Coupons security

As discussed in chapter 1, there are two types of fixed-income securities zero-coupon bonds, also known as discount bonds or strips, and coupon bonds. A zero-coupon bond makes a single payment on its maturity date, while a coupon bond makes interest payments at regular dates up to and including its maturity date. A coupon bond may be regarded as a set of strips, with the payment on each coupon date and at maturity being equivalent to a zeto-coupon bond maturing on that date. This equivalence is not purely academic. Before the advent of the formal market in U.S. Treasury strips, a number of investment banks traded the cash flows of Treasury securities as separate zero-coupon securities. 

Between the short- and long-term horizon dates is one at which the net effect of the change in reinvestment rate on the bond s future value is close to zero. At this date, the bond behaves like a single-cash-flow or zero-coupon security, and its future value can be predicted with greater certainty, no matter what the yield curve does after its purchase. Defining this date as Sh interest periods after the purchase date and Ph as the value of the bond at that point, it can be shown that the bond s rate of return up to this horizon date is the value for rntn that solves equation (16.6). 

As noted in chapter 2, a Treasury bond can be seen as a bundle of individual zero-coupon securities, each maturing on one of the bond s cash flow payment dates. In this view, the Treasury s price is the sum of the present values of all the constituent zero-coupon bond yields. Assume that the spot rates for the relevant maturities—ri,r2,rg,.rj f—can be observed. If a bond pays a semiannual coupon computed at an annual rate of C from period 1 to period N, its present value can be derived using equation (16.7). 

Because it is affected by current demand, the yield of a particular zero-coupon bond at any time may differ from the equivalent-maturity spot yield. When investors value an individual zero-coupon bond less highly as a stripped security than as part of a coupon bond s theoretical package of zero-coupon cash flows, the strip s yield will be above the spot rate for the same maturity. The opposite happens when investors prefer to hold the zero-coupon security. 

The equivalent bond yield, also referred to as the coupon yield equivalent, is reported on most bond dealers quote sheets. Us purpose is to make possible direct comparisons between the interest earned on discount securities and the yield to maturity on couponpaying bonds. Since most coupon securities pay interest on a semiannual basis, the time to maturity for the discount security is important in determining its equivalent bond yield. 

Convertible bonds are typically fixed-coupon securities that are issued with an option to be converted into the equity of the issuing company under specified terms and conditions. They have been issued as both senior and subordinated securities. The investors view on the performance of the issuing company s shares is a major factor, because investors are buying into... 

The simplest approach assumes, somewhat unrealistically, that the yield curve is flat and moves only in parallel shifts, up or down. It considers a bond to be a package of zero-coupon securities whose values are discounted and added together to give its theoretical price. The advantage of this approach is that each cash flow is discounted at the interest rate for the relevant term, rather than at a single internal rate of return, as in the conventional approach. Given the flat yield curve, however, this approach reduces to (17.3). An example of its application follows. 

Bond A long-term debt-type of security generally issued by corporations or governments to generate cash. The coupon rate is the interest rate paid to the bondholder. The maturity date is when the face value of the bond will be paid to the bondholder. 

Treasury inflation-protected securities (TIPs) are one of the most innovative financial products to appear in recent years. They pay a real coupon, plus the return on the Consumer Price Index (CPI). Thus, they automatically protect investors 100% against rising inflation, a property no other security possesses. Further, in a rising inflation environment, returns on TIPs are negatively correlated with those of bonds and other assets whose prices tend to decline when inflation rises. 

As explained in the introduction, the value of a convertible bond is the sum of two main components, the option-free bond and a call option on underlying security. The value of the option-free bond, or bond floor, is determined as the sum of future payments (coupon and principal at maturity). Therefore, the bond component is influenced by three main parameters, that is the maturity, the coupon percentage on par value and the yield to maturity (discount rate). Differently, the value of a call option can be found mainly through two option pricing models, Black Scholes model and binomial tree model. 

Unpredictable cashflows While in fixed-rate securities the coupon payments are known with certainty, with floaters we cannot predict futiue cash flows ... 

A bond, like any security, can be thought of as a package of cash flows. A bond s cash flows come in two forms—coupon interest payments and the maturity value or par value. In European markets, many bonds deliver annual cash flows. As an illustration, consider a 6% coupon... 

The most actively traded government securities for various maturities are called benchmark issues. Yields on these issues serve as reference interest rates which are used extensively for pricing other securities. Exhibit 1.2 is a Bloomberg screen of the benchmark bonds issued by the government of the Netherlands. European government bonds will be discussed in Chapter 5. As an illustration of a corporate bond. Exhibit 1.3 shows a Bloomberg Security Description screen for 4.875% coupon bond issued by Pirelli SPA that matures on 21 October 2008. 

As noted, the coupon rate is the interest rate the issuer agrees to pay each year. The coupon rate is used to determine the annual coupon payment which can be delivered to the bondholder once per year or in two or more equal installments. As noted, for bonds issued in European bond markets and the Eurobond markets, coupon payments are made annually. Conversely, in the United Kingdom, United States, and Japan, the usual practice is for the issuer to pay the coupon in two semiannual installments. An important exception is structured products (e.g., asset-backed securities) which often deliver cash flows more frequently (e.g., quarterly, monthly). 

DIHBir 1.4 Bloomberg Security Description Screen for a Zero-Coupon Bond Issued by BNP Paribus... 

