Mortgage Backed Securities PSA Model - PSA Prepayments

PSA Prepayment Model

The PSA is a numerical scale that is used to measure the rate of principal prepayments on MBSs and to make assumptions on the future rate of prepayments. The PSA assumes that homeowners tend to make very little prepayments in the first several months of homeownership, make a steadily increasing amount of prepayments each month out to twoand- a-half years, and (beyond 2.5 years) prepayments continue at a constant rate over the remaining life of the pool. Specifically, the basic PSA model assumes of 0.2% annual prepayment in month 1, 0.4% annual prepayment in month 2, 0.6% prepayment in month 3, etc. The model increases prepayments by 0.2% (annualized) each month out to 30 months, and then levels out at an annualized rate of 6% prepayment per year thereafter. Logically, this prepayment pattern makes sense. A new homebuyer has typically just spent a thousand dollars inclosing costs and down payment to buy their house. This new homeowner usually wants to spend some additional dollars on home improvements or new furniture etc. However, after being in their home several years, they may have gotten a promotion, or need more space, or found out they didn’t really like the neighborhood. So, the basic PSA model takes these tendencies into account. The PSA prepayments are expressed as a percentage of this base model.

If a MBS has principal prepayments each month dollar and penny for penny at exactly the same rate as the model, the MBS is said to be prepaying at a rate of 100% PSA. If the prepayment cash-flow are twice the amount of the base model, then prepayments would be at 200%PSA; if they are 10 times as fast, 1000% PSA, if only half as much, 50% PSA etc. If the homeowners do not make any prepayments, the collateral is said to be paying at 0% PSA.

FORECASTING PREPAYMENTS

Obviously, the PSA and CPR can be used to analyze actual prepayment history on a specific pool, but more importantly, the PSA and CPR are used to analyze projected future cash-flows, average live, maturity, and yield to evaluate a specific pool prior to purchase. In order to do this, an assumption of future prepayment activity must be made.

Opposed to simply guessing about future prepayments, there are three tangible sources of information that can be used to help formulate a prepayment assumption (forecast): Review the actual prepayment history of the MBS; review the prepayments histories of other similar MBSs; review the prepayments histories of other similar MBSs; review the forecasts of the mortgage securities experts on Wall Street ( this is often referred to as the “street assumption” or “Bloomberg Median”). These sources of prepayment history and forecasts are reviewed and then the investor applies his/her feeling about the direction of interest rates and mortgage rates, and therefore, the possibility of the homeowners wanting to refinance their mortgages. Then, a reasonable and supportable prepayment assumption can be made.

Step Up Bonds

A STEP-UP Agency debenture is a bond that has a fixed coupon rate for a period of time. It is then available to be “called” (redeemed @par) by the issuing Agency. If the note is not called, the coupon will then STEP-UP (adjust) to a new coupon rate. These various coupons and the amount of time between the step dates are established at the issuance and will not be changed over the life of the bond. (A Step-Up Bond is not considered a true floating rate security because the coupons are pre-determined at issuance and do not “float” against a market index).

Step Up Bond Example: FHLB STEP -UP: 12/31/2002-97

Opening coupon = 5.50% Callable: 12/31/97 (or anytime thereafter) Step coupon=7.00% Price @ issuance = PAR Yield to the call = 5.50% Yield to maturity=6.25% Keep in mind that each STEP-UP bond will have its own specific call features and coupon step-up features. Some recent issues have had multiple step-up dates with the coupon rate changing each year through maturity if he bond is not called. In any event, the best method of evaluation is to examine the effective yield to each available call date (taking into account the multiple coupons) and then comparing to alternative investments.

Dula Indexed Floater Bonds

A DUAL-INDEXED FLOATER is a floating rate Agency bond whose coupon is reset using a COMBINATION of two indexes, one subtracted from the other, and then adding some number of basis points. One is a long term index the other a short term index.

