Bonds prepayment

As noted, a bond may contain an embedded option which permits the issuer to call or retire all or part of the issue before the maturity date. The bondholder, in effect, is the writer of the call option. From the bondholder s perspective, there are three disadvantages of the embedded call option. First, relative to bond that is option-free, the call option introduces uncertainty into the cash flow pattern. Second, since the issuer is more likely to call the bond when interest rates have fallen, if the bond is called, then the bondholder must reinvest the proceeds received at the lower interest rates. Third, a callable bond s upside potential is reduced because the bond price will not rise above the price at which the issuer can call the bond. Collectively, these three disadvantages are referred to as call risk. MBS and ABS that are securitized by loans where the borrower has the option to prepay are exposed to similar risks. This is called prepayment risk, which is discussed in Chapter 11. 

The two most common types of embedded options are call (or prepay) options and put options. As interest rates in the market decline, the issuer may call or prepay the debt obligation prior to the scheduled principal repayment date. The other type of option is a put option. This option gives the investor the right to require the issuer to purchase the bond at a specified price. Below we will examine the price/yield relationship for bonds with both types of embedded options (calls and puts) and implications for price volatility. 

In the discussion below, we will refer to a bond that may be called or is prepayable as a callable bond. Exhibit 4.16 shows the price/yield relationship for an option-free bond and a callable bond. The convex curve given by a-a" is the price/yield relationship for an option-free bond. The unusual shaped curve denoted by a-b in the exhibit is the price/yield relationship for the callable bond. 

This discussion covers the main factors affecting bond returns in the European fixed income market, namely, the random fluctuations of interest rates and bond yield spreads, the risk of an obligor defaulting on its debt, or issuer-specific risk, and currency risk. There are also other, more subtle sources of risk. Some bonds such as mortgage-backed and asset-backed securities are exposed to prepayment risk, but such instruments still represent a small fraction of the total outstanding European debt. Bonds with embedded options are exposed to volatility risk. However, it is not apparent that this risk is significant outside derivatives markets. 

Some lending institutions penalize borrowers who retire their loans early. In the United States, prepayment penalties are levied only for commercial mortgages, not for residential ones (both are penalized in the United Kingdom). Residential lenders, therefore, cannot be certain of the cash flows they will receive. This is known as prepayment risk. The uncertainty of mortgages cash flows, and the risk associated with it, is passed on to the securities backed by the loans. In this way, an MBS is similar to a callable bond, with the call exercisable at the discretion of the borrowers, and, as will be explained later, it can be valued using a similar pricing model. 

As already noted, the exact term of a mortgage-backed bond cannot be stated with assurance at the time of issue, because of the uncertainty connected with the speed of mortgage prepayments. As a result, it is not possible to analyze these bonds using the same methods as for fixed-coupon bonds. The most common approach is to assume a fixed prepayment rate—recognizing that, in reality, it will fluctuate with changes in mortgage rates and the economic cycle—and use this to project the bond s cash flows and thus its life span. The prepayment rate selected obviously is very important. This section considers some of the ways the rate is arrived at. 

The convention is to estimate CPR using the prepayment standard developed by the Public Securities Association, or PSA, the domestic bond market trade association now named the Bond Market Association. The PSA benchmark—100 percent PSA—assumes a starting prepayment rate... 

Using a projected prepayment rate enables analysts to evaluate mortgage-backed bonds. The original PSA benchmarks were based on the observation that prepayment rates tend to stabilize after the first thirty months of a mortgage and assumed a linear increase in these rates. They do not reflect seasonal variations in prepayment patterns nor the different behavior patterns of different types of mortgages. 

PACs exhibit lower price volatility than other mortgage securities. When the prepayment rates are within the PAC band, their prices are fairly stable when rates move outside the band, volatility increases by a smaller amount than for non-PAC bonds, because the prepayment risk is transferred to the companions. For this reason, PAC issues trade at lower spreads to the Treasury yield curve than do other issues with similar maturities. The companion bonds are always priced at a wider spread than the PACs, reflecting their higher prepayment risk. 

Within the CMO structure may be some PAC bonds with less prepayment risk than others, known as Type //and Type ///PACs. A Type II PAC has a narrower band than a standard PAC, thus reducing prepayment risk. If prepayment rates remain within their narrower bands. Type II PACs trade like standard PACs if rates move outside their bands, the extra cash flow is redirected to the companions only if the rates move above the range. Otherwise, there is no excess and the companion amortization is delayed. Type II PACs are second in priority to the standard PACs and so trade at a higher yield. If prepayment rates remain high for an extended period and all the companions are redeemed, the Type II PACs take over the function of companion and, with it, the higher prepayment risk. Type III PACs function like Type II PACs, but their band ranges are even tighter. 

The prepayment rate lies above the band. If this continues, the number of companions available to receive faster prepayments will fall, and the band will narrow, its upper and lower limits converging completely when all the companion bonds have been redeemed. At that point, the PAC will trade as a conventional sequential-pay security until it is redeemed. 

The prepayment rate lies below the band. The upper limit will drift upward, because more companion bonds are available to receive a greater level of prepayments in the future the lower band may also rise by a small amount. This type of drift is relatively rare, however, since PACs have the highest priority of all classes in a CMO stmcture until the payment schedule is back on track. 

Targeted amortization class, or TAG, bonds were created to cater to investors who require prepayment protection but at a higher yield than would be available with a PAC. Essentially, a TAG is a PAC whose band consists of only one standard prepayment rate. Like PACs, TACs amortize principal according to a schedule when the actual prepayment rate accords with this standard and, when the rate moves above it, use the extra principal amounts to pay off companion bonds. They differ from PACs mainly in taking on extra prepayment risk when prepayments fall below the rate required to maintain the payment schedule, extending the issues average life. Because one element of the PAC band is removed, TACs trade at a higher yield. 

