Economics of sub p lending

On the Economics of Subprime Lending

AMY CREWS CUTTS

Office of the Chief Economist, Freddie Mac, McLean, VA, USA

E-mail: [email protected]

ROBERT A. VAN ORDER

The Wharton School, University of Pennsylvania, Philadelphia, PA, USA

E-mail: [email protected]

Abstract

US mortgage markets have evolved radically in recent years. An important part of the change has been the rise

of the Bsubprime^ market, characterized by loans with high default rates, dominance by specialized subprime

lenders rather than full-service lenders, and little coverage by the secondary mortgage market. In this paper, we

examine these and other Bstylized facts^ with standard tools used by financial economists to describe market

structure in other contexts.

We use three models to examine market structure: an option-based approach to mortgage pricing in which

we argue that subprime options are different from prime options, causing different contracts and prices; and two

models based on asymmetric informationYone with asymmetry between borrowers and lenders, and one with

the asymmetry between lenders and the secondary market. In both of the asymmetric-information models,

investors set up incentives for borrowers or loan sellers to reveal information, primarily through costs of

rejection.

Key Words: asymmetric information, licensing, option-pricing, secondary market, signaling, subprime

mortgage market

1. Introduction

US mortgage markets have evolved radically in recent years. Innovations in underwriting,

mortgage products, and mortgage funding have expanded mortgage lending and reduced

costs. An important part of the change has been the rise of the Bsubprime^ market. The

subprime market is characterized by loans with high default rates and dominance by

specialized subprime lenders. Indeed, for research and other purposes subprime loans are

generally defined by the characteristics of the lender (a specialized subprime lender)

rather than the loan.1 Subprime mortgages are now a little more than ten percent of the

mortgage market.

Two characteristics are of special interest for this paper: first, the observation cited

above that subprime is defined by lender rather than loan and that subprime lenders

have historically been separate, specialized institutions, rather than parts of the same

institution quoting different prices for different risks; and second, that the secondary

market, which is prominent in most of the prime market, has done very little

The Journal of Real Estate Finance and Economics, 30:2, 167–196, 2005# 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.

purchasing of subprime loans. In this paper, we attempt to explain these and some

other Bstylized facts^ with some standard tools used by financial economists to

describe mortgage markets and financial structure in other contexts. Our reasoning is

inductive rather than deductive, making us tinkers with our economic toolbox. This is

in part because we do not have data that are suitable for rigorous testing; some of our

stylized facts are not much more than hearsay.

The main stylized facts that characterize the subprime market (relative to the prime

market) are:2

1. High interest rates.

2. High points and fees.

3. Prevalence of prepayment penalties.

4. Lending based largely on asset value, rather than borrower characteristics, with

low loan-to-value (LTV) ratios and high rejection rates.

5. Specialized subprime lenders who cater only to subprime borrowers and who have

limited access to secondary mortgage markets.

6. Large rate differences between marginally prime and marginally subprime

borrowers.

Some of these characteristics are changing, especially as information improves. As a

result the menu of choices analyzed here is expanding.

Our focus is on whether pricing differences between prime and subprime markets can

be explained by option-based approaches to mortgage pricing and on whether or not

historic market structure can be explained by two asymmetric information models. On

the pricing side we argue that subprime options are different in some ways from prime

options, causing different contracts and prices. In both of the market structure models

asymmetric information causes investors to set up incentives for borrowers or loan

sellers to reveal information, primarily through costs of rejection. In the first model, a

combination of signaling and screening leads to a separating equilibrium in which

lenders get borrowers to reveal hidden risks through their application/rejection strategy

and down payment requirements. In the second model, loan purchasers use rejection

(through quality control sampling) as a device to get sellers to classify loans for them.

While we cannot prove that our models are all that there is to it, we do find that the

enumerated six points are largely consistent with them.

Our models assume that borrowers have better information about themselves than

lenders have about them, and that they act rationally based on that information. If this

were true in all cases, then it would be unlikely that fighting Bpredatory lending^practices, which are more concentrated in the subprime market, would be at the forefront

of public policy making as it is today.3 Richardson (2002) explores predatory lending in

the context of a market with rational borrowers seeking to refinance who cannot

determine predatory subprime lenders from good, non-predatory subprime lenders due to

weak signals.4 We do not attempt to explain predatory lending; however, Richardson’s

model is consistent with ours, and indeed, could coexist with our theoretical framework.

We do discuss some implications of borrower self-misclassification.

168 CUTTS AND VAN ORDER

2. Options and risks in the prime and subprime segments

We can think of mortgage borrowers as having three options:

1. An option to default, which can be thought of as a put option, giving the borrower

the right to put the house back to the lender in exchange for the loan.

2. A delinquency option, which can be thought of as a fixed-rate line of credit that

gives the borrower the right to borrow at the mortgage rate plus penalty.

3. An option to prepay, which can be thought of as a call option, (e.g., exercised

when mortgage rates fall, or more broadly, when the borrower can get a better

deal).

While option-based models (particularly regarding the first and third options) are well

studied in the finance and real estate literature on prime market loans, little has been done

on the options held by subprime borrowers and how their options differ from those of

prime borrowers. This is in part due to a lack of data. Simply stated, when interest rates

fall, prime borrowers will more or less ruthlessly exercise their option to refinance into a

lower rate mortgage and, if home values fall sufficiently, borrowers will more or less

ruthlessly exercise their option to default.5 Subprime borrowers hold these same options,

but they are more likely to have difficulty qualifying for a new mortgage, so they are less

likely to refinance when rates fall. However, they also hold an option to prepay and take

out a prime mortgage when their credit condition improves even if mortgage rates have

stayed level or increased. This produces an asymmetry, characteristic of all options, in

that lenders lose the good borrowers but keep the bad ones.

Additionally, subprime borrowers, due to already weaker credit histories, may also

place more value on the option to be delinquent (or less value on the cost of a worse

credit rating), without defaulting, if that option offers a lower cost way to finance their

activities. That is, in a financial emergency borrowing their mortgage payment amount at

the mortgage rate inclusive of the penalty for late payment may be lower cost than

entering the unsecuritized debt market for high-risk borrowers, drawing down assets, or

raising money informally.

Here we investigate the stylized facts that support differences in the way these options

are exercised and how the market tries to mitigate these risks.

2.1. Default risk

Option-based default models such as those surveyed in Hendershott and Van Order (1987)

and Kau and Keenan (1995) generally begin with default as a put option on the property

and focus on how the option is exercised when the option is Bin the money.^ Most analysis

and empirical work (see, for example, Deng et al., 2000) focus on both negative equity (the

measure of Bin-the-moneyness^) and some trigger event as necessary for the option to be

Bexercised.^ The stylized fact of higher default rates in the subprime segment is generally

interpreted as being due to subprime borrowers being more susceptible to trigger events

ON THE ECONOMICS OF SUBPRIME LENDING 169

and/or that they have property that is more likely to fall in value (e.g., due to neighborhood

effects). Hence, credit history is expected to be especially predictive in conjunction with

down payment (which is the extent to which the option is out of the money at origination).

Thus, higher default rates are often posited as the reason for higher interest rates in the

subprime market, even given a larger down payment.

The empirical evidence on pricing shown in Table 1 supports this correlation. For 30-

year, fixed-rate mortgages in the first week of September 2002, the average conventional

prime loan applicant was quoted a 6.14 annualized percentage rate (APR), well below

the average APR of 7.20 percent quoted for the very best, or AA+ quality, subprime

loans.6 Thus, marginally subprime and marginally prime borrowers pay substantially

different rates. Subprime loans on average were quoted a rate of 9.83 percent APR. The

riskiest subprime loans, BCC^ grade, were quoted an average APR over 6.5 percentage

points higher than the average prime loan.

