merrill lynch - valuing subordinate abs

Highlights

The role of home prices in the valuation of mortgage-backed securities has long

taken a back seat to that of interest rates. However, over the past few years, investors

have become increasingly aware of the significant impact of home prices on

performance, both in terms of prepayments and in terms of credit. This is most

pronounced in the sub-prime ABS market, where home prices may be the most

dominant factor in driving future performance, especially for subordinate securities.

This relationship has been brought to the forefront over the past several months, as

investors have sought to purchase protection in the ABS credit default swap (CDS)

market, against a downturn in the housing market. Yet, despite this flurry of activity

and exceptionally volatile spreads, there has been little consensus on the appropriate

approach to valuing these securities. In this paper, we present an innovative, option-

based approach to pricing this risk and understanding the implications of various

spread levels. In particular, we find the following:

Home price appreciation going forward may be weaker than it has been over the

past several years. Although hard evidence of a slowdown has been limited, the

most recent data seem to indicate that home price appreciation has decelerated.

Sub-prime mortgages are particularly sensitive to the rate of home price

appreciation (HPA). The rate of HPA affects prepayments, defaults, and loss

severities. Taken together, these findings imply that cumulative losses are

extremely dependent on the housing market.

Armed with the dependence of prepayments and losses on home prices, we are

able to calculate a price for each security in an ABS structure for any given

home price scenario. This immediately allows us to judge what home price

scenarios are required for an ABS subordinate to begin losing value.

Rather than choosing one home price appreciation rate, it is more reasonable to

assume a distribution of possible scenarios. We find that different home price

distributions correspond directly to various spread levels. Not only is the mean

of the distribution important, but also its standard deviation (or volatility). We

accordingly treat subordinate ABS as (short) options on home prices.

By reversing the approach and using observed market spreads to derive an

implied HPA distribution, we establish a calibration with which we can price the

HPA risk embedded in a range of securities. It also provides direct insight into

capital structure pricing and potential relative value opportunities.

In the process, we create a ABS valuation framework that incorporates home prices,

interest rates, and deal structure in a single option adjusted framework.

ASSET-BACKED SECURITIES

Contributors

Kamal Abdullah MBS Strategist, MLPF&S (1) 212 449 9308 [email protected]

Akiva Dickstein MBS Strategist, MLPF&S 1) 212 449 1759 [email protected]

Shaolin Li ABS Strategist, MLPF&S 1) 212 449 6891

[email protected]

Sarbashis Ghosh ABS Strategist, MLPF&S 1) 212 449 4457 [email protected]

Jonathan Braus MBS Strategist, MLPF&S 1) 212 449 9728

[email protected]

3 February 2006

Valuing Subordinate ABS Introducing a New Risk-Adjusted Framework Based on

Home Prices

Merrill Lynch does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report.

Investors should consider this report as only a single factor in making their investment decision.

Refer to important disclosures on page 25. Analyst Certification on page 24.

Global Securities Research & Economics Group Fixed Income StrategyRC#41403401

Valuing Subordinate ABS 3 February 2006

2 Refer to important disclosures on page 25.

CONTENTS

Section Page

Section I Introduction 3

Section II Todays Housing Market 5

Section III Home Prices and the Sub-prime Borrower 8

Section IV Pricing Housing Market Risk Credit-Adjusted OAS 12

Section V Final Thoughts and Direction for Future Work 21


Refer to important disclosures on page 25. 3

1. Introduction

Over the past several months ABS investors have been grappling with

valuation issues, as spreads on subordinate securities (Baa3, for example)

widened by up to 200 bp in October before tightening back by more than 100 bp

toward the end of 2005 and beginning of 2006. Two factors precipitated much of

this widening: i) an increasing number of investors wanting to take positions

against the housing market and ii) the belief that ABS CDS1,2 (Asset-Backed

Securities Credit Default Swaps) was the best way to do so.

Although spreads have moved dramatically over the past few months, there

remains little consensus as to their proper level. Is a spread of 200 bp rich for

Baa3 ABS? Is 400 bp cheap? What is the appropriate spread level required

to fairly capture the risk inherent in these securities?

This paper will develop a methodology for answering these questions. Our goal

is to understand precisely what kind of housing market is implied by a

particular level of spreads so that we can make informed investment

decisions.

We begin by briefly reviewing housing market trends and show that recent data

have finally indicated that the housing market may be softening. We also discuss

some of the factors that may weigh on home price appreciation going forward,

including declining affordability and a negative media effect.

We then address the impact of home price appreciation (HPA) on sub-prime

borrowers and present a historically motivated model of prepayments, defaults,

and loss severities as a function of home prices. We show that home price

scenarios play a major role in driving all three of these variables, and thereby

serve as perhaps the most critical economic determinant of cumulative losses.

Given that subordinate ABS performance is driven by cumulative losses, and these

losses are inherently driven by home prices, then valuations should depend

directly on home price appreciation.3 Consequently, we can calculate a fair

price on each subordinate security for any given home price scenario.

Of course, it is difficult to project a single home price scenario with any degree of

certainty. Rather than project a single HPA scenario, we look at value across a

probabilistic distribution. We can take any home price appreciation distribution

and calculate the associated fair value spreads on subordinate securities. These

spreads can then be compared with market spreads to assess whether ABS

subordinates are attractive or expensive. Essentially, this approach represents the

introduction of an option-adjusted framework that puts home prices on near equal

footing with interest rates.

We can also reverse this approach: rather than choosing a home price

distribution and calculating fair value spreads, we can take market spreads

and calculate an implied distribution of home price scenarios. This framework

is analogous to the familiar option-based OAS approach used throughout fixed

income. Just as OAS employs a market-implied price for interest rate risk, this

approach does the same for HPA via the burgeoning market for ABS CDS. As

1 An ABS CDS swap is a synthetic contract between a protection buyer (shorting bonds) and seller

which is modeled after the eponymous, successful corporate contract. Sector and cashflow differences

have given rise to a PAYGO or PAUG structure which is better suited to ABS cashflows. There

are minor cashflow differences between ABS CDS and their cash equivalents including interest

shortfall payments. We ignore these minor differences here. For more information see Lang Gibson,

Structured Finance CDS & Implications for the CDO Market, April 27, 2005, Merrill Lynch

Research. 2 Most recently, trading has begun in ABX.HE a set of synthetic ABS indices that enable one to trade

baskets of single-name ABS CDS. This development further facilitates our proposed methodology by

creating generic and transparent spreads for different points in the capital structure. 3 ABS prices also depend on interest rates which are usually correlated with home prices. Deal

structure, on the other hand, is fully determined at issuance it is not a driver of valuation, but rather a

predictable translation table from drivers to bond cashflows.