Example: coupon=(10 year Treasury Rate MINUS 1 month Libor)+250 Basis Points If the 10 year Treasury is 6% and 1 month Libor is 3% coupon= (6%-3%) + 2.50% = 5.50%

The key to a DUAL-INDEX floater is the basis point spread between the two indexes. In our above example, the difference between long term rates (the 10 year Treasury Rate) and short term rates (the 1 month Libor) is 3%. If the yield curve “flattens” and this spread “tightens” then the coupon on the floater will go down:

Example: 10 year CMT goes up to 7% and 1 month LIBOR goes up to 4.50% (long term rates up 100 Bps, and short term rates up 150 Bps) coupon = (7%-4.50%)+2.50%=5%

In this scenario, the general level of interest rates has gone up but the Dual-Indexed Floater’s coupon has gone down, because the yield curve has flattened. If the yield curve becomes more steep (the spread between the two indexes becomes greater), then the coupon on a Dual-Indexed Floater will go up. In effect, this floater’s coupon is a reflection of “steepness” of the yield curve more than a reflection of the general direction of interest rates. For this reason, DUAL-INDEXED Floaters are sometimes called Yield Curve Anticipation Notes (“YCANs”).

Inverse Floater Bonds

An INVERSE FLOATER Agency debenture is also a bond whose coupon rate will float with the market.

As the name implies, an Inverse Floater’s coupon moves in the opposite direction of the index. Simply put, if the general level of floating coupon is accomplished in one of two methods. First the coupon will be set by subtracting an index from a fixed rate:

Example: Coupon= (14%-1 mo. LIBOR) If the Libor rate is 3.00% coupon=14%-3%=11% If the Libor rate goes UP to 4% coupon=14%-4%=10%

As you can see the general level of interest rates is rising but the coupon on this Floater is going down, hence the name “Inverse Floater”. The other method of generating an Inverse Floater’s coupon is by multiplying an index against a negative # (called a negative multiplier) and adding some number of basis points. For example:

Example: coupon = (-1.5*1 mo. Libor) + 1500 Basis Points If the Libor rate is 3.00% coupon = (-1.5*3.00%)+15.00%=10.50% If the Libor rate goes UP to 4.00% coupon = (-1.5*4.00%)+15.00%=9.00%

Again, the general level of interest rates is rising but because of the negative multiplier, the coupon of the Inverse Floater’s interest rate is going down.

Government Agency Bonds

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A Primer on Bonds Valuation

If you follow the bond market, you can observe that prices of bonds are generally decreasing when the economic news are good and increasing when negative. An understanding of this typical valuation of bonds can explain the phenomena.

After reading this document, you will know how bonds are defined, valuated and traded. There are ts to bondholders makes bonds a good and safe investment: investors get fixed amounts of incomesfundamental factors that generate fluctuations in prices of bonds. knowing these factors leads to a better understanding of the underlying economic forces together with the valuation of bonds.

Main features of bonds

A bond is a negotiable debt security under which the issuer borrows a given amount of money, called the principal amount. In exchange, the borrower agrees to pay fixed amounts of interests, also called the coupons, during a specific period of time. Everything is well defined by the bond contract: the coupon rate is the interest rate that the issuer pays to the bondholder and the coupon dates are the dates on which the coupons are paid. Besides the issuer will repay the total amount of the principal when the bond will reach what is called maturity (or maturity date).

In short, a bond is a securitized loan.

First, we can mention the most relevant point that makes bond so attractive, especially in gloomy periods for stock markets. Indeed, the regular payments of interes and are repaid the principal value at maturity date. Bonds with maturity of one year or less are referred to as short-term bonds or debt.

Bonds with maturity of one year to ten years are referred to as intermediate bonds or intermediate notes. The long-term bonds are issued with a maturity of at least ten years and commonly up to 30 years.

A second important aspect is that all characteristics of bond are well defined in advance and the market offers different choices for each of them: coupon rate (also called coupon yield), coupon date, maturity date can vary from one bond to another but are known when investing into the given bond. It allows the investor to fit its investment strategy with its risk and return acceptable levels.

Let consider the following example: for a bond with a principal value of 1000$, a yearly coupon rate of 5% and a maturity of 2 years. As the yearly coupon rate is 5%, the issuer of those bonds agrees to pay $50 (5% x $1000) in annual interest per bond. The second year, the bondholder will receive (per bond) 50$+1000$, the coupon and the repayment of the principal value. I is exactly what you can expect if you have bought the bond as defined in this example and if the issuer of the bond is not in default!

However, at each instant, the value of your bond may fluctuate. Imagine that the market interest rate is raising to 6% in the second year of your bondholding and new bonds are issued with a coupon rate of 6%. Clearly, new investors will not pay $1000 for a bond with a performance of 5% when they can buy new bonds with an updated coupon rate of 6% for each $1000. What will happen to your specific bond (with a 5% coupon rate)?