Although the very best BAA+^ and BAA^ subprime loans are described similarly to

prime loans, they do not perform like them.7 As of June 30, 2002, the serious

delinquency rate for conventional, prime loans was 0.55 percent and the loss rate was

running at just 1 basis point of original unpaid principal balance (UPB).8 In contrast,

AA+ subprime loans had a serious delinquency rate of 1.36 percent but a loss rate of

5 basis points of UPBVfive times the loss rate of conventional prime loans. FHA

loans, which carry a rate similar to conventional prime loans but have an insurance

premium roughly equivalent to paying a 100 basis point higher rate, had a serious

delinquency rate of 4.45 percent with losses running just under 30 basis points, putting

FHA loan performance between AA+ and AA quality subprime loans.9 BC^ and BCC^grade subprime loans had the highest delinquency rates, both exceeding 21 percent, and

the highest loss rates, more than 2.6 percent of UPB, among all loan grades.

We examine the correlation between credit and collateral and loan performance in

Table 2. Serious delinquency rates for a sample of loans originated between 1996 and

2001 are shown for each market segment by borrower credit history as measured by the

borrower’s FICO\ score and the loan-to-value ratio (LTV) at origination.10 Since

average home values have increased in every state over this period, borrowers generally

have an even greater equity stake than our table demonstrates. The loans are further

divided by whether their states’ house-price appreciation has been stronger or weaker

than the national average over the period.

In both the prime and subprime segments, the incidence of serious delinquency declines as

FICO scores increase. In the prime segment, we also find that as LTV decreases (equity

increases) the rate of serious delinquency decreases. But in the subprime market, the amount

of equity a subprime borrower has in their home is not a deterrent to delinquency. For

example, in all but two subsections in the subprime panel of Table 2, borrowers with high

LTVs (equity of 10 percent or less) are less likely to be seriously delinquent than borrowers

who have between 10 and 30 percent equity in their homes.11

Differences in delinquency, default, and loss rates between the subprime and prime

segments and the relative insensitivity of subprime loan performance to LTV broadly

justify higher rates for subprime loans, even though they generally have larger down

payments. Higher servicing costs (due to more frequent and longer delinquency spells)


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for subprime loans also support higher rates. The evidence above, however, does not

indicate how much higher the rates should be.

2.2. The delinquency option

That delinquency rates decline with equity in the prime market but not in the subprime

market suggests that delinquency is a prelude to foreclosure in the prime market, but

is more like a short-term borrowing option (line of credit) in the subprime market.

This use of the delinquency option in the subprime market is reinforced by differences

in the timing of delinquency patterns. Generally, in the prime market, the proportion

of loans 60-days delinquent is lower than the share of loans 30-days delinquent, and

90-day delinquencies are lower yet. For example, in Table 1, prime 30-day delin-

quencies as of June 30, 2002 were 1.73 percent of loans outstanding, 60-day delinquen-

cies were 0.31 percent, and 90-day delinquencies were running at 0.28 percent. Only

Table 2. Relative loan performance by market segment, FICO score, LTV, and house price appreciation rate

(Percent of loans ever 90+ days delinquent).

LTV

Prime market segment Subprime market segment

Origination decision FICO score Origination decision FICO score

Low Medium High Very high Low Medium High Very high

Low house price appreciation states

High 14.10 7.21 3.21 0.99 22.53 11.51 9.58 7.15

Medium-high 10.85 6.50 2.54 0.78 26.95 17.69 12.55 9.35

Medium 9.04 5.29 1.87 0.44 29.56 17.80 11.87 11.11

Low 5.64 3.25 1.01 0.25 25.56 12.74 9.94 6.48

Medium house price appreciation states

High 12.49 5.28 2.11 0.68 27.39 13.15 8.27 3.51

Medium-high 8.41 4.37 1.64 0.47 24.12 14.74 9.45 4.56

Medium 6.01 3.02 1.00 0.23 27.42 15.52 11.01 7.39

Low 4.20 2.00 0.64 0.15 28.07 12.01 7.25 3.16

High house price appreciation states

High 12.37 4.82 1.82 0.69 20.35 9.46 6.02 3.48

Medium-high 7.05 3.46 1.38 0.42 15.45 10.13 7.33 6.33

Medium 4.33 2.09 0.72 0.18 17.86 9.48 6.98 4.86

Low 3.09 1.41 0.46 0.12 18.73 8.60 5.69 3.66

Notes: FICO Score category: Low (�620), Medium (>620 and �660), High (>660 and �720), Very high

(>720). LTV category: Low (�70%), Medium (>70% and �80%), Medium-high (>80 and <90%), High

(�90%). House-price appreciation (HPA) determined by 5-year growth rates for the period 1Q1997–1Q2002

using the Freddie Mac Conventional Mortgage Home Price Index State seriesVLow HPA states: AK, HI, ID,

ND, NM, NV, UT, WV, WY; High HPA states: CA, CO, DC, MA, ME, MN, NH, NY. Rates are relative to the

rate for prime loans with High FICO scores, Medium LTVs, and Medium HPA. Loans were originated from

1996Y2001 and observed through 2002 Q1.

Source: LoanPerformance, San Francisco, CA.


0.15 percent of prime loans go on to become foreclosed real-estate-owned (REO) or

are disposed of through foreclosure alternatives such as short sales or deed-in-lieu

transfers.

For subprime loans this trend is reversed, with increasing rates the more serious the

delinquency. Again referring to Table 1, subprime 30-day delinquencies were running at

7.35 percent of loans outstanding as of June 30, 2002, 60-day delinquencies were 2.02

percent, but 90-day delinquencies were running at 4.04 percentVdouble the 60-day rate!12

Option One Mortgage Corporation (OOMC) (2002a) reports an REO rate for subprime

loans that is less than one-third the foreclosure rate, indicating that most seriously delinquent

subprime borrowers avoid default.13 FHA loans follow a pattern similar to subprime loans.

Ninety-day delinquency rates can exceed 60-day delinquency rates only if borrowers

who fall behind in their mortgage payments miss two, then three, payments, and then begin

to pay again without making up all of the missed payments immediately, thus remaining

90-days late for an extended period. Since each period some 60-days delinquent loans will

become 90 days late, the total number of loans 90-days late will exceed that of loans 60-

days late under this scenario. Apparently, subprime borrowers tend to exercise the option

to take out short-to medium-term loans from their mortgage lenders in amounts equal to a

month or two month’s worth of mortgage payments while prime borrowers do not.

The patterns of subprime delinquencies in Tables 1 and 2 are more consistent with the

theory of borrowers getting into trouble and borrowing at the subprime mortgage-plus-

penalty rate than as a prelude to default. Presumably, prime borrowers have more to lose

from being delinquent due to their better credit record, and they have better access to

credit markets and wealth to get them through difficult times.14 Thus, the delinquency-

short-of-foreclosure option is less valuable to them.

2.3. Prepayment options

Given the very high interest rates in the subprime market and the jumps in rates between

grades within the subprime market as well as between the subprime market and the

prime market, subprime borrowers have a strong incentive to refinance their loans if their

credit records improve. Prime borrowers may also have the incentive to refinance when

their credit quality improves, but because the room for improvement in credit history is

smaller and the default cost function is relatively flat for borrowers with good credit

history, the default option is less valuable than the prepayment option motivated by

changes in interest rates. Figure 1 illustrates the co-movement of prepayment speeds with

interest rates. Prime prepayment speeds are very high when interest rates are relatively

low and when interest rates climb slightly, prime prepayment speeds slow quickly. The

subprime market prepayment speeds are relatively insensitive with respect to interest

rates, but were much higher on average over the period. Indeed, subprime prepayment

speeds generally declined over the period June 1998YDecember 2000 yet interest rates

both declined and increased significantly over that same period.15

Table 3 documents that the incentive for subprime borrowers to refinance when their

credit improves can be quick to develop. In an analysis of FICO score migration trends


by Fair, Isaac and Co. based on more than 400,000 individuals with bankcard accounts in

the late 1990s, more than 30 percent of individuals with very low FICO scores (below

600) improved their scores by 20 points or more within three months. Since high scores

are indicative of consistently good credit management, individuals with initial scores

over 700 had a much lower chance of improving their score by 20 points or more but

were also less likely to have their scores fall by more than 20 points.16 Hence, the

Figure 1. Prime and subprime prepayment trends and mortgage interest rates, 1995Y2003.