Home prices have a major

impact on prepays, defaults and

severities, and thus are a

dominant driver of cumulative

losses.

We can calculate the fair price

for any given HPA scenario.

Introducing an option-adjusted

framework: valuing ABS using

a distribution of home price

scenarios.

Market spreads can also be

used to imply a distribution of

home prices.



swaps and swaptions imply forward rates and volatilities, market spreads on

mezzanine and subordinate ABS, by analogy, imply forward home prices and their

volatility. This implied distribution can be used to value other ABS and generate

rich/cheap relationships across the capital structure.



2. Todays Housing Market

A Spectacular Run for Home Prices, Especially in Select Regions

Over the past decade, U.S. homeowners have enjoyed near continuous and, at

times, spectacular levels of home price appreciation. Geography has played a

determining role. We summarize home price appreciation by state according to

cumulative five-year HPA using the Freddie Mac/OFHEO repeat sales index

(Chart 1).4 The most recent HPA wave which started in 2004 has been even

more pronounced, with some states appreciating in excess of 25% per annum

while others have remained below 5% (shown in the percentages in Chart 1).

Chart 1: Home Price Appreciation by State

Source: OFHEO

Is the Housing Market Slowing?

Reasons that the Housing Market May Slow

There are a number of reasons to suspect that the recent run in housing prices may

slow over the next few years. First, affordability is down (Chart 2).5 The

composite and first-time homebuyer indices were 138.4 and 80.9 respectively

during 2003. These readings have deteriorated to 117.8 (a 15% decline) and 68.4

(a 16% decline) as of 3Q2005 a direct result of higher home prices and interest

rates.

4 There are numerous methods used to gauge home price growth, each with its own idiosyncrasies and

shortcomings. For the purpose at hand, we simply employ the widely used OFHEO repeat sales index

which is calculated using selected properties that back agency conforming loans. 5 An affordability reading of 100 means that a family with the median income (U.S. Census) exactly

qualifies for a mortgage loan at the national average blended arm-fixed rate on a home valued the

median home price (FHFB).

Five-Year Cumulative HPA

Red States 20-30%

Yellow States 30-60%

Blue States 60+%

Most Recent

1-Year HPA

19%

12%

30% 25% 5%

12%



Chart 2: NAR Affordability Index: Declining Affordability

0

20

40

60

80

100

120

140

160

Mar-81

Mar-83

Mar-85

Mar-87

Mar-89

Mar-91

Mar-93

Mar-95

Mar-97

Mar-99

Mar-01

Mar-03

Mar-05

Index

Composite

First-Time Buyer

Source: NAR

A second reason that housing could slow going forward is that the perception that

housing could slow going forward a perception that is growing in popularity. As

with any other asset, todays transaction prices are significantly shaped by buyer

and seller expectations of future prices. As sellers anticipate weaker prices ahead,

they are more inclined to negotiate. Buyers, similarly, are less likely to pay up. In

fact, a prevailing belief that the housing market is cooling undermines many a

buyers foundation that housing is a good investment. New buyers in particular

may feel that they can afford to wait, whereas in the past, many felt that if they did

not buy immediately, prices would only increase further. Most housing market

news presently is dedicated to questioning the housing markets sustainable

growth. For this reason alone, it might not be sustainable.

Some Hard Evidence of a Potential Slowing Has Finally Emerged

We have believed that factors such as affordability and market perceptions could

slow the housing market, but hard evidence was near absent throughout most of

2005. However, recent data suggest that the market may in fact be weaker than it

was several months ago.

For example, according to the NAR, existing single-family supply has been

climbing slowly throughout 2005 from 3.8 months (January) to 4.9 months

(November) almost reaching the indexs 10-year average value of 5.0 months.

Perhaps more importantly, home prices have actually given up ground over the

past few months, even when seasonally adjusted (Chart 3). Over the past six

months, the seasonally adjusted annualized rate of growth is now 5.4%, compared

with 8% for the prior six month period.

Could a negative media effect

also play a role in slowing the

housing market?

Hard evidence of a slowdown

has been limited but may have

recently emerged.



Chart 3: Even Seasonally Adjusted, Home Price Growth Has Flattened

Source: NAR, Merrill Lynch



3. Home Prices and the Sub-Prime Borrower The movement in ABS spreads over the past few months can be tied to investor

indecision about the future direction of home prices. The volatility of the sector

also indicates that investors may be equally uncertain about the appropriate level

of spreads for the associated risk. The goal of this paper is to address this question.

In order to do so, we first must clarify the connection between home prices and

collateral performance.

The sub-prime sector is perhaps the only arena in the mortgage backed securities

market in which home price exposure dominates that of interest rates. On the

prepayment side, lower credit borrowers display significant sensitivity to home

prices. They generally have fewer financial resources beyond their home and have

come to rely on its appreciation to fund other financial obligations through cash-

out refinances. The recent strong housing market accompanied by agreeable

interest rates led sub-prime borrowers to extract home equity through cash-out

refinancings at a record pace in 2004. Deals backed by 2003 vintage loans

routinely have been prepaying at 40-50 CPR (or more) during the past year,

despite no obvious rate incentive. On the credit side, strong home prices have

similarly kept defaults low, as borrowers who could no longer afford monthly

payments were more likely to sell the home and pocket any built up equity rather

than default on the loan and relinquish the property.

We are interested in quantifying the relationship between prepayments and

defaults on one hand and home prices on the other. It is impossible to do this on a

national level because the housing market has been too strong. Simply put, the

sub-prime market has yet to be proven in a nationally weak housing market. This

is very fortunate for borrowers and investors, but somewhat unfortunate for

researchers!

