Mortgage-backed securities (MBS), while attractive for a number of reasons, have some unique features which add risk when compared to plain vanilla bonds.

- MBS are collateralized by a pool of residential mortgages.
- Monthly payments "pass through" the originating bank on to a third-party investor.
- Besides monthly interest payments, mortgages amortize over their life, meaning some amount of principal is paid off with every monthly payment, unlike a bond, which generally pays all principal at maturity.
- In addition to scheduled amortizations, investors receive, on a pro-rata basis, unscheduled prepayments of principal due to refinancing, foreclosure and house sales. While a typical mortgage may have a term of 30 years, quite often mortgages are paid off much sooner. Because of these unscheduled prepayments, predicting the maturity of the MBS is problematic.

Focusing on the prepayment aspect of MBS, this article will introduce the concept of weighted average life (WAL), and explain its use in guarding against prepayment risk. (For background reading on MBS, see *Profit From Mortgage Debt With MBS* and *Asset Allocation Within Fixed Income*.)

**Weighted Average Life**A statistic that is commonly used as a measure of the effective maturity of a MBS is the WAL, sometimes called just "average life." To calculate the WAL, multiply the date (expressed as a fraction of years or months) of each payment by the percentage of total principal that is paid off at that date, then add up these results. Thus, the WAL registers the impact of principal paydowns over the lifetime of the security. The WAL can be visualized as a fulcrum on a timeline that runs from origination to the final maturity date. The fulcrum "balances" the principal payments, just like children of different weights balance a seesaw by having different positions on the bar. Figure 1 below depicts the WAL for a 30-year mortgage pool. (Read more about mortgage pools in

*Why Are Mortgage Rates Increasing?*)

Figure 1 |

Source: "The Duration of a Bond as a Price Elasticity and a Fulcrum" (1988) by Dr. David Smith |

**Yields on Mortgage-Backed Securities**MBS are marketable and can trade at premiums, discounts or par value, depending upon changes in current market rates. A current-coupon pass through trades at par value, while high-coupon pass throughs trade at premiums and low-coupon securities trade at discounts. The quoted yield is the internal rate of return, which equates the present value of all future cash flows with the current price of the security. Therefore, the quoted yield on a MBS is always conditional on a prepayment assumption. (Read

*An Inside Look At Internal Rate Of Return*for more on using this method of financial analysis.)

The prepayment assumption is crucial to mortgage pass-through securities. Investors know in advance that prepayment can and will occur, but do not know when and by how much. Those variables must be projected and assumed. Moreover, there is not a single, conservative assumption that can apply to all pass-throughs because of the asymmetric effect: there is an incentive to prepay more quickly on premium MBS, while the reverse is true for discount MBS. (Read more about prepayment in *Defeasance Reduces Commercial Real Estate Fees*.)

**Realized-Yield Asymmetry**The realized yield on a pass-through security is the yield that the purchaser actually receives while holding the security, based on the actual prepayments of principal, rather than on the assumed prepayments that were used to calculate the quoted yield. Prepayments that are faster or slower than expected affect premium and discount pass-throughs asymmetrically.

Suppose that the pass-through security is trading at a premium. Prepayments at par value result in cash flows that can only be reinvested at the lower, current rate. Consequently, faster-than-assumed prepayments deny the investor the high cash flows that justified the premium price in the first place. On the other hand, slower prepayments offer the investor more time to earn the higher coupon rate. Thus, slower prepayments raise the realized yield above the quoted yield, while faster prepayments lower the realized yield.

A discount pass-through benefits from faster-than-anticipated prepayments because those cash flows can be reinvested at par value in current-coupon securities. In effect, the investor can simply replace the low coupon for a higher one, since the prepayment is at par. Therefore, the realized yield will exceed the quoted yield. Just the reverse happens when prepayments are slower than expected. The investor is stuck with the lower coupons for a longer period of time, thereby reducing realized yield.

**The Prepayment Assumption**Over the years, a number of conventional specifications of assumed prepayment rates have been developed. Each has its advantages and disadvantages.

*Standard Mortgage Yield*The first and simplest specification is to assume the "standard mortgage yield" or "prepaid in 12." In this specification, it is assumed that there are no prepayments whatsoever until the twelfth year, when all the mortgages in the pool prepay in entirety.

This specification has the advantage of computational simplicity and conforms to the reality that the effective maturity of most mortgage pools is far shorter than the final maturity date. Beyond that, not much can be said for this assumption. It totally neglects the prepayments that occur in the early years of a mortgage pool; therefore, a yield calculated and quoted on the basis of this "standard" prepayment assumption seriously understates the potential yield on a pass-through security trading at a deep discount and overstates the potential yield on a premium pass-through.

*FHA Experience Method*At the other end of the spectrum, with respect to complexity and realism, is a prepayment specification based on actual experiences of the Federal Housing Authority (FHA). The FHA compiles historical data on the actual incidence of prepayment on the mortgage loans that it insures. This data covers a wide range of origination dates and coupon rates. (Read about FHA loans in

*Financing Basics For First-Time Homebuyers*.)

The FHA experience method was clearly an improvement over the standard mortgage yield, since it introduced realistic and historically validated assumptions, yet it is not without its own problems. Since the FHA publishes a new series almost every year, the secondary mortgage market faced the confusing circumstance of having securities based on series from different years. (Read more about the secondary mortgage market in *Behind The Scenes Of Your Mortgage*.)

*Constant Prepayment Rate*Another specification that has been used is the constant prepayment rate (CPR), also known as the "conditional prepayment rate." This specification assumes that the percentage of the principal balance that is prepaid during a given year is a constant.

The CPR method is easier to work with analytically than FHA experience, because the applicable prepayment rate for each year is one consistent number, not one of 30 varying numbers. Consequently, it is easier to compare quoted yields for a certain holding period across different prepayment assumptions. One subtle advantage to the CPR method is that it exposes the subjective nature of the prepayment assumption. The FHA experience approach implies a degree of precision that might be totally unwarranted.

A variant of the CPR is called "single monthly mortality" (SMM). The SMM is simply the monthly analogue to the annual CPR. It assumes that the percentage of the principal balance that is prepaid during a given month is a constant.

*PSA Standard Prepayment Model*

The most commonly used prepayment rate assumption is the standard prepayment experience offered by the Public Securities Association (PSA), an industry trade group. The PSA's goal was to bring standardization to the marketplace. The first 30 months of standard prepayment experience call for a steadily rising CPR, starting at zero and rising 0.2% each month; thereafter, a level 6% CPR is used. Sometimes, however, yields are based on a faster or slower prepayment assumption than this standard. This change in prepayment assumption is indicated by designating a percentage above or below 100%:

- An MBS quoted at 200% PSA assumes a 0.4% CPR monthly rise over the first 30 months, then a level CPR at 12%.
- An MBS quoted at 50% PSA assumes a 0.1% monthly increase in the CPR, until the 3% CPR level is attained.

**Conclusion**As discussed, using weighted average life involves assumptions and is far from precise. However, it helps investors make more realistic predictions on the yield and term of an MBS which helps reduce the inherent prepayment risk.