Table 3. 3-month credit bureau score migration by score range.

Current observation score

Migration

amount

Less

than 550

550 to

599

600 to

649

650 to

699

700 to

749

750 &

higher All

Low to j41 2.9% 8.9% 10.4% 6.7% 4.7% 3.3% 5.2%

j40 to j21 7.9% 8.8% 6.9% 7.3% 7.7% 7.9% 7.7%

j20 to +20 54.4% 50.1% 59.4% 68.2% 71.9% 83.4% 72.8%

+20 to +40 16.3% 15.9% 14.6% 11.9% 11.5% 4.8% 9.7%

+41 to high 18.2% 16.1% 8.4% 5.6% 3.9% 0.3% 4.3%

Column total 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Notes: Cells show column percentages. Migration is measured over a 90-day period for more than 400,000

accounts taken from a stratified random sample of bankcard data from the late 1990s. Fair Isaac credit bureau

scores provided by TransUnion.

Source: Fair Isaac and Co., San Rafael, CA.


stronger credit-score and weaker interest-rate prepayment propensities suggested by the

theory are consistent with the observed small interest-rate elasticity and the higher

average level of prepayment rates of borrowers in the subprime market.

Lenders and investors in the mortgage market have tried to control the optionality

inherent in mortgages by charging rates and fees that compensate them for the credit risk

inherent in the loans they originate and by encouraging the take-up of prepayment penalty

clauses that inhibit a borrower’s ability to prepay the loan. In exchange for the prepayment

limitations, borrowers receive a lower interest rate. Subprime loans are more than three

times as likely as prime loans to have prepayment penalty terms in their mortgage contract,

and the refinance (refi) lock-outs are usually in effect for two to five years.17 Prepayment-

penalty clauses are likely to be binding constraints on borrowers that have them. For

example, for many borrowers who took out loans in 1998, there was a strong refi incentive

due to falling interest rates. Average prime mortgage rates were 7.48 percent in January

1998, fell to 6.71 percent in March 1999, and rose back to 7.5 percent in December 1999.

OOMC (2002a) reports that among subprime loans originated in 1998, 10 percent of loans

with prepayment penalty clauses prepaid by the thirteenth month after origination, but

more than 20 percent of loans without prepayment penalties prepaid within 13 months.

OOMC’s experience suggests prepayment penalties are effective deterrents.

3. Market structure and separating equilibrium

Having separate prime and subprime markets rather than a single market in which different

risks are priced suggests not only imperfect information, but also asymmetric information.

Models of separating equilibrium, where lenders offer up contracts designed to get

borrowers to reveal information about themselves, are candidates for analyzing such

situations. We assume that there are three types of borrowers. Each borrower knows its

type but lenders don’t, so lenders want to induce borrowers to reveal their risk type. Two

sources of separation devices are entertained: collateral and rejection (i.e., underwriting).

Collateral (down payment) as a signal of credit risk has been investigated in a variety of

contexts. For instance, Rothschild and Stiglitz (1976) and Bester (1985), in general models,

and Brueckner (2000) and Yezer et al. (1994), in mortgage market models, produce separating

equilibrium models in which it is assumed that supplying collateral is costly, more so for the

riskiest types because they have inside information that they are riskier and as a result want to

put up less of their own money (see Freixas and Rochet (1997) for a survey). On the other

hand, research like Harrison et al. (2004) argues that if default is costly to borrowers, riskier

borrowers might signal more risk by offering to make bigger down payments.

An alternative approach is to assume that the worst borrowers are also likely to be Bcredit

constrained^ in the sense of having low-wealth endowments, making raising money for a

down payment especially costly. A reason for arguing this way is that the worst borrowers

are likely to have had the worst past experience and not have any wealth left or sources

from which to borrow it (alternately it could be assumed that they have higher personal

discount rates). In what follows we appeal to this argument, which leads to the

proposition that safer borrowers can signal their status with higher down payments.


Underwriting has a more straightforward rationale. If having an application rejected is

costly, then we should expect riskier borrowers to opt for markets with less underwriting,

and this can be a device for separating the riskiest from the safest borrowers (see Nichols

et al. (2002) and Staten et al. (1990)) because application strategy will be a signal of

creditworthiness made credible by rejection cost (along the lines in Spence (1973)).

Ben-Shahar and Feldman (2003) present a model similar to ours in which there are two

dimensions to selection and signaling-screening exists.

3.1. The separating equilibrium model

3.1.1. Assumptions

There are three, risk-neutral, borrower types: lowest risk or prime, denoted A; higher

risk or subprime, denoted B; and extremely high-risk, denoted C; and three possible

market types: prime, P; subprime, S; and Bloan shark,^ L.18 The latter is a residual

market in which any borrower can get a loan without underwriting or a down payment,

but at a high interest rate (or alternately where rates are too high and borrowers opt out).

We let i denote borrower type and j market type. There are two possible equilibrium

types: pooling, in which there is one market in which all three borrower types pay the

same rate; and separating, where there are three market types and one rate in each.

The three borrower types choose application strategies that minimize expected costs

subject to pricing constraints. Expected costs are given by the sum of:

1. The rate paid plus the cost of equity used in the down payment, all multiplied by

the probability of the loan being accepted,

2. The cost of having a loan rejected multiplied by the probability of rejection,

3. Underwriting costs, which are paid regardless of whether the loan is accepted or

rejected.

Lenders are also risk neutral, and the equilibrium market structure is assumed to be

characterized by free entry and zero profits.

To simplify the analytics and bring out the role of equity as a signal, we assume that

equity has no direct effect on defaults, working only as a signaling device.19 Thus

borrowers have simple expected default costs, dA, dB and dC, respectively. Because C

type borrowers have had especially poor credit histories and are especially risky,

collateral is more costly to supply for C than B, but we assume that it is the same for A

and B (or at least the differences are much smaller than those between B and C

borrowers). Then, letting Ei (e) be the cost of equity for the ith type borrower, we assume

EA eð Þ ¼ EB eð Þ < EC eð Þ; and 0 < E 0A eAð Þ ¼ E 0

B eBð Þ < E 0C eCð Þ: ð1Þ

Underwriting, which is essentially information gathering, has a cost that varies with the

amount of time spent, u, doing it. The cost in market j is given by U(uj), with U 0(uj) > 0.


After gathering information, the underwriters classify borrowers. We let fij(uj) be the

probability that borrower type i will be classified as relatively risky in market type j. Then

fAP (uP) is the probability that an A or Bprime^ borrower will be (mis)classified B or

Bsubprime^ (and therefore be rejected) and fBP(uP) is the probability that a subprime

borrower will be (correctly) classified as subprime in the prime market (and be rejected).

More information means better classification. Thus, it is assumed that in the prime market

f 0APðuPÞ < 0; f 0

BPðuPÞ > 0;

f 00APðuPÞ > 0; f 00

BPðuPÞ < 0;ð2Þ

representing the notion that underwriting helps safer borrowers, hurts riskier ones, and

there are diminishing returns to underwriting. We further assume (at least because

probabilities are bounded) that fAP0 (uP) and fBP

0 (uP) both approach zero as u increases.

