Redemptions payments

Revolutionary legislation in France, rather than abolishing tithes outright, attempted to phase them out with temporary tithe redemption payments. Popular defiance was so massive and intractable that the payments were finally abandoned. See James C. Scott, Resistance Without Protest and Without Organization Peasant Opposition to the Islamic Zakat and the Christian Tithe, Comparative Study in Society and History 29, no. 3 (1987) 417-52. 

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 ... 

A conventional bond s cash flows are the interest payments or coupons that are paid during the life of the bond, together with the final redemption payment. It is possible to determine the cash flows with certainty only for conventional bonds of a fixed maturity. So for example, we do not know with certainty what the cash flows are for bonds that have embedded options and can be redeemed early. 

Collecting funds from the issuer and paying these out to investors as coupon and redemption payments. 

The first bond in figure 1.2 matures in precisely six months. Its final cash flow will be 103.50, comprising the final coupon payment of 3-50 and the redemption payment of 100. The price, or present value, of this bond is 101.65- Using this, the six-month discount factor may be calculated as follows ... 

The fair price of a bond is the sum of the present values of all its cash flows, including both the coupon payments and the redemption payment. The price of a conventional bond that pays annual coupons can therefore be represented by formula (1.12). 

A bond paying a semiannual coupon has a dirty price of 98.50, an annual coupon of 3 percent, and exactly one year before maturity. The bond therefore has three remaining cash flows two coupon payments of 1.50 each and a redemption payment of 100. Plugging these values into equation (1.20) gives... 

It is possible to shorten the procedure of computing Macaulay duration longhand, by rearranging the bond-price formula (2.1) as shown in (2.10), which, as explained in chapter 1, calculates price as the sum of the present values of its coupons and its redemption payment. The same assumptions apply as for (2.1). 

Up to this point the discussion has involved plain vanilla bonds. But duration applies to all bonds, even those that have no conventional maturity date, the so-called perpetual, or irredeemable, bonds (also known as annuity bonds), which pay out interest for an indefinite period. Since these make no redemption payment, the second term on the right side of the duration equation disappears, and since coupon payments can stretch on indefinitely, n approaches infinity. The result is equation (2.12), for Macaulay duration. 

The majority of bonds in the market are coupon bonds. As noted above, such bonds may be viewed as packages of individual strips. The strips corresponding to the coupon payments have face values that equal percentages of the nominal value of the bond itself, with successively longer maturity dates the strip corresponding to the final redemption payment has the face value and maturity date of the bond. 

Credit-linked notes are hybrid securities, generally issued by an investment-grade entity, that combine a credit derivative with a vanilla bond. Like a vanilla bond, a standard CLN has a fixed maturity structure and pays regular coupons. Unlike bonds, all CLNs, standard or not, link then-returns to an underlying asset s credit-related performance, as well as to the performance of the issuing entity. The issuer, for instance, is usually permitted to decrease the principal amount if a credit event occurs. Say a credit card issuer wants to fond its credit card loan portfolio by issuing debt. To reduce its credit risk, it floats a 2-year credit-linked note. The note has a face value of 100 and pays a coupon of 7.50 percent, which is 200 basis points above the 2-year benchmark. If more than 10 percent of its cardholders are delinquent in making payments, however, the note s redemption payment will be reduced to 85 for every 100 of face value. The credit card issuer has in effect purchased a credit option that lowers its liability should it suffer a specified credit event—in this case, an above-expected incidence of bad debts. 

Figure 11.2 is a one-period binomial interest rate tree, or lattice, for the six-month interest rate. From this lattice, the prices of six-month and 1-year zero-coupon bonds can be calculated. As discussed in chapter 3, the current price of a bond is equal to the sum of the present values of its future cash flows. The six-month bond has only one future cash flow its redemption payment at face value, or 100. The discount rate to derive the present value of this cash flow is the six-month rate in effect at point 0. This is known to be 5 percent, so the current six-month zero-coupon bond price is 100/(1 + [0.05/2]), or 97.56098. The price tree for the six-month zero-coupon bond is shown in FIGURE 11.3. 

Deriving the one-year bonds price at period 0 is straightforward. Once again, there is only one future cash flow— the period 2 redemption payment at face value, or 100—and one possible discount rate the one-year interest rate at period 0, or 5.15 percent. Accordingly, the price of the one-year zero-coupon bond at point 0 is 100/(1 + [0.0515/2] ), or 95 0423-At period 1, when the same bond is a six-month piece of paper, it has two possible prices, as shown in figure 11.4, which correspond to the two possible sbc-month rates at the time 5.50 and 5.01 percent. Since each interest rate, and so each price, has a 50 percent probability of occurring, the avert e, or expected value, of the one-year bond at period 1 is [(0.5 x 97.3236) + (0.5 x 97.5562)], or 97.4399. 

Certain countries have markets in bonds whose coupon or final redemption payment, or both, are linked to their consumer price indexes. Generally, the most liquid markets in these inflation-indexed, or index-linked, debt instruments are the ones for government issues. Investors experiences with the bonds differ, since the securities were introduced at different times in different markets and so are designed differently. In some markets, for instance, only the coupon payment, and not the redemption value, is index-linked. This makes comparisons in terms of factors such as yield difficult and has in the past hindered arbitrageurs seeking to exploit real yield differences. This chapter highlights the basic concepts behind indexed bonds and how their structures may differ from market to market. 

Current pt. Current-pay bonds have been issued in Turkey. They are similar to interest-indexed bonds in that their redemption payments at maturity are not adjusted for inflation. They differ, however, in their term cash flows. Current-pay bonds pay an inflation-adjusted coupon plus an indexed amount that is related to the principal. In effect, they are inflation-indexed floating-rate notes. 

TIPS periodic coupon payments and their final redemption payments are both calculated using an inflation adjustment. Known as the inflation compensation, or IC, this is defined as in expression (12.2). 

EXAMPLE TIPS Coupon and Redemption Payment Calculation ... 

FIGURE 17.15 shows the cash flow for the Treasury s principal strip. Its yield is 4.0751 percent, corresponding to a price of 67.10027 per 100 nominal, which represents a spread above the gross redemption yield of the coupon Treasury. This relationship is expected, given a positive yield curve. There is only one cash flow the redemption payment, which equals 1 million for a holding of 1 million nominal. The principal strip s convexity is higher than the coupon bond s, as is its duration, again as expected. 

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