Zero Coupon Bond Study

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Zero-Coupon Bond
What Does Zero-Coupon Bond Mean? A debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value. Also known as an "accrual bond". Read more: http://www.investopedia.com/terms/z/zero-couponbond.asp#ixzz1UvgmpRzk Investopedia explains Zero-Coupon Bond Some zero-coupon bonds are issued as such, while others are bonds that have been stripped of their coupons by a financial institution and then repackaged as zero-coupon bonds. Because they offer the entire payment at maturity, zero-coupon bonds tend to fluctuate in price much more than coupon bonds. Read more: http://www.investopedia.com/terms/z/zero-couponbond.asp#ixzz1Uvgp945U What is the difference between a zero-coupon bond and a regular bond? Read more: http://www.investopedia.com/ask/answers/06/zerocouponregularbond.asp#ixzz1UvgwNtw G The difference between a zero-coupon bond and a regular bond is that a zero-coupon bond does not pay coupons, or interest payments, to the bondholder while a typical bond does make these interest payments. The holder of a zero-coupon bond only receives the face value of the bond at maturity. The holder of a coupon paying bond receives the face value of the bond at maturity but is also paid coupons over the life of the bond. Zero-coupon bondholders gain on the difference between what they pay for the bond and the amount they will receive at maturity. Zero-coupon bonds are purchased at a large discount, known as deep discount, to the face value of the bond. A coupon-paying bond will initially trade near the price of its face value. In other words, a zero-coupon bond gains from the difference between the purchase price and the face value, while the coupon bond gains from the regular distribution of interest. For example, imagine that you have the choices between a one-year zero-coupon bond with a face value of $1,000, which can be purchased for $952.38 or a one-year 5% semi-annual coupon bond trading at its face value of $1,000. If you bought the zero-coupon bond for $952.38, you would receive $1,000 at maturity, which is a gain of 5% ($47.62/$952.38). If you bought the coupon bond, you would have received two coupon payments of $25 each during the year for a total of $50, which also represents a 5% gain ($50/$1,000). So in this case, no matter which bond you buy, you will get the same return, even though the source of the return is different. This is not always true, as each case is different. Read more: http://www.investopedia.com/ask/answers/06/zerocouponregularbond.asp#ixzz1Uvh01vew

zero-coupon bond
Definition
A bond which pays no coupons, is sold at a deep discount to its face value, and matures at its face value. A zero-coupon bond has the important advantage of being free of reinvestment risk, though the downside is that there is no opportunity to enjoy the effects of a rise inmarket interest rates.

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Also, such bonds tend to be very sensitive to changes in interest rates, since there are no coupon payments to reduce the impact of interest rate changes. In addition, markets for zero-coupon bonds are relatively illiquid. Under U.S. tax law, the imputed interest on a zero-coupon bond is taxable as it accrues, even though there is no cash flow.
Read more: http://www.investorwords.com/5377/zero_coupon_bond.html#ixzz1Uvh9ZOVV

Zero Coupon Bond (ZCB): An attractive investment opportunity as well as low-cost source of fund
Mohammad Ferdous Mazid MBA Issuance of bond is one of the sources of fund under debt securities. One common term among bond investors is a "coupon". It refers to interest paid on bonds. Therefore, "zero coupon" means "no interest". Zero coupon bond holders are not entitled to enjoy an interest payment on maturity. The interest accrues and the value of the bond increases. The investor can then sell it for the face value once it matures. A Zero Coupon Bond (ZCB) makes no periodic interest payments. The bond is issued at a discount from the face value. The offered rate of return of the bonds determines the level of discounting. The investor of such a bond receives the rate of return by the gradual appreciation of the bond, which is redeemed at face value on a specified maturity date. The interest on the bond may compound at quarterly and monthly rest. The accrued interest of the bond will be added to the issue price. The investor receives the face value on maturity of the bond. This face value comprises the principal amount and the interest earned on the bond. Features: Zero coupon bonds have some really attractive features to them. One is that a potential investor can buy zero coupon bonds at a deep discount. This means that an investor pays lesser than the bond's par value, the amount it is worth at maturity. As the bond matures, the interest is accrued and the bond increases in value. ZCBs are easily transferable. Any bondholder is entitled to transfer the bonds easily to any third party. An application for transfer of bonds is required to be accompanied by a properly completed transfer instrument (117 Form), duly executed by the transferee and transferor with each bond certificate. Issuer shall keep a Register of Transfers and therein shall fairly and distinctly enter the particulars of every transfer of the bonds. The Company shall register transfer of bond only when a proper instrument of transfer executed by or on behalf of the transferor and by or on behalf of the transferee has been delivered to the Company, along with the Bond Certificate for registration. The ZCB can be pledged as security like any other financial instruments to banks or financial institutions for obtaining bank loans or any other credit facilities. However, investors have to comply individual bank's or financial institution's (FIs) credit policy. The ZCB may be listed with the stock exchanges to trade over the counter (OTC). This type of bonds is not convertible into common shares and must be redeemed at maturity. The ZCB is more secured as the issuer keeps provision for a first ranking specific floating charge on the movable/floating assets of the company, equivalent to the face amount of the issued bonds and/or corporate guarantee on the total bond face amount and also for post-dated cheque for the full bond amount in the name of the Trustee. Denomination or minimum lot for investment may be customized and convenient for the investors. Process of issuance of ZCB: Issuance of the ZCB is carried out phase by phase. Initial stage issuer of the ZCB i.e. the company has to decide its objective that how much fund it requires, up to what extant they are capable of making the bond secured in term of repayment and utilization of raising fund. In this regard credit rating of the entity and the bond is necessary.

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Issuer is required to appoint Trustee as a custodian of investor's interest backed by security charged on fixed/ floating assets of the company. Simultaneously the issuer has to consult on designing of the ZCB in a way that is most appropriate for it (the issuer) as well as attractive to the prospective investors. According to the bond designing, the issue price and the face value on maturity are determined. Credit rating of bond and security of Trustee depends upon proper bond designing. In this regard, Bond Designing is the crucial part of the total issue process. Shareholders, approval is required for the listed companies before issue of a ZCB. After credit rating and appointment of trustee, the issuer is required to take 'No Objection Certificate' (NOC) from their regulatory authority. For banks and financial institutions the Bangladesh Bank issues clearance and then the other regulatory authority, capital market watch-dog -- the Securities and Exchange Commission (SEC) -- issue consent, upon completion of required information. Funding through the ZCBs is most convenient for the investors due to tax exemption on income from ZCBs as per SRO No. 159 dated June 28, 2007 by the National Board of Revenue (NBR). It is needless to mention that ZCB is the most attractive option for financing and investment for the corporate bodies and institutions as it is a win-win situation both for the investor and issuer. An issuer of ZCB can get the fund at cost of 9.0% to 11.0% whereas this will generate tax effective return of 16.36% to 20.00% to the institutional investor of 45% tax bracket. The main attraction of the ZCB is tax benefit, which gives the opportunity of raising low-cost fund for the issuer as well as attractive investment opportunity for tax-paying corporate institutions and individuals. The Industrial and Infrastructure Development Finance Company Limited (IIDFC) is the pioneer in the area of issuing ZCB. In the year 2003, they got approval from the regulatory authority for issuance of ZCB, amounting Bangladesh Taka (BDT) 5.0 billion in trenches of BDT 1.0 billion each, having three years maturity and considering simple discount rate at 10%. However the IIDFC is not yet listed with the stock exchanges of Bangladesh. Recently, some listed financial institutions are encourage to raise fund through ZCBs like LankaBangla Finance Limited for BDT 1.0 billion, IDLC Finance Limited for BDT 3.0 billion, Uttara Finance and Investments Limited for BDT 5.0 billion, United Leasing Company Ltd. for BDT 1.0 billion, IPDC for BDT 2.0 billion etc. Besides these there are some other types of ZCBs like asset backed, securitized, series strips etc. However, in a true sense ZCBs need not to be securitized but must be secured for bullet payment at the time of redemption i.e. not a series of payments like principal and interest. Better credit rating, corporate guarantee, sinking fund provision and ultimate yield of the bond make the instrument more attractive. Internationally, the ZCB is very popular as fixed income securities. Generally, government, municipal corporation and very good credit worthy companies issue this type of bonds, so that investors can rely on long term investment. five to twenty years' ZCB are very much available in the USA and UK market. Investors can purchase different kinds of zero coupon bonds in the secondary markets that have been issued from a variety of sources, including the U.S. Treasury, corporations, and state and local government entities. Because zero coupon bonds pay no interest until maturity, their prices fluctuate more than other types of bonds in the secondary market. In addition, although no payments are made on zero coupon bonds until they mature, investors may still have to pay federal, state, and local income tax on the imputed or "phantom" interest that accrues each year. Some investors avoid paying tax on the imputed interest by buying municipal zero coupon bonds (if they live in the state where the bond was issued) or purchasing the few corporate zero coupon bonds that have tax-exempt status. However, in Bangladesh income from the ZCB is fully exempted from tax burden. In fine, it can be mentioned here that there are immense opportunities to develop the bond market. The capital market in Bangladesh is still at a growing stage. After the debacle of '96, the country's share market general index has, again, become stable at 3000 level. It indicates the market is more mature and investors are more educated and behave rationally then that of '96. Now it is time to for all concerned to contribute to the development of the capital market - from the policy-making ministry of finance, the Securities and Exchange Commission, the Dhaka and the Chittagong stock exchanges and merchant bankers, to

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member houses of the capital market. Introduction of new products in the capital market is also needed to give a better alternative to the prospective investors. The writer is Deputy General Manager of AAA Consultants & Financial Advisers

Zero Coupon Bonds
Zero coupon bonds are bonds that do not pay interest during the life of the bonds. Instead, investors buy zero coupon bonds at a deep discount from their face value, which is the amount a bond will be worth when it "matures" or comes due. When a zero coupon bond matures, the investor will receive one lump sum equal to the initial investment plus the imputed interest, which is discussed below. The maturity dates on zero coupon bonds are usually long-term²many don¶t mature for ten, fifteen, or more years. These long-term maturity dates allow an investor to plan for a long-range goal, such as paying for a child¶s college education. With the deep discount, an investor can put up a small amount of money that can grow over many years. Investors can purchase different kinds of zero coupon bonds in the secondary markets that have been issued from a variety of sources, including the U.S. Treasury, corporations, and state and local government entities. Because zero coupon bonds pay no interest until maturity, their prices fluctuate more than other types of bonds in the secondary market. In addition, although no payments are made on zero coupon bonds until they mature, investors may still have to pay federal, state, and local income tax on the imputed or "phantom" interest that accrues each year. Some investors avoid paying tax on the imputed interest by buying municipal zero coupon bonds (if they live in the state where the bond was issued) or purchasing the few corporate zero coupon bonds that have taxexempt status. The Securities Industry and Financial Markets Association has more information about zero coupon bonds on its website. http://www.sec.gov/answers/zero.htm

Pros and Cons of Zero-Coupon Bonds
I am 42 years old and interested in zero-coupon bonds to supplement my retirement savings. What are the pros and cons?

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With retirement years away for you and today's low interest rates, we'd advise against buying zeros. These bonds don't make regular interest payments. Instead, they're sold at a big discount to face value; when they mature, you collect the full amount. Their big advantage is that you know how much you'll collect a certain number of years from now. In mid June, for example, you could have bought a U.S. Treasury zero for $341 that matures in August 2027 at a face value of $1,000. That's an annualized return of 5.4%. But inflation, which has averaged about 3% over the past 20 years, will eat up a big part of that return. ³Amounts due at maturity may not have the purchasing power you thought they would,´ says Paul Winter of Five Seasons Financial Planning in Salt Lake City. And if interest rates continue to rise, as they did in late spring, zeros, unlike regular bonds, don't give you the opportunity to reinvest your interest at higher yields. Moreover, if you hold zeros in a regular account, you'll have to pay taxes each year on so-called phantom income from interest you haven't yet received. With 20 years or so to go before you retire, you'll almost certainly do better with a diversified portfolio of stocks, although they'll probably offer a bumpier ride along the way. If the certainty of zeros still appeal to you, Winter suggests this strategy: Put some money in zeros that mature in 20 years. Five years from now, buy more zeros that mature 20 years from that point, and so on. If interest rates rise, you'll be able to invest at least some of your money at higher yields.

Zero Coupon Bonds
Zero coupon bonds are a special type of bond that does not pay interest. Instead, it is redeemed at full face value at the maturity date. Zero coupons tend to fluctuate in price much more than other type of bonds. These resources and informational articles should provide you with a firm foundation for understanding zero coupon bonds. Savings Bond Calculator Savings bond calculators can help you determine the value of your various U.S. Government savings bonds, including EE, HH, and I series. These savings bond ... http://beginnersinvest.about.com/od/bondcalculator/Savings_Bond_Calculator.htm Bond Duration - What It Is and How to Calculate It One of the biggest dangers to bond investors can be calculated by ... provides a calculator for figuring how to usebond duration to hedge risks in other ... http://beginnersinvest.about.com/lw/Business-Finance/Personal-finance/Understanding-Bond-Duration.htm Online Calculators & Conversion Tables You'll also find calculators for pH, temperature, molecular weight, and other ... This site will calculate molecular properties (bond lengths, angles, ... http://chemistry.about.com/od/convertcalculate/Online_Calculators_Conversion_Tables.htm Zero Coupon Bonds Zero coupon bonds are a special type of bond that does not pay interest. Instead , it is redeemed at full face value at the maturity date. http://beginnersinvest.about.com/od/zerocouponbonds/Zero_Coupon_Bonds.htm Loan Amortization Calculator - A Free Online Loan Amortization ... The loan amortization calculator can be used for any straight-line amortized loan. You'll see what your monthly payment is, and you can see where you stand ... http://banking.about.com/library/calculators/bl_LoanAmortizationCalculator.htm

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HH Savings Bonds This means that, unlike the EE bond, the HH bond itself doesn't increase in value. When an HH bond is issued, you pay the face amount for the HH bond and ... http://beginnersinvest.about.com/od/hhsavingsbonds1/HH_Savings_Bonds.htm Bonds and Fixed Income Investing Bond Basics (13) · Bond Calculator (3) · Bond Funds (8) ... that results in an investor lending money to the bond issuer in exchange for interest payments. ... http://beginnersinvest.about.com/od/bondsandfixedincome/Bonds_and_Fixed_Income_Investing.htm Inflation - How to Protect Yourself From Inflation To find out each bond's return, go to the Treasury Department's Savings Bond Calculator. Learn more at the U.S. Treasury web site. ... http://useconomy.about.com/od/inflationfaq/f/protect_Infla.htm Investment for Beginners Savings bond calculators can help you determine the value of your various U.S. Government savings bonds, including EE, HH, and I series. ... http://beginnersinvest.about.com/mlibrary.htm Bond Basics - Basic Concepts of Bonds Explained A bond is an IOU issued by a corporation, government, or governmental agency to ... best done with a computer program or programmable business calculator. ... http://stocks.about.com/od/understandingstocks/a/bondbas102604.htm Zero Coupon Bonds - Understanding Zero Coupon Bonds Zero coupon bonds are sold at a deep discount and redeemed at full face value. http://stocks.about.com/od/bonds/a/Zeroone012505.htm Zero Coupon Bonds Zero coupon bonds are a special type of bond that does not pay interest. Instead , it is redeemed at full face value at the maturity date. http://beginnersinvest.about.com/od/zerocouponbonds/Zero_Coupon_Bonds.htm Zero-Coupon Bonds: What Are Zero Coupon Bonds and "Strips" and Who ... Zero-Coupon Bonds are sold at a deep discount to their face value. In many cases , interest is compounded and paid at maturity rather than during the life of ... http://bonds.about.com/od/bonds101/a/zeros.htm Zero-Coupon Bonds - Investing Zero-coupon bonds can be issued by companies, government agencies, or municipalities. http://www.netplaces.com/investing/types-of-bonds/zero-coupon-bonds.htm What Are Zero Coupon Bonds? Zero coupon bonds offer significant opportunities for some investors. STRIPs are the most prominent form of zero coupon bonds. http://stocks.about.com/od/bonds/a/061211-What-Are-Zero-Coupon-Bonds.htm Zero Coupon Bonds - How to Use Zero Coupon Bonds You can use zero coupon bonds to reach a variety of financial goals, but watch out for the tax consequences. http://stocks.about.com/od/bonds/a/ZeroTwo012505.htm Zero-Coupon Bond A zero-coupon bond is a bond that has no coupon rate (interest rate) attached to it so it pays no interest during its life. Instead, it is sold to investors ... http://bizfinance.about.com/od/glossaryz/g/zero-coupon-bond.htm What Are Zero Coupon Bonds? Jun 13, 2011 ... Zero coupon bonds are sold at a deep discount and redeemed for full face value, which means you receive the interest payments when you ... http://stocks.about.com/b/2011/06/13/what-are-zero-coupon-bonds.htm Bond Investing Strategies: Diversifying and Bond Laddering Zero-coupon bonds and "strips" are bought at a discount to face value. Interest is compounded annually, but isn't paid until the bond matures. ... http://bonds.about.com/od/bondinvestingstrategies/Bond_Investing_Strategies_Building_a_FixedIncome_Portfolio.htm Muni Bonds: Learning the Pros and Cons of Investing in Tax-Free Munis Zero-Coupon Bonds are sold at a deep discount to their face value. In many cases , interest is compounded and paid at maturity rather than during the life of ... http://bonds.about.com/od/munibonds/Muni_Bonds_Investing_in_TaxFree_Munincipal_Bonds.htm

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VALUING ZERO COUPON BONDS

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Many investors assume that the value of a zero coupon bond, or 'zero', is derived in the same manner as the yield to maturity on a par coupon bond, such as a Government of Canada bond. This is not the case. Yields on zero coupon bonds involve greater mathematical sophistication in order to account for the individual cash flows and unique maturity dates. This is where the 'bootstrapping' method of deriving a yield curve comes to bear rewards for investors and dealers alike.