Similarly, in the subprime market the Bs have lower credit cost than Cs and

f 0BSðuSÞ < 0; f 0

CSðuSÞ > 0;

f 00BSðuSÞ > 0; f 00

CSðuSÞ < 0;ð3Þ

where fBS(uS) > 0 and fCS (uS) are the probabilities that B and C, respectively, will be

classified as BC^ or extreme-risk within the subprime market (and therefore be rejected).

We also assume that fBS0 (uS) and fCS

0 (uS) both approach zero.

For the separating equilibrium model to work, there has to be a cost to borrowers of

being rejected and the expected cost will have to be highest for the highest risks. We

assume that the cost of rejection comes from reapplying and eventually borrowing at a

higher rate as well as incurring further underwriting and delay costs. Assume that these

(gross) costs are given by Kij (uj). Then the expected net cost of rejection is defined as the

probability of rejection times the difference between Kij (uj) and the borrowing rate Rj

plus equity cost Ei (eij). This net cost is given by Tij(uj), which is assumed to be given by

a fixed cost, tj, which is the same for all borrower types within a market but can differ

across markets, times the probability of being rejected, which is the probability of being

classified as a B in the A prime market or as a C in the B subprime market. Thus, in the

subprime segment, B’s expected rejection costs are TBS(uS) = tS fBS (uS).

Borrowers choose application strategies that minimize total expected cost, which vary

by borrower and market. For borrower type i in market type j expected costs are given by

Wijðuj; ei j;RjÞ ¼ bRj þ EiðeijÞc b1 � fijðujÞc þ KijðujÞfijðujÞ þ UðujÞ¼ Rj þ EiðeijÞ þ tj fijðujÞ þ UðujÞ:

ð4Þ

We assume that underwriting costs U(uj) are passed along to the borrower, for example

through an application fee, regardless of the lending decision.

3.1.2. Equilibrium

Equilibrium is given by conditions for borrowers minimizing cost, zero profit for lenders,

and nonnegative levels of e and u. We begin by looking at equilibrium in the subprime


market assuming that the As have been separated out, and then we move to the prime

market and show how the As are separated out. We first need to show that a pooling

equilibrium is not possible, which is common in models like this one (see Freixas and

Rochet (1997)). In particular, a pooling equilibrium, in which all borrowers are offered

the same rate and terms, can be broken by offering the Bs a slightly better rate in

exchange for more equity, which, because equity is less costly for the Bs, will separate

the Bs from the Cs. Hence, if there is to be an equilibrium, it will have to be a separating

one, and only one rate will be charged in each market. We now turn to characterizing a

separating equilibrium that sorts borrowers by specifying a minimum down payment and

an amount of underwriting.

The zero profit condition implies that lenders set rates at break-even costs. Then

letting Dj be the expected default cost in the jth market

Rj ¼ Dj: ð5Þ

Then substituting for Rj into Wij(), we have

Wij eij; uj jDj

� �¼ Dj þ Ei eij

� �þ Tij uið Þ þ U uj

� �ð6Þ

with

@Wijðeij; uj jDjÞ=@eij > 0 and

@Wijðeij; uj jDjÞ=@uj > 0ð7Þ

for ij = BP or CS (i.e., positive effects on costs of e and u for the riskier applicants)

@Wij eij; uj jDj

� �=@eij > 0 and

@Wij eij; uj jDj

� �=@uj >< 0

ð8Þ

for ij = AP or BS (i.e., ambiguous effect of u for the safer applicants).

From (1)

@WAP eP; uP jDPð Þ=@eP ¼ @WBP eP; uP jDPð Þ=@eP and

@WBS eS ; uS jDSð Þ=@eS < @WCS eS ; uS jDSð Þ=@eS :ð9Þ

Furthermore, in a separating equilibrium

DP ¼ dA;

DS ¼ dB and

DL ¼ dC

ð10Þ

Because ¯Tij (uj) /¯uj approaches zero, we expect that ¯Wij (eij, uj |Dj) /¯uj > 0 if u is

large enough. If we assume for simplicity that Tij (uj) is the only source of nonlinearity

(through the probability of rejection), then borrower costs become

Wij ej; uj jDj

� �¼ Dj þ �iej þ Tij uj

� �þ �uj: ð11Þ


Then the isocost curves (incorporating the zero profit condition) are of the form

eij ¼ � Dj þ Tji uj

� �þ �uj

� �=�i þ$ Iij uj

� �ð12Þ

and their shape depends on the shape of T() and in turn fij (uj)), and the relative sizes of

the �i. Note that expected rejection costs are indeed higher for riskier borrowers in each

market because while cost given rejection is constant within markets, riskier borrowers

are more likely to be rejected.

From (8) we know that for the better borrowers, underwriting has an ambiguous effect

on costVbecause it increases underwriting cost but also increases the probability of

being well classified, which lowers expected rejection cost. For the worst borrowers,

underwriting unambiguously raises cost. Then in both the prime and subprime markets

Iij(uj) is decreasing in u for the riskier class (the Bs in the prime market and Cs in the

subprime), so that their isocost curves are always downward sloping, and from condition

(3), convex to the origin. However, for the safer class in either market (the As in the

prime market and Bs in the subprime), the shape is ambiguous. Hence, the isocost curves

in these cases can be upward sloping, but they are eventually downward sloping. From

(2) and (3) the second derivative for safe borrowers is positive, so that from (8) the

isocost curves are concave to the origin in any case.

A separating equilibrium in the subprime market has to be such that Cs apply only to

the L (or Bloan shark^) market and Bs only to the S (or subprime) market, and profits are

zero and costs are minimized. Then for a given level of u and e in the L market,

equilibrium requires that u and e in the B market be enough to keep the Cs from applying

in the S market. If e and/or u in the L market are positive, then for any level of e and u

in the S market that is a candidate for equilibrium a lower level of both e and u in the S

market will make Cs better off without affecting Bs. Hence, equilibrium requires that e

and u both be zero in the L market, u and e be set in the S market so they are just enough

to keep the Cs out and costs be minimized for Bs.

Then, using (10), the separating equilibrium levels of e and u are determined by solving

Min WBSðeS ; uS jdBÞ subject to

WCSðeS ; uS jdBÞ � WCLð0; 0jdCÞð13Þ

This is depicted in Figure 2, with isocost curves shown for Bs and Cs in the subprime

market. The positive slope at low levels of u for the Bs reflects the possibility that the

benefits of underwriting might offset its costs at low levels of underwriting. The

tangency solution is given by g and the equilibrium levels of e (the minimum down

payment) and u are indicated by eS* and uS*. Because the isocost curves for Cs are

convex, the curves for B concave and �C > �B, there can be an interior solution.

If the isocost curves of WBS (eS, uS |dB) have an upward sloping part there will always

be at least some underwriting, but we cannot rule out a corner solution with no down

payment minimum. As is generally the case in models like this, it cannot be proven that

this equilibrium exists. In particular, if there are few C borrowers then neither

underwriting nor down payment will be worth their cost in the subprime market, but

the pooling equilibrium is still broken for the reasons given above.


Now we go to the prime market. Assume, as discussed above, that A and B have the

same collateral cost, �A = �B, so that collateral reveals nothing about As versus Bs. In this

case, the Bs are the riskier type. The solution requires setting e and u in the prime market

at levels high enough to keep the Bs (and Cs) out of the prime market, P. If eS* and uS* are

the equilibrium levels of e and u in the subprime market, then the equilibrium in the P

market is given by solving

Min WAPðeP; uP jdAÞ subject to

WBPðeP; uP jdAÞ � WBSðe*S ; u*S jdBÞð14Þ

The isocost curves are similar to those in the subprime market; the only difference in

costs is due to expected rejection costs. From (2) and �A = �B, the isocost curves for As

are always flatter than those for Bs. This is depicted in Figure 3. The solution must be a

corner solution, at h in the figure, with no down payment restrictions in the prime

market, and just enough underwriting to keep the Bs from applying.