This relationship, though, can still be addressed through the use of a horizontal

analysis in which HPA variations by geography correlated with local loan

performance serve as a proxy. For example, if two pools with identical

characteristics (FICO, LTV, grade ) were located in Texas and California, the

performance of each would be tied to local HPA. If Texas and California pools

prepay at 25 CPR and 50 CPR respectively, the disparity would be attributed to

differences in state level HPA (say 4% and 20% per annum).6

We utilize this approach using Metropolitan Statistical Area (MSA) level home

prices and performance. We provide historical sub-prime prepayments and

defaults by HPA level (Charts 4a & 4b). We have included all securitized sub-

prime loans originated between 1999 and 2005.7,8

6 This approach has two shortcomings. First, other relevant variables at the geographic level are

subsumed in to the HPA variable (unemployment, etc). Second, loan performance in a national

housing downturn could be unlike that observed locally. Nonetheless, the horizontal analysis of HPA is

the only empirically available method of extracting home price driven performance. 7 The average LTV = 80%, the average FICO = 618, 75% of the loans have prepayment penalties, and

the product mix is 25% FRM / 55% 2/28 Hybrids / 20% Other. The observation period is 1999-2005. 8 The additional structure visible is due to inclusion of all loan types (fixed, 2/28s, 3/27s, all penalty

types.)

The sub-prime sector is

especially sensitive to the

housing market.

Use a horizontal analysis to

tie HPA to loan performance

With home prices mainly rising,

how do you quantitatively

determine their impact?



Chart 4a: Historical Subprime Prepayments by Age and HPA

0

10

20

30

40

50

60

70

80

3 6 9 12 15 18 21 24 30 36 48 60

Age (months)

CPR

< 2.5%

5%

10%

15%

20%

Source: Merrill Lynch and Loan Performance

Chart 4b: Historical Subprime Defaults by Age and HPA

0

2

4

6

8

10

12

14

16

3 6 9 12 15 18 21 24 30 36 48 60

Age (months)

CDR

< 2.5%

5%

10%

15%

20%

Defaults are defined as 90+ days delinquent Source: Merrill Lynch and Loan Performance

The sensitivity of sub-prime loan performance to home prices is astounding. A

pool exposed to 15% HPA versus flat home prices prepays 20 CPR faster.

Similarly, by month 36, the same pool would be defaulting at only 8 CDR instead

of 12 CDR.

An interesting observation involves the < 2.5% HPA and 5% HPA buckets.

Although both prepay at nearly the same speeds, they exhibit marked default

differences with age. This makes sense because there is a financial threshold

below which cashout refinances are not feasible. Nevertheless, just 5% equity

growth per year materially reduces default likelihood.

Loss severity, like prepayments and defaults, is a crucial ingredient when

accounting for deal performance. As can be seen, HPA profoundly shapes it as

well (Chart 5).9

9 The observed loss severity seasoning curve can be explained for newer loans by

Subprime performance goes

hand-in-hand with home price

appreciation.

High HPA low loss severity.



Chart 5: Loss Severity versus Home Price Appreciation

-

5

10

15

20

25

30

35

40

45

50

3 6 9 12 15 18 21 24 30 36 48 60

Age (months)

Lo

ss

Se

ve

rit

y (

%)

HPA < 2.5%

HPA=5%

HPA=10%

HPA=15%

HPA=20%


The are several reasons for this dependence of severity on HPA:

Resale environment recovered properties are more easily resold in a strong

market, reducing upkeep and servicer corporate advances.

Process time the period from foreclosure to resale can typically require

anywhere from 6 to 18 months. Any home price appreciation during that

period applies directly to the homes value and diminishes severity

accordingly. In high HPA environments (e.g., recent California experience),

this can give rise to near zero severities.

Resolution method how the property is transferred and ultimately sold is

also influenced by home prices. Less costly methods such as a short sale or

deed-in-lieu of foreclosure make more sense to both borrowers and lenders in

a strong housing environment.

These factors prepayments, defaults, and severities interact and nonlinearly

contribute to cumulative loss. As higher HPA accelerates voluntary prepayments,

loans that would otherwise fail are able to refinance / payoff and thus make the

investor whole. Fewer loans default anyway and those that do experience lower loss

severities. We schematically show this compounded HPA sensitivity (Chart 6).

The underlying property is still near appraisal value.

The property has spent limited time on its way to foreclosure.

Total advances are lower.

Faster prepayments arising

from high HPA also minimize

cumulative losses



Chart 6: A Schematic of Deal Losses and Home Prices

High HPA

Faster Prepayments

Fewer Defaults

Lower Losses

Deal Structure

Lower Loss

Severity

Source: Merrill Lynch

We provide historical cumulative sub-prime losses by HPA and loan age in Chart

7. The underlying data are the same as those in Charts 4a and 4b.

Chart 7: Cumulative Loss versus Age by Home Price Appreciation

0

1

2

3

4

5

6

7

3 6 9 12 15 18 21 24 30 36 48 60 82

Age (months)

Cu

m L

os

s (

%)

HPA=1.5%

HPA=5%

HPA=10%

HPA=15%

HPA=20%


Investors concerned about

losses should focus first on the

housing market.



4. Pricing Housing Market Risk Credit Adjusted OAS (COAS)

Relating HPA Scenarios to ABS Spreads

The analysis in the previous section revealed that housing price appreciation

plays a major role in determining sub-prime cumulative losses prepayments,

and enabled us to quantify the relationship between the two. The next key

step is to relate these findings to an understanding of ABS spreads.

Because ABS prepayments and losses are directly related to home price

appreciation, there is validity in the concept of buying protection on ABS CDS as

a way of making a bet that home price appreciation will decelerate. However,

buying protection (shorting a bond) has a cost: the spread on the security must be

paid. In the Treasury market, at a given price, even bearish investors might be

induced to own a security for its yield. In the mortgage market even those who

believe that prepayments are increasingly efficient will take the convexity risk at

the right price. The same should be true for a sub-prime subordinate bond and

home price risk. Given any prior beliefs about the direction of the housing market,

there is some price or spread where a bonds expected value is acceptable. The

question before us, then, is how to value a subordinate security given its

exposure to home prices.

In one sense, this task is far more challenging than determining the impact of

interest rates on MBS. Interest rate risk has long been tamed quantitatively via

familiar financial tools such as term-structure models and OAS, both of which are

predicated on the existence of a liquid interest rate derivatives market. By contrast,

there has been no such market for home prices,10 though the Chicago Mercantile

Exchange will begin trading home price futures as of 2Q06.11

Our approach is three-pronged:

First, we will use the information in the previous section to value ABS

securities under any given home price scenario. This allows investors with

a firm view of future home prices to choose bonds appropriately.