As we are aware by this point in our travels through The Financial Pipeline, a traditional interest bearing bond is comprised of the principal portion, which will be repaid to the holder of the bond, in full, at maturity and the interest portion of the bond, consisting of coupon payments which the holder of the bond receives at regular intervals, usually every 6 months. Since the traditional par bond is made up of unique cash flows, it is possible to separate the two components, or strip, the bond into its constituent components. This process is done by taking the interest bearing coupons as one distinct and unique security, known simply as 'coupons', and the principal, the residual, as another distinct security. The traditional measure for comparing the value of bond investments has been the yield to maturity. For example, when calculating the price on a traditional interest bearing bond the yield to maturity (for this example assume 7%) is utilized on all cash flows to discount the value of those cash flows from the maturity date to the present date in order to determine the present value of all the cash flows. Since each of the coupon related cash flows are received at different distinct points of time in the future, each of these cash flows is subject to reinvestment risk. In order to compensate for the reinvestment risk, a 'spot' curve must be constructed. This will allow the investor to utilize the discount rate appropriate to the specific date associated with each cash flow. Since the residual and coupons are the constituent parts of the original bond, the 'spot' curve should theoretically value the individual cash flows to equal the price of the regular par bond at a given yeild to maturity. The sum of the parts should be equal to the whole. Since we know that the yield to maturity calculation for a par bond utilizes the same discount rate for all of the cash flows associated with the bond, namely the yield to maturity, to derive the price of the par bond, a series of yields must be derived which will make all the cash flows associated with the distinct stripped securities equal to the yield to maturity of the par bond. The derivation of the unique discount rates, or yields, at various intervals along the yield curve is referred to as the term structure of interest rates. It is this 'spot' term structure which we are interested in deriving in order to value zero coupon bonds. The spot curve may be determined through a method known as bootstrapping. The term structure of interest rates refers to the relationship between bonds of different terms. When interest rates of bonds are plotted against their terms, this is called the yield curve. Economists and investors believe that the shape of the yield curve reflects the market's

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future expectation for interest rates and the conditions for monetary policy. Bootstrapping is an iterative process which determines an appropriate discount rate associated with a unique maturity solving for the unknown 'zero' rate. By starting at the front end of the yield curve with a known 6 month t-bill rate and a known one year Government bond yield, a forward rate may be determined to equate a single 1 year security with two six month securities: one starting today and maturing in six months, and one starting in six months and maturing one year from now. This same methodology is utilized along the yield curve in six month intervals to derive the 'spot' curve. If the six month yield to maturity is 6%, and the 1 year yield to maturity is 7%, then the 1 year spot rate will be approximately 7.02%. This difference in observed yields versus derived spot yields becomes more pronounced the further out the yield curve the spot rate is calculated. Let the following table act as an example of a fictitious yield curve and the associated spot curve. Term (in years) 0.5 1.0 1.5 2.0 2.5 3.0 Yield (in %) 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% Zero or Spot Yield (in %) 6.00% 7.02% 8.05% 9.12% 10.21% 11.35%

If the yield curve is positively slopped, then the theoretical spot curve will lie above the yield curve, as in the example above. This is due to the fact that the greater the maturity, the greater the yield. As the maturity increases along the yield curve, the appropriate discount rate associated with each distinct cash flow must also increase in order to maintain the yield to maturity/zero coupon value equilibrium. When the equilibrium price becomes out of line arbitrage opportunities exist to either strip more bonds or reconstitute current stripped bonds. The opposite is true when the yield curve is inverted: the spot curve will lie below the yield curve. Due to the nature of the distinct cash flows associated with various coupon bearing bonds there are certain bonds which are more likely to be stripped than others. The effect of the coupon size on the present value of future cash flows has a direct bearing on stripping. A high coupon bond (example: 15%) has a larger portion of its present value derived from its coupon cash flows than a low coupon bond (example: 4%). This is due to the fact that every six months the high coupon bond holder will receive $7.50 for each $100 of par value they hold, while the low coupon bond holder will receive $2.00. Over the life of a ten year bond the total cash flow received from the high coupon bond is $150, where as the low coupon pays only $40. Due to the significant difference in cash flows, the economics of the spot

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curve favours stripping high coupon bonds over low coupon bonds. When considering adding zero coupon bonds to your portfolio remember that 'bootstrapping' is the way to determine the value of the security you are considering. It is not a simple task to construct the 'spot' curve of iterated forward spot yields, but the effort can pay-off in a better understanding of the value of your securites.

What in the world is a zero-coupon bond?
By Dorothy Rosen ‡ Bankrate.com

Hearing the finer points of bonds explained leaves you feeling like you're listening to a foreign language. No matter how many times you get it pounded into your head that a bond's yield moves in the opposite direction of its price, you still find your eyes glazing over and your head starting to nod. So the concept of the zero-coupon bond is going to be a real snooze, right? Well, I can't promise to turn bond investing into John Woo directing Jackie Chan, but I can give you a pretty clear idea of what you're getting into when you step up to the plate with one of these securities. First, some definitions might be useful. A bond is essentially an IOU sold by governments and companies to investors that guarantees that borrowers will repay borrowed money to the lenders, at certain interest rates by a certain time. A coupon is the interest an investor receives on bonds he or she owns -- a check arrives every six months until the bond's principle is due. Back in the dark ages, bonds actually used to come with small, detachable coupons that bondholders would physically redeem to receive the interest they were owed. Today, bond interest is usually paid through electronic transfer, but the anachronistic term persists. Two other useful definitions are face value, which is the value of the bond at the time it's redeemed, and maturity date, which is the date at which you are able to redeem your bond for cash at face value. For example, if a bond with a $1,000 face value matures on Dec. 31, 2000, you will receive $1,000 on that date. It doesn't matter if interest rates are up or if the Dow and Nasdaq are in the toilet. Unless the borrower defaults, the investor will receive the face value of her bond on its maturity date. A zero-coupon bond is a bond that is bought at a deep discount from its face value. It pays zero annual interest during its life, but pays full face value on its maturity date. If you buy a $10,000 zero-coupon bond for $5,000, you are buying it at a deep discount. The discount -- in this case $5,000 -- is actually the interest that will accumulate during the life of the bond. Most people buy

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zeros issued by the U.S. Government or state and local municipalities. Some investors favor the zero because it provides the comfort of a secure investment. If you buy a non-callable zero -- one that the issuer cannot make you redeem before its maturity date -- you effectively have a sure thing if you hold the bond to maturity. If you need $10,000 in three years for school tuition, or $30,000 in seven years to pay off a mortgage, the non-callable zero will get you there. But to achieve this comfort level, you need to be sure you're not going to have to cash it in before its maturity date, because that would mean selling it on the open market in competition with newer bonds that may be cheaper. If interest rates have climbed since you bought it, then the interest offered on a new bond will be more than $5,000, which drops the purchase price of your bond below the amount you paid. If you sell your bond, you may lose money. Tax wise, if you buy municipal zeros, you're spared the federal tax that is levied on Treasuries for each year's imputed interest. Investors who buy Treasury zeros often get around the tax disadvantage by putting them in taxdeferred retirement accounts, like an IRA, or the kids' accounts, if the children are in a low-to-no income tax bracket.
DOROTHY ROSEN has a master's degree in finance, with a specialization in accounting, from the Kellogg Graduate School at Northwestern University in Evanston, Ill. Rosen has more than 15 years of experience in the financial arena, serving in Illinois and Florida as a certified public accountant, financial consultant, expert witness and educator. She is owner of Dorothy Rosen, CPA, a public accounting firm that serves individuals and small businesses.

Subject: Bonds - Zero-Coupon
Last-Revised: 28 Feb 1994 Contributed-By: Art Kamlet (artkamlet at aol.com)

Not too many years ago every bond had coupons attached to it. Every so often, usually every 6 months, bond owners would take a scissors to the bond, clip out the coupon, and present the coupon to the bond issuer or to a bank for payment. Those were "bearer bonds" meaning the bearer (the person who had physical possession of the bond) owned it. Today, many bonds are issued as "registered" which means even if you don't get to touch the actual bond at all, it will be registered in your name and interest will be mailed to you every 6 months. It is not too common to see such coupons. Registered bonds will not generally have coupons, but may still pay interest each year. It's sort of like the issuer is clipping the coupons for you and mailing you a check. But if they pay interest periodically, they are still called Coupon Bonds, just as if the coupons were attached. When the bond matures, the issuer redeems the bond and pays you the face amount. You may have paid $1000 for the bond 20 years ago and you have received interest every 6 months for

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the last 20 years, and you now redeem the matured bond for $1000. A Zero-coupon bond has no coupons and there is no interest paid. But at maturity, the issuer promises to redeem the bond at face value. Obviously, the original cost of a $1000 bond is much less than $1000. The actual price depends on: a) the holding period -- the number of years to maturity, b) the prevailing interest rates, and c) the risk involved (with the bond issuer). Taxes: Even though the bond holder does not receive any interest while holding zeroes, in the US the IRS requires that you "impute" an annual interest income and report this income each year. Usually, the issuer will send you a Form 1099-OID (Original Issue Discount) which lists the imputed interest and which should be reported like any other interest you receive. There is also an IRS publication covering imputed interest on Original Issue Discount instruments. For capital gains purposes, the imputed interest you earned between the time you acquired and the time you sold or redeemed the bond is added to your cost basis. If you held the bond continually from the time it was issued until it matured, you will generally not have any gain or loss. Zeroes tend to be more susceptible to prevailing interest rates, and some people buy zeroes hoping to get capital gains when interest rates drop. There is high leverage. If rates go up, they can always hold them. Zeroes sometimes pay a better rate than coupon bonds (whether registered or not). When a zero is bought for a tax deferred account, such as an IRA, the imputed interest does not have to be reported as income, so the paperwork is lessened. Both corporate and municipalities issue zeroes, and imputed interest on municipals is tax-free in the same way coupon interest on municipals is. (The zero could be subject to AMT). Some marketeers have created their own zeroes, starting with coupon bonds, by clipping all the coupons and selling the bond less the coupons as one product -- very much like a zero -- and the coupons as another product. Even US Treasuries can be split into two products to form a zero US Treasury. There are other products which are combinations of zeroes and regular bonds. For example, a bond may be a zero for the first five years of its life, and pay a stated interest rate thereafter. It will be treated as an OID instrument while it pays no interest. (Note: The "no interest" must be part of the original offering; if a cumulative instrument intends to pay interest but defaults, that does not make this a zero and does not cause imputed interest to be calculated.) Like other bonds, some zeroes might be callable by the issuer (they are redeemed) prior to

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maturity, at a stated price.

How a Zero-Coupon Bond Works
The following information on Zero-Coupon Treasury Bonds was designed to give investors a basic understanding on the subject listed below. The information provided on Zero-Coupon Treasury Bonds should not be construed as investment advice, tax advice or a recommendation to purchase any security. Always consult a licensed professional and your personal tax advisor to determine if Zero-Coupon Treasury Bonds are right for you.

Zero-coupon treasury bonds (STRIPS) are purchased at a discount price below the face (par) value of $1,000 and are noncallable. When a zero is purchased, the investor is promised a fixed rate of return for the life of security called the yield to maturity (YTM). If the investor holds the zero until maturity, the investor receives the maturity (face) value of $1000. Example: Let's assume a 10-year zero was purchased with a yield to maturity (YTM) of 7%. As one can see on the present value chart, the current value of this zero would be approximately $503. In 10 years, at 7% compounded semiannually, the value of this zero at maturity will be the face value of $1,000. So $503 is the present value of $1,000 (face value) which matures in 10 years at a rate of 7%. The difference between the discount price and the face value of $1000 is the return to the investor. The return is the interest earned on the principal invested compounded semiannually at the original interest rate (YTM). Bonds that are not zero-coupons have a fixed-coupon rate that pay periodic interest payments. Zeros do not have a fixed-coupon rate, hence the name zero-coupon, and do not make periodic interest payments to the holder. Instead of making regular interest payments, the value of the bond accrues each year by the interest rate (YTM) until the zero matures at face value providing the investor holds the bond until maturity. However, if a zero is sold before maturity, the investor could realize a gain or loss

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because the market price could be more or less than the purchase price plus the amount of interest (and the inflation adjustment to principal in the case of inflation-indexed notes and bonds) that has accrued between the time the security was purchased and the sale date. The current value of a zero before it matures will fluctuate according to fluctuations in the interest rate. The bond value is inversely related to interest rates. This means, as interest rates rise, the value of the bond will fall and as interest rates fall, the value of the bond will increase. However, if you hold the security until maturity, your return is backed by the full faith and credit of the U.S. Government. See thePresent Value Chart for an example of how changes in interest rates reflect on the present value of a zero coupon bond. On the Present Value Chart, long-term zeros have lower market prices than shortterm zeros, because long-term zeros accrue interest over a longer period of time. For example, assume that three zeros are quoted in the market at a yield of 6.50 percent. The price for zeros with 25 years remaining to maturity would be $202.07 per $1,000 face amount; the price for zeros with 10 years remaining to maturity would be $527.47 per $1,000 face amount, while that for 2-year zeros would be $879.91 per $1,000 face amount. Zero-coupons (STRIPS) issued by the Treasury are generally considered the safest because they are obligations of the Treasury and are backed by the full faith and credit of the United States. Zeros represent direct ownership in interest of principal payments on U.S. treasury notes or bonds. Thus, when held to maturity, zeros are relatively safe because they are directly secured by the U.S. Government. However, the current market price is not guaranteed. Furthermore, market prices of zeros fluctuate more than the prices of fully constituted securities of the same maturity. The market price of a zero reflects the fact that there is only one payment on a specific date in the future. The market price of a fully constituted Treasury note or bond reflects the fact that there is a series of semiannual interest payments and a final payment at maturity. Zeros provide investors with assured growth in three ways. 1. They will know exactly how much money they will receive when the bond matures. 2. They will know exactly when they will receive that money. 3. They do not have to worry about reinvesting the small amounts of interest

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regular full-coupon bonds pay. In short, if the investor holds the treasury zero until maturity, they will know exactly how much money they will have and when they will have it backed by the full faith and credit of the U.S. Government. The annual growth or accreted value of zeros is taxed by the IRS as ordinary income even though no interest is paid. This is known as phantom income because an investor is taxed on income that is being reinvested or compounded and not actually received during the year. Because of the compounding, an increasing tax liability will result as the investment approaches maturity. However, it should be noted that the accreted value, or phantom income, is generally exempt from state and local taxation for treasury zeros. Every investor in zeros receives a report each year displaying the amount of zeros interest income from the financial institution, government securities broker, or government securities dealer that maintains the account in which the zeros are held. This statement is known as IRS Form 1099 - OID, the acronym for original issue discount. The income-reporting requirement has meant that zeros are attractive investments for tax-deferred accounts, such as individual retirement accounts (IRAs), SEP, SIMPLE, profit-sharing, custodial accounts, and 401(k) plans, and for non-taxable accounts, which include pension funds. The income tax treatment of zeros also takes into account market discount and capital gains or losses, if any. Therefore, an investor would be well advised to review possible income tax implications before investing in zeros. For further information on the tax treatment of STRIPS and other zero-coupon securities, see Internal Revenue Service Publication 550, "Investment Income and Expenses" on the Internal Revenue Service website at: Yields will vary with the maturity chosen and general market conditions at the time of purchase. In general, the longer the maturity, the higher the yield. Zeros mature on the 15th of February, May, August, and November every year from 1 to 30 years. This availability makes it simple for you to pick the maturity that fits your needs. Zeros have one of the largest and most active secondary markets in the debt market. The market value of zeros depend upon interest rates because they have an inverse relationship with each other . When interest rates rise, the market value

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of zeros fall and when interest rates fall, the market value of zeros rise. In addition, the market value of zeros fluctuates more than interest (coupon) bearing treasury bonds of similar maturity. As with most other debt-based investments, generally the longer the maturity of an issue, the more it will fluctuate in value. Zeros are traded on a principal (markup or markdown) basis, Thus, short-term trading of zeros may not be profitable. The Present Value Chart indicates the approximate present (accreted) value of a zero at its respective years to maturity and at various interest rate levels. To compute the present value of a zero after interest rates have changed, follow the example. Example: Let's assume a 10-year zero was purchased with a yield to maturity (YTM) of 7%. Based on thePresent Value Chart, we can see the zero would have a present value of $503. This can be found by intersecting the Interest Rate column (7%) by the Years to Maturity row (10-year). To see the inverse relationship interest rates have on the value of zeros, look at the value of the zero if interest rates fluctuate by 1% (100 basis points). If interest rates rise 1% to 8% in one year, this zero would be worth approximately $494 (a decrease in value of 1.789% or $9). However, if interest rates fall by 1% to 6%, the zero would be worth $587 (an increase in value of 16.7% or $84). This is why zero coupon treasury bonds are so attractive. If you were to purchase the bond above, you are guaranteed a 7% return if you hold the bond for 10 years. If interest rates were to fall by 1% in one year, your invest would increase by 16.7% ( The return in this example does not reflect the impact of transaction costs when buying and selling which would reflect a lower net return). If the above zero matured in 20 years instead of 10 years, the present value would be $253. If interest rates rise 1% to 8% in one year, this zero would be worth approximately $225 (a decrease in value of 11.0672% or $28). However, if interest rates fall by 1% to 6%, the zero would be worth $325 (an increase in value of 28.458% or $72). Note: The longer the maturity of zeros (STRIPS), the greater is the potential market price fluctuation.
Present Value Chart

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The present or accreted value of zeros as illustrated in this table should be used only as an approximation.
Zero-Coupon Bond
A bond that pays no interest. It is sold at a discount from par and matures at par. These are fairlyilliquid investments because they do not benefit from changes in interest rates. However, they tend to be low-risk. Zero-coupon bonds fluctuate in price, sometimes dramatically, with changes in interest rates. Sometimes zero-coupon bonds are issued as such; other times they are bonds stripped of their coupons by a financial institution and resold as zero-coupon bonds. A zero-coupon bond is less formally known as a zero.