3.2. Comments

1. The above describes a separating equilibrium in all three markets: the Cs will only

apply to the L market, the Bs to the S market, and the As to the P market.

2. There are three distinct lending markets, but just two mortgage markets; the third

being a loan shark market, with no down payment or underwriting.

3. There is less underwriting in the subprime market even though that would appear

to be where it is where it is most Bproductive.^

Figure 2. Equity and underwriting as a separating equilibrium in the subprime market.


4. The subprime market has minimum down payments, but the prime market does

not.20 In both mortgage markets, there can be LTV pricing (if we introduce the

realistic assumption that LTV directly affects risk) subject to the minimum in the

subprime market.

3.3. Rejections

The model, so far, has no rejections because everyone applies to the right market. Table 1

suggests that there are significant rejections and subprime markets have much higher

rejection rates than prime markets. Our model is consistent with a reasonable model of

rejections in which rejections are mistaken applications, (e.g., because applicants do not

know their own credit category or the lenders’ standards). If the prime market is more

uniform and/or its participants more financially sophisticated, then it can have lower

rejections relative to the subprime market, where borrowers are more likely to be first-

time borrowers or are likely to be less financially sophisticated or experienced.21

3.4. Self-misclassification

The model requires that people who classify themselves as B or C be, as a group,

more likely to default than those who classify themselves as A or B, but that need

not be true of all members. Some As and Bs may simply misclassify themselves by

overestimating their risk category, in which case they will cross-subsidize borrowers who

Figure 3. Equity and underwriting as a separating equilibrium in the prime market.


really are riskier. A benefit of better underwriting is that such misclassification will be

less likely.

4. The secondary market and market structure

We posited above that the bifurcation of the subprime and prime markets is because the

markets elicit signals from borrowers that lead to a separating equilibrium. The model is

of some historical interest, but the recent trend toward use of the Internet to apply for

loans and the advent of banks with subprime subsidiaries that send applications to the

subsidiary suggests that rejection costs may be falling. Here we focus on information

asymmetries between types of lenders rather than between borrowers and lenders,

leading to bifurcation between primary and secondary mortgage markets. It has been

posited by Lax et al. (2004) that subprime borrowers pay rates that are higher than the

differences in prime and subprime default rates would indicate. We examine why this

might be true by allowing the distribution of credit risk types to be continuous rather than

having just three distinct types.

The basic model is that banks originate loans, which are modeled as having put options

on the property securing the loans, and then either hold them or sell them to the secondary

market, SM; but they have better information and can select against SM. However, SM

has lower costs. For instance, banks may have better local information than SM, and/or

SM may not, for regulatory reasons, be able to use the information, or while both SM and

banks may have access to borrower credit history (e.g., FICO score), bank underwriting

may help predict which low FICO score borrowers will improve (e.g., because the reason

for the low score was a temporary setback, like an illness). Alternatively, there may be

lenders who choose not to underwrite, and they run a loan shark market.

This model has an equilibrium, which might restrict SM to the worst part of the

market, like the loan shark segment above, and perhaps to a very small part of it. To

obtain a secondary market like the one we actually observe today, we bring back a

version of the costly rejection model in the previous section by assuming that SM

chooses a cutoff point for loan quality, rejects loans below the cutoff, and punishes

sellers who deliver bad loans.

4.1. The model

We begin with a simple, discrete heuristic model with just two types of loans: Bgood^ in

which case default and transaction costs for banks is $5; or bad, in which case cost is

$10. For SM, costs are $1 less than for banks in each case, but SM cannot distinguish

good loans from bad. Assume that banks have two good loans and one bad loan. By

offering a guarantee fee just under $10, the SM can just induce the bank to part with the

bad loan, but it will have to offer $5 to get the two good loans as well. But at $5, it will

lose $4 on the bad loan and only make $2 on the two good ones. The competitive

equilibrium (zero profit) is for SM to hold only the risky loan, and it will have a $9 price.


The banks will hold the safe loans, and their price will be $5. This will continue to be the

case if there are three good loans, but if there are four good loans SM will be indifferent

between holding just the bad loan and taking over the entire market. At five good loans

there will be a discrete change in price (to $4 from $9 for bad loans and to $4 from $5 for

good loans) and market structure, and SM will suddenly take over the entire market.

However, if one bad loan is added to the available pool or SM’s cost advantage falls to

just $.50, the equilibrium will revert back to one with SM taking only the bad loans.

Hence, equilibrium will depend on the shape of the risk structure as well as the

difference in costs between the two markets. This simple model shows that despite its

lower costs the secondary market can be confined to a small part of the market and that

market structure might be Bfragile^ in the sense of being sensitive to small changes in

cost or risk structure. This suggests incentives for SM to improve information, because

while a large part of the mortgage market has relatively low cost there is a sizeable

segment with much higher costsVwhich can affect market structureVso there is an

incentive to try to separate this risky Bsubprime^ segment from the prime market.

4.2. Actors and loans

We assume there are two types of risk neutral financial institutions, banks and the

secondary market, SM. The loans are originated by the banks, which may or may not sell

them to SM. Loans are divided into submarkets defined by the publicly available

information shared by all loans in the submarket. For a particular submarket, we assume

that there is a fixed supply of loans given by N .22 The portion of the submarket held by

SM is denoted by s, and the portion held by the banks is b, so that N ¼ b þ s. We assume

that the loans are for one period and are secured by the borrower’s house. The value of

the property securing the loan is a random variable, X. It is assumed that loans take the

form of discount bonds that pay $1 at the end of the period. Interest, credit, and other

costs are paid by the firm in the form of an upfront discount. At the end of the period, the

borrower maximizes wealth by paying off the loan if X Q $1 and defaulting otherwise.23

Hence, the borrower has a put optionVto sell the property back to the lender at a price

equal to the payment due on the loan. All loans are the same size; the only question is

who holds the loans.

Associated with every loan are two costs. The first is the basic cost of funds, which

does not vary with risk. This cost is denoted by cx, x = b, s, and cb > cs, (i.e., for reasons

discussed above, SM has lower funding costs than banks). The second is default cost,

which is the value of the put option on the property.

4.3. Information structure

SM has an information disadvantage. We assume that monitoring loans ex ante is

sufficiently costly to SM relative to benefits that it does not take place. We discuss ex

post monitoring and rejection in the next section. There are two types of information:

that which is known to everyone; and that which is known exactly to the banks but only


in a distribution sense to SM, which defines a submarket. The second type of information

is the source of the model’s information asymmetry.24

Within a submarket, the relevant information is the expected cost of default. Because

everyone knows at least the distribution of default cost across borrowers, everyone can

order the expected costs of default from the safest to the riskiest loans. This ordering

produces the offer curve faced by SM as well as its marginal cost curve, and we assume

that the ordering can be used to represent default costs by the function C(N), N 2 0;N� �

,

which gives (increasing) default costs as we vary the number of loans, N from the safest

(N = 0) to the riskiest N ¼ N� �

.

C(N ) comes from the option to default and give up the collateral at the end of the

period if the value of the collateral is less than one. Hence, the value of the option

depends on the distribution function of the level of X at the end of the period, denoted

by X1, which in turn will be conditional on the value of X at the beginning of the period,

denoted by X0. We represent the value of the option by V(X0).

Let F(X0) be the distribution function of X0 across borrowers. Then F(X0) gives the

number of borrowers for whom N is less than or equal to X0, and the inverse of F(),

G(N ), N 2 0;N� �

, ranks borrowers from riskiest to safest according to their level of X0.