In a conventional sequential-pay structure, the other classes in the CMO receive some of their principal prepayments from the Z bond, which lowers their average-life volatility. Z bonds are an alternative for investors who might otherwise purchase Treasury zero-coupon bonds. Like zero coupons, these bonds have no reinvestment risk, but they have higher yields than Treasury strips with similar average lives. 

The PO bond is similar to a zero-coupon in that it is issued at a discount to par value. The PO bondholders return is a function of the rapidity at which prepayments are made the quicker the prepayment, the higher the return. This is like the buyer of a zero-coupon bond receiving the maturity payment ahead of the redemption date. The highest possible return for the bondholder would occur if all the mortgages were prepaid the instant after the PO bond was bought. A low return occurs if all the mortgages are held until maturity, so that there are no prepayments. 

The price of a PO bond fluctuates with mortgage interest rates. As noted earlier, the majority of mortgages are fixed-rate loans. If mortgage rates fall below the PO bond s coupon rate, the volume of prepayments should increase as the individuals holding the underlying loans refinance them, speeding the stream of payments to the bondholder. The PO s price will rise both because of the faster cash flows and because the flows are now discounted at a lower rate. The opposite happens when mortgage rates rise. 

An lO bond has no par value, since it is essentially just a stream of cash flows, consisting of the interest payments on the underlying mortgage principal outstanding. These cash flows cease once the principal is redeemed, so a higher rate of prepayment depresses the lO price. The risk for investors is that prepayments occur so quickly that they don t receive enough interest payments to cover what they paid for their bond. 

Senior/subordinated structures are the most common type of internal credit enhancement encountered in the market. Essentially, the CMO is divided into two classes of bonds, one senior and the other subordinated. The latter absorbs all the losses arising from default or other cause, leaving the senior class unaffected. The subordinated bonds clearly have higher risk than the senior class and so trade at a higher yield. Most senior/ subordinated arrangements incorporate a shifting interest structure, which redirects prepayments from the subordinated to the senior class. This alters the cash flow characteristics of the senior notes, whether or not defaults or similar events occur. 

As explained in chapter 2, a bond s modified or Macaulay s duration is the average time to receipt of its cash flows, weighted according to their present values. To compute a mortgage-backed bond s duration, it is necessary to project its cash flows using an assumed prepayment rate. These projections, together with the bond price and the periodic interest rate, derived from the yield, may then be used to arrive at the bond s periodic duration, which is divided by twelve (or four, in the case of a bond that pays quarterly) to arrive at its duration in years. 

There are a number of ways to calculate the yield on a mortgage-backed bond. One of the most common is the static cash flow model. This assumes a single prepayment rate to estimate the cash flows for the bond and does not take into account how changes in market conditions might affect the prepayment pattern. 

Cash flow yield calculated in this way is essentially a redemption yield calculated assuming a prepayment rate to project the cash flows. As such, it has the same drawbacks as the redemption yield for a plain vanilla bond it assumes that all the cash flows will be reinvested at the same interest rate and that the bond will be held to maturity. In fact, the potential inaccuracy is even greater for a mortgage-backed bond because the frequency of interest payments is higher, which makes the reinvestment risk greater. The final yield of a mortgage-backed bond depends on the performance of the mortgages in the pool—specifically, their prepayment pattern. 

The cash flows of lO and PO bonds are dependent on the cash flows of the underlying pass-through security, which is itself dependent on the cash flows of the underlying mortgage pool. To calculate the prices of these strips, their cash flows must be estimated using a prepayment rate. The price of an lO is the present value of the projected interest payments the price of the PO is the present values of the projected principal payments, comprising the scheduled principal payments and the projected principal prepayments. 

The prepayment option of the holders of mortgages underlying a mortgage security is essentially a call option. Not surprisingly, then, mortgage securities often behave like callable bonds. 

The optionality of a mortgage-backed bond, and the volatility of its yield, frequently have a negative impact on the bondholders. This is for two reasons the actual yield realized during the holding period has a high probability of being lower than the anticipated yield, which was calculated on the basis of an assumed prepayment level, and mortgages are frequently prepaid when the bondholders will suffer the most—that... 

Because OAS analysis takes into account a mortgage-backed bond s option feature, it is less affected by a change in interest rates or the yield curve, which affect prepayments, than the bond s yield spread. Assuming a flat yield curve, the relationship between the OAS and the yield spread is expressed in equation (14.18). 

This relationship can be observed when yield spreads on current-coupon mortgages widen during declines in interest rates. As the possibility of prepayment increases, the cost of the bonds option feature rises put another way, the option feature gets closer to being in the money. To adjust for the increased value of the option, traders price higher spreads into the bond, which keeps the OAS more or less unchanged. 

The modified duration of a bond measures its price sensitivity to a change in yield. It is essentially a snapshot of one point in time. It assumes that no change in expected cash flows will result from a change in market interest rates and is thus inappropriate as a measure of the interest rate risk borne by a mortgage-backed bond, whose cash flows are affected by rate changes because of the prepayment effect. 

The first component can be estimated by assuming a prepayment rate during the holding period the second entails assuming a reinvestment rate. For the third, two assumptions are necessary one concerning the bond s bond-equivalent yield at the end of the holding period, and another about the prepayment rate projected by the market at this point, which is a function of the projected yield. 

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