Coupons cash flows

This is the observation that, due to demand and liquidity reasons, zero-coupon bonds sourced from the principal cash flow of a coupon bond trade at a lower yield than equivalent-maturity zero-coupon bonds sourced from the coupon cash flow of a conventional bond. 

With an eight-month lag, we will know the next coupon cash flow and possibly the subsequent one, but no others. The formula takes the latest known RPI value and from that month projects all future monthly RPI values using an inflation assumption (currently 3%), which is a market convention. So an unknown RPI in month t is given by... 

The long end of the swap curve is derived directly from observable coupon swap rates. These are generic plain vanilla interest rate swaps with fixed rates exchanged for floating interest rates. The fixed swap rates are quoted as par rates and are usually compounded semiannually (see Exhibit 20.2). The bootstrap method is used to derive zero-coupon interest rates from the swap par rates. Starting from the first swap rate, given all the continuously compounded zero rates for the coupon cash flows prior to maturity, the continuously compounded zero rate for the term of the swap is bootstrapped as follows ... 

Another problem with YTM is that it discounts a bond s coupons at the yield specific to that bond. It thus cannot serve as an accurate basis for comparing bonds. Consider a two-year and a five-year bond. These securities will invariably have different YTMs. Accordingly, the coupon cash flows they generate in two years time will be discounted at different... 

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 assumptions of this study are premised on the commitment to a multi trillion dollar, centralized H2 production and delivery system in the U.S. over a thirty-year time period. Therefore, it is believed that the capital structure assumptions of 30% equity capital and 70% debt are more realistic for the assumed scale of capital investments. In addition, there are cash flow benefits to financing capital budgeting projects with debt capital rather than equity capital because interest on debt is tax deductible whereas dividends payments are not. The 7% interest rate for 30-year coupon bonds is a reasonable assumption for the assumed scale of investments, particularly so if a national H2 plan is adopted with government regulation and guaranteed bond issues. 

The asset swap is an agreement that allows investors to exchange or swap future cash flows generated by an asset, usually fixed rates to floating rates. It is essentially a combination of a fixed coupon bond and an IRS. We define it thus ... 

At the same time, the investor enters in the swap contract, paying fixed cash flows equal to the coupon payment and receiving a fixed spread over the interbank rate, that is the asset-swap spread. Figure 1.1 shows the asset-swap mechanism. 

The zero-coupon curve is used in the asset-swap analysis, in which the curve is derived from the swap curve. Then, the asset-swap spread is the spread that allows us to receive the equivalence between the present value of cash flows and the current market price of the bond. 

As shown in Eigures 1.4 and 1.5, with this swap structuring, the asset-swap spread for HERIM is 39.5 bp and for TKAAV is 39.1 bp. These represent the spreads that will be received if each bond is purchased as an asset-swap package. In other words, the ASW spread provides a measure of the difference between the market price of the bond and the value of the cash flows evaluated using zero-coupon rates. 

Z-spread is an alternative spread measure to the ASW spread. This type of spread uses the zero-coupon yield curve to calculate the spread, in which in this case is assimilated to the interest-rate swap curve. Z-spread represents the spread needful in order to obtain the equivalence between the present value of the bond s cash flows and its current market price. However, conversely to the ASW spread, the Z-spread is a constant measme. 

For the calculation, we cancel out the principal payments of par at maturity. We assume that cash flows are annual and take place on the same coupon dates. The breakeven asset-swap spread A is calculated by setting the present value of all cash flows equal to 0. From the perspective of the asset swap seller, the present value is ... 

As above, assuming a constant average inflation rate, which is then used to calculate the value of the bond s coupon and redemption payments. The duration of the cash flow is then calculated by observing the effect of a parallel shift in the zero-coupon yield curve. By assuming a constant inflation rate and constant increase in the cash flow stream, a further assumption is made that the parallel shift in the yield curve is as a result of changes in real yields, not because of changes in inflation expectations. Therefore, this duration measure becomes in effect a real yield duration ... 