The information asymmetry is that banks know X0 for each loan, but SM only knows

F(X0).

Then if V(X0) and G(N ) are both well-behaved, C(N ) is given by

C Nð Þ ¼ V G Nð Þð Þ: ð15Þ

We assume that costs accelerate as we move from safest to riskiest loans, which makes

C(N ) convex. The convexity assumption is important, and it is consistent with a wide

range of models, particularly those that model default as an option on the underlying

collateral.25 For instance, Van Order (2003) shows that if ln X (that is, the change in

valuation) follows a random walk, then X1 has a lognormal distribution, and if traders are

risk-neutral (or markets are sufficiently complete), then V(X0) can be represented by the

Black and Scholes (1973) model. Then if F(X0) is given by a uniform distribution then

C(N) is convex and looks like the Black-Scholes representation of the value of a put

option as a function of the initial price of the asset on which the put is written (where N

is the initial price), and it is convex in N. If F(X0) is lognormal or has an BS^ shape, then

C(N) is convex for low levels of N but could be concave at high levels, for instance if

there is a small number of very safe loans. The key property of C(N ) is that it be convex

for low levels of N.

4.4. Behavior

Because banks have full information about risk they find it optimal to engage in risk-

based pricing, and assuming perfect competition among banks, the pre-SM price equals

marginal cost of each loan conditional on the index of risk level, N. That is, the up front

price charged by banks, rb(b), for taking credit risk is given by

rb bð Þ ¼ cb þ C bð Þ: ð16Þ


Because SM does not know the quality of any loan it purchases, it charges only one

price, rs(s), regardless of quality, and the loans that are purchased by SM are those with

cost to banks greater than rs(s). Hence, equation (16) becomes an offer (average revenue)

curve for SM, or

rsðsÞ ¼ cb þ C N � s� �

ARs; ð17Þ

As in the heuristic model above, the secondary market starts with the riskiest loan, N ,

and can bid it away from the banks by charging a rate, rs(s), just under cb þ C N� �

; as SM

decreases rs(s), it sweeps in more (successively less risky) loans, and rs(s) is the rate paid

by borrowers for loans purchased by SM.

The cost of adding one more loan to the portfolio of SM is given by the marginal

default cost plus SM ’s funding costs, or

MCs ¼ cs þ C N � s� �

: ð18Þ

Total revenue for SM is given by

TRs ¼ cbs þ C N � s� �

s; ð19Þ

and marginal revenue is given by

MRs ¼ cb þ C N � s� �

� C0 N � s� �

s: ð20Þ

Total cost is

TCs ¼ css þZ N

N � s

C ð Þd: ð21Þ

Subtracting total costs from total revenue produces total profits, which are given by

�s ¼ cb � csð Þs þ C N � s� �

s �Z N

N � s

C ð Þd: ð22Þ

Because the demand and marginal cost curves are downward sloping and parallel,26 price

cannot equal marginal cost, so we cannot have a perfectly competitive equilibrium with

all borrowers paying their marginal cost and SM ’s transaction costs.

4.5. Equilibrium

We consider the monopoly solution.27 SM maximizes profit, (22), with respect to s,

s 2 0;N� �

. Letting SM ’s funding advantage be denoted by � = cb j cs > 0, the profit

maximizing first order condition with respect to changes in s is either

� ¼ sC 0 N � s� �

if 0 � s < N or ð23Þ

� > sC 0 N � s� �

and s ¼ N : ð24Þ


Because � is positive and C 0 is bounded, s = 0 cannot be a solution. Equation (23) is

equivalent to MRs = MCs, and (17) applies to a corner solution, where SM takes over the

entire market. The monopoly model and solution with C(N ) are depicted in Figure 4.

Values of s that satisfy equation (23) occur at the intersections marked A and C, and the

value that satisfies equation (24) is marked E.28

4.6. Comments

1. There may not be an intersection if � is large enough. In that case the economies

of the secondary market completely dominate the selection problems, and s ¼ N.

2. If � is small enough, there is at least one interior solution. For the riskiest loan,

there is no selection problemVit will always go to SM because of SM ’s lower

costs.29

3. There can be two intersections. In the monopoly case MRs and MCs can intersect

twice, first at A, the Bloan shark^ equilibrium, as in the previous section, where the

secondary market takes the worst of the loans, as is typical of Akerlof (1970)-type

lemons models. It is a local maximum, but the second solution, at C, is a minimum.

4. There is a second possible equilibrium, the corner solution, for N sufficiently

large,30 shown in Figure 4 in the monopolist case as the point E. Marginal revenue

exceeds marginal cost at E, and E could be more profitable than A. Hence, the

monopolist will either operate as a loan shark based on A, or will serve the entire

market at E. In the free entry case, if N is to the right of D, then competition

Figure 4. Average and marginal cost and revenue functions for the secondary market.


among SM traders will force price from E (the monopoly outcome) to F, where N

and ACs intersect. Shifts from interior to corner solutions are discontinuous,

implying some instability of market structure (see Van Order (2003)).

5. The model applies to submarkets. Within a submarket, SM gets selected against and

has higher default rates than banks have. But this may not hold across submarkets.

For example, markets with steep slopes will have small SM shares, and markets

that are flat will have large shares. Hence, the model is consistent with SM having

lower default rates overall than banks, despite higher default rates in each market.

4.7. Rejections and market structure

The solution to this simple model is not entirely satisfactory to SM. It will have a loan

shark type equilibrium, where the worst is assumed of any loan that is delivered to SM,

or unless � is sufficiently large, an equilibrium that is fragile. Hence, SM is being

prevented from fully exploiting its lower costs. As is noted above in Tables 1 and 2, the

Bprime^ market is relatively large and has rather small variation in delinquency rates and

from other data we know it has rather little variance in default cost. On the other hand,

the subprime/high-FICO part of the market is smaller and has much larger variation in

delinquency rates. This suggests strong incentives to try to find ways to induce banks to

deliver only Bprime^ loans.

We introduce these incentives by reintroducing rejections, in this case of loans sold by

banks to SM. In particular, we allow SM to reject loans below some quality level,

typically labeled Binvestment quality.^ The historical mechanism for this has been for

SM to do quality control sampling of loans sold to it (by assumption, it is too costly to

underwrite all loans) and to require banks to repurchase loans that fail the investment

quality test. It is assumed that this is costly to banks (e.g., because of penalty charges,

bad reputation, etc.) and that this leads to a separating equilibrium, where the banks do

not deliver loans below the cutoff. This is equivalent to providing a Blicense^ to banks

that sell good loans, and our model is similar to the licensing model in Leland (1979).

Hence, we assume that SM can carve out a separating equilibrium, and we analyze how it

chooses the cutoff and the implications of that choice.

4.8. A rejection model

The contract for the banks specifies a minimum quality standard, N*, which can be

thought of as the prime/subprime cutoff, below which loans will be rejected with some

probability and cost, such that banks choose not to violate the contract,31 and we assume

that the banks engage in adverse selection so long as doing so does not violate their

licensing contracts with SM. We assume that the distribution of collateral value, F(X0),

across properties is s-shaped, so that, as discussed above, C(N ) can be concave over

some range of the safest loans.


