SecuritizationChapter 181 Chapter 18: Analysis of Credit Sensitive MBS Andrew Davidson Anthony B. Sanders Lan-Ling Wolff Anne Ching

SecuritizationChapter 182 Analysis of credit sensitive MBS  Through securitization, the mortgage market protects most investors from the risk of default on the underlying loans. Credit risk is borne primarily by mortgage insurance companies, Fannie Mae and Freddie Mac, the US Government, through FHA and VA, and the holders of lower rated and unrated, subordinated classes of private passthroughs. In many cases, the originating lender retains the subordinated classes, particularly the most risky first-loss piece. (Lenders may also bear credit risk due the representations and warranties they make to buyers of securities.)  Because default risk is concentrated in relatively few players, the analysis of the valuation of credit risk is not as well developed as the analysis of interest rate risk and prepayment risk. In fact, many leading analytical systems provide limited ability for investors to assess credit risk. Furthermore, much of the analysis that does exist is proprietary.

SecuritizationChapter 183 Methodology  The fundamental question that needs to be addressed in assessing credit risk is what is the amount of losses that an investment may experience due to credit losses.  First, it is necessary to establish a methodology. Generally market participants use either yield spreads, or stress scenarios to assess credit risk. Here we will describe a probability driven approach.  Next it is necessary to assess the risk of the collateral. To measure default risk it is necessary to understand all aspects of the collateral that will affect the securities created with the loans. Generally this means that prepayments, defaults, losses and delinquencies need to be considered.

SecuritizationChapter 184 Methodology  Based on an analysis of the collateral, the cash flows of the securities can be generated following the specific rules for that deal. This chapter includes a sample senior/subordinated transaction to demonstrate some of the important issues in structuring.  The DAS framework uses a theoretical construct similar to that used to derive OAS. Calculating DAS involves estimating the cost of the default option, adding the cost of the default option to offered price of the subordinated MBS, calculating the new yield at the offered price plus the default option cost, and subtracting the yield from cost of capital to get the DAS.

SecuritizationChapter 185 Prepayment risk  Evaluating collateral involves an analysis of prepayment risk and default risk. Generally collateral that has greater default risk has reduced prepayment risk. Figure 18.1 shows the relative prepayment speeds of several MBS with different kinds of collateral. It is clear from the chart that there is an interaction between credit risk and prepayment sensitivity at the collateral level. The high quality jumbo loans and agency MBS exhibit greater prepayment sensitivity than Alt-A and lower quality HEL collateral.

SecuritizationChapter 186 Relative prepayment speeds

SecuritizationChapter 187 Credit risk  For the rest of this chapter we will focus primarily on the credit risk of MBS.  The valuation method described in this chapter requires an understanding of the dispersion of possible losses as well as the mean expected losses.  To assess these probability distribution of losses, information about ratings upgrades and downgrades, as well as the ultimate default percentages by initial rating class are valuable.  While each individual loan and each pool of loans may have its own unique credit situation, rating agencies strive to create consistency across ratings classes.  Thus the default probability by rating class can provide insight into the distribution of potential losses of a pool of loans.

SecuritizationChapter 188 Credit risk  The rating agencies publish statistics on ratings changes. Ratings changes reflect upgrades or downgrades. A security that defaults generally has passed through a series of downgrades prior to default. Table 18.1 is a sample transition matrix from Standard & Poor's.

SecuritizationChapter 189 Ratings transition

SecuritizationChapter 1810 S&P probability transition matrix  The S&P probability transition matrix defines the percentages of a MBS that migrated from one credit rating to another over a ten- year period. For example, of the securities whose original rating was AAA, percent remained AAA securities, and 1.38 percent were downgraded to AA, a 0.10 percent were downgraded to A and so on. The last column labeled D represents the probability of the original security defaulting. While no AAA rated securities in the sample defaulted, 5.63 percent of the BBB rated securities defaulted. This table represents only securities that existed for ten-year periods during 1978 to In order to include more securities, it is possible to use one-year transition matrices and compound the results, using matrix multiplication to produce results for longer time periods.