zero-coupon bond
A bond that provides no periodic interest payments to its owner. A zero-coupon bond is issued at a fraction of its par value (perhaps at $3 to $5 for each $100 of face value for a long-term bond) and increases gradually in value as it approaches maturity. Thus, an investor's income from a zerocoupon bond comes solely from appreciation in value. Zero-coupon bonds are subject to very large price fluctuations. The tax consequences of taxable issues often make zero-coupon bonds more suitable for tax-deferred accounts such as IRAs than for regular investments. Also called accrual bond, capital appreciation bond, zero. Case Study Zero-coupon bonds offer advantages, at least to some investors. Zero-coupon bonds present an investor with the certainty that the rate of return earned on reinvested interest payments will be zero because no payments will be available for reinvestment. Zero-coupon bonds accumulate interest each period until they become worth their face value on the scheduled maturity date. Buy a 7% zero and you will earn 7% both on your original investment and also on the interest that is added to your original investment every six months. A fixed reinvestment rate is an advantage if you believe interest rates are likely to fall there is no concern about reinvesting interest payments at a rate lower than 7%. Of course, if interest rates subsequently increase, the owner of a zero-coupon bond will be worse off because interest payments could have been reinvested at a rate higher than 7%. This is a downside to earning the guaranteed rate. Zero-coupon bonds, especially issues with long maturities, tend to have very volatile prices. Buy a zero-coupon bond with a 25-year maturity and watch the price plummet if market interest rates increase. Of course, the opposite also holds true. A long-term zero-coupon bond will produce substantial gains in value when market rates of interest decline. Invest in a 7% zero-coupon bond before a major decline in interest rates and you will own a very valuable asset. The price volatility of long-term zero-coupon bonds subjects an investor to substantial risk in the event the bond must be sold prior to maturity. Zero-coupon bonds also often suffer from a lack of liquidity and so may be difficult to sell at a fair price before maturity. Again, liquidity is important if you may be required to sell the security on relatively short notice. However, if you plan to hold the bond to maturity, a lack of liquidity is not a problem. It is important to recognize that interest accumulations on corporate and U.S. government zero-coupon bonds must be reported as taxable income each year even though you do not receive any interest payments. This may result in a cash flow problem since money (specifically, taxes) will be going out and no money (for example, interest income) will be coming in. If interest from the bond is exempt from taxes (such as with an obligation of a state or municipality), or if a taxable issue is held in a tax-sheltered retirement account, taxability will not be an important issue. What are the advantages and disadvantages of buying zero-coupon bonds? Who should buy them? Zero-coupon bonds are quite useful in financial planning because they permit you to plan with certainty for specific rates of growth on the monies invested in them, provided that those monies will be left intact until maturity. If, however, you need to liquidate your zero-coupon bonds before their maturity, you will find that since you purchased your bonds, their prices will have moved dramatically in a direction opposite that of interest rates. These bonds have the most volatile price movements of any bonds in their respective credit quality and maturity group because they pay no coupon interest to

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cushion the blow of any change in interest rates. Another important aspect of zero-coupon bonds relates to their taxation. Income is accrued on zero-coupon bonds even though they do not pay any interest before maturity. If the bond is taxable (that is, it is a U.S. Treasury bond or a corporate bond), you will have to pay annual federal income tax on the accrued income even though you did not receive any cash flow from the bond before maturity. The income is based on the accretion of the bond from the discount price at which you bought it to the par value it will grow to have at maturity. If your bond is a municipal zero-coupon, the accretion is still calculated each year, but the bond's accretion is not taxed at the federal level. (Consult your state's tax laws regarding the taxation of the accretion.) This accretion affects the municipal bond's book value, however, which in turn influences the portion of any capital gain subject to federal income tax. Taxable zero-coupon bonds are often used in retirement plans and in children's custodial accounts because of the predictability of their values at maturity and the fact that income earned in accounts of this sort is generally able to grow tax-deferred or is taxed at a low federal income tax rate. Tax-exempt zero-coupon bonds are often used to form a "Side-IRA," which means that a pool of money is able to grow, free of taxation, with its anticipated use being to enhance the pool of money that is allowed to grow within an IRA. The obvious result is that more money will be available at the time of retirement because of careful planning for tax savings and the continuous compounding of the tax-favored rate of return. Stephanie G. Bigwood, CFP, ChFC, CSA, Assistant Vice President, Lombard Securities, Incorporated, Baltimore, MD

Zero-Coupon Bond
A bond that pays no interest. It is sold at a discount from par and matures at par. These are fairlyilliquid investments because they do not benefit from changes in interest rates. However, they tend to be low-risk. Zero-coupon bonds fluctuate in price, sometimes dramatically, with changes in interest rates. Sometimes zero-coupon bonds are issued as such; other times they are bonds stripped of their coupons by a financial institution and resold as zero-coupon bonds. A zero-coupon bond is less formally known as a zero.

Zero-coupon bond. Zero-coupon bonds, sometimes known as zeros, are issued at a deep
discount to par value and make no interest payments during their term. At maturity, the bondholder receives par value, which includes the interest that has accrued since issue. For example, you may purchase a zero-coupon bond with a six-year term for $13,500, and collect $20,000 at maturity. One advantage of zeros is that you can invest relatively smaller amounts and choose maturity dates to coincide with times you know you'll need the money -- for example, when you expect college tuition bills to come due. One drawback of zeros, however, is that income taxes are due annually on the interest that accrues, even though you don't receive the actual payment until the bond matures. The exception occurs if you buy tax-exempt municipal zeros, on which no tax is due either during the term or at maturity. Another drawback is that zero coupon bonds are volatile in the secondary market, so if you have to sell before maturity, you might have a loss. These bonds get their name -- zero coupon -- from the fact that coupon means interest in bond terminology, and there's no periodic interest.

Zero-Coupon Bond

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What Does Zero-Coupon Bond Mean? A debt security that does not pay interest (a coupon) but is traded at a deep discount and paid in full at face value upon maturity; also called an accrual bond. Investopedia explains Zero-Coupon Bond Some zero-coupon bonds are issued as such, whereas others are bonds that have been stripped of their coupons by a financial institution and then repackaged as zero-coupon bonds. Because they offer the entire payment at maturity, zero-coupon bonds tend to fluctuate in price more than coupon bonds do. Related Terms: ‡ Bond ‡ Coupon ‡ Discount Rate ‡ Face Value ‡ Maturity

Bond
A security representing the debt of the company or government issuing it. When a company or government issues a bond, it borrows money from the bondholders; it then uses the money to invest in its operations. In exchange, the bondholder receives the principal amount back on a maturity datestated in the indenture, which is the agreement governing a bond's terms. In addition, the bondholder usually has the right to receive coupons or payments on the bond's interest. Generally speaking, a bond is tradable though some, such as savings bonds, are not. The interest rates on Treasury securities are considered a benchmark for interest rates on other debt in the United States. The higher the interest rate on a bond is, the more risky it is likely to be. There are several different kinds of bonds. The most basic division is the one between corporate bonds, which are issued by private companies, and government bonds such as Treasuries ormunicipal bonds. Other common types include callable bonds, which allow the issuer to repay theprincipal prior to maturity, depriving the bondholder of future coupons, and floating rate notes, which carry an interest rate that changes from time to time according to some benchmark. Along with cashand stocks, bonds are one of the basic types of assets.

bond
1. A long-term promissory note. Bonds vary widely in maturity, security, and type of issuer, although most are sold in $1,000 denominations or, if a municipal bond, $5,000 denominations. 2. A written obligation that makes a person or an institution responsible for the actions of another

Bond
A security representing the debt of the company or government issuing it. When a company or government issues a bond, it borrows money from the bondholders; it then uses the money to invest in its operations. In exchange, the bondholder receives the principal amount back on a maturity datestated in the indenture, which is the agreement governing a bond's terms. In addition, the bondholder usually has the right to receive coupons or payments on the bond's interest. Generally speaking, a bond is tradable though some, such as savings bonds, are not. The interest rates on Treasury securities are considered a benchmark for interest rates on other debt in the United States. The higher the interest rate on a bond is, the more risky it is likely to be. There are several different kinds of bonds. The most basic division is the one between corporate bonds, which are issued by private companies, and government bonds such as Treasuries

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ormunicipal bonds. Other common types include callable bonds, which allow the issuer to repay theprincipal prior to maturity, depriving the bondholder of future coupons, and floating rate notes, which carry an interest rate that changes from time to time according to some benchmark. Along with cashand stocks, bonds are one of the basic types of assets.

Bond. Bonds are debt securities issued by corporations and governments.
Bonds are, in fact, loans that you and other investors make to the issuers in return for the promise of being paid interest, usually but not always at a fixed rate, over the loan term. The issuer also promises to repay the loan principal at maturity, on time and in full. Because most bonds pay interest on a regular basis, they are also described as fixed-income investments. While the term bond is used generically to describe all debt securities, bonds are specifically long-term investments, with maturities longer than ten years.

bond
A certificate that provides evidence of a debt or obligation.

Bond
What Does Bond Mean? A debt investment in which an investor lends money to an entity (corporate or government) that borrows the funds for a defined period at a fixed interest rate. Bonds are used by companies, municipalities, states, and U.S. and foreign governments to finance a variety of projects and activities. Bonds commonly are referred to as fixedincome securities and are one of the three main asset classes, along with stocks and cash equivalents. Investopedia explains Bond The indebted entity (issuer) issues a bond stipulating the stated interest rate (coupon) to be paid and a date when the loaned funds (bond principal) are to be returned (maturity date). Interest on bonds usually is paid every six months (semiannually); bond categories include corporate bonds, municipal bonds, and U.S. Treasury bonds, notes, and bills (³Treasuries´). Two features of a bond²credit quality and maturity²are the principal determinants of the interest rate of a bond. Bond maturities can range from a 90-day Treasury bill to a 30-year government bond. Corporate and municipal bonds typically go out 3 to 10 years. Related Terms: ‡ Callable Bond ‡ Convertible Bond ‡ Corporate Bond ‡ Junk Bond ‡ Yield to Maturity

Bond
A note obliging a corporation or governmental unit to repay, on a specified date, money loaned to it by the bondholder. The holder receives interest for the life of the bond. If a bond is backed by collateral, it is called a mortgage bond. If it is backed only by the good faith and credit rating of the

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issuing company, it is called a debenture.

Coupon
The contractual interest obligation a bond or debenture issuer covenants to pay to its debtholders.

Coupon
The interest paid on a bond. That is, the coupon is the amount that the issuer must pay to the holderof each bond in exchange for investing in that bond. Coupons usually are paid every six months. They are called coupons because formerly they were represented by physical coupons on the bond certificate that had to be clipped and returned to the issuer to receive the interest payment. With the advent of computers, this has become much less common.

coupon
1. The annual interest paid on a debt security. A coupon is usually stated in terms of the rate paid on a bond's face value. For example, a 9% coupon, $1,000 principal amount bond would pay its owner $90 in interest annually. A coupon is set at the time a security is issued and, for most bonds, stays the same until maturity. 2. The detachable part of a coupon bond that must be presented for payment every six months in order to receive interest. See also clip, coupon clipping.

Coupon
The interest paid on a bond. That is, the coupon is the amount that the issuer must pay to the holderof each bond in exchange for investing in that bond. Coupons usually are paid every six months. They are called coupons because formerly they were represented by physical coupons on the bond certificate that had to be clipped and returned to the issuer to receive the interest payment. With the advent of computers, this has become much less common.

Coupon. Originally, bonds were issued with coupons, which you clipped and presented to the
issuer or the issuer's agent -- typically a bank or brokerage firm -- to receive interest payments. Bonds with coupons are also known as bearer bonds because the bearer of the coupon is entitled to the interest. Although most new bonds are electronically registered rather than issued in certificate form, the term coupon has stuck as a synonym for interest in phrases like the coupon rate. When interest accumulates rather than being paid during the bond's term, the bond is known as a zero coupon.
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Coupon
The contractual interest obligation a bond or debenture issuer covenants to pay to its debtholders.
Copyright © 2011, Campbell R. Harvey. All Rights Reserved.

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Coupon
The interest paid on a bond. That is, the coupon is the amount that the issuer must pay to the holderof each bond in exchange for investing in that bond. Coupons usually are paid every six months. They are called coupons because formerly they were represented by physical coupons on the bond certificate that had to be clipped and returned to the issuer to receive the interest payment. With the advent of computers, this has become much less common.

Farlex Financial Dictionary. © 2009 Farlex, Inc. All Rights Reserved

coupon
1. The annual interest paid on a debt security. A coupon is usually stated in terms of the rate paid on a bond's face value. For example, a 9% coupon, $1,000 principal amount bond would pay its owner $90 in interest annually. A coupon is set at the time a security is issued and, for most bonds, stays the same until maturity. 2. The detachable part of a coupon bond that must be presented for payment every six months in order to receive interest. See also clip, coupon clipping.
Wall Street Words: An A to Z Guide to Investment Terms for Today's Investor by David L. Scott. Copyright © 2003 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.

Coupon
The interest paid on a bond. That is, the coupon is the amount that the issuer must pay to the holderof each bond in exchange for investing in that bond. Coupons usually are paid every six months. They are called coupons because formerly they were represented by physical coupons on the bond certificate that had to be clipped and returned to the issuer to receive the interest payment. With the advent of computers, this has become much less common.

Farlex Financial Dictionary. © 2009 Farlex, Inc. All Rights Reserved

Coupon. Originally, bonds were issued with coupons, which you clipped and presented to the issuer or the
issuer's agent -- typically a bank or brokerage firm -- to receive interest payments. Bonds with coupons are also known as bearer bonds because the bearer of the coupon is entitled to the interest. Although most new bonds are electronically registered rather than issued in certificate form, the term coupon has stuck as a synonym for interest in phrases like the coupon rate. When interest accumulates rather than being paid during the bond's term, the bond is known as a zero coupon.
Dictionary of Financial Terms. Copyright © 2008 Lightbulb Press, Inc. All Rights Reserved.

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Coupon
What Does Coupon Mean? The interest rate stated on a bond when it is issued. The coupon typically is paid semiannually. This also is referred to as the coupon rate or coupon percent rate. Investopedia explains Coupon For example, a $1,000 bond with a coupon of 7% will pay $70 a year. It is called a coupon because some bonds literally have coupons attached to them. Holders receive interest by stripping off the coupons and redeeming them. This is less common today as more records are kept electronically. Related Terms: ‡ Bond ‡ Interest Rate ‡ Premium ‡ Yield ‡ Zero-Coupon Bond

Discount rate
The interest rate that the Federal Reserve charges a bank to borrow funds when a bank is temporarily short of funds. Collateral is necessary to borrow, and such borrowing is quite limited because the Fed views it as a privilege to be used to meet short-term liquidity needs, and not a device to increaseearnings. In context of NPV or PV calculations, the discount rate is the annual percentage applied. In the context of project financing, the discount rate is often the all-in interest rate or the interest rate plus margin.

Discount Rate
The interest rate at which the Federal Reserve makes short-term loans to member banks. The discount rate is an indicator of the direction in which the Federal Reserve is trying to push the broadereconomy. In general, a low interest rate indicates that it is trying to promote growth by making liquidityeasily available, and a high interest rate shows that the Fed is concerned about inflationary pressures on the economy and trying to reduce the amount of money in the economy. Along with the sale ofTreasury securities and the determining of the fed funds rate, setting the discount rate is one of the primary ways the Federal Reserve sets the monetary policy of the United States.

discount rate
1. The interest rate charged by the Federal Reserve on loans to its member banks. A change in this rate is viewed as a strong indicator of Fed policy with respect to future changes in the money supply and market interest rates. Generally, a rise in the discount rate signals increasing interest rates in the money and capital markets. 2. The rate at which an investment's revenues and costs are discounted in order to calculate its present value.

Discount Rate
The interest rate at which the Federal Reserve makes short-term loans to member banks. The discount rate is an indicator of the direction in which the Federal Reserve is trying to push the broadereconomy. In general, a low interest rate indicates that it is trying to promote growth by making liquidityeasily available, and a high interest rate shows that the Fed is concerned about inflationary pressures on the economy and trying to reduce the amount of money in the

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economy. Along with the sale ofTreasury securities and the determining of the fed funds rate, setting the discount rate is one of the primary ways the Federal Reserve sets the monetary policy of the United States.

Discount rate. The discount rate is the interest rate the Federal Reserve charges on loans it
makes to banks and other financial institutions. The discount rate becomes the base interest rate for most consumer borrowing as well. That's because a bank generally uses the discount rate as a benchmark for the interest it charges on the loans it makes. For example, when the discount rate increases, the interest rate that lenders charge on home mortgages and other loans increases. And when the discount rate is lowered, the cost of consumer borrowing eventually decreases as well. The term discount rate also applies to discounted instruments like US Treasury bills. In this case, the rate is used to identify the interest you will earn if you purchase at issue, hold the bill to maturity, and receive face value at maturity. The interest is the difference between what you pay to purchase the bills and the amount you are repaid.

discount rate
The rate at which the Federal Reserve loans money to lenders to cover short-term cash needs, usually for overnight loans. Increases or decreases in the discount rate almost always signal similar increases or decreases in bank loan rates to customers, even though the two are not directly tied to each other.

Discount Rate
What Does Discount Rate Mean? (1) The interest rate that an eligible depository institution is charged to borrow short-term funds directly from a Federal Reserve Bank. (2) The interest rate used in determining the present value of future cash flows. Investopedia explains Discount Rate (1) This type of borrowing from the Fed is fairly limited. Institutions often seek other means of meeting short-term liquidity needs. The Federal funds discount rate is one of two interest rates the Fed sets, the other being the overnight lending rate, or the Fed funds rate. (2) Let's say you expect $1,000 in one year's time. To determine the present value of this $1,000 (what it is worth to you today), you would need to discount it by a particular rate of interest (often the risk-free rate but not always). Assuming a discount rate of 10%, the $1,000 in a year's time would be the equivalent of $909.09 to you today (1,000/[1.00 + 0.10]). Related Terms:

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‡ Federal Funds Rate ‡ Federal Open Market Committee ‡ Interest Rate ‡ Monetary Policy ‡ Prime Rate

Face Value
The amount of money stated on a bond or (rarely) a stock certificate. For example, if a bond certificate says $1,000, the face value is $1000. Bonds pay the face value at maturity, and calculate coupons as a percentage of the face value. Many bonds are issued at their face value, though discount bonds are not. The face value is also called the par value or simply par.

Face Value
The amount of money stated on a bond or (rarely) a stock certificate. For example, if a bond certificate says $1,000, the face value is $1000. Bonds pay the face value at maturity, and calculate coupons as a percentage of the face value. Many bonds are issued at their face value, though discount bonds are not. The face value is also called the par value or simply par.

Face value. Face value, or par value, is the dollar value of a bond or note, generally $1,000.
That is the amount the issuer has borrowed, usually the amount you pay to buy the bond at the time it is issued, and the amount you are repaid at maturity, provided the issuer doesn't default. However, bonds may trade at a discount, which is less than face value, or at a premium, which is more than face value, in the secondary market. That's the bond's market value, and it changes regularly, based on supply and demand. The death benefit of a life insurance policy which is the amount the beneficiary receives when the insured person dies. It's also known as the policy's face value.

face value
The value of an instrument (promissory note, bond, stock, etc.) as stated on the face of the instrument.The face value does not always equal the market value. Example: A 5-year-old mortgage note with a face value of $100,000 and an amortization term of 20 years at 2.8 percent interest is worth far less than $100,000 for two reasons: (1) The principal balance is now a little under $80,000. (2) Why would anyone invest even $80,000 to earn 2.8 percent interest when he or she can get better returns in the marketplace? For both reasons, an investor would pay much less than the $100,000 face value to buy the mortgage.