Second, we will use a distribution of these home price scenarios to price

the ABS securities. This is a risk-based pricing approach that allows us to

balance the spread and the risk on these securities. We will show how

choosing the mean and standard deviation of the distribution plays a major

role in subordinate valuation, and discuss the concept of viewing subordinate

ABS as options struck on home prices.

Finally, we will examine the concept of using the ABS CDS market to

imply a distribution of home prices. In purchasing protection, an investor is

buying insurance. The spread paid is therefore the price of risk. We can find

the distribution of home prices which best fits the observed pricing of

subordinate CDS. We can then use this distribution to derive a rich/cheap

relationship across the credit spectrum.

A Reference Deal

In order to be concrete, we choose a reference deal that is representative of recent

sub-prime production in terms of collateral, structure, originator-servicer

reputation, and ratings coverage. Ameriquest 2005-R5 is triple rated by Moodys,

10 As such, housing market risk has not been diversifiable a risk that is readily measured and is

explicitly hedgable. In economics, an investor is not compensated for taking such risk. To illustrate, a

Agency CMO buyer might compare bonds on an OAS basis and then use swaps to dynamically hedge

the purchased bond. A subprime BBB buyer, on the other hand, has had no simple way to hedge home

price exposure and accordingly could not price the risk. 11 http://www.cme.com/trading/prd/env/housingover16250.html

We now turn to the critical

question: How do we relate

HPA to spreads?

Three approaches to the

valuation question.

ABS CDS are indirect bets on

home prices their spreads

indicate implied home price

expectations.



S&P, and Fitch for all classes in the deal. We detail the lower mezzanine structure

and collateral backing it in Tables 1a & 1b.

Table 1a: Ameriquest 2005-R5 Mezzanine Structure

Class Moodys Coupon (bp) Cash (bp) ABS CDS (bp) Initial Size C/E

Senior Classes

M6 A3 70 80 80 1.26% 4.70%

M7 Baa1 122 140 135 1.01% 3.70%

M8 Baa2 135 185 190 0.96% 2.75%

M9 Baa3 175 300 300 0.55% 2.20%

M10 Ba1 300 725 765 0.55% 1.65%

Subordinate Classes

Market spreads as of 11/24/05 Source: Ameriquest, INTEX, and Merrill Lynch

Table 1b: Ameriquest 2005-R5 Collateral

ARM / Fixed 81% / 19%

Owner Occ 98%

SF / PUD 90%

Avg FICO 613

Orig LTV 77%

Full Doc 75%

IO 9%

CA 15%

Avg Loan Size $150k

Source: Ameriquest, Bloomberg

We restrict our attention to the lower mezzanine (A3 and below) capital structure

because the performance of these classes is most sensitive to home price

appreciation in the region of common interest. Home prices would have to drop

dramatically in order for the A1A (Aaa rated) class to incur a loss a possible,

albeit very unlikely, event. The lower mezzanine classes, on the other hand, are

more sensitive to future home prices.

Having chosen our example transaction, we are now ready to discuss our three

approaches to valuation.

Capital Structure Valuation Under Static Pricing

Our first approach (which will also be used as a stepping stone for the later

approaches) is to value each security under the spectrum of possible HPA

outcomes. To do this, we use the collateral models from the previous section;

specify the HPA scenario and interest rate assumptions along with a discount

margin to statically price a given bond.12

12 Its imperative that one not confuse the various components involved in pricing. The external drivers (interest rates and home prices) represent the risks. The models (prepayment, default, delinquency, and

loss severity) are predetermined functions that map rates and home prices into collateral cashflows.

Finally, the deal structure (fully determined and available via INTEX) allocates these cashflows among

the bonds contingent on rates and collateral performance.

Focus on lower mezzanine

classes.



Chart 8: Pricing using HPA, Interest Rates, and a Discount Margin

Prepayments

Defaults

Delinquencies

Loss Severity

Deal

Structure Price

HPA

Int Rates

DM


Throughout this approach, we discount cash flows at LIBOR flat (discount

margin = 0). At first glance, this might seem surprising given that subordinate

ABS offer significant margins. However, if we were to use the bonds stated

margin, we would find that in scenarios where the bond does not incur a loss, the

price is todays market price, but the price is significantly lower at times when the

bond incurs a loss. In other words, prices would have nowhere to go but down.

We believe this is not only awkward but also misses the point: subordinate ABS

investors earn handsome margins by accepting the risk of losses. In scenarios

without losses, the value of a L+300 security should be greater than its initial

market price in order to balance those in less favorable scenarios.13

In Chart 9, we calculate the prices of the various securities in the capital structure

as a function of HPA assuming a fixed LIBOR of 4.5%.

Chart 9: Bond Price versus HPA for fixed LIBOR

0

20

40

60

80

100

120

140

-15% -7% -3% 1% 5% 9% 13%

HPA

Bond P

rice

M6 (A3)

M7 (Baa1)

M8 (Baa2)

M9 (Baa3)

M10 (Ba1)

M11 (Ba2)


13 This approach is also analogous to interest rate derivatives, in which a term structure model is adjusted so that each security has 0 OAS.

How does the capital structure

stand up to home prices?



Chart 9 reveals the breaking point for each bond in the capital structure. The

more complex features arise from the interaction of the collateral model with the

deals structure.14

This simple approach significantly extends the usual first-loss coverage multiple

analysis. Rather than calculating just a single multiple of the default model at

which a bond incurs its first dollar of principal loss, we can size up precisely what

levels of HPA lead to bond price declines and principal losses. The impact of

structure is readily seen.

For example, if one anticipates flat home prices (HPA=0%), an investment

portfolio containing Baa2 and above credit is recommended.

Toward a Risk-Based Pricing Methodology

While Chart 9 gives us the value of each security in a given home price scenario, it

makes more sense to value a security across a range of possible home price and

interest rate scenarios, just as we value interest rate options or mortgages using a

distribution of interest rate scenarios.

To do this, we combine the calculation of the bonds price under each scenario

(we did this in the previous section) with a probability of such a scenario

occurring. The option-adjusted price of the bond will then be the probability-

weighted average of the prices across the various scenarios. We therefore require:

a prescribed interest rate distribution

a prescribed home price appreciation distribution

a correlation between these two15

We present a schematic of the option adjusted pricing method in Chart 10.