SM chooses N* by maximizing profits with both s and N* as choice variables, s 2(0, N*), N* 2 0;N

� �. The new profit function is

�s ¼ cb � csð Þs þ C N* � sð Þs �Z N*

N*�s

C ð Þd: ð25Þ

The first order conditions for an interior solution (0 < s < N*) are

d�s=ds ¼ �� sC 0 N* � sð Þ½ � ¼ 0; ð26Þ

and

d�s=dN* ¼ sC 0 N* � sð Þ � C N*ð Þ � C N* � sð Þ½ � ¼ 0: ð27Þ

For � > 0 neither s nor N* can be 0, so the only corner solution possibility is

where s = N* (SM takes over the entire prime market). Equations (26) and (27) can be

rewritten as

C 0 N* � sð Þ ¼ C N*ð Þ � C N* � sð Þð Þs

; ð28Þ

and

�� C N*ð Þ � C N* � sð Þ½ � ¼ 0: ð29Þ

Additionally, once N* and s are chosen to satisfy (28) and (29), SM may have

additional profit opportunities within the remaining (loan shark) segment of the market

containing all loans riskier than N*. In that remaining segment if C(N ) is convex over

the entire range, only (26) applies. The equilibrium in the risky, loan shark market is

exactly the same as the one where there is no licensing, (the loan shark equilibrium),

with SM holding the riskiest loans in the remaining segment. Hence, steepness of C(N ) in

the riskiest region limits SM share. Neither the new equilibrium nor the old loan shark

solution exhibits the possibility of fragility that occurred in the previous model without a

quality cutoff.

The equilibrium is depicted in Figure 5. The key condition is that the slope at D

equal BE (the difference between the largest and smallest values of C(N )) divided by s,

the size of the market. Note that this condition requires that C(N ) have a concave region;

if not the solution is s = N*, and SM takes over the whole prime market. From (29), SM

covers the large homogeneous (or long flat) part of the market, with the difference

between the best and worst default being equal to �. It does not reach for the safest

borrowers because they are few in number and the one price policy that is optimal for SM

implies that to do so would mean foregoing profits from the more heavily populated

middle range.32

The market can have four distinct segments. Two segments have fixed prices: the loan

shark part of the market, denoted by s2, and the prime-quality SM segment, given by s1,

characterized by (28) and (29). The subprime lenders operate in the segment N2 (which

could have zero length) with risk-based pricing, and prime bank lenders operate along

N1, which could also have zero length, again with risk-based pricing.


4.9. Comments

1. The model shows how SM can choose its market by choosing an Binvestment

quality^ cutoff. This market is not the high-risk, loan shark market, but SM can

also be in that market. Its role is limited by the curvature of C(N ) because the

range of the market is limited by �. It is straightforward to see that if C(N ) is very

flat then SM will take over the entire market, but steepness will keep it out of the

high-risk end. Intuitively, the steepness of the curve is a measure of the degree of

adverse selection. SM chooses its cutoff in a way that keeps it away from the

adverse selection. In the high-risk section, SM’s role is limited as before by

adverse selection, and the steeper the curve the less high-risk business it will do.

Neither market exhibits the fragility possible in the model without a quality cutoff.

Hence, the investment-quality cutoff produces a type of stability.

2. There can be distinct discontinuous price jumps between the different segments as

shown in Figure 6. For the far right or Bsuper-prime^ segment of the market,

N 2 N � N1;N� �

, the banks engage in risk-based pricing and prices increase

continuously from cb þ C N� �

(equal to cb in the figure) to P1sm as loan quality

decreases. The traditional prime segment, s 2 N*;N � N1

� �, is covered by SM,

which charges everyone the same price, P1sm, and rations its purchases. The third

segment from the right, the subprime segment, N 2 [s2, N*], is once again served

by the banks and reverts back to risk-based pricing, but for loans with risk level

N* + " interest rates will be exactly � more than borrowers at N*. Thus, the

Figure 5. Profit maximization if SM defines Binvestment quality:^ concave and convex case.


difference to a borrower of being just to the right or left of N* is significant due to

the discontinuity in pricing.

3. The discrete jumps in pricing between market subsegments coupled with con-

tinuous pricing within a subsegment are supported by actual market pricing. In

Table 4, the rates for different subprime grades are presented.33 Within each

grade, prices vary by FICO score of the borrower and by LTV ratio. The pricing

differentials are much higher between similar loans in different grades than

between slightly different loans within a grade. For example, for a 65 percent LTV

loan with a 580 FICO score, the price jumps from 8.85 to 9.30 between the A and

B subprime grades, but within the A subprime grade having a slightly worse FICO

score, say 560, only raises price to 9.05.

4. Improved information increases the number of identifiable market segments. For

instance, historically the secondary market did not collect credit history for

individual loans but instead did quality control sampling, which did look at credit

history on individual loans, and punished (e.g., via repurchase) sellers who

delivered low-quality loans. Now credit history in the form of FICO scores is

available at close to zero marginal cost, so that market segments can be identified

by FICO score range. This however, does not end the selection problem. For

example, as described above, low FICO scores tend to migrate back up. At least

some of this can be predicted with local information, for instance about whether or

not the borrower was unlucky (e.g., sick) or is chronically bad at paying debts, and

some information that can be used in selling loans (e.g., some detailed location

variables) cannot be used in buying loans.

Figure 6. Profit maximization if SM defines Binvestment quality:^ concave and convex case.


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5. Final observations

Our study suggests that some standard economic models can explain the main

characteristics of the subprime market. Specifically, option-based models of subprime

markets are consistent with pricing and loan characteristics, particularly after taking into

account the FICO option, (i.e., the option to refinance after improved credit history).

Similarly, the separating equilibrium model describing the segmentation between

different lendersVthose specializing in prime loans and those specializing in subprime

loansVis consistent with sorting borrowers through signaling mechanisms.

The adverse-selection models presented here describe the stylized history of the sec-

ondary market reasonably well. Fixed pricing and jumps from the prime market to the

subprime market can be explained as a tug-of-war between the lower costs of the sec-

ondary market and the information advantages of the primary market. Improved

information and modeling technology have led to an increased (but still small) role of

the secondary market into riskier markets as well as some pricing on the basis of risk, by

expanding the number of market segments. In these models prices are still constant

within classes of risk, making it costly to the borrower who just misses the cutoff to the

next-lowest risk class. However, the borrowers in each risk class pay equal or lower rates

than they would in the absence of the secondary market’s presence in that market

segment.

Acknowledgments

Most of the work for the paper was done while Van Order was Chief International

Economist at Freddie Mac. The opinions expressed in this paper are those of the authors

and do not necessarily reflect the views of Freddie Mac or its Board of Directors. The

authors would like to thank: Ralph DeFranco and Sheila Meagher at LoanPerformance,

San Francisco, CA; and Craig Watts at Fair Isaac Corporation, San Rafael, CA, for their

generous assistance in providing data tables used in this paper. We also wish to thank

Richard Green, David Nickerson, Michael Fratantoni, and Peter Zorn, and participants

at the Credit Research Center Subprime Lending Symposium, the Federal Trade

Commission Research Roundtable on the Home Mortgage Market, and the Haas School

of Business Real Estate Seminar for their comments and suggestions.

Notes

1. For example, subprime loans are identified in Home Mortgage Disclosure Act (HMDA) data by whether

they were originated by a subprime lender; subprime lenders are identified by the US Department of

Housing and Urban Development (HUD) within the list of HMDA reporting institutions.

2. Many of these characteristics are documented in Lax et al. (2004) and Courchane et al. (2004); we also

provide some empirical evidence in the sections that follow.

3. For a description of alleged predatory practices see, for example, the text of the Predatory Lending


Consumer Protection Act of 2002 (http://www.senate.gov/~banking/chairman.htm) proposed by Senator

Paul Sarbanes (D-MD).

4. Large disparities between the demographic characteristics of prime and subprime borrowers are well

documented. See, for example, Lax et al. (2004), Courchane et al. (2004), and US Department of Housing

and Urban Development (2000). The reasons for these disparities and correlations between them and the

mortgage market structure are not explored here.

5. See the theory surveys by Hendershott and Van Order (1987), and Kau and Keenan (1995) on mortgage

options in the prime market. Two recent additions to the literature on prepayments are Bennett et al. (2000)

and Ambrose and LaCour-Little (2001). Prepayments motivated by a move are another option held by

borrowers, but this option has received relatively little attention in studies of prepayment behavior.