Face Value
What Does Face Value Mean? The nominal or dollar value of a security at the time it is issued. For stocks, it is the original cost of the stock shown on the certificate. For bonds, it is the amount paid to the holder at maturity (generally $1,000). Also known as par value or par. Investopedia explains Face Value

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In bond investing, face value, or par value, commonly refers to the amount paid to a bondholder at the maturity date, assuming the issuer does not default. However, bond prices on the secondary market fluctuate with interest rates. For example, if interest rates are higher than a bond's coupon rate, the bond is sold at a discount (below par). Conversely, if interest rates are lower than the bond's coupon rate, the bond is sold at a premium (above par). Related Terms: ‡ Bond ‡ Fair Value ‡ Market Value ‡ Par Value ‡ Premium

Maturity
For a bond, the date on which the principal is required to be repaid. In an interest rate swap, the date that the swap stops accruing interest.

Maturity
The time when the issuer of a bond or other debt security must repay the principal or when a borrowermust repay a loan in full. For example, if a company issues $1 million in bonds with a maturity of 10 years, the company must repay $1 million to bondholders 10 years after the issue. The amount owed at maturity is usually the same as the debt or loan's face value. After maturity, the loan or debt ceases to exist, assuming all parties have fulfilled their obligations. See also: Expiration.

maturity
The date on which payment of a financial obligation is due. In the case of a bond, the maturity date is the one on which the issuer must retire the bond by paying the face value of the bond to its owners. Shares of stock do not have specific maturity dates. Case Study In late 1995, BellSouth became only the fifth company in 40 years to issue bonds with 100-year maturities. The AAA-rated bonds carried a 7% coupon that was 70 basis points higher than 30-year Treasury bonds yielded when the BellSouth bonds were priced. Because it is impossible to know what the next 100 years will bring, bonds with such long maturities subject investors to substantial risk. Renewed inflation, for example, could undermine the purchasing power of the interest payments a bondholder received. Likewise, competition in the communications industry might shake the financial stability of a company long protected by regulation. In addition, changes in market rates of interest have a significant impact on the price of bonds with long maturities. On the plus side though, this BellSouth bond presented investors with a chance to lock in for a long period what at the time appeared to be an attractive yield. If inflation and interest rates remain low for decades, the bonds could turn out to be a profitable investment.

Maturity
The time when the issuer of a bond or other debt security must repay the principal or when a borrowermust repay a loan in full. For example, if a company issues $1 million in bonds with a maturity of 10 years, the company must repay $1 million to bondholders 10 years after the issue. The amount owed at maturity is usually the same as the debt or loan's face value. After maturity, the loan or debt ceases to exist, assuming all parties have fulfilled their obligations. See also: Expiration.

maturity
The date on which the remaining balance of a promissory note is due.

Maturity
The period until the last payment is due.

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The maturity is usually but not always the same as the period used to calculate the mortgage payment

Maturity
What Does Maturity Mean? (1) The length of time until the principal amount of a bond must be repaid. (2) The end of the life of a security. Investopedia explains Maturity In other words, the maturity is the date on which the borrower must pay back the money he or she borrowed through the issuance of a bond. Related Terms: ‡ Bond ‡ Interest Rate ‡ Long-Term Debt ‡ Par Value ‡ Yield to Maturity

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zero-coupon bond
Definition
Bond that (1) pays no interest but instead is sold at a deep discount on its par-

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value, or (2) an interest paying bond that has been stripped of its coupon which is sold separately as a security in its own right. Bondholder'sincome is determined by the difference between the bond'sredemption value on maturity and its purchase price. Also called non-interest bearing Bond, zero interest bond, orzero rated bond. See also deep discount bond.

What Are Zero-Coupon Bonds and "Strips"?
Zero-coupon bonds, or zeros, are sold at a discount to face value. Interest is compounded during the term of the bond, but unlike other bonds, those interest payments aren't made until the bond matures. With zero-coupon bonds, an investor buys a $1,000 bond for considerably less than that amount. There are no payments received until the bond matures - perhaps as far into the future as 30 years. However, investors can buy and sell the bonds prior to maturity -- realizing a gain or loss depending on how prices have changed since the original purchase. The most popular forms of zero-coupon bonds are sold by the U.S. government. U.S. Savings Bonds such as the EE Series are zero-coupon investments. Treasury bills, which mature in one year or less, are also zero-coupon investments. Another form of zero-coupon investment is called a "strip." Strips, or Separate Trading of Registered Interest and Principal Securities, are created from traditional, interest-paying bonds. A financial institution buys the bond and then "strips" out the interest payment -- creating two distinct investments: a zero-coupon bond and a collection of interest coupons. They can be sold separately. Why Buy a Zero-Coupon Bond? Institutional investors such as pension funds and insurance companies often like long-maturity zeros because of a complicated valuation concept known as duration. Zeros have a high duration, which means they can be used to mitigate interest rate risks associated with money that must be paid in the future (insurance policies, pensions, etc.) But zeros may also appeal to some average investors. 1. Zeros are inexpensive: Say you're looking to set aside money for retirement in 30 years. For every $1,000 you'd want to have then, you must pay $1,000 today for an interest-paying bond. As an alternative, you can "lock in" that future $1,000 by buying a zero-coupon today for closer to $250. 2. Most zeros are very safe. The most popular form of zero-coupon bonds are U.S. Treasury Strips. Given that they are created from government debt offerings that are backed by the full faith and credit of the U.S. government, the risk of default is nil. On the Other Hand ... Reasons to Avoid Zeros There are also three good reasons for the average investor to think twice before buying zeros. 1. 2. 3. You'll owe taxes on the interest before you receive the interest. A quirk in U.S. tax law makes the holder of a zero responsible for taxes on interest as it accrues. So the owner must pay taxes every year on interest that he won't receive until the bond matures. The prices of zeros fluctuate wildly in the secondary market. If you have to sell before maturity, you could lose money. Locking yourself into a zero exposes you to inflation risk. If you don't sell before maturity, the money you

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collect at the end of the term may have lost some of its value. In other words, your investment may not keep up with inflation.

Types of Bonds
Introduction

Types of Zero Coupon Bonds The three largest categories of zero coupon securities available are zero coupon Treasury bonds, zero coupon corporate bonds and zero coupon municipal bonds, which are issued by the U.S. Treasury, corporations, and state and local government jurisdictions, respectively. Generally, zero coupon Treasury bonds are considered the safest zero coupon bonds because they are backed by the full faith and credit of the U.S. government. Zero coupon corporate bonds and municipal bonds offer a potentially higher rate of return commensurate with additional credit risk, which will vary based on the issuing entity. Zero coupon municipal bonds are the only zero coupon securities that pay interest that is exempt from federal income tax and, in many cases, state and local taxes. This section will discuss zero coupon municipal bonds.

Size of the Municipal Zero Coupon Market Zero coupon bonds were introduced to the fixed-income market in 1982. The municipal zero coupon market is substantially larger today than it was in 1982, when there were 58 new offerings totaling $2.2 billion in issuance. In 2009, there were 380 new issues totaling $17.2 billion. More than 164.4 billion of zero coupon municipal bonds have been issued in the past ten years.* To understand how zero coupon municipal bonds work, it is important first to become acquainted with the principal characteristics of both municipal bonds and the zero coupon structure.

Zero Coupon Bond Value
Click Here or Scroll Down for Zero Coupon Bond Calculator

A zero coupon bond, sometimes referred to as a pure discount bond or simply discount

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bond, is a bond that does not pay coupon payments and instead pays one lump sum at maturity. The amount paid at maturity is called the face value. The term discount bond is used to reference how it is sold originally at a discount from its face value instead of standard pricing with periodic dividend payments as seen otherwise. As shown in the formula, the value, and/or original price, of the zero coupon bond is discounted to present value. To find the zero coupon bond's value at its original price, the yield would be used in the formula. After the zero coupon bond is issued, the value may fluctuate as the current interest rates of the market may change. Example of Zero Coupon Bond Formula A 5 year zero coupon bond is issued with a face value of $100 and a rate of 6%. Looking at the formula, $100 would be F, 6% would be r, and t would be 5 years.

After solving the equation, the original price or value would be $74.73. After 5 years, the bond could then be redeemed for the $100 face value. Example of Zero Coupon Bond Formula with Rate Changes A 6 year bond was originally issued one year ago with a face value of $100 and a rate of 6%. As the prior example shows, the value at the 6% rate with 5 years remaining would be $74.73. In this example, we suppose that the interest rates have changed to 5% since it was originally issued. The formula would be shown as

After solving the equation, the value would be $78.35.

Zero Coupon Bond Calculator
Face Value (F) Rate/Yield (r) Time to Maturity (t) =
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Zero-Coupon Bond
What It Is: A zero-coupon bond is a bond that makes no periodic interest payments and is sold at a deep discount from face value. The buyer of the bond receives a return by the gradualappreciation of the security, which is redeemed at face value on a specified maturity date.

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[InvestingAnswers Feature: 10 Highest Paying Work-at-Home Careers] How It Works/Example: The price of a zero-coupon bond can be calculated by using the following formula: P = M / (1+r)n where: P = price M = maturity value r = investor's required annual yield / 2 n = number of years until maturity x 2 For example, if you want to purchase a Company XYZ zero-coupon bond that has a $1,000 face value and matures in three years, and you would like to earn 10% per year on the investment, using the formula above you might be willing to pay: $1,000 / (1+.05)6 = $746.22 When the bond matures, you would get $1,000. You would receive "interest" via the gradualappreciation of the security. The greater the length until a zero-coupon bond's maturity, the less the investor generally pays for it. So if the $1,000 Company XYZ bond matured in 20 years instead of 3, you might only pay: $1,000 / (1+.05)40 = $142.05 Zero-coupon bonds are very common, and most trade on the major exchanges. Corporations, state and local governments, and even the U.S. Treasury issue zero-coupon bonds. Corporate zero-coupon bonds tend to be riskier than similar coupon-paying bonds because if the issuer defaults on a zero-coupon bond, the investor has not even received coupon payments -- there is more to lose. For tax purposes, the IRS maintains that the holder of a zero-coupon bond owes income tax on the ir that has accrued each year, even though the bondholder does not actually receive the cash until maturity. The IRS calls this imputed interest. [InvestingAnswers Feature: 50 Surprising Facts You Never Knew About Gold] Why It Matters: Zero-coupon bonds are usually long-term investments; they often mature in ten or more years. Although the lack of current income provided by zero-coupons bond discourages some investors, others find the securities ideal for meeting long-range financial goals like college tuition. The deep discount helps the investor grow a small amount of money into a sizeable sum over several years.

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Because zero-coupon bonds essentially lock the investor into a guaranteed reinvestment rate, purchasing zero-coupon bonds can be most advantageous when interest rates are high. They are also more advantageous when placed in retirement accounts where they remain taxsheltered. Some investors also avoid paying taxes on imputed interest by buying municipal zerocoupon bonds, which are usually tax-exempt if the investor lives in the state where the bond was issued. The lack of coupon payments on zero-coupon bonds means their worth is based solely on their current price compared to their face value. Thus, prices tend to rise faster than the prices of traditional bonds when interest rates are falling, and vice versa. The locked-in reinvestment rate also makes them more attractive when interest rates fall. What It Is: The measuring principle allows traders to set a specific minimum price target when trading a stock. This technique works with any well-defined technical analysis pattern, such as a head and shoulders, rectangle or triangle.

How It Works/Example:
To use the measuring principle to calculate the minimum target for an expected share price move, first establish the height of the pattern. In the case of the S&P chart below, we have a potential four-month topping pattern, with a peak at 1295 and clear support at 1245. If support is broken, then the pattern would take the form of a head and shoulders top. Using this example, the simple calculation looks like this: Peak: 1295 Support: 1245 Difference: 50 points Once the height of the pattern has been established, either subtract that amount from the broken support level or add it to the level where the stock breaks out above resistance. In this case, the break will be below support, so we will subtract. Breakout level: 1245 Less: Height of pattern: 50 Minimum Target: 1195 Once this target is established, traders should then determine if it makes sense with the rest of the technical picture. The S&P's major trendline is at 1200, so a break of key support would lead to a pullback to that trendline. The lower Bollinger band is at 1175 in the example below, so a decline would end above the band. In my mind, this kind of additional reasoning gives further credence to the target.

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Why It Matters: The measuring principle may have no fully logical explanation, yet it works uncannily well in most cases. However, if the market begins to send a different message, then the trader should be prepared to adapt. After all, the measuring principle is just a principle, not a law.

zero-coupon bond investment & finance
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definition
A bond that pays no interest until it matures. It is priced at a deep discount to make up for the lack of income. These bonds are commonly called zeros. A bond that provides no periodic interest payments to its owner. A zero-coupon bond is issued at a fraction of its par value (perhaps at $3 to $5 for each $100 of face value for a long-term bond) and increases gradually in value as it approaches maturity. Thus, an investor's income from a zero-coupon bond comes solely from appreciation in value. Zerocoupon bonds are subject to very large price fluctuations. The tax consequences of taxable issues often make zero-coupon bonds more suitable for tax-deferred accounts such as IRAs than for regular investments. Also called accrual bond, capital appreciation bond, zero. Case Study Zero-coupon bonds offer advantages, at least to some investors. Zero-coupon bonds present an investor with the certainty that the rate of return earned on reinvested interest payments will be zero because no payments will be available for reinvestment. Zerocoupon bonds accumulate interest each period until they become worth their face value on the scheduled maturity date. Buy a 7% zero and you will earn 7% both on your original investment and also on the interest that is added to your original investment every six months. A fixed reinvestment rate is an advantage if you believe interest rates are likely to fall²there is no concern about reinvesting interest payments at a rate lower than 7%. Of course, if interest rates subsequently increase, the owner of a zero-coupon bond will be worse off because interest payments could have been reinvested at a rate higher than 7%. This is a downside to earning the guaranteed rate. Zero-coupon bonds, especially issues with long maturities, tend to have very volatile prices. Buy a zero-coupon bond with a 25-year maturity and watch the price plummet if market interest rates increase. Of course, the opposite also holds true. A long-term zero-coupon bond will produce substantial gains in value when market rates of interest decline. Invest in a 7% zero-coupon bond before a major decline in interest rates and you will own a very valuable asset. The price volatility of long-term zerocoupon bonds subjects an investor to substantial risk in the event the bond must be sold prior to maturity. Zero-coupon bonds also often suffer from a lack of liquidity and so may be difficult to sell at a fair price before maturity. Again, liquidity is important if you may be required to sell the security on relatively short notice. However, if you plan to hold the bond to maturity, a lack of liquidity is not a problem. It is important to recognize that interest accumulations on corporate and U.S. government zero-coupon bonds must be reported as

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taxable income each year even though you do not receive any interest payments. This may result in a cash flow problem since money (specifically, taxes) will be going out and no money (for example, interest income) will be coming in. If interest from the bond is exempt from taxes (such as with an obligation of a state or municipality), or if a taxable issue is held in a tax-sheltered retirement account, taxability will not be an important issue. What are the advantages and disadvantages of buying zero-coupon bonds? Who should buy them? Zero-coupon bonds are quite useful in financial planning because they permit you to plan with certainty for specific rates of growth on the monies invested in them, provided that those monies will be left intact until maturity. If, however, you need to liquidate your zero-coupon bonds before their maturity, you will find that since you purchased your bonds, their prices will have moved dramatically in a direction opposite that of interest rates. These bonds have the most volatile price movements of any bonds in their respective credit quality and maturity group because they pay no coupon interest to cushion the blow of any change in interest rates. Another important aspect of zero-coupon bonds relates to their taxation. Income is accrued on zero-coupon bonds even though they do not pay any interest before maturity. If the bond is taxable (that is, it is a U.S. Treasury bond or a corporate bond), you will have to pay annual federal income tax on the accrued income even though you did not receive any cash flow from the bond before maturity. The income is based on the accretion of the bond from the discount price at which you bought it to the par value it will grow to have at maturity. If your bond is a municipal zero-coupon, the accretion is still calculated each year, but the bond's accretion is not taxed at the federal level. (Consult your state's tax laws regarding the taxation of the accretion.) This accretion affects the municipal bond's book value, however, which in turn influences the portion of any capital gain subject to federal income tax. Taxable zero-coupon bonds are often used in retirement plans and in children's custodial accounts because of the predictability of their values at maturity and the fact that income earned in accounts of this sort is generally able to grow tax-deferred or is taxed at a low federal income tax rate. Tax-exempt zero-coupon bonds are often used to form a ³SideIRA,´ which means that a pool of money is able to grow, free of taxation, with its anticipated use being to enhance the pool of money that is allowed to grow within an IRA. The obvious result is that more money will be available at the time of retirement because of careful planning for tax savings and the continuous compounding of the tax-favored rate of return. Stephanie G. Bigwood, CFP, ChFC, CSA, Assistant Vice President, Lombard Securities, Incorporated, Baltimore, MD

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zero-coupon bond business definition
A bond that provides no periodic interest payments to its owner. A zero-coupon bond is issued at a fraction of its par value and increases gradually in value as it approaches maturity. Thus, an investor's income from a zero-coupon bond comes solely from appreciation in value. Zero-coupon bonds are subject to very large price fluctuations. The tax consequences of taxable issues often make zero-coupon bonds more suitable for tax-deferred accounts such as IRAs than for regular investments. Also called accrual bond, capital appreciation bond, zero. See also Separate Trading of Registered Interest and Principal of Securities.

Zero-Coupon Bondsby Michele Cagan, CPA
Zero-coupon bonds can be issued by companies, government agencies, or municipalities. Known as zeros, these bonds do not pay interest periodically as most bonds do. Instead, they are purchased at a discount and pay a higher rate (both interest and principal) when they reach maturity. Don't buy zeros (or zero-coupon bonds) for liquidity in your portfolio. As for taxes, despite the fact that you do not receive any interest payments, you need to report the amount the bond increases each year. The interest rate is locked in when you buy the zero-coupon bond at a discount rate. For example, if you wanted to buy a five-year $10,000 zero in a municipal bond, it might cost you $7,500, and in five years you would get the full $10,000. The longer the bond has until it reaches maturity, the deeper the discount will be. Zeros are the best example of compound interest. For example, a twenty-year zero-coupon bond with a face value of $20,000 could be purchased at a discount, for around $7,000. Since the bond is not paying out annual or semiannual dividends, the interest continues to compound, and your initial investment will earn the other $13,000. The interest rate will determine how much you will need to pay to purchase such a bond, but the compounding is what makes the discount so deep.