Chart 10: Option Adjusted Price From Rate and HPA distributions

Forward interest rate probability distribution (already known from usual term structure)

Correlation

Each scenario uses modeled cashflows

Option Adjusted Price

Forward HPA probability distribution Either we specify or infer from ABS CDS / ABX.HE


14 With lower HPA, losses increase and prepayments decline causing bonds to extend and rely on overcollateralization when available. Ultimately, under sufficiently weak HPA, write-downs ultimately

extinguish the bonds. 15 Home prices and rates may be inversely correlated, at least locally. As rates rise, homes become less affordable and demand accordingly wanes. As rates fall, demand increases. This correlation is relevant

because typical deal structures involve moving parts that are codependent on rates and collateral

prepayments and defaults, both of which depend on home prices. Because home prices are a direct

input in this approach (instead of estimating them from interest rates using the correlation), correlation

specification is less critical.

Dont go below Baa2 if you

expect flat home prices.

Introduce an option framework

to price risk.

Calculate option adjusted price

from HPA and interest rate

probability distributions.



One of the two risk dimensions in Chart 10 is already known. Forward LIBOR and

its volatility (probability shape) are well determined by the familiar capital

markets instruments and can be applied directly. The home price distribution can

either be specified a priori or inferred from ABS CDS (next section).

Investor Beliefs and Pricing

We now consider two hypothetical investors: a housing Bull and a housing

Bear. The Bear anticipates a distribution of housing prices centered around 4%

HPA per year, while the Bull more optimistically predicts a distribution centered

around 11% HPA per year a continuation of recent trends. Both claim a

reasonably modest uncertainty of 7%. Chart 11 compares HPA expectations.

Chart 11: Housing Bear and Bull HPA Outlook

Expected Home Price Appreciation

0%

1%

2%

3%

4%

5%

6%

7%

-15 -5 5 15 25

HPA (%)

Probability

Bullish HPA

Bearish HPA


How would these two interpret the actual market portrayed in Table 1a? Given

their different projected home price distributions, each would calculate a different

fair value price for the securities. In other words, while the two investors may

agree on the price of the security under any given home price scenario, they

weight those scenarios quite differently and as a result arrive at very different fair

value (or option-adjusted) prices. We can translate these fair value prices into a

breakeven or fair value spread at which each investor finds the market cash

prices fair. We show the actual spread along with the Bears and Bulls

breakevens in Table 2.

Table 2: Housing Bear and Bull Breakeven Spreads (Volatility=7%)16

Class Moodys Market Cash Price $

Market ABS CDS Spread (bp)

Bull B/E Spread (bp)

Bear B/E Spread (bp)

M6 A3 99-21 80 10 137

M7 Baa1 99-19 135 24 236

M8 Baa2 98-04 190 82 481

M9 Baa3 95-25 300 184 778

M10 Ba1 86-02 765 359 1170

Rich Cheap


16 as of November 29, 2005

A housing Bull and Bear

will have different views of

whether spreads are attractive.



When the breakeven spread is above (below) the cash spread, the bond appears

rich (cheap). In this example, the Bull finds all bonds cheap while the Bear finds

all bonds rich.

Impact of Volatility: Thinking of Subordinate Bonds as Options

In the above example, we found that the Housing Bear believes that all of the

bonds are expensive at current levels. Yet, under a 4% HPA scenario (Chart 9)

the Bears mean HPA the Baa2 and even the Baa3 security incur no decline in

price. Why then do they appear so rich according to the Bear? The answer lies not

in the Bears mean of 4%, but in the significant tail of the Bears distribution

(Chart 11, left side). The significant probability that HPA could be lower than 4%

is what makes the Bears distribution indicate that spreads are too tight.

This implies that we need to consider not only the mean of the distribution,

but also its standard deviation. In the prior example, we used a standard deviation

of 7%. What would happen if we reduced this to 4%, thus tightening both

distributions?

The Bull now finds the Baa3 extremely cheap, as it is trading at DM of 300 bp, but

its fair value is 24 bp. Even the Bear, who previously thought that the Baa3

should be trading at 778 bp, would now be content with a spread of just 562 bp

(Table 3).

In fact, with a 4% volatility, the Bear actually believes that the A3 and the Baa1

classes are cheap. Lowering the volatility materially reduces the likelihood of

these classes incurring losses. The Baa1 only begins to lose value at an HPA of

around -4% per year; with the lower volatility this scenario is two standard

deviations below the 4% mean of the Bear (Chart 11).17

Table 3: Housing Bear and Bull Breakeven Spreads (Volatility=4%)

Class MoodysMarket Cash

Price $Market ABS CDS

Spread (bp) Bull B/E Spread

(bp)Bear B/E Spread

(bp)

M6 A3 99-21 80 1 -19

M7 Baa1 99-19 135 -2 2

M8 Baa2 98-04 190 0 208

M9 Baa3 95-25 300 24 562

M10 Ba1 86-02 765 101 1105

Rich Cheap


Having introduced HPA volatility into the analysis, we can now think of

subordinate ABS as being short options on home prices. Remarkably, if we

review Chart 9 and consider the shape of the price distribution for any given class,

we find that it remarkably resembles a put option on HPA (with a few structural

nuances). Consequently, it makes sense that subordinate securities, as with interest

rate options, should be valued using a volatility assumption for home price

scenarios. Each bond in the capital structure corresponds to being short a put

option with a different strike in HPA space. The Ba2 class is struck closest to-the-

money and accordingly offers the greatest spread in return for the greatest risk.

17 As volatility drops, there can even be scenarios in which the Bear would pay more for a bond than

the Bull; indeed, this is shown in the A3 pricing in Chart 9, where the Bear believes the bond is worth

L-19 while the Bull has L+1. The reason is that while both believe that writedowns are highly

unlikely, the expected price of this class is higher at 2% HPA than at 11%. This effect is due to bond

extension arising from lower prepayments and deal paydown rules. In other words, the Bear is

compensated for his HPA brinkmanship he expects HPA to be much lower than it is today but is

confident that it will not go negative by much under this volatility assumption.

Volatility (uncertainty) is an

essential component in risk

valuation.