SecuritizationChapter 1811 Historical default probabilities Figure 18.2 shows the probability of loss for various ratings categories. The three sets of bars represent the 10-year mortgage transitions, the 10- year corporate bond transitions and an implied 10-year transition for mortgages, based on compounding of one-year transition results.

SecuritizationChapter 1812 Structure  Just as the CMO structure can allocate prepayment risk, the senior/subordinated structure can allocate credit risk. The modeling of senior/subordinated securities can be quite complex, due to the shifting priorities of cash flows depending on the performance of the collateral. Accurate modeling of deal cash flows may also depend on documents and information that is not readily available.

SecuritizationChapter 1813 Senior/subordinated example  In order to understand more fully how a senior/subordinated structure works to protect senior security holders from default risk, we have created a very simple senior/subordinated transaction in order to illustrate how cash flows are allocated among the senior and subordinated classes within the deal. Let’s assume that we start out with collateral of $100 million in mortgage loans. The WAC is 12.0 percent and the WAM is 360 months. We assume a constant prepayment rate of 25 CPR. We assume defaults are zero for the first year, increase at a constant rate over the second year and peak at an annualized rate of 6.0 percent.  They remain constant until month 60 and then decline at a constant rate over two years to half the peak rate or 3.0 percent.

SecuritizationChapter 1814 Example  Figure 18.3 shows the composition of cash flows produced by the underlying collateral.  Notice that voluntary prepayments represent the largest proportion of cash flows while scheduled principal payments represent the smallest proportion, barely visible on the graph.  The area below the x-axis represents the volume of defaults.

SecuritizationChapter 1815 Collateral cash flow

SecuritizationChapter 1816 Outstanding senior securities and OC amounts  Figure 18.4 compares the balances of the outstanding senior securities and OC amount. Notice that the initial OC level starts at $2.0 million in month 0, gradually rises to $5.0 million and remains at that level until about month 30. That is because in this example the target OC level is set at 5.0 percent of the original collateral balance or $5.0 million. Any excess interest that would otherwise be paid to residual holders is used to pay down the principal of the senior class until the OC amount reaches the target level of $5.0 million. It is a common feature of senior/subordinated transactions to require that initial OC requirements increase to a target level over a specified period because of the problem of “adverse selection” created by prepayments early on in a transaction’s life.

SecuritizationChapter 1817 Senior bond and O/C balance

SecuritizationChapter 1818 Monthly cash flows to senior class  Figure 18.5 shows the monthly cash flows paid to the senior class. What stands out the most from this graph is that principal payments, which include both scheduled principal and voluntary prepayments, represent the largest proportion of monthly cash flow to the senior class. The sharp dip in principal cash flows around month 30 can be explained by the fact that the target OC level has been reached and excess interest can now be directed to the residual class, so as long as the OC level does not fall below the required amounts.

SecuritizationChapter 1819 Monthly cash flows to senior class

SecuritizationChapter 1820 Residual cash flows  The cash flow available to the residual will depend on the exact formulation of each individual transaction. This sample transaction provides some indication as to the sources of cash flow. Excess cash flow created by the structure can be used to increase overcollateralization levels, or to make payments to the residual holder if the over collateralization requirement have been met. The sources of excess cash flow consist of excess interest and the principal and interest payments on the current balance of OC while negative cash flow results from defaults or credit losses as shown in Figure 18.6.

SecuritizationChapter 1821 Sources of residual cash flows

SecuritizationChapter 1822 Residual cash flows and over-collateralization balance  Figure 18.7 shows the residual cash flow and the OC balance over time. The available excess cash flow is first used to build the OC balance until the OC requirements are met. The first spike in residual cash flow occurs when the target OC level has been reached and excess interest can now be diverted from paying down the principal of the senior class to the residual class. The reason for the drop around month 20 is that defaults have reached their peak rate and the amount of excess cash flow has declined. The second spike occurs in month 30 because of the “step-down” in target OC level.

SecuritizationChapter 1823 Residual cash flows and over-collateralization balance

SecuritizationChapter 1824 Results  Table 18.2 shows a sample calculation of Default Adjusted Spread (DAS). The bond has a default option cost of 2.4 points and a resulting DAS of –16 basis points.

SecuritizationChapter OAS calculation for generic BBB security