What Are Zero-Coupon Bonds and "Strips"?
Zero-coupon bonds, or zeros, are sold at a discount to face value. Interest is compounded during the term of the bond, but unlike other bonds, those interest payments aren't made until the bond matures. With zero-coupon bonds, an investor buys a $1,000 bond for considerably less than that amount. There are no payments received until the bond matures - perhaps as far into the future as 30 years. However, investors can buy and sell the bonds prior to maturity -- realizing a gain or loss depending on how prices have changed since the original purchase. The most popular forms of zero-coupon bonds are sold by the U.S. government. U.S. Savings Bonds such as the EE Series are zero-coupon investments. Treasury bills, which mature in one year or less, are also zero-coupon investments. Another form of zero-coupon investment is called a "strip." Strips, or Separate Trading of Registered Interest and Principal Securities, are created from traditional, interest-paying bonds. A financial institution buys the bond and then "strips" out the interest payment -- creating two distinct investments: a zero-coupon bond and a collection of interest coupons. They can be

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sold separately. Why Buy a Zero-Coupon Bond? Institutional investors such as pension funds and insurance companies often like long-maturity zeros because of a complicated valuation concept known as duration. Zeros have a high duration, which means they can be used to mitigate interest rate risks associated with money that must be paid in the future (insurance policies, pensions, etc.) But zeros may also appeal to some average investors. 1. Zeros are inexpensive: Say you're looking to set aside money for retirement in 30 years. For every $1,000 you'd want to have then, you must pay $1,000 today for an interest-paying bond. As an alternative, you can "lock in" that future $1,000 by buying a zero-coupon today for closer to $250. 2. Most zeros are very safe. The most popular form of zero-coupon bonds are U.S. Treasury Strips. Given that they are created from government debt offerings that are backed by the full faith and credit of the U.S. government, the risk of default is nil. On the Other Hand ... Reasons to Avoid Zeros There are also three good reasons for the average investor to think twice before buying zeros. 1. 2. 3. You'll owe taxes on the interest before you receive the interest. A quirk in U.S. tax law makes the holder of a zero responsible for taxes on interest as it accrues. So the owner must pay taxes every year on interest that he won't receive until the bond matures. The prices of zeros fluctuate wildly in the secondary market. If you have to sell before maturity, you could lose money. Locking yourself into a zero exposes you to inflation risk. If you don't sell before maturity, the money you collect at the end of the term may have lost some of its value. In other words, your investment may not keep up with inflation.

Understanding Zero Coupon Bonds
Does paying tax on interest you haven¶t received sound like a good idea? That¶s what you do with zero coupon bonds and it can make good sense in the right circumstances. Zero coupon bonds or zeros don¶t make regular interest payments like other bonds do. You receive all the interest in one lump sum when the bond matures. You purchase the bond at a deep discount and redeem it a full face value when it matures. The difference is the interest that has accumulated over the years. Zero coupon bonds generally come in maturities from one to forty years. The U.S. Treasury issues are the most popular ones, along with municipalities and corporations. Here are some general characteristics of zero coupon bonds: Issued at deep discount and redeemed at full face value Some issuers may call zeros before maturity You must pay tax on interest annually even though you don¶t receive it until maturity Zero coupon bonds are more volatile than regular bonds Of the three kinds of zero coupon bonds, U.S. Treasury bonds are the most popular.

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However, the U.S. Treasury doesn¶t issue them directly; you have to buy ³STRIPS´ from qualified financial institutions or brokers. STRIPS stands for Separate Trading of Registered Interest and Principal of Securities and it means a financial institution has taken a regular U.S. Treasury issue and separated the principal and interest payments into two separate securities. The normal income is packaged and sold to investors who need a reliable cash flow and the principal becomes a zero coupon bond. Full Faith and Credit Although you buy the STRIP (they come in other names also) from brokers and financial institutions, they still carry the full faith and credit of the U.S. government making them the safest of investments from a credit risk perspective. Municipalities and corporations also issue zero coupon bonds. They have the same basic feature of being sold at a deep discount and redeemed in the future at full face value. However, some of these issues may have call features allowing the issuer to redeem them before maturity. Be sure a check what if any those provisions are before you invest. Municipal zero coupon bonds are free from federal income tax like regular municipal bonds. The major credit agencies rate most zero coupon bonds for credit worthiness. This rating can change during the life of the bond, which can affect the price. Risk of Default Corporate zero coupon bonds carry the most risk of default and pay the highest yields. Many of these have call provisions. How big of a discount will you pay? The U.S. Treasury provided this example: ³For example, assume that three STRIPS are quoted in the market at a yield of 6.50 percent. The price for STRIPS with 25 years remaining to maturity would be $202.07 per $1,000 face amount That for STRIPS with 10 years remaining to maturity would be $527.47 per $1,000 face amount That for 2-year STRIPS would be $879.91 per $1,000 face amount.´

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As you can see, the farther out you go the lower your front-end cost and the more work compounding does to get you to the full face value. Conclusion You buy zero coupon bonds a deep discount to face value. You receive no interest until maturity; however, in most cases you do owe taxes annually on the interest as it accrues.

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In Part Two In part two, we¶ll look more closely at the tax implications of zero coupon bonds and examine how you can use zeros to meet your financial goals.

Back to Bond Information Center

Suggested Reading Bond Basics Understanding Bond Types Understanding Bond Prices and Interest Rates Related Articles y Zero Coupon Bonds - How to Use Zero Coupon Bonds y Zero-Coupon Bonds: What Are Zero Coupon Bonds and "Strips" and Who Should B... y Bond Basics - Basic Concepts of Bonds Explained y U.S. Treasury Bonds - An Easy Guide to the 30-Year U.S. Treasury Bond y Bond Yields and Taxes - Personal Finance in Your 40s & 50s

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How to Use Zero Coupon Bonds
Part Two
Zero coupon bonds have some unique features that make them effective tools for reaching certain financial goals; however, they are not tax-friendly so use caution. In the first part of this two-part series, we looked at some of the characteristics of zero coupon bonds and some of the organizations that issue them. In this part, we¶ll turn our attention to how to use zero coupon bonds and the tax consequences. Like regular bonds, zero coupon bonds are great for targeting a financial need in the future ± for example, a child¶s college education or your retirement. (For more information on bonds see my article Bond Basics Unlike regular bonds, you won¶t receive any interest payments along the way. The trade off is that you can buy the bonds at a great discount. This means you might only need to come up with 70% or 80% of the face value of a 20-year or longer bond. No Interest Payments This reduces your need to lay out a large sum of money upfront. The trade off is you won¶t be receiving any interest payments, but you will get nicked for the taxes just the same (more about taxes in a minute). There is a secondary market for zero coupon bonds, although not a robust as for regular bonds. If you need to get rid of a zero coupon bond, its value will be determined by prevailing market rates, years remaining and credit worthiness of issuer. Hold to Maturity The advantage of zero coupon bonds is in keeping them until maturity. Many investors use them to provide a solid base against a volatile stock market.

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For example, suppose you had $100,000 to invest. You might take $25,000 or so and buy a $100,000 STRIP (U.S. Treasury issue) maturing in 20 years. You might then take the remaining $75,000 and invest it in stocks appropriate for your financial goals. The worst that can happen is in 20 years you¶ll get your money back. (Of course, I¶ve ignored fees and taxes, but you get the point. I trust that you would do better than lose all your money.) This very simple example may open the door to other ideas for you. For example, instead of buying one bond for $100,000, you could build a bond ladder. Taxing Situation Zero coupons are taxed just like regular bonds even though they don¶t pay interest until maturity. Every year the issuer will send a statement telling you how much interest accrued to the bond that year. There are some things you can do to offset the tax on ³phantom´ interest. Municipal zero coupon bonds are free of federal income tax and may be free of state and local tax where issued Zero coupon bonds work great in retirement accounts where they can grow free from tax on current interest If you are using one to fund a child¶s college education, consider putting the bond in the child¶s name. Your broker can help you set up a custodial account. Because of the lower limits on investment income for children, it may take some time before any tax is owed and then at the child¶s rate. Be sure you check with a qualified tax professional to get this done correctly. Even if you have to pay tax as you go, the good news is when the bond matures, all the taxes are paid.

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Conclusion Zero coupon bonds can be a good choice for funding a future financial goal, especially if you don¶t have a large sum to put down now and can solve or live with the tax consequences. Back to Part One

Why Is the Interest I Earn on my Bonds Called a Coupon?
When you begin to invest in bonds for the first time, you may hear your broker or other investors refer to the ³coupon´. A $25,000 bond that paid 8% interest might be said to have an 8% ³coupon´. For new investors who don¶t know the history of the stock market or the bond market, this may be confusing and seem odd. Where the Term Coupon Originated for Bonds Back in the days before computers, when an investor bought a bond, he or she was given a physical, engraved certificate. They would then go lock these in a safe deposit box. It was important that they be kept secure because it was the proof that they had lent money to the bond issuer and it was what entitled them to receive their money back, plus interest. Each of these bond certificates included an attached section of ³coupons´ with dates printed on them. Twice a year, when the interest was due on their bond, the investor would go down to the bank, open the safe deposit box, and physically clip the proper coupon with the current date. They would take the coupon and deposit it, just like cash, into their bank account or mail it in to the company to get a check, depending upon the terms and the circumstances. An Example of How the Bond Coupon Would Work

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If an investor wanted to buy a $25,000 Coca-Cola bond with a 30 year maturity and an 10% coupon, it would work like this: He would send in the $25,000 from his savings account and get a $25,000 engraved bond certificate in exchange. After 30 years, he would be able to get his whole $25,000 back from the Coca-Cola company (of course, he can always sell it before then if he needs the money). Every year, he¶s entitled to receive 10% interest on the money he lent, or $2,500. Since most companies in the United States pay interest semi-annually, he would likely have 60 coupons attached to his bond for $1,250 each. Every June 30th and December 31st, the investor would go down, clip the proper coupon, send it in, and get their money. Today, bonds don¶t work like this. In most cases, you will buy them through a brokerage account and the interest payment will just show up as a deposit in your account. In other cases, they are held in ³book entry´, which means that the company records your ownership in a computer program and mails the coupon payment to you when it¶s due (in some cases, you could provide your bank information and the money will be electronically deposited into your account). Although the practice is now defunct, the terminology stuck and interest payments on bonds will forever be known as coupons. More Bond Investing Articles What Percentage of My Portfolio Should Be Invested in Bonds? Which Is a Better Investment - Bond or Bond Funds? Bonds 101 - Guide for the Total Beginners Related Articles y Making Money from Investing in Bonds y Coffee Talk: Your Financial Questions Answered Edition 2 y What is a Bond y Zero Coupon Bonds - How to Use Zero Coupon Bonds y Coupon

y y y

Zero-coupon Bond
A zero-coupon bond is a bond that does not pay interest but instead is sold at adiscount, i.e., for less than its face value. For example, a zero-coupon bond with a face value of $5,000 may sell for only $4,200. When the zero-coupon bond matures years later, the bond buyer receives the full $5,000; the $800 difference is the "interest" earned on the zero-coupon bond. A

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well-known example of a zero-coupon bond is the series EE savings bond sold by the U.S. Treasury. This bond sells for half its face value, which ranges as high as $10,000. One advantage to issuing a zero-coupon bond is that the issuer does not need to make periodic interest payments to its bondholders. One possible disadvantage to bond investors is that zero-coupon bond prices are more volatile on the secondary bond market, since the lack of periodic interest payments is viewed as risky. A zero-coupon bond is also known as an accrual bond.

zero-coupon bond
A debt security that does not offer any interest (a coupon), but trades at a deep discount of face value, offering the potential for return when the instrument matures at full face value.

Zero coupon bonds may be issued in the primary market with no interest, or repackaged by financial institutions as such for sale in the secondary market. Since they offer payment only upon maturity, and in forgoing regular income until that date investors are forced to set longer term and more nimble predictions on return, zero coupon bonds tend to be more volatile in price than traditional interest earning debt instruments. Also known as Accrual Bond.

Related Words
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coupon discount bond

coupon
An offer made in response to another offer.,

Related Words
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interest rate collar fixed investment trust date of issue par value nominal rate

discount bond

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Outside of the traditional, rather obvious laymen definition - Discount also applies to bond pricing, where a bond price is less than the par value. The discount is the difference between the price paid for the bond and the bond's listed price. Example: If the par value of a bond is $1000 and the bond is currently bid at 950 - it is currency selling at a discount. This condition will occur when the bond is high risk or offers a coupon rate well below prime. Noun 1. zero coupon bond - a bond that is issued at a deep discount from its value at maturity and pays no interest during the life of the bond; the commonest form of zero-coupon security zero-coupon bond governing, government activity, government, governance,administration - the act of governing; exercising authority; "regulations for the governing of state prisons"; "he had considerable experience of government" corp, corporation - a business firm whose articles of incorporation have been approved in some state bond certificate, bond - a certificate of debt (usually interest-bearing or discounted) that is issued by a government or corporation in order to raise money; the issuer is required to pay a fixed sum annually until maturity and then a fixed sum to repay the principal zero coupon security, zero-coupon security - a security that makes no interest payments but instead is sold at a deep discount from its face value
Based on WordNet 3.0, Farlex clipart collection. © 2003-2008 Princeton University, Farlex Inc.

The zero coupon bond matures at par, thereby guaranteeing the investor's capital, while the call option maintains the upside exposure required. Structured products: structured products are investments that combine ...by Donnellon, Brien / Swiss News For example, you might purchase a zero coupon bond today for $500 that will mature in 10 years for $1,000. Arkansas college saving bonds: not just for kids by Martin, James /Arkansas Business Under the original issue discount rules, the interest implicit in the amortization of the discount on the zero coupon bond component of the SIGNs would be taxed annually over the life of the instrument. Interpreting SIGNs by Finnerty, John D. / Financial Management More results

How To Buy Zero Coupon Bonds
Posted by jenifer on May 8, 2011

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A zero coupon bond is an investment instrument that does not pay interest throughout the life of the bond, but accrue interest during the life of the bond, and reinvest it at the same interest rate. The principal and interest are payed out to the investor upon the bonds maturity date. Zero coupon bonds are regarded as a more conservative investment that other asset classes such as stocks if you hold onto them until they mature, although they do not come without risk. These types of bonds are purchased at a deep discount which is much less than their face value at maturity. It is important to understand how these bonds work, to carefully consider your time frame for investing, and your unique investment objectives prior to committing any capital. Online brokerage ETradeoffers their Bond Center to help you with how to buy zero coupon bonds, including education, research, and purchasing.

How To Buy Zero Coupon Bonds
While these bonds are not 100% risk-free, buying zero coupon bonds is a considerably less risky alternative to investing in stocks or other assets. These types of securities are more predictable than other investments, as if you are able to hold onto your bond until it matures, you will receive a lump-sum payment. Zero coupon bonds should be seen as a long-term investment, and your risk can be reduced by keeping these bonds until they mature. Zero coupon bonds are excellent investment for long-term goals such as a child¶s education, or the purchase of a new home. How to buy zero coupon bonds. You can postpone paying federal taxes on income from your bonds by buying zero coupon bonds through your retirement account. The interest on this type of bond is charged in the current tax year, although you do not receive it in the same year as the interest is reinvested. By

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purchasing a zero coupon bond through your retirement fund, you do not have to pay taxes on the profits until you reach retirement.

How To Buy Zero Coupon Bonds: Tax Advantages
You can avoid paying federal taxes all together on your earnings from a zero coupon bond when you invest in municipal zero coupon bonds, which are tax-free. These bonds are issued through local agencies such as counties and states, and you usually receive tax-free interest payments with these types of securities. The more you pay for a bond, the lower your yield is. As an example, if you pay $500 for a bond that is worth $1000 when it matures you know that the interest earned on the bond will be $500 when it matures. If the bond is purchased for $700 you would make $300 in interest when it matures. How to buy zero coupon bonds. You can purchase these bonds through discount brokerages such as ETrade, or through your full-service broker. Markups and commissions will vary in cost, although the face value will be the same, so it pays to shop for the best rates and commissions. No related content found.

Banglalion plans Tk 400cr zero coupon bond
THURSDAY, 11 AUGUST 2011 AUTHOR / SOURCE : STAFF REPORTER

Dhaka, Aug 10: For expanding the countrywide network of 4G WiMax telecommunication service, Banglalion Communication Ltd, one of the two WiMax service providers in the country, plans to raise Tk 400 crore through issuance of a Zero Coupon Bond. Banglalion, the lone cent percent locally-owned telecom service provider, initiated such bond for the first time in the telecom industry as market price of the bond is much more stable than that of common stocks in Bangladesh capital market. The company laid bare its plan on Tuesday at a road show at Ruposhi Bangla hotel in the city. Zero coupon bond is a debt instrument that has no periodic interest. At maturity, the face value of the bond is repaid or redeemed, which includes both principal and interest of the bond. Major (rtd) Abdul Mannan, Banglalion¶s chairman, told The Independent: ³We¶ve launched zero coupon bond, as the government is promoting the bond market as an alternate source of investment for infrastructure projects.´ As return of any zero coupon bond is almost fixed in nature, investors of such bond do not have to panic during any market turmoil, Mannan pointed out. He said of the Tk400 crore, 70 percent or Tk 280 crore will be raised from private investors and the rest will be raised from public investors. ³The primarily targeted private investors are the non-residential Bangladeshis (NRBs) living in the United Kingdom and the Middle Eastern countries. On his company¶s future plans, Mannan said Banglalion eyes installing another 700 base trans-receiver systems (BTS) across the country to expand the WiMax network and take benefits of internet to the doorsteps of the people in the next few years. ³Each BTS costs us more than Tk 1 crore. We are launching the zero coupon bond to raise the money for expanding our netwrok´, he said. ³Two years ago we started with 35 BTS and now we have over 500 BTS and more than 1.5 lakh subscribers. WiMax is still a new technology but it has enormous potential. We have given 30 Mhz of bandwidth and we had to pay only $ 31 million for that. In USA, one Mhz of bandwidth now costs $1 billion´, he said. The Banglalion boss said, ³Bangladesh will hopefully see a digital revolution soon and the mission of Banglalion is to empower a smarter, more connected world with the fastest, most cost-efficient and highest 4G network for the countrymen.´ Khondker Shafiqur Rahman, head of structured finance of Infrastructure Development Finance Company Limited

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(IIDFC), the facility arranger and the trustee for the Banglalion bond, said the new bond has 11 percent discount rate and 18 percent conversion. ³Its total maturity is seven years. Banglalion¶s ordinary share will be traded in the country¶s stock exchanges within the third year of the issuance of zero coupon bond,´ Rahman said, adding that 18 percent of the bond¶s face value will be converted into ordinary shares in the last audited Net Asset Value.