Clapp et al. (2001) examine prepayments motivated by moves separately from loan refinances and found

statistically strong evidence in support of doing so. Van Order and Zorn (2000) analyze default and

prepayment by location, income, and race/ethnicity. See the references cited within these articles for other

excellent studies on the exercising of default and prepayment options in the prime market.

6. Option One Mortgage Corporation, the source for our subprime interest-rate information, uses unique

subprime grade classifications not commonly used within the subprime market. Their AA+, AA, and A

grade loans are similar to what are commonly referred to as BAlt-A^ and BA-minus^ subprime grade loans,

and their CC grade loans are similar to what are commonly referred to as BD^ grade subprime loans in the

mortgage industry.

7. Table 4 provides a description of how Option One Mortgage Corporation, the basis of our subprime

performance information, defines different subprime loan grades.

8. Serious delinquency is defined as loans 90+ days late or in foreclosure (we do not have comparable data for

loans actually going through foreclosure). Losses are total net cumulative losses including revenues from

the sale of foreclosed properties and are net of mortgage insurance payouts. Delinquency rates are from

LoanPerformance, San Francisco, CA (updated information based on LoanPerformance (2002)), and losses

are based on Freddie Mac’s experience as a proxy for all conventional prime loans. See Freddie Mac

(2002a).

9. FHA loans are generally viewed as being of prime quality, however, higher delinquency and loss rates are

to be expected relative to conventional prime loans because of the emphasis of the FHA program on

creating low-cost funding for first-time homebuyers. FHA losses are from Weicher (2002); FHA

delinquency rates are from LoanPerformance, San Francisco, CA.

10. BFICO score^ is the common reference for the credit bureau score developed by Fair Isaac and Co. and

came into widespread use in the mortgage industry in the early 1990s, followed by the development of

automated underwriting systems in the latter 1990s. Straka (2000) provides similar evidence for loan

performance by FICO score and LTV and the efficacy of automated underwriting.

11. Ideally, we would like to examine default (REO) rates rather than serious delinquencies, but such data are

not available at this level of detail. We have less complete comparable data on loans that have gone into

foreclosure, but from the data we have the results look similar.

12. LoanPerformance also provided subprime performance statistics through June 30, 2002: 30-day

delinquencies at 3.33 percent; 60-day delinquencies at 0.96 percent: 90-day delinquencies at 3.5 percent;

and foreclosures at 4.21 percent. Because Option One Mortgage Corporation (OOMC) (2002aYc) provided

statistics on all loan grades, Table 1 reports the OOMC values for all subprime loans.

13. A loan in foreclosure is considered seriously delinquent (as are 90-day delinquent loans). Because it can

take years for the foreclosure process to clear, foreclosure rates can exceed 90-day delinquent rates even if

borrowers do not exercise the option to be delinquent without defaulting. Default, in the context of this

discussion, occurs when the lender successfully forecloses on the property or negotiates a foreclosure

alternative such as deed-in-lieu transfer or a short sale. The comparison is not as clean as we would like it

because these are flows. Better would be an analysis of conditional transition rates such as the likelihood of

becoming REO conditional on being in foreclosure.

14. Courchane et al. (2004) find that prime borrowers have a much larger financial safety net than do subprime

borrowers; specifically prime borrowers report having more savings, greater family resources, and better

credit opportunities than do subprime borrowers based on a survey conducted by Freddie Mac in 2001.


15. Subprime mortgage rates do generally track major benchmarks like the 10-year U.S. Treasury note rate, but

may not be as sensitive as prime rates to changes in these benchmarks.

16. According to Fair Isaac and Co. (2000), roughly 60 percent of the population has a FICO score of 700 or

more.

17. A survey of subprime borrowers conducted by Freddie Mac in 2001 (the basis of the Courchane et al.

(2004) study) shows that 41 percent of subprime first-lien mortgages have prepayment terms but just 12

percent of prime loans have them. Just 9.6 percent of prepayment lock-out periods are for one year or less

and 12.7 percent are for periods of five or more years. A Bbest practices^ trend in subprime lending started

in 2001 has decreased the length of generally acceptable prepayment lock-out periods from five to three

years. See Freddie Mac (2002b) and OOMC (2002d).

18. In the context of our model, A, B, and C are just names and do not necessarily correspond to any particular

grade of mortgage loans. Similarly, P, S, and L do not necessarily refer to any particular existing market

segment.

19. This is not quite as silly as it might appear. We should expect the interest rate to decline as equity increases

because increased equity takes the option to default further out of the money. But the option is a zero sum

game, which affects borrowers and lenders symmetrically, at least in the simplest models. We can consider

the rate above to be net of the option cost, increasing or decreasing because of the added cost of certain risk

types, which we could model as being due to different strike prices. Then the model implies full LTV

pricing as long as equity, e, is above the minimum determined by the model.

20. This is because �A = �B. If �A < �B < �C but the difference is smaller than in the subprime market, then there

might be a down payment requirement in the prime market that is smaller than in the subprime market.

21. Note that this model is complicated by lack of correspondence between the Dj and di default rates.

22. Alternatively, we can assume that loans are determined endogenously, by the banks. What we do not

assume is the possibility of moral hazard in the form of banks originating Bbad^ loans solely for the

purpose of selling to the secondary market.

23. It is assumed that fundraising takes the form of loans rather than equity investment. A reason for this might

be that outside investors cannot verify the level of X in which case (e.g., see Townsend (1979), Gale and

Hellwig (1985), and Krasa and Villamil (2000)) the standard debt contract assumed is optimal (the lender

only needs to verify the state variable if there is a default). One could also appeal to incomplete contracting

models as in Hart (1995).

24. For example, banks are assumed to know the true value of the underlying collateral, and hence the true

loan-to-value of the collateral, but SM knows only the appraisal of the value of any specific collateral,

which is subject to error and manipulation. However, SM knows the distribution of true value given the

appraisal. Hence, the banks can select against the SM by delivering loans with high appraisals relative to

value.

25. This and more general option-based models can be priced with models like the classic Black and Scholes

(1973) model (e.g., see Kau and Keenan (1995)), given the initial loan-to-value ratio of the collateral. It is

well known that the price of such options is a convex function of the value of the collateral. Van Order

(2003) discusses more general models and shows that convexity of C(N ) is consistent with a wide range of

option-type models.

26. That is, the vertical distance between the curves is constant.

27. Use of the monopoly scenario does not, of course, mean that we believe that the real world SM is a

monopoly. It is simply the easiest model to use in some situations, especially the licensing model that

follows. The free-entry, competitive equilibrium has similar properties.

28. If there is no cost to entry, new entrants into the secondary market can take away SM’s initial business by

undercutting it, eventually driving profits to zero. We get the solution to this by setting equation (15) equal

to zero. This is depicted by the intersections of average revenue and average cost in the exhibit at points B

and D.

29. The caveat to this outcome is when there are nontrivial start-up costs for the secondary market. In this case,

it may not be profitable for the secondary market to exist at all.

30. That is, where the second intersection of MRs and MCs (or ARs and ACs) occurs to the left of N.

31. Of course, it is not quite so simple because banks have the option of cheating and exiting the industry


before the loans can be sent back. Hence, in practice, the licensing contract is enforced by auditing banks

and limiting the number of banks that SM deals with to sellers with long-term interests in not cheating.

32. Note that the solution does not maximize market share subject to (29) for SM; doing so (for an interior

solution) would require equating slopes of C() at both ends of the market, which cannot be the case given

the first order conditions, which require that the slope at B be steeper than at D.

33. These are again from the subprime lender Option One Mortgage Corporation and are based on its naming

conventions for loan grades.

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Economics of sub p lending

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