It will be sold by many bondholders who are willing to invest on the new bonds at 6%, and consequently, the face value of your bond will decrease in order to make it more competitive against current bonds. Inversely, if interest rates are decreasing, your bond value will increase as there will be more buyers.

Intermediate Summary

A Bond is a debt investment in which an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate. Bonds are used by companies, municipalities, states and U.S. and foreign governments to finance a variety of projects and activities. The indebted entity (issuer) issues a bond that states the interest rate (coupon) that will be paid and when the loaned funds (bond principal) are to be returned (maturity date). Note that bonds have a certain similarity with the Certificates of Deposit (CDs) and savings accounts. Indeed, investors who deposit money in CDs (or savings accounts) are lending money to banks. Banks pay the investor interests over their deposits and later repay them the principal when CDs reach maturity.




The risks of investing in bonds

Investing in bonds is not without risks. In fact, every investment in bonds carry some risks, although the degree of risk varies with the type of debt and the issuer.

The main risk is the credit risk (or default risk). In this scenario, the issuer is not be able to pay the interests and repay the principal in the pre-established dates. The credit risk is then a function of the credit trust of the issuer of the debt. The creditworthiness refers to the ability that the issuer has in making scheduled payments and repaying the principal at maturity date. Obviously, the credit risk varies with bond issuers. US Treasury issues carry virtually no risk of default because of the full faith and credit of the US Government guarantees interest and principal payments.

As a direct consequence, US Government bonds will offer a lower yield than more risky bond issuers. Indeed, US Government bonds are "absolutely" safe with no risk, then no big returns can be expected.

Another risk consists in the interest rate risk, only if you do not keep your bond till maturity. We have already mentioned this process in the previous section of this document: bond values are varying with the interest rates in a simple way. During the high period of the interest, if you sell your bonds (purchased at lower yield), you will loose some money, only if you sell before maturity.

For bond holder (till maturity), a major risk is obviously driven by a rising inflation, as it will have a corrosive impact on your bond investment. Indeed, you lock up your money for a long period, then inflation plays against you. Of course, the longer the maturity, the larger the impact of inflation. Then, we expect some pair trades to be active between short term and long term maturities during rising inflation periods.

The Yield Curve
The yield curve is defined as the two-dimensional graph of the bond yields to maturity (YTM) as a function of the maturity (Year) of bonds (with the same risk level).

You expect a positive slope curve as the longer the maturity, the greater the bondholder exposure to risk. For this reason, bond issuers will pay more (higher yield) to compensate investors for the risk involved with longer maturities.

An inverted curve is generally atypical, it indicates that by extending maturities investors are taking greater risks for smaller returns. It indicates a worsening of the economic situation.

The shape of the yield curve is changing on a daily basis with the changes in yield because of fluctuations in the rates of interest market. Then, you can decide whether you are willing to invest in long or short-term maturity bonds, based on the shape of the yield curve.

The purchasing process of bonds

Bonds are quoted in hundreds, but negotiated in denominations of thousands. A bond price quote of $86 ¾ means that the bond is negotiated not at $86.75, but rather at $867.50 per bond. The bid price is the highest price that a buyer would pay for a bond. For example, when someone sells a bond whose market price is 94 ½ , the highest point that a buyer would offer would be $945.00 per bond. The ask price is the lowest price offered for a bond buy the seller. For example, an investor that buys a bond with a bid of 94 ½ and an ask price of $94 5/8 would pay for the bond $946.25 (the lowest price that a seller of this bond will accept).

The spread is the difference between the bid and the ask price of the bond, part of which is a commission to pay to the broker or dealer. A large spread indicates a bond inactively traded. Bonds are bought in similar way as stocks.

Although a large part of the bonds is bought and sold through brokerage firms, one can purchase some bonds through banks or directly from issuers.
The different type of purchase orders (market and limit orders) used to buy stocks are also applicable to purchase bonds.

Note that finding current bid and ask prices of a bond can be difficult because the bond market is a dealer market in which the same bonds can be offered at different prices. For example, a dealer offers a General Motors bond with a maturity date of 2028 at a price of $867.50 and other dealer asks for $900 for the same bond.


Oliver Schoeffel for the Stock Code Group: [http://www.thestockcode.com]

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