What Are Zero Coupon Bonds?
What are Zero Coupon Bonds? Zero coupon bonds are bonds which do not make interest payouts, known as coupon payments, to the bond holder. Instead the bond holder buys the bond at a discount price off the face value amount, earning zero coupon bonds the nicknames discount bonds or even deep discount bonds. Essentially the trade-off in a discount bond is one makes their money, what would be in essence interest of their investment, from the difference between what they pay for the bond below its par value and the amount they receive, the face value, when the bond reached maturity. Deep discount bonds were once very popular in the 1960¶s when there existed a very significant tax loophole: no income taxes paid on the profit from discount bonds. This loophole has since been closed and zero coupon bond holders now are taxed on the amount of money they make over their initial investment amount as income.

Deep Discount Bonds In The Market
In the marketplace deep discount or zero coupon bonds take on different roles. These bonds can be issued short or long term. They can be any time of bond in the bond marketplace; they simply must be stripped of their coupon payments to fit the parameters of a discount bond. Short term zero coupon bonds issued by the US Treasury department are referred to as bills. Currently these bills make up the largest market share of discount bonds. Long-term zero coupon bonds can run anywhere from 10-15 years in maturity length. Most of these bonds are traded on the secondary bond market and the original investor is rarely the same who holds the bond when it matures. As bond rates rise or fall bond investors will look to sell these discount bonds at a profit or invest in them when their value is lowered.

Zero-coupon bond
Description From Wikipedia, the free encyclopedia A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments, or have so-called "coupons," hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value. Examples of zero-coupon bonds include U.S. Treasury bills, U.S. savings bonds, long-term zerocoupon bonds, and any type of coupon bond that has been stripped of its coupons. In contrast, an investor who has a regular bond receives income from coupon payments, which are usually made semiannually. The investor also receives the principal or face value of the investment when the bond matures. Some zero coupon bonds are inflation indexed, so the amount of money that will be paid to the bond holder is

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calculated to have a set amount of purchasing power rather than a set amount of money, but the majority of zero coupon bonds pay a set amount of money known as the face value of the bond. Zero coupon bonds may be long or short term investments. Long-term zero coupon maturity dates typically start at ten to fifteen years. The bonds can be held until maturity or sold on secondary bond markets. Short-term zero coupon bonds generally have maturities of less than one year and are called bills. The U.S. Treasury bill market is the most active and liquid debt market in the world. Source Description above from the Wikipedia article Zero-coupon bond, licensed under CC-BY-SA full list of contributors here. Community Pages are not affiliated with, or endorsed by, anyone associated with the topic.

What Are Tax Free Bonds?
What are Tax Free Bonds? Tax free bonds are government issued bonds, often called Treasury notes as they are issued by the US Treasury Department, which pay interest to the bond holder which is not taxed as income by the federal government. In some cases, such as with I Bonds, there is no state income tax to be paid either. At a minimum, all government bonds will not require the holder to pay tax on the interest they receive. For this reason, among others such as confidence in repayment, government bonds have many advantages over corporate bonds. No tax bonds issued by the government should be compared to corporate bonds in a manner which truly reflects their potential for income. Corporate bonds, bonds issued by private companies in order to raise capital, often-times offer seemingly much higher interest or coupon rates. While the interest on their corporate bonds is not a trick, one must consider the interest which will be paid on these bonds when compared to tax free bonds. Government no tax bonds have low interest payouts, but there is more there than meets the eyes. For example if considering the following two bonds, to really compare them one must really see beyond the numbers. These two bonds offer very different interest rates, however the government bond actually pays the investor more:

Corporate bond: 10 years, face value $10,000. Coupon interest rate 10%. Government bond: 10 years, face value $10,000. Coupon interest rate 4% While there is an obvious and seemingly attractive interest rate advantage of 6% over the government bond, the corporate bond fails to inform the investor they will pay tax on the entire 10% of interest paid annually, both Federal and State tax considered as income. On average the actual interest will be only 2-3% after included the tax liability.

More Tax Free Bond Advantages
Tax free bonds offer more than just a good and predictable interest rate without tax liability worries: they are also guaranteed by the US Government. Corporate bonds will usually pay a decent return but one should remember just like a stock purchase, there is inherent risk investing in a private entity. A corporation can lose assets, have legal liabilities freezing funds, or simply cease to exist. Government bonds however are all but a guaranteed payback. A very safe investment in turbulent financial times.

Pricing of Bonds

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Table of Contents Chapter 1: Categories of Bonds Chapter 2: Pricing of Bonds Chapter 3: Calculating Yield and Understanding Yield Curve Chapter 4: Duration of Bonds Chapter 5: Relationship Between Price, Yield and Duration Navigate This Page Chapter 2: Pricing of Bonds - Why Do Bond Prices Change - Premium and Discount - Understanding Present Value of Future Payments - Calculating Bond Prices - Pricing a Plain Vanilla Bond - Pricing a Zero Coupon Bond - Dirty and Clean Bond Prices - Calculating Accrued Interest Chapter 2: Pricing of Bonds When bonds are issued, they are usually sold at their par value, which is also referred to as their face value. For most corporate bond issues, this par value is $1,000, while some of the government bonds can have a par value of $10,000. This is the principal amount of a bond and it is returned to the investors when the bond matures. However, during the term of a bond, market forces make the value of the bond change. At any time, the bond could be selling at a value higher than its par, lower than its par or at its par value. Why Do Bond Prices Change The main reason behind this change in bond value is change in interest rates. Interest rates in the economy are dynamic and they are constantly adjusted by the Federal Reserve in response to changing economic situation. When the economy is not doing well, the Fed can lower interest rates to encourage lending and to give a boost to economic activity. But when there are serious inflationary expectations in the economy, the Fed can lower interest rates to cool things down. Such decisions can have a significant impact on the bond market, and prices of bonds always respond to changes in interest rates. Inverse Relationship with Interest Rates: Bond prices have an inverse relationship with interest rates. When interest rates in the economy go up (all other things being equal), bond prices go down, and vice versa. It is easy to understand why this happens. Let¶s say you have invested in a plain vanilla bond at a par value of $1,000 and a coupon rate of 5%. When interest rates in the economy go up, future bond issues will have to pay a higher coupon rate, let¶s say 6%. In such a scenario, an investor will be willing to buy your bond from you only if you sell it at a value lower than its par such that the buyer is compensated for the lower interest payments. The opposite of this happens when interest rates go down. Now future bonds will be issued at a lower interest rate and buyers will be willing to pay you more as your bond offers higher



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interest earnings. This will increase the price of the bond in the market.



Impact of Creditworthiness: Another reason that can have a huge effect on bond prices is a change in the creditworthiness of the issuer. For example, if a company is facing financial difficulties that can adversely impact its ability to repay its obligations, credit rating agencies can decide to lower its credit rating. When that happens, markets will react by lowering the prices of bonds issued by the company as there is now a much greater risk of default associated with those bonds. The same thing can happen to countries and it is not uncommon to see the prices of bonds issued by a national government change drastically in response to bad economic data.

It should be noted that the bond market does not always wait for a credit rating agency to lower the rating of the issuer before lowering the price of its bonds. Large market participants are well aware of the risks that an issuer faces and expectations of default are always factored in bond prices. Premium and Discount When a bond is selling at a value higher than its par, it is said to be selling at a premium. On the other hand, when the price of a bond falls below its par, it is said to be selling at a discount. When listing bond prices, the prices are mentioned in terms of percentage of premium or discount, irrespective of what the par value of the bond is. When a bond is selling at par value, it¶s price is listed as 100. When it is selling at a 10% discount, its price is listed at 90. Similarly, let¶s say when it¶s selling at a 5% premium, its price is listed as 105. This kind of quoting convention allows bonds to be compared directly and easily. Finding the true price of the bond is easy. The price of a bond listed as 105 and having a par value of $1,000 can be calculated as 105% of $1,000, which comes to $1050. Understanding Present Value of Future Payments Bonds assure a stream of future payments to the investor. For a plain vanilla bond, you receive regular interest payments from the bond issuer until the bond matures, and at maturity, you receive the par value of the bond. Therefore, the price that you should be willing to pay for a bond is the value that you can attach to these future payments. However, valuing future payments is not very simple. This is where you have to understand one of the most fundamental concepts of finance ± time value of money. Think about two straightforward scenarios, one where you get $1,000 immediately and one where you get $1,000 one year later. Any smart investor will prefer the first scenario. Why? Because if you receive the money today, you can invest it somewhere and earn interest on it. If you could get 5% interest on your investment, one year from now, you would have $1,050 in the first scenario, while in the second scenario, you would just have $1,000. In other words, any future payments are not worth the same amount that they would be if the payment was made today. To determine the µpresent value¶ of a future payment, you would have to discount it. The farther you go in future, the more this discounting would be. The present value of a $1,000 payment one year from now should be the amount that if you had today and invested in the market would yield $1,000 one year later. This amount would always be lower than the

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future payment. In the previous example, it is clear that the rate of discounting a future payment should be the interest that you can realistically earn on your investment. This interest is known as the required rate of interest or the required yield. If you had $1,000 today, it would be worth $1,050 one year from now if the required rate of interest is 5%. This is equivalent to saying that the present value of a payment of $1,050 one year from now is $1,000. The present value of any payment can be calculated using this formula: PV = F/ (1+r)^n Here: PV is present value F is future payment r is required rate of return n is the number of periods after which the payment would be made Applying this formula in the previous example, we can easily calculate the present value of a $1,000 payment one year from: PV = $1,000 / (1+.05) ^ 1 = $953.38 Calculating Bond Prices The price of a bond is equal to the present value of all its future interest payments and the repayment of par value at maturity. We can use the formula for present value of future payments to determine the value of a bond. But keep in mind that as coupon payments come at different points in time, the discounting factor for each of them will be different, with payments coming later having a heavier discount. The price of a bond can be represented as the following formula: Price = [I / (1+r)] + [I / (1+r)^2] + « + [I / (1+r)^n] + [Par Value / (1+r)^n] Here: I is the interest or coupon payment paid at the end of every period r is the required rate of return n is the number of periods after which the bond will mature This series of periodic payments in a plain vanilla bond is referred to as an ordinary annuity. This formula assumes that the first coupon payment will be made one period from the present time and the end of every subsequent period, the next coupon payments will be made. Note that period here could be anything, but typically bonds pay coupon semi annually or annually, so one period will be 6 months or 12 months long. Also note that the last coupon payment and the par value of the bond are paid together. It is clear from the formula that the payments that come farther in the future have a lower present value. Another thing evident from the formula is the inverse relationship between bond prices and interest rates. As interest rates go up in the economy, the required rate of return (r) also goes up. This increases the discounting factors in the formula and the price of the bond will be lower. The bond pricing formula given above can be simplified as: Price = I x [1- [1 / (1+r)^n ] ] / r + [Par Value / (1+r)^n] When you use this formula, you wouldn¶t have to calculate the present value of each coupon

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payment separately, and the price can be determined simply by plugging in the value of these variables. The same formula can be used irrespective of the nature of the bond. Here is an illustration of how this formula can be applied when determining the price for different kinds of bonds. Pricing a Plain Vanilla Bond Let¶s consider a plain vanilla bond with a par value of $5,000, maturity period of 5 years, and a coupon rate of 5%, paid semi-annually. Let¶s assume that the required rate of return is 10%. Here are the values of different variables that we¶ll need in the formula. n = 10 (Coupon payments are made with a periodicity of 6 months. There are 10 such periods in 5 years) I = $5,000 * 2.5% = $125 (Although coupon rate is 5%, this is the annual interest rate. For semi annual payments, coupon rate will be half of the annual rate) r = 5% (For a 10% annual required rate of return, the semi-annual required rate will be 5%) Par Value = $5,000 Plugging these values in the bond price formula: Price = $125 x [1- [1 / (1+.05)^10 ] ] / .05 + [$5,000 / (1+.05)^10] = $4,034. 7 You can see this value in light of our previous discussion on bonds selling for a premium or a discount. In this case, the required rate of return is significantly higher than the coupon paid by the bond. That is why the bond is selling at a heavy discount, as otherwise investors will have no reason to purchase this bond. Now, let¶s see what happens when the coupon rate of the bond is 15%. The coupon payment in this case (I) will be $5,000 * 7.5% = $375. All the other variable for the formula remain the same. This will result in the bond being priced as: Price = $375 x [1- [1 / (1+.05)^10 ] ] / .05 + [$5,000 / (1+.05)^10] = $5,965.2. The bond is offering a higher coupon rate than the interest rate investors can earn in the market, which is why the bond is now selling at a premium. Pricing a Zero Coupon Bond A zero coupon bond does not make any interest payments throughout the life of the bond. There is only a single cash flow, at the time of maturity of the bond, when the par value of the bond is returned to the investors. Pricing such a bond is much simpler. Let¶s consider a zero coupon bond with a par value of $5,000 and a maturity period of 5 years. Let¶s assume that the required rate of return is 10%. Plugging these values in the bond pricing formula: Price = [$5,000 / (1+.05)^10] = $3069.5 Compare this price with the price of the plain vanilla bond that we calculated in the last example. You can see that as there are no coupon payments made by the bond issuer, investors need a much larger incentive, in the form of a bigger discount, to purchase the bond. Of course, in case of zero coupon bonds, there is no question of the bond selling at a premium, or even at par. No investor would be ready to pay $5,000 (or more) today, just to get $5,000 back a few years from now. You would have noticed that we assumed a periodicity of 6 months in the formula despite the fact

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that a zero coupon bond pays no interest. This is done so that these bonds can be easily compared with other bonds that pay coupon on a semi-annual basis. Dirty and Clean Bond Prices So far, the bond pricing that we¶ve discussed misses out on one crucial point ± accrued interest. In the formula that we used to find out bond prices, we did not take into account the fact that the price of a bond will change as coupon payment date comes closer. We simply assumed that the next coupon payment is exactly one period away. At any given date between two coupon payments, the price of a bond should include the interest that has been accrued so far since the last coupon payment. This is the interest that the bond investor has already earned by holding the bond, but it has not bee paid to him yet. You can also think of this change in price between two coupon payments in terms of time value of money. Let¶s say a bond paid coupon on June 31 and the next payment is scheduled for Dec 31. As the next payment and all future cash flows come closer, their time value should increase, which means that the price of the bond should increase. However, this has not been accommodated in the formula so far. Bond prices that include accrued interest are known as dirty bond prices while those excluding accrued interest are referred to as clean bond prices or flat prices. Typically, quoted prices of bonds are flat prices. The reason behind this is that a clean price allows investors to evaluate the quality of the bond on the basis of issuer risk, interest rates etc. It also enables easier comparison between two bonds, without complicated assessment of when the last coupon was paid and how much interest has been accrued. The dirty price of a bond moves in a saw tooth pattern throughout the life of the bond (assuming interest rates and issuer risk do not change in that period). The price of the bond keeps increasing from the date of coupon payment as more and more interest gets accrued. On the subsequent coupon payment, the price falls to its minimum level again and starts rising in the same manner from the next day onwards. Calculating Accrued Interest As you would have guessed, to be able to calculate the accrued interest, we need to first determine the exact number of days that have passed since the last coupon payment. Different day counting conventions are used for different bonds. In an actual / actual day-count convention, you need to count the exact number of days that have passed so far since the last coupon payment and evaluate interest assuming that it accrues on every day. This convention is used for treasury securities. Consider a situation where the last coupon payment on a treasury bond was made on July 1 and the next payment is scheduled for January 1. To price the bond on September 1, we¶ll have to count the exact number of days between July 1 and September 1. Accrued interest in this case will be calculated for 62 days, which is the number of days that have passed since the last payment. In a 30 / 360 convention, it is assumed that each month of the year has 30 days and that there are 360 days in a year. This somewhat simplifies the calculation for the number of days, as you don¶t have to think about which month has 30 days, which has 31, if it is a leap year, and so on. This convention is typically used for corporate bonds and municipal bonds. If in our previous

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example, the bond was issued by a company, the accrued interest would have been calculated on 60 days instead of 62 days. But in this case, the daily accrual of interest will be calculated assuming that there are only 360 days in the year, i.e. interest will be divided into 360 periods. Accrued interest can be calculated using the following formula: Accrued interest = I x [d/D] Here: I = Coupon payment d = Number of days since last payment D = Total number of days between payments Let¶s consider a corporate bond, where the last coupon payment was made on July 1, the next payment is due on January 1, and we are calculating accrued interest on October 1. The coupon rate is 10%, paid semi-annually, and the par value of the bond is $5,000. I = $5,000 x (10% / 2) = $250 d = 90 days (as all months are assumed to have 30 days and exactly 3 months have passed since last coupon payment) D = 180 days (coupon payments are semi-annual, so periodicity is 6 months, with each month assumed to have 30 days) Accrued Interest = $250 x [90 / 180] = $125 This accrued interest should be added to the clean price of the bond (as calculated from the bond pricing formula) to arrive at the true value of the bond on October 1. This is the price that you¶ll have to pay if you want to buy the bond from the secondary market. Next Chapter: Calculating Yield and Understanding Yield Curve Related posts: 1. 2. 3. 4. 5. Duration of Bonds Understanding Bond Terminology Categories of Bonds Categories of Bonds Factors to Consider Before Buying Bonds

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Chapter 2: Pricing of Bonds When bonds are issued, they are usually sold at their par value, which is also referred to as their face value. For most corporate bond issues, this par value is $1,000, while some of the government bonds can have a par value of $10,000. This is the principal amount of a bond and it is returned to the investors when the bond matures. However, during the term of a bond, market forces make the value of the bond change. At any time, the bond could be selling at a value higher than its par, lower than its par or at its par value. Why Do Bond Prices Change The main reason behind this change in bond value is change in interest rates. Interest rates in the economy are dynamic and they are constantly adjusted by the Federal Reserve in response to changing economic situation. When the economy is not doing well, the Fed can lower interest rates to encourage lending and to give a boost to economic activity. But when there are serious inflationary expectations in the economy, the Fed can lower interest rates to cool things down. Such decisions can have a significant impact on the bond market, and prices of bonds always respond to changes in interest rates. Inverse Relationship with Interest Rates: Bond prices have an inverse relationship with interest rates. When interest rates in the economy go up (all other things being equal), bond prices go down, and vice versa. It is easy to understand why this happens. Let¶s say you have invested in a plain vanilla bond at a par value of $1,000 and a coupon rate of 5%. When interest rates in the economy go up, future bond issues will have to pay a higher coupon rate, let¶s say 6%. In such a scenario, an investor will be willing to buy your bond from you only if you sell it at a value lower than its par such that the buyer is compensated for the lower interest payments. The opposite of this happens when interest rates go down. Now future bonds will be issued at a lower interest rate and buyers will be willing to pay you more as your bond offers higher interest earnings. This will increase the price of the bond in the market. Impact of Creditworthiness: Another reason that can have a huge effect on bond prices is a change in the creditworthiness of the issuer. For example, if a company is facing financial difficulties that can adversely impact its ability to repay its obligations, credit rating agencies can decide to lower its credit rating. When that happens, markets will react by lowering the prices of bonds issued by the company as there is now a much greater risk of default associated with those bonds. The same thing can happen to countries and it is not uncommon to see the prices of bonds issued by a national government change drastically in response to bad economic data. It should be noted that the bond market does not always wait for a credit rating agency to lower the rating of the issuer before lowering the price of its bonds. Large market participants are well aware of the risks that an issuer faces and expectations of default are always factored in bond prices. Premium and Discount When a bond is selling at a value higher than its par, it is said to be selling at a premium. On the other hand, when the price of a bond falls below its par, it is said to be selling at a discount. When listing bond prices, the prices are mentioned in terms of percentage of





