Optional redemption

The optional redemption featnres of the master trust transactions are essentially the same as those for a pass-through transaction. The issuer typically has the option to call the notes for any of the following circumstances ... 

The legal maturity of the deal is 99 years, but due to the optional redemptions described below, the deal is expected to be terminated in about 12 years. 

The Senior Notes shall be redeemed (in whole but not in part) by the Issuer at the direction of the holders of more than 50% of the aggregate principal amount outstanding as at the Final Closing Date of the Junior Notes. Any such redemption is subject to the following conditions (a) no such redemption may occur on any date other than an Interest Payment Date (b) other than as a result of the occurrence of certain tax events, no such redemption may occur prior to the end of the Reinvestment Period and (c) no optional redemption of the Senior Notes may occur unless there are sufficient proceeds to repay all the Senior Notes and any accrued and unpaid fees and expenses. 

This feature can be assimilated as an embedded put option by which the investor will receive the par value, in the case of deflation, or the redemption value linked to the inflation. The payoff is given by Equation (6.16) ... 

Bonds with embedded options are debt instruments that give the right to redeem the bond before maturity. As we know, the yield to maturity represents the key measure of bond s return (although, of course, it is an anticipated return that is seldom realised in practice). The calculation of the return is particularly easy for conventional bonds because the redemption date is known with certainty, as their value. In contrast, for callable bonds, but also for other bonds such as putable and sinking fund bonds, the redemption date is not known with certainty because the bonds can be redeemed before maturity. If we want to calculate... 

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. 

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. 

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. 

The yield calculation for conventional bonds is relatively straightforward. This is because their redemption dates are fixed, so their total cash flows—the data required to calculate yield to maturity— are known with certainty. Less straightforward to analyze are bonds with embedded options—calls, puts, or sinking funds—so called because the option element cannot be separated from the bond itself The difficulty in analyzing these bonds lies in the fact that some aspects of their cash flows, such as the timing or value of their future payments, are uncertain. 

If a bond s actual redemption date differs from the assumed one, its return computed this way is meaningless. The market, therefore, prefers to use other methods to calculate the return of callable bonds. The most common method is option-adjusted spread, or OAS, analysis. Although the discussion in this chapter centers on callable bonds, the principles enunciated apply to all bonds with embedded options. 

A bond with early redemption provisions is essentially a portfolio consisting of a conventional bond having the same coupon and maturity and a put or call option on this bond. The value of the bond is the sum of the values of these portfolio elements. This is expressed formally as (11.1). 

If the issuer of a callable bond is entitled to call it at any time after the first call date, the bondholder has effectively sold the issuer an American call option. However, as figure 11.1 illustrates, the redemption value may vary with the call date. This is because the value of the underlying bond at the time the call is exercised is composed of the sum of the present values of the remaining coupon payments that the bondholder would have received had the issue not been called. Of course, the embedded option does not trade on its own. Nevertheless, it is clear that embedded options influence significantly not only a bonds behavior but its valuation as well. 

The market quotes bonds with embedded options in terms of yield spreads. A cheap bond trades at a high spread, a dear one at a low spread. The usual convention is to quote the spread between the redemption yield of the bond being analyzed and that of a government bond having an equivalent maturity. This is not an accurate measure of the actual difference in value between the two bonds, however. The reason is that, as explained in chapter 1, the redemption yield computation unrealistically discounts all a bond s cash flows at a single rate. 

To calculate the modified duration of a bond with an embedded option, the bondholder must assume a fixed maturity date based on the bond s current price. When it is unclear what redemption date to use, modified duration may be calculated to both the first call date and the final maturity date. This is an unsatisfactory compromise, however, since neither date, and so neither measure, may be appropriate. The problem is more acute for bonds that are continuously callable or putable from the first call or put date until maturity. 

The modified duration and convexity methods we have described are only suitable for use in the analysis of conventional fixed-income instruments with known fixed cash flows and maturity dates. They are not satisfactory for use with bonds that contain embedded options such as callable bonds or instruments with unknown final redemption dates such as mortgage-backed bonds. For these and other bonds that exhibit uncertainties in their cash flow pattern and redemption date, so-called option-adjusted measures are used. The most common of these is option-adjusted spread (OAS) and option-adjusted duration (OAD). The techniques were developed to allow for the uncertain cash flow structure of non-vanilla fixed-income instruments, and model the effect of the option element of such bonds. 

The option element in a convertible cannot be stripped out of the bond element, and so is termed an embedded option. The valuation of the bond takes into account this embedded optionality. Note also that unlike a straight equity option, there is no additional payment to make on conversion the holder simply exchanges the bond for the specified number of shares. One could view the price paid for exercising the option as being the loss of the bond element, which is the regular coupon and redemption proceeds on maturity, but this should be viewed as more of an opportunity cost rather than a payment. This bond element is often referred to as the bond floor, which is the straight debt element of the convertible. The bond floor can be viewed as the level at which a vanilla bond issued by the same company would trade, that is, its yield and price. It generally accounts for between 50 percent and 80 percent of the total value. 

Some convertibles are callable by the issuer, under prespecified conditions. These are known as convertible calk and remove one of the advantages of the straight convertible—that conversion is at the discretion of the bondholder—because by calling a bond the issuer is able to force conversion, on terms potentially unfavorable to the investor. There are two types of call option. Hardcall is nonconditional while soficall is conditional. If a bond is hardcall protected for any time after issue, then the issuer may not early-redeem the bond. During softcall protection, early redemption is possible under certain conditions, normally that the underlying share price must trade above a certain level for a specific period. This level is usually around 130 percent of the conversion price. 

Investors rarely convert voluntarily. They may during an event such as a call or a tender offer, or if the share price has risen by a considerable amount. The main reason why early redemption is not generally in the investors interest is because it will erode the time value of the option element, as well as remove the yield advantage of holding the convertible. It also removes the downside protection afforded by the bond. That is... 

The convertible price accounts for both the conventional bond element and the embedded option element. If we assume the share price in period t< is 97.01, then in period 6o the share can assume only one of two possible values, 106.25 or 92.24 (see Figure 13.6). In these cases, the value of the call option Ch and Cl will be equal to the higher of the bonds conversion value or its redemption value, which is 106.25 if there is a rise in the price of the underlying or 102.50 if there is a fall in the price of the underlying. This is the range of possible final values for the bond however, we require the current (present) value, so we discount this at the appropriate rate. 

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