Mortgage-Backed Securities 定價與風險

課程內容 CASH FLOWS ANALYSIS PREPAYMENT MODEL YIELDS RISKS

Basic Principles of valuation of MBS

Monthly payments consisting of – Interest on the mortgage – Scheduled principal repayments. – Unscheduled principal repayments Project Monthly Mortgage Interest, servicing and guarantee I t = MB t-1 . i NIt = MB t-1 (i - s - g) St = MB t-1 s Gt = MB t-1 g It = projected monthly interest for month t. NIt = projected interest net of servicing and guarantee fee St = projected servicing fee for month t Gt = projected guarantee fee for month t s = servicing fee rate

PREPAYMENT MODEL There are four methods of measuring prepayment speeds Prepayment based on FHA experience Constant Prepayment Rates (CPR) Single Monthly Mortality (SMM) PSA Standard Prepayment Benchmark

PREPAYMENT MODEL

Constant Prepayment Rates (CPR) Assumes a constant percentage of the remaining principal in pool is prepaid each month for the remaining term of the mortgage A 10% CPR means we can expect 10% of the remaining mortgage balance to be prepaid each and every future year The CPR is based on the characteristics of the pool, current and expected future economic environment Its advantage is simplicity and ease of application It suffers from disadvantage that prepayments are treated as constant

Single Monthly Mortality (SMM) The CPR is annual prepayment rate. The annual rate is converted into monthly prepayment rate called the single monthly mortality rate (SMM) as follows SMM = 1 - (1 - CPR)1/12 PSA Standard Prepayment Benchmark Developed by Public Securities Association (PSA) The standard PSA prepayment curve, called 100% PSA is as follows: – it assumes 0.2% CPR for the first month. – the rate increases by 0.2% per month until the 30th month (top of the ramp) when it reaches a CPR of 6% per year . – it remains at 6% per year for the remaining stated maturity of the pool if t £ 30, CPR = (6%)(t)/30, if t > 30, CPR = 6% where t is the number of months since mortgage origination.

Factors Affecting Prepayment Assumable and Nonassumable mortgages Burnout: after a pool has stayed in refinancing range for some time prepayments decrease. This is call burnout Seasoning: aging of mortgage loans and associated changes in prepayments Path Dependence: future prepayment for a mortgage pool are dependent on that pool’s past prepayments, which in turn are dependent on the path interest rates have taken since pool’s origination. Prevailing mortgage rate and market conditions –spread between contract rate and prevailing mortgage rate –path dependence –refinancing burnout –level of mortgage rates –housing turnover and affordability

Factors Affecting Prepayment Seasonal factors – home buying starts in spring and reaches its peak in summer – in fall and winter home buying declines Characteristics of the underlying mortgage Loans – contract rate – conventional versus FHA/VA – amount of seasoning – FRMs versus ARMs – pool factor – geographical location of underlying properties General economic activity – general economic activity affects prepayment through its effects on housing turnover as growing economy increases personal income and opportunities for worker migration

Evaluating Mortgage-Backed Securities Pricing Concepts Weighted Average Coupon (WAC) –average of underlying mortgage rate weighted by dollar balance of each mortgage as of date of issue Stated Maturity Date of Pool –longest maturity date for any mortgage in the pool assuming zero prepayment Weighted Average Maturity (WAM) –remaining term of underlying mortgages weighted by principal balance Weighted Average Life (WAL) –average number of years until investors principal is returned weighted by each principal balance Pool Factor –outstanding balance divided by beginning balance

Cash flow yields Semiannual yield (IRR) = (1 + ym)6 - 1 Bond Equivalent Yield (BEY) BEY = 2[(1 + ym)6 - 1], ym= monthly yield or IRR To convert the bond equivalent yield to a monthly yield ym = [1 + (0.5)(BEY)]1/6 - 1 Suppose an investor requires a BEY of 8.13%, then the corresponding monthly interest rate is ym = [1 + (0.5)(.08130]1/6 - 1 = 0.006667 The projected cash flow can then be discounted at ym = 0.6667% Price is simply the present value of the projected cash flow.

Yield-to-Maturity for 8 percent, 30-year MBS*   Price Paid No Prepayments 100% PSA 300% PSA 500% Premium 105 7.550 7.302 6.744 6.177 Par 100 8.077 8.051 7.995 7.938 Discount 95 8.640 8.871 9.368 9.868 *Bond equivalent yeild (%)

Price/Yield Relationship for Option -Free Bond

Price/Yield Relationship for Callable

Bonds Option Adjusted Spread Option Adjusted Spread analysis attempts to include the cost of prepayment option ( and other factor, delays) when calculating the spread the passthrough security offers above the Treasury yield curve. The first step in calculating OAS is running a Monte Carlo simulation of numerous possible future interest rate paths. Next future monthly cash flows are calculated based upon prepayment model for each interest rate path. An average yield above Treasury yield is then calculated for each path. The OAS for a security is the average of individual spreads calculated for each future interest rate paths.