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premium or discount, irrespective of what the par value of the bond is. When a bond is selling at par value, it¶s price is listed as 100. When it is selling at a 10% discount, its price is listed at 90. Similarly, let¶s say when it¶s selling at a 5% premium, its price is listed as 105. This kind of quoting convention allows bonds to be compared directly and easily. Finding the true price of the bond is easy. The price of a bond listed as 105 and having a par value of $1,000 can be calculated as 105% of $1,000, which comes to $1050. Understanding Present Value of Future Payments Bonds assure a stream of future payments to the investor. For a plain vanilla bond, you receive regular interest payments from the bond issuer until the bond matures, and at maturity, you receive the par value of the bond. Therefore, the price that you should be willing to pay for a bond is the value that you can attach to these future payments. However, valuing future payments is not very simple. This is where you have to understand one of the most fundamental concepts of finance ± time value of money. Think about two straightforward scenarios, one where you get $1,000 immediately and one where you get $1,000 one year later. Any smart investor will prefer the first scenario. Why? Because if you receive the money today, you can invest it somewhere and earn interest on it. If you could get 5% interest on your investment, one year from now, you would have $1,050 in the first scenario, while in the second scenario, you would just have $1,000. In other words, any future payments are not worth the same amount that they would be if the payment was made today. To determine the µpresent value¶ of a future payment, you would have to discount it. The farther you go in future, the more this discounting would be. The present value of a $1,000 payment one year from now should be the amount that if you had today and invested in the market would yield $1,000 one year later. This amount would always be lower than the future payment. In the previous example, it is clear that the rate of discounting a future payment should be the interest that you can realistically earn on your investment. This interest is known as the required rate of interest or the required yield. If you had $1,000 today, it would be worth $1,050 one year from now if the required rate of interest is 5%. This is equivalent to saying that the present value of a payment of $1,050 one year from now is $1,000. The present value of any payment can be calculated using this formula: PV = F/ (1+r)^n Here: PV is present value F is future payment r is required rate of return n is the number of periods after which the payment would be made Applying this formula in the previous example, we can easily calculate the present value of a $1,000 payment one year from: PV = $1,000 / (1+.05) ^ 1 = $953.38 Calculating Bond Prices The price of a bond is equal to the present value of all its future interest payments and the repayment of par value at maturity. We can use the formula for present value of future

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payments to determine the value of a bond. But keep in mind that as coupon payments come at different points in time, the discounting factor for each of them will be different, with payments coming later having a heavier discount. The price of a bond can be represented as the following formula: Price = [I / (1+r)] + [I / (1+r)^2] + « + [I / (1+r)^n] + [Par Value / (1+r)^n] Here: I is the interest or coupon payment paid at the end of every period r is the required rate of return n is the number of periods after which the bond will mature This series of periodic payments in a plain vanilla bond is referred to as an ordinary annuity. This formula assumes that the first coupon payment will be made one period from the present time and the end of every subsequent period, the next coupon payments will be made. Note that period here could be anything, but typically bonds pay coupon semi annually or annually, so one period will be 6 months or 12 months long. Also note that the last coupon payment and the par value of the bond are paid together. It is clear from the formula that the payments that come farther in the future have a lower present value. Another thing evident from the formula is the inverse relationship between bond prices and interest rates. As interest rates go up in the economy, the required rate of return (r) also goes up. This increases the discounting factors in the formula and the price of the bond will be lower. The bond pricing formula given above can be simplified as: Price = I x [1- [1 / (1+r)^n ] ] / r + [Par Value / (1+r)^n] When you use this formula, you wouldn¶t have to calculate the present value of each coupon payment separately, and the price can be determined simply by plugging in the value of these variables. The same formula can be used irrespective of the nature of the bond. Here is an illustration of how this formula can be applied when determining the price for different kinds of bonds. Pricing a Plain Vanilla Bond Let¶s consider a plain vanilla bond with a par value of $5,000, maturity period of 5 years, and a coupon rate of 5%, paid semi-annually. Let¶s assume that the required rate of return is 10%. Here are the values of different variables that we¶ll need in the formula. n = 10 (Coupon payments are made with a periodicity of 6 months. There are 10 such periods in 5 years) I = $5,000 * 2.5% = $125 (Although coupon rate is 5%, this is the annual interest rate. For semi annual payments, coupon rate will be half of the annual rate) r = 5% (For a 10% annual required rate of return, the semi-annual required rate will be 5%) Par Value = $5,000 Plugging these values in the bond price formula: Price = $125 x [1- [1 / (1+.05)^10 ] ] / .05 + [$5,000 / (1+.05)^10] = $4,034. 7 You can see this value in light of our previous discussion on bonds selling for a premium or a discount. In this case, the required rate of return is significantly higher than the coupon paid

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by the bond. That is why the bond is selling at a heavy discount, as otherwise investors will have no reason to purchase this bond. Now, let¶s see what happens when the coupon rate of the bond is 15%. The coupon payment in this case (I) will be $5,000 * 7.5% = $375. All the other variable for the formula remain the same. This will result in the bond being priced as: Price = $375 x [1- [1 / (1+.05)^10 ] ] / .05 + [$5,000 / (1+.05)^10] = $5,965.2. The bond is offering a higher coupon rate than the interest rate investors can earn in the market, which is why the bond is now selling at a premium. Pricing a Zero Coupon Bond A zero coupon bond does not make any interest payments throughout the life of the bond. There is only a single cash flow, at the time of maturity of the bond, when the par value of the bond is returned to the investors. Pricing such a bond is much simpler. Let¶s consider a zero coupon bond with a par value of $5,000 and a maturity period of 5 years. Let¶s assume that the required rate of return is 10%. Plugging these values in the bond pricing formula: Price = [$5,000 / (1+.05)^10] = $3069.5 Compare this price with the price of the plain vanilla bond that we calculated in the last example. You can see that as there are no coupon payments made by the bond issuer, investors need a much larger incentive, in the form of a bigger discount, to purchase the bond. Of course, in case of zero coupon bonds, there is no question of the bond selling at a premium, or even at par. No investor would be ready to pay $5,000 (or more) today, just to get $5,000 back a few years from now. You would have noticed that we assumed a periodicity of 6 months in the formula despite the fact that a zero coupon bond pays no interest. This is done so that these bonds can be easily compared with other bonds that pay coupon on a semi-annual basis. Dirty and Clean Bond Prices So far, the bond pricing that we¶ve discussed misses out on one crucial point ± accrued interest. In the formula that we used to find out bond prices, we did not take into account the fact that the price of a bond will change as coupon payment date comes closer. We simply assumed that the next coupon payment is exactly one period away. At any given date between two coupon payments, the price of a bond should include the interest that has been accrued so far since the last coupon payment. This is the interest that the bond investor has already earned by holding the bond, but it has not bee paid to him yet. You can also think of this change in price between two coupon payments in terms of time value of money. Let¶s say a bond paid coupon on June 31 and the next payment is scheduled for Dec 31. As the next payment and all future cash flows come closer, their time value should increase, which means that the price of the bond should increase. However, this has not been accommodated in the formula so far. Bond prices that include accrued interest are known as dirty bond prices while those excluding accrued interest are referred to as clean bond prices or flat prices. Typically, quoted prices of bonds are flat prices. The reason behind this is that a clean price allows investors to evaluate the quality of the bond on the basis of issuer risk, interest rates etc. It also enables easier

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comparison between two bonds, without complicated assessment of when the last coupon was paid and how much interest has been accrued. The dirty price of a bond moves in a saw tooth pattern throughout the life of the bond (assuming interest rates and issuer risk do not change in that period). The price of the bond keeps increasing from the date of coupon payment as more and more interest gets accrued. On the subsequent coupon payment, the price falls to its minimum level again and starts rising in the same manner from the next day onwards. Calculating Accrued Interest As you would have guessed, to be able to calculate the accrued interest, we need to first determine the exact number of days that have passed since the last coupon payment. Different day counting conventions are used for different bonds. In an actual / actual day-count convention, you need to count the exact number of days that have passed so far since the last coupon payment and evaluate interest assuming that it accrues on every day. This convention is used for treasury securities. Consider a situation where the last coupon payment on a treasury bond was made on July 1 and the next payment is scheduled for January 1. To price the bond on September 1, we¶ll have to count the exact number of days between July 1 and September 1. Accrued interest in this case will be calculated for 62 days, which is the number of days that have passed since the last payment. In a 30 / 360 convention, it is assumed that each month of the year has 30 days and that there are 360 days in a year. This somewhat simplifies the calculation for the number of days, as you don¶t have to think about which month has 30 days, which has 31, if it is a leap year, and so on. This convention is typically used for corporate bonds and municipal bonds. If in our previous example, the bond was issued by a company, the accrued interest would have been calculated on 60 days instead of 62 days. But in this case, the daily accrual of interest will be calculated assuming that there are only 360 days in the year, i.e. interest will be divided into 360 periods. Accrued interest can be calculated using the following formula: Accrued interest = I x [d/D] Here: I = Coupon payment d = Number of days since last payment D = Total number of days between payments Let¶s consider a corporate bond, where the last coupon payment was made on July 1, the next payment is due on January 1, and we are calculating accrued interest on October 1. The coupon rate is 10%, paid semi-annually, and the par value of the bond is $5,000. I = $5,000 x (10% / 2) = $250 d = 90 days (as all months are assumed to have 30 days and exactly 3 months have passed since last coupon payment) D = 180 days (coupon payments are semi-annual, so periodicity is 6 months, with each month assumed to have 30 days) Accrued Interest = $250 x [90 / 180] = $125

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This accrued interest should be added to the clean price of the bond (as calculated from the bond pricing formula) to arrive at the true value of the bond on October 1. This is the price that you¶ll have to pay if you want to buy the bond from the secondary market. Next Chapter: Calculating Yield and Understanding Yield Curve Related posts: 1. 2. 3. 4. 5. Duration of Bonds Understanding Bond Terminology Categories of Bonds Categories of Bonds Factors to Consider Before Buying Bonds

Zero Coupon Bonds - Why Are they so Special?
Created in 1982, zero coupon bonds intention was to offer a financial instrument to guarantee long-term investments in securities, backed up by big and stable organizations, like states or transnational companies.

TYPES OF ZERO COUPON BONDS
Also known as strip bonds, there are four types of them. The first one is known as zero coupon municipal bonds. Also known as government zero coupon bonds, they have the advantage of not being affected by federal taxes. And in some cases, they are not even affected by state or local taxes. As a consequence, the Return Over Investment (ROI) may be higher than other kind of zero coupon bonds. Another advantage is that they don't require a huge amount of capital. You only need a minimum of US$5000, an easily achievable figure in the USA. Additionally, it is rated as an A or even triple A investment, which has a high degree of liquidity. This is very practical if you need the money and wish to sell your securities. All of these reasons have created a market of US$124 billion for this type of bond. Another kind is the zero coupon corporate bond. Although their ROI is higher than any other kind of bond, they are affected by federal taxes. But there are some other advantages. You may choose a wide portfolio of bond investments for you or your clients (many companies issue zero coupon bonds), they have a fair liquidity and are well ranked as instruments for investment. The third type is known as zero coupon treasury bonds. This kind of bond is issued by the Treasury of the United States and is considered the safest type of bond since it is backed up by the United States government, a country that has existed for more than two hundred years. Finally, the fourth type is called short term zero coupon bond. They reach their period of maturity in one year and are also known as bills. The US Treasury bill market is considered the most liquid debt market in the whole world. But issuing zero coupon bonds ain't an easy task. Any organization, public or private, who wishes to follow this path, needs to comply with a series of requirements that guarantees the money of their investors. That's why there are entities that rate the risk of bonds. Remember that a higher risk means a higher ROI, but also the possibility to lose your money.

Why Zero Coupon Bonds Are Different from other Bonds
The main difference is that zero coupon bonds don't pay interests over the life of the bond, but at the end. That means that at the end of the period, let's say, twenty years, the investor will receive the initial amount of money that he invested, the interests over his investment and any additional money consequence of inflation. The second principal difference is the period of maturity of the bond. While traditional bonds can last only for some months, a common period for a zero coupon bond is of thirty years.In the case of normal bonds, the investor receives semiannual payments (depending on the conditions of the bond) during the life of the bond. But, as in the case of a zero coupon bond, he will receive the original amount of money only at the end of the term.

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WHAT IS THEIR PURPOSE?
The principal interested for this kind of financial instrument is a pension fund. Since they need to leverage their portfolio of high risk investments, they immediately look at the bond market as a counterweight for any misshapen. From all the reasons indicated above, a zero coupon bond is one of the most recurred security by these entities. Another kind of sector interested in these instruments are insurance companies, who manage huge amounts of money and have to search for different kind of financial services in which to invest. Families and individuals are also keen to invest in zero coupon bonds. They usually use it as part of their retirement plan or as a long term investment for their kid's education.

WHERE DO I GET THEM?
If you are interested in buying zero coupon bonds, you may start at a mutual fund. They should have a variety of zero coupon bonds that are available in the market. You can also go to a broker and ask for the zero coupon bonds that they can offer. At either of these options you should receive advice on which type of zero coupon bond you should acquire. They have the experience and knowledge to understand their clients and offer them the one that best suits their needs. From all of these options, it seems that zero coupon municipal bonds are the most adequate for the small investor since it only requires a reasonable amount of money and offers a good ROI. But take note about this, you only can buy it if you live within the zone where it was emitted. In the case of pension funds and other kind of financial entities, the other type of zero coupon bonds seem as a more adequate choice for their kind of business. Zero balance account (ZBA). A disbursement bank account on which cheques are written even though the balances in the accounts are maintained at zero. Debits are covered by a transfer of funds from a master account at the same bank.
See also Master account

Zero balancing A method of cash concentration whereby funds are moved between a group of accounts leaving all but one (the main account) with a zero balance.
See also Cash concentration

Zero based An approach to planning as if each planning period were the first in operation. All structures and activities should be justified as if they were new proposals.
See also Zero based budgeting

Zero based budgeting (ZBB). This requires department managers to present their budgets as if each year were the first in operation ± all aspects of the budget should be justified afresh.
See also Budget Flexible budgeting Zero based

Zero cost 1. A zero cost collar is an options hedging structure which has a zero net premium payable by the hedging entity. The profit for the provider - and the true cost for the hedger - is built in to the related strike prices of the options, from which the collar is constructed. 2. Any structure which has no cost, or which may appear to have no cost.
See also Collar hedge

Zero coupon Zero coupon instruments pay only a single amount at their final maturity. They do not pay any intermediate interest.

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Investors in zero coupon instruments are not exposed to reinvestment risk, because the whole of their return is enjoyed via the capital gain up to maturity, which is fixed from the investment date. (So long as they hold their investment for its full life up to final maturity.)
See also Reinvestment risk Zero coupon bond Zero-coupon swap

Zero coupon bond (ZCB). Securities which pay no intermediate coupons, but only a redemption amount, so that the whole of the return to investors is represented by their capital gain from their investment date to the redemption of the bond at its final maturity. This may be beneficial for some taxpayers, especially high-income individuals.
See also Coupon bond Reinvestment risk Zero Zero coupon Zero coupon yield

Zero coupon rate (ZCR). Near enough the same as Zero coupon yield.
See also Zero coupon yield

Zero coupon yield The rate of return on an investment today, for a single cashflow at maturity of the instrument. Equal to the current market rate of return on zero coupon bonds of the same maturity. Also known as the Zero coupon rate, spot rate, or spot yield.
See also Bootstrap Flat yield curve Forward yield Spot rate Yield curve Zero Zero coupon bond

Zero Rated VAT. VAT at a rate of 0%.
See also Lower rated VAT

Zero-coupon swap A swap in which a fixed rate payer makes a single payment, on the maturity date, and the other party makes payments periodically.
See also Swap Zero coupon

Zero Coupon Bond Calculator
Face value of bond: Rate or yield: Time to maturity:
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About This Tool
The online Zero Coupon Bond Calculator is used to calculate the zero coupon bond value.

Zero Coupon Bond Definition
A zero coupon bond is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity. It does not make periodic interest payments. When the bond reaches maturity, its investor receives its face value. It is also called a discount bond or deep discount bond.

Formula
The zero coupon bond value calculation formula is as following: Zero coupon bond value = F / (1 + r) Where: F = face value of bond r = rate or yield t = time to maturity
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6.3 The Zero Coupon Bond Case n the cash matching section, you saw that you can control all interest rate risk perfectly if you construct the exact synthetic equivalent of the underlying position. The problem with this approach is that large positions imply tens of thousands of different cash flow points over time. It is unlikely that the markets exist to create a synthetic equivalent. Even if sufficient markets were available, the transaction cost associated with creating such a security would be onerous.

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This leads us to a question: Do simpler "solutions" exist that would allow a trader to manage the exposure of a position to interest rate risk using fewer securities? Investment Example In this example, we will consider the impact of large yield curve shifts upon a small position. Consider the following position, which generates cash flows at the end of each year for four years. The cash flows associated with each component are described by the following set of timelines: Security Units Security I -14

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Cash in 1-year money market line $5,300 2-Year zero-coupon bond 51 3-Year zero-coupon bond 0 The following timelines describe the cash flow from each security. Timeline for Per Share Cash Flows from Security I

Timeline for Cash Flows from 1-Year Money Market Line

Timeline for Cash Flows from 2-Year Zero-Coupon Bond

Timeline for Cash Flows from 3-Year Zero-Coupon Bond

Online, you can work with this problem using the interactive online calculator below. You can click on the cell besdie Security 1 under Value (307.20) to bring up the exposure profile for the coupon bond.:

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To access the The default dataset is the problem at hand. By clicking on the Cash Flows button (beside Numeric) you can see the cash flows associated with the four securities. The fifth "security" is $100 cash at time zero.