Holders of subordinate ABS are

writing put options on home

prices.

We begin to consider

subordinate ABS as short

options on HPA.



Market Implied Home Prices

An Analogy With Swaptions: Using CDS to Derive an Implied HPA

Distribution

In the prior section, we imposed our own views of the distribution of HPA

scenarios and calculated fair value spreads, which we then compared with actual

market spreads. However, how are we to know the appropriate distribution of

HPA scenarios? In this section, we consider using the market itself to reveal the

implied distribution.

Readers familiar with interest rate derivatives will immediately recognize this

problem as very similar to the daily calibration of forward curves and implied

volatility to fit observed rate levels and swaption and cap prices. The implied

forward rate curve is not guaranteed to be realized rather it is a convenient

representation of the markets current price for interest rate risk.

In order to apply a similar methodology to home prices, we simply need a family

of spreads referencing different bonds in a single deal, such as the one in our

example; this provides adequate information to deduce a market-implied HPA

distribution. By analogy to the Black model for interest rates, we employ a

normal distribution to model market implied HPA. Using forward interest rates

and volatility from the swaps market and fitting the HPA mean and standard

deviation accordingly, we arrive at an implied distribution of HPA scenarios that

best fits the current ABS spreads.

We label the option-adjusted framework that prices the risk arising from home

prices as well as that arising from interest rates as COAS Credit and (Rate)

Option Adjusted Spread. 18 Both home prices and interest rate expectations are

implied by market prices.

It turns out that the distribution that best fits ABS CDS spreads in our example has

a mean of 8% and standard deviation of 7%, situating it right between our Bull

and Bear investors.19 The three distributions are shown in Chart 12.

Chart 12: Market Implied Home Price Appreciation

0%

1%

2%

3%

4%

5%

6%

7%

-15 -5 5 15 25

HPA (%)

Probability

Implied Forward HPA

Bullish HPA

Bearish HPA


18 Credit used in this context refers to home prices and all correlated drivers of borrower default. Note

also that we allow interest rates to vary as well as home prices. We also allow for correlation between

rates and home prices, with higher rates implying lower rates of growth for home prices, as has been

suggested by empirical evidence. 19 as of November 29, 2005.

The crucial step: infer the

market implied HPA

distribution from ABS CDS

spreads.

The ABS CDS market implied

HPA is centered about 8% per

annum.



This outcome is surprisingly reasonable. ABS CDS spreads are primarily

determined by the balance between synthetic CDO originators sourcing synthetic

collateral and, on the other side, macro hedge funds buying protection thereby

shorting the consumer. The true valuation of these spreads is quite complex: it

requires a model for prepays, defaults, and losses in terms of home prices and

interest rates as well as a model for translating those relationships into price terms.

Yet despite this complexity, the current market equilibrium appears to be at least

roughly in the realm of reasonableness. Of course, aggressive ABS CDS

protection buyers, including some macro hedge funds, might find an implied 8%

( = 6.8%) HPA distribution is far too optimistic. They, accordingly, may want

to purchase protection at todays levels.

Capital Structure Arbitrage

Once the market implied HPA distribution is determined and prices are generated

for each attachment point in the capital structure, comparison to actual prices

provides a natural relative value framework within the capital structure. In

particular, the residuals from the fits used to build the HPA curve provide a rich /

cheap analysis framework. This is because the HPA curve above is the best fit on

average across all the tranches. There remain residual errors on individual

tranches: some appear too tight (rich) while others appear too wide (cheap). We

identify arbitrage opportunities in Chart 13, using pricing (Table 1a) and implied

HPA distribution (Chart 12). The rich/cheap amount in basis points is on the left

hand y-axis and denoted by bars. The overall spread levels are denoted by the line

and presented on the right hand y-axis.

Chart 13: Quantitative Capital Structure Arbitrage

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

A3 Baa1 Baa2 Baa3 Ba1

Class

Ric

h / C

heap

(b

p)

0

100

200

300

400

500

600

700

800

900

CD

S S

pread

(b

p)

Rich / Cheap

CDS Spread


The Baa2 and especially the Baa3 classes appear rich. This is not a surprise given

the CDO bid for the two classes. At the same time, the Ba1/Baa3 swap appears

170 bp cheap.20,21 One could buy the Ba1 and buy protection on the Baa3 a

positive carry trade, albeit with financing considerations.

Another way to take advantage of the Baa3 richness would be to own Baa2s and

Ba1s versus Baa3s; this also is a positive carry trade which only loses in the

narrow band of scenarios in which the Ba1 incurs losses but the Baa3 remains

mostly whole. 20 We caution that AB CDS spreads were volatile during this analysis and marking an accurate Ba1

spread is difficult due to infrequent trading. 21 Due to funding issues, this cash swap should always be cheap. Typical repo haircuts for the Baa3

class are 15%-25% where as that for the Ba1 are closer to 30%-40%. In theory, one would execute both

legs synthetically by selling protection on the Ba1 and purchasing protection on the Baa3.

Capital structure relative value.

Sell Baa3, buy Ba1 or Baa1.



Housing Risk Metrics

Now that we have presented subordinate bonds as short options and derived an

implied distribution of HPA scenarios from current pricing, it makes sense to

consider the next step. In dealing with interest rate options, we usually consider

their risk in terms of duration, convexity, and vega. Suppose we applied a similar

approach to subordinates, but rather than calculate the exposure to interest rates,

we calculate the exposure to home prices. These metrics applied at the portfolio

level would provide a windfall of valuable exposure information to todays

investor.

We provide an example using our reference deal and the implied HPA distribution

determined in the previous section (Chart 12). The duration (delta) is the

percentage change in a securitys price for a 1% change of the mean of the

distribution, while the gamma represents the convexity associated with moving the

mean by 1% up relative to 1% down (Table 4).

As expected, the ABS are all long delta on HPA they all benefit from a rise in

HPA and all are negatively convex relative to HPA they lose more for a 1%

decline in HPA than they gain from a 1% rise. This is makes sense given that they

are effectively short put options.

Finally, the vega gives the percent change in option-adjusted bond price for a 1%

increase in the standard deviation; as can be seen, the Baa3 has the most vega as

well as the greatest gamma.

