securitizationchapter 181 chapter 18: analysis of credit sensitive mbs andrew davidson anthony b....

Securitization Chapter 18 1

Chapter 18: Analysis of Credit Sensitive MBS

Andrew DavidsonAnthony B. SandersLan-Ling WolffAnne Ching


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.


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.


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.


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.


Relative prepayment speeds

0

10

20

30

40

50

60

70

-100 -50 -25 0 50 100 150 200

Jumbo

WFMBS 02-20

Agency MBS

FNMA 6.5

GNMA 6.5

ALT-A

CWALT 2002-2 A2

CWALT 2002-13 A1

HEL

CFLAT 2002-C1(CHASE)

CWL 2002-4 (Countrywide)


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.


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.


Ratings transition

End 10 Year Transition 1978-2001Start AAA AA A BBB BB B CCC CC C D

AAA 98.49% 1.38% 0.10% 0.02% 0.01% 0.01% 0.00% 0.00% 0.00% 0.00%AA 45.68% 43.08% 8.00% 1.54% 0.64% 0.57% 0.10% 0.07% 0.00% 0.30%A 27.50% 21.45% 39.26% 6.70% 1.66% 0.76% 0.41% 0.38% 0.02% 1.90%BBB 13.84% 15.66% 16.45% 34.24% 6.07% 6.72% 0.98% 0.96% 0.05% 5.63%BB 4.17% 5.35% 11.65% 18.10% 28.81% 8.53% 1.82% 2.57% 0.09% 18.43%B 1.41% 1.21% 2.67% 6.96% 13.60% 37.11% 2.55% 3.63% 0.13% 30.68%CCC 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.08% 4.66% 0.01% 95.25%CC 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 5.86% 0.00% 94.14%C 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00%D 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00%


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, 98.49 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 2001.

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.


Historical default probabilities

0

1

2

3

4

5

6

7

8

9

AAA AA A BBB

MBS 10 yr transitions Corporate 10 yr transitions MBS implied 10 yr transitions

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.


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.


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.


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.


Collateral cash flowFigure 18.3 Collateral Cash Flow

($500)

$500

$1,500

$2,500

$3,500

$4,500

0 60 120

Months

$th

ou

san

ds

('00

0)

-$500

$500

$1,500

$2,500

$3,500

$4,500

Interest Sched.Principal Prepayment Default


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.


Senior bond and O/C balance

$-

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Months

(in thousa

nds)

O/C Balance Senior Bond Balance


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.


Monthly cash flows to senior class

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Months

(in

$th

ou

sa

nd

s)

Bond Interest Bond Principal


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.


Sources of residual cash flows

-$270

-$170

-$70

$30

$130

$230

$330

$430

0 60 120 180 240 300

Months

$th

ou

sa

nd

s (

'00

0)

Excess Interest OC Interest OC Principal Losses


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.


Residual cash flows and over-collateralization balance

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Months

OC

Ba

lan

ce

($

mil

lio

ns

)

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

OC

Re

lea

se

($

mil

lio

ns

)

OC Balance (left axis) Residual Cash Flow (right axis)


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.


2001 OAS calculation for generic BBB security

2001 DAS Calculation for Generic BBB Security

Rating Cum Loss Probability PriceNo Loss 0.000% 0.00% 93.94$ NA 0.031% 14.51% 93.94$ NA 0.125% 37.12% 93.94$ B 0.250% 25.22% 93.94$ BB 0.500% 13.84% 93.94$ BBB 0.850% 5.80% 90.94$ A 1.350% 2.41% 34.69$ AA 2.200% 0.88% 22.48$ AAA 4.000% 0.22% 15.33$

Price at Zero Losses 93.94Expected Price less 91.54Default Option 2.40

Market/Offered Price 92.06Default Option plus 2.40Default Adjusted Price 94.46

Default Adjusted Yield 7.79%WACC less 7.95%Default Adjusted Spread (bp) (16)

securitizationchapter 181 chapter 18: analysis of credit sensitive mbs andrew davidson anthony b....

Documents

risk of default

credit risk of mbs

analysis of prepayment

valuation of credit

rate risk

greater default risk

credit losses

credit riskfor