In this piece, we address the critical issues related to why and how prepayments impact the performance of, and risks associated with, mortgage-backed securities.

Traders looking to value and hedge MBS use prepayment speeds that are either generated directly from historical experience or through a forward-looking model. Many applications in Eikon allow users to specify either historical prepayment speeds or modeled speeds obtained from different 3rd party financial libraries.

Many traders like to use historical prepayment speeds as their benchmark, since they are easily obtained and ostensibly free from modeling biases. Historical prepayment data can be obtained for an individual pool or security, for the issuance vintage (e.g., 2015 Fannie 3.5s), or for the coupon in aggregate. Others will look to utilize prepayment projections generated by econometric models (which, of course, utilize historical experience as a primary input). Model-generated speeds have the advantages of both being forward-looking and allowing the user to take different rate scenarios into account. However, since there are no industry-wide models or methodologies, the output from different models can vary widely.

Given the dispersion of model results, one useful feature in Eikon is the inclusion of the MIAC “Mortgage Industry Medians” (MIMs) survey as an option. The survey uses prepayment model projections from a variety of sources and generates consensus speeds in both the base case (i.e., an unchanged rates regime) as well as under various interest rate scenarios. The consensus speeds are reported as both CPRs and PSAs, and are available as the “survey” prepayment source in a number of applications, including the MBS Analysis and Basis Monitor apps.

**Prepayment Speeds and MBS Yields**

By definition, the yield on any fixed-income security represents the discount rate that equates the present value of all cash flows with the security’s market value. By implication, calculating a bond’s yield involves generating its expected principal and interest cash flows. For callable instruments such as corporate and municipal bonds (so-called “bullet” securities where principal is paid at maturity) yields are calculated by assuming the issue is called at different points of time (e.g., the most likely time or the most inopportune time) as well as at maturity. Mortgage-backed securities are unique, however, both because the underlying instruments (mortgages) are designed to amortize over time (rather than pay a lump sum at maturity) and the call decisions are dispersed among the numerous individuals whose mortgages comprise the MBS pools.

This has a number of implications. The expected yields and returns on MBS can’t be calculated unless some prepayment function is first utilized to generate the expected cash flows. By implication, changing prepayment expectations have a material impact on projected returns, and realized returns on MBS are in turn highly dependent on the actual prepayments experienced on a security or portfolio. Finally, the risks associated with MBS are directly related to both the expected level of prepayments as well as changes in prepayment expectations resulting from fluctuating interest rates.

The impact of prepayments on the yield of an MBS depends on its market price. Faster prepayments reduce the yield on premium MBS in the same fashion as the early call of a premium bullet bond. In both cases, cash flows for which the investor paid a premium are returned at par value, and must be reinvested at lower interest rates. However, faster prepayments increase the yield on discount securities; principal valued below parity are returned at face value and can be reinvested at (higher) current market rates.

This concept can be better understood by examining the impact of changing prepayment rates(whether a one-time call or faster prepayments) on the principal and interest components of bond cash flows. A few simple examples will illustrate the concepts. First imagine an investor that was due a lump-sum payment in 10 years instead receives his/her invested principal back immediately; the investor garners a windfall profit, receiving cashflows back at face value that previously had a present value much less than par. This is comparable to the early call of the principal portion of a bond’s cash flows. Alternatively, a retiree who bought a 20-year annuity that can only make payments for five years would suffer a significant loss on the investment, and is analogous to the impact of an early call or calls on a bond’s interest component.

** ** Prepayments and MBS Interest Rate Risk

In addition to their impact on value, changing prepayment speeds alter the interest rate risks associated with MBS. The interest rate risk for non-callable bonds (i.e., their “durations,” discussed below) is roughly linear, meaning that the relationship between a change in interest rate and the bonds’ values is fairly constant irrespective of the level of rates. This makes hedging them relatively easy and inexpensive. By contrast, the ability of mortgagors to prepay their loans is an option which collectively makes the risk profile of the resulting MBS curved or non-linear, and always works against the interest of the bondholder.

To understand this, first consider a rising rate environment where prepayment speeds are slowing. Slower prepayments always result in MBS that are longer in average life and duration, which means that the investors’ portfolios are getting longer or “extending” at exactly the time when rational investment managers would look to reduce their exposure to interest rates. Alternatively, when interest rates decline homeowners look to refinance mortgages carrying above-market note rates, which shorten the loans and securities; unfortunately, this occurs at precisely the time that investment managers seek to extend their portfolios and gain greater exposure to falling rates. These behaviors result in a price profile that, unlike that of the bullet bond, has a distinct curvature, and is illustrated in the accompanying hypothetical chart. While the price of the bullet bond moves monotonically with changes in rates, the prices for the MBS lag the bullet when rates move in either direction. This behavior of MBS and other callable bonds is called “negative convexity.”

A brief digression to explore the meaning of a few terms will be helpful here. The terms “duration” and “convexity” refer to the sensitivity of a bond’s price to a change in market yields. Duration is the first-order effect, and is defined as the percentage change in price given some change in yield. It is analogous to the physical concept of speed, defined as the distance covered over some defined period of time (measured, for example, as miles per hour or feet per second). Convexity is a second-order effect and represents the degree of curvature of the price/yield function at any particular level of rates. It is comparable in the physical world to acceleration, which is the rate of change *of* the rate of change (measured as feet per second per second). Mortgages are “negatively convex,” meaning that their price change are projected to underperform their duration; the price of the security will either rise less, or decline more, than implied by the duration at any given rate level.