It is possible that the spread widening toward the end of 2005 reflected changing

investor views on both the mean and standard deviation of the HPA distribution:

as investors became more bearish on housing and more uncertain about its future,

the price of subordinate ABS declined.

Table 4: HPA Risk Measures

Class Moodys Price ($) Spread (bp) HPA Delta HPA Gamma HPA Vega

M6 A3 99-21 80 0.6% -0.19% -1.3%

M7 Baa1 99-19 135 1.0% -0.28% -1.9%

M8 Baa2 98-04 190 1.9% -0.38% -2.6%

M9 Baa3 95-25 300 3.0% -0.42% -3.0%

M10 Ba1 86-02 765 4.0% -0.36% -2.6%


These risk measures could be used in a number of different ways.

They represent the response of the security to changes in perceptions of the

housing market. In our view, the prices of subordinate bonds should move as

new housing data become available. Of course, changes in HPA are not as

apparent as changes in rates, but on days when home price information is

released, we believe subordinate prices should move. So far, we have not

seen this kind of response in the market, but perhaps that is no surprise as this

methodology is relatively new.

These exposures can be used for constructing trades which are duration-

neutral not only to rates but also to home prices. Eventually, we might want

to calculate similar measures for agency securities as well. For example,

agency IOs have negative HPA deltas a decline in HPA would slow down

speeds and raise the value of the IO. This immediately suggests that

subordinate ABS could be an appropriate hedge for agency IOs; calculating

accurate HPA deltas and gammas would be critical for determining a hedge

ratio.

The Greeks for housing?



5. Final Thoughts and Direction for Future Work

Final Thoughts

Our main findings concerning this new approach to understanding and valuing

subordinate ABS securities are summarized below.

Sub-prime prepayments, defaults, and loss severities are all highly correlated

with home price appreciation. Consequently, cumulative losses for a given

pool are driven in large part by HPA. Using these relationships, we can value

subordinate securities under different HPA assumptions.

Imposing a weighting on HPA and interest rate scenarios generates an option-

adjusted fair value price for each security. This price, in turn, implies a fair

spread on the security for the chosen distribution.

We explore the impact of different distribution means and standard deviations

on valuation, and suggest that investors begin thinking of subordinate ABS as

being short options on home prices.

As a further step, letting the market imply an HPA distribution is similar to

the approach taken with other types of options. An implied distribution

captures the markets pricing of risk and, to some degree, its expectations.

These techniques readily lend themselves to quantitative relative value

recommendations.

This approach naturally sheds light on capital structure arbitrage and relative

value across different tranches. It also allows the calculation of risk exposures

to the housing market.

We hope this discussion and analysis has helped investors gain a better

understanding of ABS subordinates. We plan to work on putting this analytical

framework into automated production in order to track and value a wide variety of

ABS. The recently introduced liquid benchmark ABX index is likely the best

source for calibrating an implied HPA distribution. In addition to these goals, we

believe that there remain a number of possible avenues for further research, and

we now turn to a discussion of these.

Directions for Future Work

There are many possible avenues for further work along these lines. Here we

explore five: i) ABS relative value; ii) cross-sector opportunities; iii) further study

of implied and actual HPA distributions; iv) the prospect of a full Monte Carlo

simulation; and v) exchange traded HPA futures and options.

ABS Relative Value

In this paper, we have developed a new methodology for the valuation of ABS

spreads in a single transaction. By considering collateral, structure, HPA, and

interest rates in an unified framework, we back out an implied home price

distribution given market spreads. As we continue to build our capabilities in this

area, we would like to apply the same technique to a wider variety of structures,

seasoning, and collateral. We suspect that this approach will illuminate some very

interesting relative value opportunities.

A good application is the calculation of fair payups for seasoned bonds, say

between 2004 and 2005 vintage deals. The more seasoned bond would have lower

current LTV and greater subordination, but slightly less structural integrity given

tighter rating agency 2005 rate stresses. Credit-Adjusted OAS would capture the

impact of each in a form that is most appropriate, namely price. It would also

provide a quantitative window on the impact of rating agency guidelines.



Cross Sector Possibilities

Beyond the realm of just ABS, there are possibilities for the extension of this

framework to other areas of the MBS market. Thus far, residential ABS CDS

trading has been restricted to sub-prime transactions. However, home price

information gleaned from spreads using sub-prime models could be useful in

valuating other sectors as well. As an illustration, one could use the implied HPA

distribution extracted from ABS CDS spreads and apply to non-agency

subordinate MBS. In theory, investors could also use the implied HPA

distribution to project a distribution of prepayments on agency pass-throughs or

derivatives. In either of these endeavors, there would certainly be challenges, as

different models could give rise to biases, and the two markets have very different

participants. Nevertheless, adapting and transferring housing market information

embedded in ABS CDS to other sectors may be well worth pursuing.

Further Study of the Implied and Historical HPA Distribution

In calculating the implied HPA distribution from ABS spreads, we made the

simplified assumption of a normal distribution. This could potentially be

incorrect. After all, interest rate traders and researchers still debate over normal or

log-normal rate distributions, even with a quarter century of data and wisdom. We

did test a few other distributions and found few differences in the resulting

valuations.

An even more interesting topic, in our view, is the relationship between the

implied HPA distribution and the actual, historical distribution. Chart 14 shows

the historical distribution of home price appreciation rates for the U.S. since 1980.

The data are recorded quarterly and represent year-over-year HPA.

Chart 14: Historical HPA for the United States (1980 2005)

Source: Merrill Lynch, OFHEO

Comparing the historical distribution to the implied in Chart 12, we find that

todays implied HPA volatility of 7% is more than twice the historical average

over the past 25 years. The implied mean of 8% is also higher that the historical

average of 5.7%. This makes sense: the nation has just enjoyed a sustained period

of high HPA and is at a juncture characterized by uncertainty.

Generally speaking, when implied volatility exceeds actual volatility one

considers selling options, e.g., buying subordinate ABS in our case. However, we

also see that the historical mean of 5.7% is below the implied 8% in Chart 12; this

suggests the opposite trade. The risk measures presented in Table 4 can help

quantify these issues, but we plan to develop this analysis further in future work.