To obtain the price of an inflation-linked bond, it is necessary to determine the value of coupon payments and principal repayment. Inflation-linked bonds can be structured with a different cash flow indexation. As noted above, duration, tax treatment and reinvestment risk, are the main factors that affect the instrument design. For instance, index-aimuity bmids that give to the investor a fixed annuity payment and a variable element to compensate the inflation have the shortest duration and the highest reinvestment risk of aU inflation-linked bonds. Conversely, inflation-linked zero-coupon bonds have the highest duration of all inflation-linked bonds and do not have reinvestment risk. In addition, also the tax treatment affects the cash flow structure. In some bond markets, the inflation adjustment on the principal is treated as current income for tax purpose, while in other markets it is not. 

The price of an inflation-linked bmid is determined as the present value of future coupon payments and principal at maturity. Like a conventional bond, the valuation depends on the cash flow structure. We can have three main cash flow structures of index-linked bonds. 

Table 6.2 illustrates the cash flow structure of an inflation-linked bond with zero-coupon indexation. 

TABLE 6.2 The Cash Flow Structure with Zero-Coupon Bond Indexation... 

Considering the example shown in Table A1 of a hypothetical bond with coupons and principal linked to the inflation. We assume a 5-year inflation-linked bond with a 2% annual coupon payment. The expected cash flows, coupons and principal, are discounted with a discount rate of 3%. The valuation is performed by the following steps. 

Z-spread The Z-spread or zero volatility spread calculates the yield spread of a corporate bond by taking a zero-coupon bond curve as benchmark. Conversely to other yield spreads, the Z-spread is constant. In fact, it is found as an iterative procedure, which is the yield spread required to get the equivalence between market price and the present value of all its cash flows. The Z-spread is given by Equation (8.2) ... 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

Let us now consider the following example. ABC pic has issued a 5-year convertible bond with a market price of 112.2 and an underlying share with a market price of 0.65. The bond has also a coupon of 5.5%, while the dividend yield of the underlying stock is 2%. If an investor buys just 1 00 and the bond may be converted into 1 51.7 shares, the premium over a direct purchase of the ordinary shares expressed in basis points is equal to (112.2 - 98.6) or 1 3.6 per bond, in which 98.6 is obtained by multiplying the conversion ratio of 151.7 by the current stock price of 0.65. The compensation for this premium is the cash flow differential between the convertible and underlying shares, which is calculated as ( 1 00 x 5.5%) -(98.6 x 2%) or 3.5. The payback period measure is 13.6/3.5 or 3.86 years and the concept is similar to payback period used in corporate finance analysis. 

Determining the Value of an Option-Free Bond The fair value of an option-free bond is the sum of the present values of aU its cash flows in terms of coupon payments and principal repayment. The bond value is given by Equation (9.5) ... 

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

Yield to call This method calculates the yield for the next available call date. The yield to call is determined assuming the coupon payment until the call date and the principal repayment at the call date. For instance, the yield to first call is the rate of return calculated assuming cash flow payments until first call date. When interest rates are less than the ones at issue, the yield to call is useful because most probably the bond will be called at next call date ... 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

To calculate the value of these bonds, it is preferable to use the binomial tree model. The value of a straight bond is determined as the present values of expected cash flows in terms of coupon payments and principal repayment. For bonds with embedded options, since the main variable that drives their values is the interest rate, the binomial tree is the most suitable pricing model. 

It is important for a zero-coupon yield curve to be constructed as accurately as possible. This because the curve is used in the valuation of a wide range of instruments, not only conventional cash market coupon bonds, which we can value using the appropriate spot rate for each cash flow, but other interest-rate products such as swaps. 

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... 

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). 

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. 

An index-linked bond has its coupon or maturity value or sometimes both linked to a specific index. When governments issue index-linked bonds, the cash flows are linked to a price index such as consumer or commodity prices. Corporations have also issued index-linked bonds that are connected to either an inflation index or a stock market index. For example, Kredit Fuer Wiederaufbau, a special purpose bank in Denmark, issued a floating-rate note in March 2003 whose coupon rate will be linked to the Eurozone CPI (excluding tobacco) beginning in September 2004. Inflation-indexed bonds are detailed in Chapter 8. 

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. 

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