Taken together, duration and convexity allow traders and investors to both estimate how different securities will perform given changes in rates and accurately lay off their exposure through hedging. However, the convexity associated with MBS means durations and hedge ratios adjust as market rates change. As a result, hedged positions must be continually monitored and adjusted to account for the changes in duration resulting from varying prepayment speeds. Note that this phenomenon is not limited to MBS; any class of securities that contain embedded options will exhibit comparable behavior. What makes MBS unique is the difficulty and uncertainty involved in projecting prepayment speeds. While callable bond deals are managed by informed and rational managers with one clear objective (i.e., obtain the lowest cost of funds), individual homeowners make prepayment decisions based on a range of personal and financial considerations. Anticipating the decisions of thousands of individual “managers” creates unique challenges for prepayment modelers and results in significant variations in the output of different models.

**MBS Price Movements and Prepayments**

A few concepts can be clarified at this juncture. While fast prepayments always impair the value of premium securities, they don’t necessarily result in negative convexity for MBS; it’s not prepayment speeds themselves but rather *changes* in speeds, and the sensitivity of prepayments to interest rates, that cause the non-linearity of their durations and result in higher hedging costs. A security that exhibits fast but predictable prepayment speeds is much easier to hedge than one with highly variable and rate-dependent speeds.

In addition, while powerful and useful to investors, duration and convexity only explain some of the changes in bond prices. Other factors such as spreads and volatility also impact MBS prices, the latter due to the embedded refinancing option held by virtually all borrowers. As a result, price changes for MBS that are attributed to negative convexity may be caused by other factors. For example, premium MBS often underperform their hedge ratios when rates decline. In many cases, negative convexity only contributes to the underperformance, with a larger factor being simple “spread widening” representing investors’ reluctance to pay increasingly high premiums that can be eroded by a few months of very fast prints. Conversely, MBS prices have historically underperformed in major selloffs. The most glaring example of this behavior took place in 1994, when the Fed surprised the market with a series of increases in financing rates. Investors arguably overreacted to a few months of unexpectedly slow prints by pricing MBS using extremely conservative prepayment assumptions that were much slower than those generated by valuation and risk models. As a result, virtually all MBS dramatically underperformed their hedge ratios and widened in spread, even as models were calculating progressively longer durations.

**Valuing a Prepayment Advantage**

MBS investors and traders use a variety of methods to calculate the incremental value of an enhanced prepayment profile. The simplest way is to calculate the price of a security at a given yield or spread using a different prepayment speed. Let’s use as an example an originator selling a Fannie 3.5% pool that is expected to prepay about 25% slower than the aggregate over its life. The one-month speed for the aggregate coupon (i.e., the speed for all Fannie 3.5s ever issued) is right around 22% CPR, which for TBAs trading at 104-28 equates to roughly a 2.05% yield. The price of the MBS generated at the same yield run but calculated at 16% CPR, however, is greater than 106-16, a significant increase in value.

However, it’s unlikely that an investor would pay the full amount of the price difference calculated in this fashion for a number of reasons. One is that the slower speed increases the pool’s average life and duration; the WAL of the pool at 16% CPR is 5.1 years versus 3.8 years at 22% CPR speed. Since the Treasury yield curve typically slopes upward (i.e., rates increase with maturity), assuming a longer average life given some yield results in a tighter spread to the Treasury curve. Investors will typically account for this by pricing to a constant (or, sometimes wider) spread over the Treasury curve, which implies a higher yield if all else remains constant. Nonetheless, the pool is certainly worth more than generic issuance (i.e., that would be delivered in TBAs) based on this relatively straightforward analysis.

Sophisticated investors often gauge incremental value by using an Option Adjusted Spread (OAS) framework. While the analytics are quite elaborate, the model generates and values the security’s cash flows over a range of interest rate scenarios. The results are reported as a single spread over the entire yield curve, and take into account factors such as the shape of the yield curve, the security’s refinancing response (i.e., the shape of the S-curve), the timing of the different cash flows, and the expectations for volatility in the market. The incremental value is often generated by first running the OAS for a generic security, and then using that spread as an input to calculate a revised price on the MBS in question.

An alternative way of assessing relative value is to calculate how much the slower speed is worth in incremental carry over some horizon period. The roll calculator contained in the MBS Basis Monitor is useful for this purpose. The break-even drop for the Fannie 3.5% roll for good-day November to December 2016 is currently 4/32s, using 1-month LIBOR as a funding cost and 22% CPR as the speed. Brand-new pools, however, don’t generally prepay at all for the first two months, as discussed below. As shown in the accompanying display, inputting 0 as the CPR results in a calculated break-even value of 7 3/8 ticks, or about 3 ticks per month of incremental carry. Therefore, if investors expected zero prepayments over the first two months of the pool’s life, they might be willing to pay up 6/32s or more for the pool, all else the same.