0

5

10

15

20

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Year-over-Year HPA

# P

erio

ds

USA

USA Fit Normal

= 5.7%

= 2.8%



It may also be important to consider differences in home price behavior across

geographical regions. As we discussed in earlier, regional differences have

dominated home price behavior across the U.S. The historical standard deviation

of home price appreciation rates in California over the past 25 years has been far

greater than that of the Midwestern states. This may be due to many factors, but

one of them is almost certainly the fact that the supply of land in many areas on

the coasts is limited. Consequently, changes in demand associated with variables

such as income, rates, or consumer confidence will have a greater impact in these

areas than in areas where land is more readily available. We compare year-over-

year historical HPA volatility for Ohio and California in Chart 15.

Chart 15: Historical HPA for Ohio and California (1980 2005)

0

5

10

15

20

25

30

35

40

-6%

-3%

0%

3%

6%

9%

12%

15%

18%

21%

24%

27%

30%

Year-over-Year HPA

# P

erio

ds

OH

CA

OH Fit Normal

CA Fit Normal

Ohio

= 4.5%

= 1.3%

California

= 7.1%

= 8.6%

Source: Merrill Lynch, OFHEO

These types of comparisons and the exposure of the different tranches to both the

mean and the standard deviation could also create some interesting opportunities

for relative value. For example, Ba1 securities are particularly sensitive to the

mean of the distribution because even some low level of positive HPA could bring

these closer to losses. On the other hand, Baa1 securities are more exposed to the

standard deviation, because it is only in the tail of the distribution that they incur

losses, and a lower standard deviation suggests a lower likelihood of a negative

HPA regime. Perhaps one should look for Baa1 and higher-rated securities with

higher concentrations in the low volatility Midwest areas of the country.

Toward a Full Monte Carlo Simulation?

Although we have moved toward a probabilistic HPA approach, we are still using

only static interest rate and HPA scenarios. A stochastic implementation, on the

other hand, would allow home prices and rates to vary over time. It would include

valuable whip-saw scenarios in which both risks vary in time and interact with

bond structures. This would be more analogous to the standard Monte Carlo

simulation approach used for OAS in MBS and CMOs.

Although there are certainly advantages to moving to a Monte Carlo approach,

there are some reasons not to leap to this stage as well:

First, our current approach is more transparent, easier to understand, and

better adapted to the manner in which ABS trade today: static spreads and

speeds. Given that a probability-weighted HPA approach is completely new

to the ABS market, we might not want to go for the full black box approach in

which the results are sometimes more difficult to grasp intuitively.



Second, the calibration of a home price term structure model is likely quite

difficult. After all, unlike interest rate derivatives, existing ABS CDS (or for

that matter existing cash ABS) are not available for an arbitrarily chosen

forward time period. Different models could yield quite different results; for

example, whether HPA is mean reverting or not could become an important

question. Another question is whether one should run HPA series purely on a

national level or on a regional level; if we choose the latter there will be

issues of the correlation between the regions and their individual volatilities.

Nonetheless, a Monte Carlo simulation could be a reasonable next step at some

point in the future.

Potential for Using Traded HPA Futures; The Analogy to MBS

In this paper, we derived an implied HPA distribution from the market prices of

ABS CDS, making an analogy to the common practice of calculating implied

interest rate volatility from the market prices of caps and swaptions. It would be

even more convenient, however, if we could obtain the implied HPA distribution

not from ABS CDS, but rather from an external source that directly references

home prices. When the Chicago Mercantile Exchange begins to trade home price

futures, this may become a real possibility if that market becomes sufficiently

deep and if an options market develops.

If this does become reality, then the treatment of housing risk and interest rate risk

would be nearly symmetric. We would derive both from their respective derivative

markets.

This would greatly enhance the current methodology. Given only one source of

securities which depend on HPA distribution, we are forced to choose between

imposing our own distribution (based on view or history) or using the CDS

spreads themselves to imply a distribution. Neither approach allows us to take an

independent, market implied distribution and assess the Credit-Adjusted Spread of

the ABS based on that distribution. This, in fact, is the standard approach in

valuing MBS, and would be a very exciting development in our view.

The authors would like to thank Tim Isgro for his valuable contributions to

this work.

Analyst Certification

We, Kamal Abdullah, Akiva Dickstein, Shaolin Li, Sarbashis Ghosh and Jonathan

Braus hereby certify that the views each of us has expressed in this research report

accurately reflect each of our respective personal views about the subject

securities and issuers. We also certify that no part of our respective compensation

was, is, or will be, directly or indirectly, related to the specific recommendations

or view expressed in this research report.



Important Disclosures

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Highlights1. Introduction2. Today's Housing MarketA Spectacular Run for Home Prices, Especially in Select RegionsChart 1: Home Price Appreciation by State

Is the Housing Market Slowing?Chart 2: NAR Affordability Index: Declining AffordabilityChart 3: Even Seasonally Adjusted, Home Price Growth Has Flattened

3. Home Prices and the Sub-Prime BorrowerChart 4a: Historical Subprime Prepayments by Age and HPAChart 4b: Historical Subprime Defaults by Age and HPAChart 5: Loss Severity versus Home Price AppreciationChart 6: A Schematic of Deal Losses and Home PricesChart 7: Cumulative Loss versus Age by Home Price Appreciation

4. Pricing Housing Market Risk - Credit Adjusted OAS [COAS]Relating HPA Scenarios to ABS SpreadsA Reference DealTable 1a: Ameriquest 2005-R5 Mezzanine StructureTable 1b: Ameriquest 2005-R5 Collateral

Capital Structure Valuation Under Static PricingChart 8: Pricing using HPA, Interest Rates, and a Discount MarginChart 9: Bond Price versus HPA for fixed LIBOR

Toward a Risk-Based Pricing MethodologyChart 10: Option Adjusted Price From Rate and HPA distributionsChart 11: Housing Bear and Bull HPA OutlookTable 2: Housing Bear and Bull Breakeven Spreads [Volatility=7%]Table 3: Housing Bear and Bull Breakeven Spreads [Volatility=4%]

Market Implied Home PricesChart 12: Market Implied Home Price AppreciationChart 13: Quantitative Capital Structure ArbitrageTable 4: HPA Risk Measures

5. Final Thoughts and Direction for Future WorkFinal ThoughtsDirections for Future WorkChart 14: Historical HPA for the United States [1980 - 2005]Chart 15: Historical HPA for Ohio and California [1980 - 2005]

Analyst Certification

merrill lynch - valuing subordinate abs

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