In contrast to a conpon rate that remains unchanged for the bond s entire life, a floating-rate security or floater is a debt instrument whose coupon rate is reset at designated dates based on the value of some reference rate. Thus, the coupon rate will vary over the instrument s life. The coupon rate is almost always determined by a coupon formula. For example, a floater issued by Aareal Bank AG in Denmark (due in May 2007) has a coupon formula equal to three month EURIBOR plus 20 basis points and delivers cash flows quarterly. 

There are several features about floaters that deserve mention. First, a floater may have a restriction on the maximum (minimum) coupon rate that be paid at any reset date called a cap (floor). Second, while a floater s coupon rate normally moves in the same direction as the reference rate moves, there are floaters whose coupon rate moves in the opposite direction from the reference rate. These securities are called inverse floaters. As an example, consider an inverse floater issued by the Republic of Austria. This issue matures in April 2005 and delivers semiannual coupon payments according to the following formula ... 

The cash flows of a fixed-income security can be denominated in any currency. For bonds issued by countries within the European Union, the issuer typically makes both coupon payments and maturity value payments in euros. However, there is nothing that prohibits the issuer from making payments in other currencies. The bond s indenture can specify that the issuer may make payments in some other specified currency. There are some issues whose coupon payments are in one currency and whose maturity value is in another currency. An issue with this feature is called a dual-currency issue. 

Some bonds include a provision in their offer particulars that gives either the bondholder and/or the issuer an option to enforce early redemption of the bond. The most common type of option embedded in a bond is a call feature. A call provision grants the issuer the right to redeem all or part of the debt before the specified maturity date. An issuing company may wish to include such a feature as it allows it to replace an old bond issue with a lower coupon rate issue if interest rates in the market have declined. As a call feature allows the issuer to change the maturity date of a bond it is considered harmful to the bondholder s interests therefore the market price of the bond at any time will reflect this. A call option is included in all asset-backed securities based on mortgages, for obvious reasons. 

Cash flow is simply the cash that is expected to be received in the future from owning a financial asset. For a fixed-income security, it does not matter whether the cash flow is interest income or repayment of principal. A security s cash flows represent the sum of each period s expected cash flow. Even if we disregard default, the cash flows for some fixed-income securities are simple to forecast accurately. Noncallable benchmark government securities possess this feature since they have known cash flows. For benchmark government securities, the cash flows consist of the coupon interest payments every year up to and including the maturity date and the principal repayment at the maturity date. 

For securities that fall into the first category, a key factor determining whether the owner of the option (either the issuer of the security or the investor) will exercise the option to alter the security s cash flows is the level of interest rates in the future relative to the security s coupon rate. In order to estimate the cash flows for these types of securities, we must determine how the size and timing of their expected cash flows will change in the future. For example, when estimating the future cash flows of a callable bond, we must account for the fact that when interest... 

The preceding three scenarios illustrate an important general property of present value. The higher (lower) the discount rate, the lower (higher) the present value. Since the value of a security is the present value of the expected future cash flows, this property carries over to the value of a security the higher (lower) the discount rate, the lower (higher) a security s value. We can summarize the relationship between the coupon rate, the required market yield, and the bond s price relative to its par value as follows ... 

To illustrate what happens to a bond selling at a premium, consider once again the 4-year, 6% coupon bond. When the discount rate is 5%, the bond s price is 103.546. Suppose that one year later, the discount rate is still 5%. There are only three cash flows remaining since the bond is now a 3-year security. We compute the present value of the coupon payments in the same way as before ... 

The approach described above for valuing a bond is to discount every cash flow using the same interest or discount rate. The fundamental flaw of this approach is that it views each security as the same package of cash flows. For example, consider a 5-year French government bond with a 4% coupon rate. The cash flows per 100 of par value would be four payments of 4 every year and 104 five years from now. In the... 

The discussion is easily expanded to include risky floaters (e.g., corporate floaters) without a call feature or other embedded options. A floater pays a spread above the reference rate (i.e., the quoted margin) to compensate the investor for the risks (e.g., default, liquidity, etc.) associated with this security. The quoted margin is established on the floater s issue date and is fixed to maturity. If the market s evaluation of the risk of holding the floater does not change, the risky floater will be repriced to par on each coupon reset date just as with the default-free floater. This result holds as long as the issuer s risk can be characterized by a constant markup over the risk-free rate. 

To illustrate, we will value the same hypothetical 4-year floater assuming that the required margin is now 20 basis points. For this to occur, some dimension of the floater s risk or the market must have increased since the floater s issuance. Now in order to be reset to par, our floater would hypothetically have to possess a coupon rate equal to 3-month LIBOR plus 20 basis points. Since the quoted margin is fixed, the floater s price must fall to reflect the market s perceived increase in the security s risk. 

We will illustrate the sources of euro returns using an example. In early July 2003, the 5-year German government bond (i.e., bund) was trading at 100.103 assuming a settlement date of 9 July 2003. The security description screen from Bloomberg is presented in Exhibit 3.8. This bond carries a coupon rate of 3% and matures on 11 April 2008. Cou-... 

The source of dollar return called reinvestment income represents the interest earned from reinvesting the bond s interim cash flows (interest and/or principal payments) until the bond is removed from the investor s portfolio. With the exception of zero-coupon bonds, fixed income securities deliver coupon payments that can be reinvested. Moreover, amortizing securities (e.g., mortgage-backed and asset-backed securities) make periodic principal repayments which can also be invested. 

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