The Option Pricing Methodology passthrough price = noncallable passthrough price - call option price

Option-Adjusted Spread Methodology

Advantages of Option-Adjusted Spread Analysis OAS analysis gives investors a way to place values on the options inherent in MBSs. OAS methodology analyzes a security over a large number of interest rate paths, provides a summary of almost all possible scenarios, and incorporate the security’s dynamic cash flow into the analysis. Several studies of OAS-based trading strategies for MBSs, like Hayre and Lauterbach (1990), have shown OAS analysis performing well.

Risks Risks faced by mortgage finance intermediaries Credit risk: risk that money lent might not be repaid. Cash flow risk: risk that market conditions will alter scheduled cash flows. – prepayment risk – inflation risk – exchange risk – interest rate risk Liquidity risk: risk that money will be needed before it is due.

Risk to investors The mortgage security investor is exposed to three types of risk - prepayment risk, market risk, and credit risk - which are present in all callable securities. Prepayment risk Market risk Credit risk

Prepayment risk Prepayment, or option, risk is the chance that borrowers prepay their mortgages faster or more slowly than expected, thereby affecting the investment's average life and perhaps its yield.  Although a borrower may enter into a mortgage with a term of up to 30 years, most mortgages are paid off before that time. Any payment of all or part of a mortgage debt before it is due is called "prepayment." Whether or not a mortgage loan is prepaid is almost entirely controlled by the borrower. Most mortgages may be prepaid at any time without penalty. The borrower has the 4 c option" either to pay scheduled installments of principal and interest over the entire term of the mortgage, or to make additional principal payments to retire the debt early. Borrowers are most likely to exercise the prepayment option at a time when it is least advantageous to investors.

Prepayment risk Prepayment behavior is important to mortgage security investors because, unlike Treasury bonds and traditional corporate securities, which provide periodic payments of interest and lump sum repayment of principal upon maturity, each mortgage security payment is likely to include a return of principal as well as interest. Generally, the most important factor affecting prepayments is refinancing to take advantage of lower interest rates. When long-term interest rates fall, so do mortgage rates. Prepayments tend to increase during periods of declining interest rates. Borrowers take advantage of these rates by refinancing higher rate mortgages with lower rate mortgages and may repeat this process several times. On the other hand, when rates rise fewer borrowers refinance their loans and prepayments slow.

Prepayment risk Some tranches (e.g., PACs or TACs) are structured to mitigate prepayment risk by shifting it to companion, or support, tranches. Some tranches are dramatically affected by prepayment patterns. Actual yields and average lives of classes like IOs, POs, floating-rate, inverse floating-rate, and certain companion tranches may widely fluctuate with prepayment changes. Under certain scenarios, investors in I0s and inverse floating-rate tranches may not receive their initial investment back, resulting in an actual loss on the investment. For this reason it is essential that investors understand the actual security that they are purchasing, as well as the underlying mortgages that provide the cash flows to the security.

Market risk Market risk is the risk that the price of the security may fluctuate over time. As mentioned above, the price of any bond is a function of prevailing interest rates, the length of time the security is expected to be outstanding, and the liquidity of the issue. The price of mortgage securities is generally very sensitive to these factors.

Market risk It is very important that an investor consider the impact of changing interest rates on the performance of the mortgage securities. Interest rate movements have a greater impact on mortgage securities than on other fixed-income instruments because they directly influence prepayment behavior rates, which affects the average life and yield of the mortgage securities. When rates fall, and prepayments speed up, investors in mortgage securities may receive their principal sooner than anticipated, so they will be in a position of reinvesting it at lower prevailing rates. This is known as "call risk." The opposite of call risk is "extension risk." When rates rise, prepayments slow and the average life of the security extends. The investor will not have the opportunity to reinvest in other higher yielding securities.

Market risk Investors should also consider the potential lack of liquidity of REMIC investments. There may be situations (such as periods of unstable interest rates) that decrease demand for certain REMIC classes, particularly those classes whose price and yield fluctuate broadly. Investors wishing to sell these securities may find few, if any, purchasers available or the price offered for them may be far less than the investor expects. The investment community often facilitates resale of these securities into what is known as the "secondary market," but no institution has an obligation to do so.

Credit risk Credit risk in mortgage securities is the risk that the investor may not receive all or part of the principal invested because the issuer or credit enhancer of the security defaulted in its financial obligations.

Credit risk The largest issuers of REMIC securities are Fannie Mae and Freddie Mac. Both Standard and Poor's and Moody's rating agencies have recognized the standard MBS that underlie these agency REMICs as AAA quality, the highest rating given any investment grade security. The MBS backing Fannie Mae REMIC issuances carry a guaranty of timely payment of both principal and interest. MBS backing Freddie Mac-issued REMICs also carry the guaranty of payment of principal and interest. REMICs issued by these two institutions carry a reduced possibility of a credit-related loss. Investors must be aware, however, that Fannie Mae's and Freddie Mac's obligations are not backed by the full faith and credit of the U.S. government, and the performance of those obligations is based on the financial health of the respective entities. Both Fannie Mae and Freddie Mac addressed the risk of default by the borrower by imposing quality guidelines on all mortgages used in their MBS.

Credit risk Ginnie Mae also has begun to guaranty REMICs. REMICs guaranteed by Ginnie Mae are backed by the full faith and credit of the U.S. government. There are also private label REMICs, which are issued by private institutions. It is very important that the investor understand the credit risks associated with these issuers and the methods they use to enhance the credit of their securities.