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Click on Done and then Enter the position as follows:

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Security Units Security I -14 Cash in 1-year money market (Security 5) $5,300 2-Year zero-coupon bond (Security 3) 51 3-Year zero-coupon bond (Security 4) 0 Note: You enter a position directly online by double clicking on the appropriate cell under Units, and typing the number directly into the cell followed by Return or Enter. If you make an error you can use the delete or backspace keys. Your entered position should appear as follows: Note: Be sure to click beside Portfolio and then click on OK

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The exposure of this position to interest rate risk appears as follows:

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Online above you can also specify the size of the initial shift in the yield curve (in basis points). In the following screen, a total shift of +/- 2000 basis points (20%) with 2 partitions either side of the current 25% is specified: Online Enter under Basis Points 2000 and Intervals 10 then click beside Portfolio and finally click OK. This gives a finer plot of the interest rate bucket shifts.

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Online, you can see, this position benefits from an increase in interest rates and is hurt by a decrease.

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Numerically, the value of these two securities can be viewed by clicking on the Numeric button:

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The origin is the flat yield curve of 25% and the shifts are +/1 10% and 20%. You can see that the present value of the portfolio is exposed to shifts in the yield curve. For example, let the current spot yield curve be flat and equal to 25% for Years 1 4. If the yield curve remains at 25%, then the current value of this position is: -$1,036.80 + $5,300 = $4,263.20 From the above you can see that Cash = $5300 plus long positions (assets) = 3264.00 and short positions (liabilities) = 4300.80. The aggregate value is $5300 + $3264.00 - $4300.80 = $4,263.20. In practice, we must consider the effects of a yield curve shift at the end of some period of time. That is, the position is invested at the current spot rate and then during the period the yield curve shifts to a new level. To consider the effects of this scenario, compute the value of this position at the end of the year: $4,263.20 * 1.25 = $5,329 Online, you can verify this by computing the future value of cash flows at the end of Year 1 assuming 25%, 25%, 25%. The end of year value of this position when there is no change in the yield curve is obtained by moving View Period forward 1-period (as illustrated below) and checking the checkbox "Reinvest.":

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Numerically, $5329 = $5300*1.25 + $4080.00 - $5376.00. $5,329 = $5,300 * 1.25 - $1,296 To see this click on the Numeric button and view the 0 Yield Shift.

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Now, suppose the yield curve shifts up during the first year so that at year end it is a flat 35%. This shift reduces the value of both the asset (i.e., the long position) and the liability (i.e., the short position). Overall, the total value increases to: $5,300*1.25 - $840.38 = $5,784.62 Which you can see above in the Portfolio Values window beside 10.00 (i.e., shift up by 10% in yield) and View Period 1 and click on the Numeric button:

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You can verify for other realizations in the same way that the end of year position value equals: Yield Curve at end of Year 1: Value of Position (1-, 2-, and 3-year spot rate) at end of Year 1 5%, 5%, 5% $3785.69 15%,15%,15% $4693.45 25%,25%,25% $5329 35%,35%,35% $5784.62 45%,45%,45% $6117.61 That is, this position (when invested at the current spot rates) benefits from an increase in interest rates but is hurt by a decrease in interest rates. Hedging Interest Rate Risk How can you ensure that this position never falls below $5,000? An easy solution is to cash out. At the current yield curve this locks you into $5,329, which satisfies your constraint with a little excess to spare. However, at any point in time, a firm's position consists of two types of short (liabilities) and long (assets) positions: those that are held for trading purposes and those that are not intended to be liquidated during the firm's normal course of business over the current period. Suppose the liability, -14 units of Security I, cannot be traded but you still want to manage the interest rate risk associated with this position. In particular, you want to ensure that by year end its value does not fall below $5,000 over the given range of yield curve shifts. How can you achieve this? Consider buying 84 3-year zeroes and selling 51 2-year zeroes.

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Online, a very different picture emerges. The present value of this position appears as follows:

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Numerically, this appears as above. Note that in the above you need to enter your final position. That is, you sold 51 units at $80 and bought 84 units at $64.00. As a result, at time 0 you only have $4263.20 cash to invest because 84 units at $64 costs more than the revenue generated from selling 51 units at $80. Click on the Numeric button to see the range of fluctuations in actual position value by first scrolling to View Period 1.00 as below:

In other words our position is now staying above $5000 at year end, for a wide range of yield curve fluctuations! That is, your position is hedged against fluctuations in the yield curve. In summary to hedge this position recall that you engaged in the following transactions at the beginning of the year: i. Sold 51 units of Security 3 at $64 (the present value of $100 at the end of Year 2 using the spot flat 25% yield curve). This equals $3,264 (51*$64). ii. Bought 84 units of Security 4 at $51.20 (the present value of $100 at the end of Year 3 using the spot flat 25% yield curve). This equals $4,300.80 (84*$51.20). iii. Invested the remaining balance of cash in the money market at 25%. This equals $4,263.20*1.25 ($5,300 + $3,264 - $4,300.80 = $4,263.20). Numerically, the year-end value of this position, if there is no shift in the yield curve, equals: $4,263.20 * 1.25 - 14 * $384 + 84 * $64 = $5,329

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Yield Curve at end of Year 1: Value of Position (1, 2, and 3 year spot rate) at End of Year 1 5%, 5%, 5% $5251.60 (= $5,329 - $77.40) 15%,15%,15% $5314.27 (= $5,329 - $14.73) 25%,25%,25% $5329 35%,35%,35% $5319.90 (= $5,329 - $9.10) 45%,45%,45% $5299.61 (= $5,299.61 - $29.39) You can see that this new position satisfies the $5,000 constraint over a range of 2,000 basis points shift in the yield curve. In this trading approach to hedging interest rate risk be sure to distinguish between the time of adjusting the position (the beginning of the year) with the time for which protection is desired (at the end of the year). You may be wondering whether some general principle underlies this example. That is, what guided the choice of selling 51 units of Security 2 and buying 84 units of Security 3? It turns out that a general principle does exist. This example was constructed by applying an important theorem, the bond immunization theorem. We develop this theory in the next topic, Macaulay's Duration, and then return to this example in topic 6.5 to see how it applies.

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Investments Lecture 3: Yield curves
Philip H. Dybvig Washington University in Saint Louis
y y y y y

The term structure of interest rates Relations among yield curves: intuition Conventions and complications in practice Continuous compounding Duration and effective duration

Copyright © Philip H. Dybvig 2000

The term structure of interest rates
Generically, we refer to the term structure of interest rates (term structure for short) the pattern of interest rates for different maturities implicit in quoted bond prices on a single date. Even in riskless securities (still our main focus in this lecture), there are different ways of representing the term structure using the forward rate curve, or the yield curve. Indeed, there are many different yield curves, for discount bonds and for coupon bonds of different moneyness. Using the basic no-arbitrage relationships and algebra, we can understand the connections among the various sorts of yield curves. The forward, zero-coupon, and par-coupon yield curves all start at the same place at short time-tomaturity, but the forward rate curve is steepest, the zero-coupon next-steepest,
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and the par-coupon the least steep. This is because the zero-coupon rate at some maturity is a sort of average of forward rates at that and earlier maturities, and the par-coupon rate at some maturity is a similar average that puts more weight on earlier maturities.

Connecting various yield curves: intuition
The various interest rates and yields correspond to different time-patterns of investing. The forward rate corresponds to investing during the future year. The zero-coupon rate corresponds to investing from now until some future date, and is approximately the average of all the forward rates along the way. The parcoupon rate combines investing to maturity with investing for shorter periods until the various coupons are paid. Like the zero-coupon rate, the par coupon rate is an average of futures rates from now until maturity, only with more weight placed on nearby forward rates than for the zero-coupon rate. The diagram on the following slide illustrates the intuition. For forward investing (corresponding to f(0,10)), the position is undertaken 9 years from now and liquidated 10 years from now. For an investment in a zero-coupon bond (corresponding to z(0,10)), the position is undertaken now and liquidated 10 years from now. The value is constant in time 0-value terms (although it is falling in dollar terms). Not surprisingly, the appropriate yield an average of forward rates across the 10 years. For a par coupon bond (c(0,10), assumed to be 5%), the value invested is falling over time as coupons are paid. For a coupon bond, the yield is an average of forward rates that puts some more weight on early rates than does the zero-coupon rate. The par-coupon rate is also a weighted average of zero-coupon rates. Finally, for a self-amortizing bond (coupons but no principal, like a mortgage), the present values declines more quickly as coupons are paid, so in this case the yield puts even more weight on early forward rates.

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Rates intuition diagram

Connecting the different term structures: some algebra
Forward rates and zero-coupon rates are connected by the expression
/ T \ 1/T 1 T z(0,T) = | Prod (1+f(0,s)) | - 1 ~ - Sum f(0,s). \ s=1 / T s=1

This can be proven using the simple expressions for the discount factor in terms of the forward rates and in terms of the zero-coupon rates. The approximation is very good provided the interest rates are not too large. Zero-coupon and par-coupon rates are connected by the expression
T c(0,T) = Sum w(0,s)f(0,s) s=1

91

where the positive weights w(0,s) are defined by
/ T w(0,s) = D(0,s) / Sum D(0,t) / t=1

sum to one and are positive are decreasing in s.

A recent yield curve

Computing the term structure from Treasury STRIPs
The previous plot was computed using Treasury STRIPs that are claims to individual principal or coupon payments from Treasury Bonds or Notes. Originally, claims to individual cash flows from Treasury issues were created

92

by investment banks as claims to funds that held the Treasury issues in trust. Now, these claims are created as a service by the Treasury, and the Treasury will strip or reconstitute securities you hold for a modest fee. One curious feature of the program is that cash flows from principal repayment (at the end) and coupon interest (though the life of the bond) are not interchangeable. In order to reconstitute a bond, you need the right principal (corpus) but you can use interest stripped off other bonds. This means the market for coupon interest strips is, at least in principle, more liquid than the market for principal strips. However, the two types of STRIP usually trade within a few basis points of each other.

Constructing the yield curve: issues
Some details need to be decided upon when constructing a yield curve, even once we have decided to use Treasury STRIP prices. For example,
y y y y y y

Use bid price, ask price, spread midpoint? Frequency of data to use (monthly? semi-annual?) Smooth data or use quotes directly? Round to an integer number of periods? Use continuously-compounded yield or bond-equivalent yield? How to extrapolate beyond available data or interpolate between available data?

Often these choices do not matter much, especially if you are consistent. It depends in part on how you will use the data and the precision required.

STRIP quotes and zero-coupon yield
Strips are quoted in dollars and 32nds per $100 of face value. For example, the strip maturing in May 2010 used in constructing the yield curve in the previous picture is quoted (the ask price) at 51:21 or 51 + 21/32 = $51.65625 per $100 of payment 10 years from now. The bond equivalent zero-coupon yield y used in the figure can be computed approximately from the formula
-10*2 D = .5165625 = (1+y/2) . 0,10

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(Recall that by definition, a^(-b) = 1/(a^b).) Solving for y, we have that
-1/20 y = 2*(.5165625 - 1) ~ 6.7%

This gives the semi-annually compounded interested rate quoted as an annual rate. In the computation used in the figure, there is an adjustment for the time between the settlement of a trade today and the middle of the month when a coupon would be received. This adjustment is approximate (I assume settlement the next day and a whole number of months from the 15th for each stripped coupon) but for more precise work you would look at the actual number of days until each stripped coupon.

Forward rates
The forward rates are computed using pairs of STRIP prices. (Recall the arb from the previous lecture: forward lending is replicated by buying a longer STRIP using proceeds from selling short just enough of a shorter STRIP.) For example, we can use the previously noted May, 2010 strip price of 51:21 (= 51 21/32 or 51.65625) and the Nov 2009 strip price of 53:14 (= 53 14/32 or 54.4375) to compute the forward rate for lending from 9 1/2 years out until 10 years out as
/53.4375 \ y = 2| -------- - 1 | \51.65625 / ~ 6.89%

One surprising feature of the yield curve plot is the irregular appearance of the forward rate. This is actually spurious detail. The forward rates are obtain by differencing STRIP prices, and differencing magnifies relative errors. (For example, think about 100 - 99, when 100 and 99 are both accurate plus or minus 2%.) Given the problems with the quotes and the spread, we cannot rule out the specific shape in the plot, but we also cannot rule out more reasonablelooking shapes.

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Smoothing to remove spurious forward rate irregularities
The following two figures illustrate the effect of smoothing (using a technique to be described shortly) on the discount STRIP prices and on the forward rates. It is interesting to see how smoothing that cannot be seen easily in the plot of zero-coupon rates can make the forward rate curve much smoother. This underlines the fact that the detail in the forward rate curve is not significant. Using the smoothed curve is good psychologically because it eliminates distracting and irrelevant features. It also can be used as an input to simulation or other analysis (as we will do later) in which we want to be sure the results are not driven by spurious features.

Zero-coupon bond prices, with and without smoothing

95

Yield curves from smoothed zero-coupon bond prices

Smoothing the yield curve
We have seen that an almost imperceptible adjustment to the original STRIP data makes the forward rate curve much smoother. (The only part that is really unclear is the very short end. The short end is important in practice; to have a closer look we would use many more STRIPs and T-Bills to nail it down.) This smoothing is important for looking at the yield curve and for communication without the spurious detail. I used linear regression to smooth the yield curve. The functions I chose as covariates (or independent variables) in the regression were picked to capture the overall features of the yield curve without too many sudden changes. The specific regression I fit to the yield curve was:

96

z(0,t) = a + b exp(-t) + c exp(-t/3) + d exp(-t/9) + e exp(-t/27) + error .

I used ordinary least squares to estimate the parameters a, b, c, d, and e, and I replaced the zero-coupon rates by the fitted values (the same equation without the error term). Then I derived the discount factors and various rates from the fitted values.

Smoothing the yield curve: tips
y y y y y

Using too many functions overfits and does not smooth Using too few functions underfits and will not match the STRIPS well Fit the yield curve, not the raw bond prices Use functions that can mimic features you believe to be important Avoid functions that have unwanted sharp changes

Self-amortizing loan yield curve
A self-amortizing loan pays the same amount, say c per period, in every period until the loan is paid off. The yield is computed in the usual way, so the price (or amount borrowed initially) should be the present value of the cash flows given the yield. If y is the bond-equivalent yield of a self-amortizing loan with semi-annual coupons maturing n/2 years from now, we have that
n P = Sum c D(0,s/2) s=1 n c = Sum -------- . s=1 s (1+y/2) c / 1 \ = --- | 1 - -------- | , y/2 | n | \ (1+y/2) /

where the last expression is the annuity formula (What is the underlying arb?). Therefore, the self-amortizing loan yield s(0,t) is the value of y that solves the equation:
2 / -2t\ n

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- | 1 - (1+y/2) y \

| - Sum D(0,s/2) = 0. / s=1

Since the left-hand side is a decreasing function of y, it is easy to solve this numerically. Note that we can also compute the payments (given the amount borrowed) from these expressions.

Continuously-compounded yields
Compounding k periods per year at a fixed annual rate r grows our money in T years by a factor
kT (1+r/k)

As k increases, this factor gets larger due to interest on interest or the magic of compounding. It is an interesting mathematical fact that as k increases without bound, this factor tends to the limit
rT e = exp(rT)

where e ~2.71828... is a transcendental number called the base of the natural logarithm. Naturally, the growth factor exp(rT) is called continuous compounding, and r is called the continuously-compounded interest rate. There is corresponding discounting with a factor 1/exp(rT) = exp(-rT). We have been working with bond-equivalent yields, which assume compounding twice a year; continuous yields correspond to continuous discounting. In some cases (for example, in computing the zero-coupon rate) it is useful to use the (natural) logarithm, which is the inverse of the exponential function: exp(log(x))=log(exp(x))=x. This is the logarithm base e. Usually, beyond high school we usually use the natural logarithm (or log base 2 for some applications in information science), while in high school and before we usually see the log base 10 (the inverse of 10^x: 10^(log_10(x))=log_10(10^x)=x).

Non Zero Coupon Bond Price
What is the formula to find price of a non zero coupon bond with example calculation. On this page we define a non zero coupon bond and provide a formula for valuation of such bonds along with an example calculation to find valuation of non zero coupon bonds. Stop wasting time with crappy templates - we bet, here you will find all you need!

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Online Bond Price Calculation
You may visit this page to see step by step non zero bond price calculation

How do you define a non zero coupon bond
Non Zero Coupon Bonds have finite maturity , thus we must consider not only the interest stream but also the terminal value or maturity value (face value) in valuing the bond.

What is the formula for Valuation of non zero coupon bond?
The valuation equation for such a bond that pays interest at the end of each year is

Finding Bond's Price in MS Excel
You may want to visit this page that show you how to find Bond Price in MS Excel with step by step explanation.

Bond Price Example
Let me illustrate finding price of a non zero coupon bond with and example. Microsoft has issued a bonds with a face value of $1000 having a coupon of 8%. The bond matures in 10 years time and interest rate for similar bonds is 9%. Bond makes annual interest payments. How do we find the market price of this bond from Microsoft Corp.

Bond Price Calculation
The bonds pays an annual interest in amount of $80 (computed as $1000 x 8 / 100). Thus we would discount each of these 10 annual payments at the market rate of 9% and add its sum to the discounted par value. Let us set this up in tabular form so that you can see all the calculations

Bond Price at 9% YTM
Year 1 2 3 4 Interest Payment $80 $80 $80 $80 PVIF @ 9% 0.917 0.842 0.772 0.708 Present Value $73.36 $67.36 $61.76 $56.64

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5 6 7 8 9 10

$80 $80 $80 $80 $80 $1080

0.650 0.596 0.547 0.502 0.460 0.422 Price

$52.00 $47.68 $43.76 $40.16 $36.8 $455.76 $935.44

Price for bonds with semi-annual payments
How would you calculate the bond price when bond pays semi-annual interest payments. To answer this question we will amend the bond price formula such that we divide the interest payment in half and double the number of periods till maturity. As an illustration, say Johnson and Johnson Company has issued a $1000 semi annual coupon bond at 10% with 10 years till maturity. Similar bonds on the market have a yield of 12%. How do we find the price of this bond with semiannual compounding of interest payments.

Bond Price at 10% semi annual compounding
Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Interest Payment $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 $50 PVIF @ 6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592 0.558 0.527 0.497 0.469 0.442 0.417 Present Value $47.15 $44.5 $42 $39.6 $37.35 $35.25 $33.25 $31.35 $29.6 $27.9 $26.35 $24.85 $23.45 $22.1 $20.85 100

16 17 18 19 20

$50 $50 $50 $50 $1050

0.394 0.371 0.350 0.331 0.312 Price

$19.7 $18.55 $17.5 $16.55 $327.6 $885.45

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