018 and is due to mature on March 1, 2028 has an original maturity of ten years. On March 1, 2019, the bond will have nine years remaining to maturity, but its original maturity will always be ten years. A par value, or face value, which is usually $1,000 or some multiple thereof. It is clearly marked on the face of the bond. A coupon interest rate (or coupon rate), which is the percentage of the par value that the holder of the bond will earn annually. Thus, a $1,000 par value bond with a 4.50% coupon rate will pay $45.00 in interest per year. Interest payments are typically made semiannually (twice a year), and so the investor in this case would receive $22.50 interest per bond every six months. Most bonds have fixed interest payments, but there are some variable interest rate bonds. Variable rate bonds tend to have their interest payments tied to some other rate, such as the LIBOR (London Interbank Offer Rate), or the rate of inflation. For this chapter, we will assume that the bonds in question have a fixed coupon rate. Note that there are bonds without coupons, known as zero coupon bonds, or zeros. These are bonds whose time to maturity is less than one year...
eBook - ePubIntroduction to Fixed Income Analytics
Relative Value Analysis, Risk Measures and Valuation
- Frank J. Fabozzi, Steven V. Mann(Authors)
- 2010(Publication Date)
- Wiley(Publisher)
...More specifically, assuming that the discount rate does not change, a bond’s value: 1. Decreases over time if the bond is selling at a premium. 2. Increases over time if the bond is selling at a discount. 3. Is unchanged if the bond is selling at par value. 25 At the maturity date, the bond’s value is equal to its par or maturity value. So, as a bond’s maturity approaches, the price of a Discount Bond will rise to its par value and a premium bond will fall to its par value—a characteristic sometimes referred to as “pull to par value.” Time Path of a Premium Bond To illustrate what happens to a bond selling at a premium, consider once again the 4-year 6% coupon bond. When the discount rate is 5%, the bond’s price is $103.5851. Suppose that one year later, the discount rate is still 5%. There are only six cash flows remaining since the bond is now a 3-year security. We compute the present value of the coupon payments in the same way as before: The present value of the maturity value is The bond’s value is then $102.7541 ($21.5104 + $82.0747). As the bond moves toward maturity with no change in the discount rate, the price has declined from $103.5851 to $102.7541. What are the mechanics of this result? The value of a coupon bond can thought of as the sum of two present values—the present value of the coupon payments and the present value of the maturity value. What happens to each of these present values as the bond moves toward maturity with no change in the discount rate? The present value of the coupon payments falls for the simple reason that there are fewer coupon payments remaining. Correspondingly, the present value of the maturity value rises because it is one year closer to the present. What is the net effect? The present value of the coupon payments fall by more than the present value of the maturity value rises so the bond’s value declines or is pulled down to par. The intuition for the result reveals a great deal about bond valuation...
eBook - ePubAccounting for Investments, Volume 2
A Practitioner's Handbook
- R. Venkata Subramani(Author)
- 2011(Publication Date)
- Wiley(Publisher)
...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...
eBook - ePubFixed Income Securities
Concepts and Applications
- Sunil Kumar Parameswaran(Author)
- 2019(Publication Date)
- De Gruyter(Publisher)
...Such a bond is said to be trading at a discount to the par value and is therefore referred to as a Discount Bond. If the price of the bond is greater than its face value, then it is said to be trading at a premium to its face value and consequently is referred to as a premium bond. If the price is equal to the face value, then the bond is said to be trading at par. As you see from the pricing equation, price and yield are inversely related. If the rate of return offered by the issuer is equal to that demanded by the market, then the bond obviously trades at par. However, if the market demands a higher rate of return, it then brings the price down until the desired yield is obtained. On the other hand, if the desired yield is lower than the coupon, then traders will be willing to pay a price that is higher than the face value of the bond. Influence of Variables on the Bond Price Let’s first differentiate the price with respect to the face value, keeping other variables constant: (2.1) ∂ P ∂ M = c 2 y 2 1 − 1 (1 + y 2) N + 1 (1 + y 2) N > 0 Thus the partial derivative of the price with respect to the face value is positive. That is, keeping other variables constant, the higher the face value, the higher the bond price. Now consider the derivative with respect to the coupon rate: (2.2) ∂ P ∂ c = M 2 y 2 1 − 1 (1 + y 2) N > 0 Thus the partial derivative with respect to the coupon rate is positive. That is, keeping other variables constant, the higher the coupon rate is, the higher the bond price. Let’s now consider the derivative of the price with respect to the time to maturity. Unlike other variables, the number of coupons can only increase in increments of 1. When there are N coupons remaining until maturity, the price is given by: (2.3) P 0 = M c y × 1 − 1 (1 + y 2) N + M (1 + y 2) N When there are N + 1 coupons remaining until maturity, the price is given...
eBook - ePubQuantitative Finance
A Simulation-Based Introduction Using Excel
- Matt Davison(Author)
- 2014(Publication Date)
- Chapman and Hall/CRC(Publisher)
...Chapter 11 Fundamentals of Fixed Income Markets 11.1 CHAPTER SUMMARY This chapter provides a quick overview of some of the “nitty-gritty” details of government (i.e., risk-free) bond markets. It begins with a description of bonds in Section 11.2. In Section 11.3, a relationship between the price of a bond and the yield of a bond is provided for a variety of “rate conventions.” The discount factor concept is also introduced in Section 11.3. Section 11.4 develops some bond pricing equations. Section 11.5 discusses how bonds are auctioned and traded in Canada. Returning to nitty-gritty details, Section 11.6 describes the so-called “clean” and “dirty” bond prices and the ever-popular “day count convention.” 11.2 What Are Bonds? Like loans, bonds represent a mechanism for shifting cash flows from the present to the future. Borrowers want to spend money now and repay it later, and investors/lenders want to invest money now and have it returned to them later (with interest). Bonds can be used for relatively short mismatches between income and expenditures (in which case they mature rapidly and likely do not need intermediate payments)—for instance, the Tbill market. Bonds can also be used to pay for an asset that gives benefits over a long time period but which must be purchased today—for example, a mortgage, a hydro dam, or a highway. It is unlikely that the lender will want their money tied up for long periods of time with no ability to consume anything from it, so they will want some periodic payments. In this case, the borrower might not mind making periodic payments, either ending in a zero balance (mortgage or sinking fund) or ending in a final lump sum payment (most bonds). This explains the distinction between bills and bonds (Americans also discuss an intermediate category of “notes”). 11.2.1 Debt Markets versus Borrowing from Small Number of Large Entities There are advantages in using capital markets to borrow money...
