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Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in

Chinas Housing Market

Yongheng Deng and Peng Liu

First Version: October 2005This Version: March 2007

Keywords: Mortgage, Prepayment, Default, Credit Risk, Forward Contract

JEL Classification Number: G12, G14, G21, H31

Contact author: Peng Liu, F605 Faculty Building #1900, Haas School of Business, University of California, Berkeley,CA 94720, Tel: 510-6438543, Email: peliu@haas.berkeley.edu; Yongheng Deng, University of Southern California,School of Policy, Planning, and Development, 650 Childs Way, RGL 201A,Los Angeles, CA 90089-0626, Tel: 213-821-1030, Email ydeng@usc.edu. We thank Mark Carhart, Pierre Collin-Dufresne, Tom Davidoff, Kent Daniel, RobertEdelstein, Dwight Jaffee, John Quigley, Richard Stanton, Adam Szeidl, Sheridan Titman, Nancy Wallace and seminar

participants at Cornell University and U.C. Berkeley for helpful comments. All errors are ours.

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Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in

Chinas Housing Market

ABSTRACT

Forward housing market, which enables the consumer to lock in future housing price, is verycommon in Asian countries. Most condominiums in China are sold forward on a pre-sale market,where purchasers and developers transact at the date of pre-sale on an underlying property, whichis not yet completed. During the pre-sale period there is significant default risk of developers.However home buyers can borrow mortgages from banks so that they can share the forwardcontract risk with the banks. This explains the phenomena of irregularly high early stage defaultand prepayment rates observed in residential mortgage lending in China where there is little or nofinancial incentives for mortgage borrowers to exercise either put or call options. An investor(home buyer) in Chinas forward housing market will choose to default her mortgage contract ifthe developer defaults the forward housing contract. If forward house is delivered, the investor

may choose to prepay the loan depending on her liquidity constraints and returns in alternativeinvestment channels.

Mortgages collateralized by forward housing asset are riskier than those with underlyingassets traded on the spot market. However, currently the Chinese mortgage banks charge the samerate to all mortgage borrowers. This results a cross subsidization between mortgage borrowersgroups in the forward and spot housing markets. Cross-subsidization, where one group pays arelative high price and thus enables another group to pay a relatively low price is pervasivephenomenon in both product market and financial market. This paper uses a rich set of data froma leading mortgage lender in China. The loan history data set contains not only mortgage loancharacteristics, but also borrowers and developers information. The unique data set allows us to

study the mortgage borrowers prepayment and default behavior with embedded forward contractrisks. The finding of this study will provide valuable insight about emerging housing andmortgage markets in China as well as those in other transition economy.

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1. INTRODUCTION

The residential mortgage market in China has grown rapidly since 1998 with an average

annual growth rate of roughly 100%. By the end of first quarter of 2005 the outstanding balance

of residential mortgages reached 1.7 trillion RMB Yuan, approximately $207 billion US dollars.

1

There are two highly distinctive features of the Chinese mortgage market: first, the Peoples Bank

of China (the Central Bank) set a uniform mortgage rate which is applied to all types of

borrowers. There is a long history of not using risk-based interest rates in China or other central-

planning economies. It is also a tradition that in those countries a unified product or service is

provided to all consumers. Second, beyond the standard spot market for housing transactions,

there is an active forward real estate market in the sense that the developer can sell housing unit

before its completion, sometimes even before construction begins. During pre-sale period there is

significant default risk of developers. However, the home buyer in China is allowed to borrow a

standard mortgage from a bank to finance the pre-sale unit. As a result, home buyers in the pre-

sale housing market can share the forward contract risk with the banks. This explains the

phenomena of irregularly high early stage default and prepayment rates observed in residential

mortgage lending in China where there is little or no financial incentives for mortgage borrowers

to exercise either put or call options. An investor (home buyer) in Chinas forward housing

market will choose to default her mortgage contract if the developer defaults the forward housing

contract. If forward housing unit is delivered, the investor may choose to prepay the loan

depending on her liquidity constraints and returns in alternative investment channels. Because of

the embedded risk of developer default, the mortgages collateralized on pre-sold property are

more risky than their counterparts on the spot market.

This paper studies the competing risks of mortgage prepayment and default with

embedded forward contract risk of developers default. The economic model is based upon Cox

proportional hazard model (Cox, 1972, 1975) of mortgage termination. The empirical analysis is

based upon a rich set of mortgage lending data from a leading mortgage lender in China. The loan

history data set contains not only mortgage loan characteristics, but also borrowers and

developers information. The unique data set allows us to study the mortgage borrowersprepayment and default behavior with embedded forward contract risks. The finding of this study

will provide valuable insight about emerging housing and mortgage markets in China as well as

those in other transitional economy. The remainder of the paper is organized as follows. Section 2

describes the Chinese mortgage market in detail, including both the single mortgage rate

1As of March 2007 the exchange rate of Chinese Yuan (CNY)is one U.S. dollar = 7.74 CNY.

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constraint and the forward market for new units. Section 3 describes the data used in this study.

Section 4 lays out the empirical methodology. Section 5 presents a discussion of empirical results.

A brief conclusion follows.

2.THE MORTGAGE AND REAL ESTATE MARKETS IN CHINA

There is long history of Real Estate market and consumer loan market in China before

1949, when China adapted the central planning system after the Communist Party took over. The

earliest real estate transaction can be traced back to 20 BC, Eastern Han Dynasty 2 . Before

adapting the central planning system in 1949, active real estate and mortgage markets had already

existed in China especially in big cities, such as Shanghai and Beijing. For a long period of time

under central planning regime, housing in China had been social welfare product administrated

and delivered by state agencies (e.g. state-owned enterprises and housing bureaus) for its people.

Under such a welfare-oriented system, a private housing market and housing mortgage system

extinguished. The mission of Chinese Banks was to act as a government directed funding source

for SOEs.

Since the early 1980s, China has gradually restructured its housing system. Market

mechanisms, with the objectives to eliminate state housing allocation, promote privatization of

public housing and encourage private housing development, were introduced in stages to replace

the welfare housing system. Although China's first modern residential mortgage loan was issued

in 1986 by China Construction Bank (CCB), the mortgage market did not play an important role

in the Chinese residential housing market for another decade. By the end of 1997, the total

outstanding mortgage balance in People's Republic of China was only approximately 19 billion

RMB Yuan (USD $2.35 billion). In 1998, the People's Bank of China, which functions as the

central bank of China, and the State Council of China announced several administrative laws to

speed up housing construction and intensify urban housing reform. Among them, the State

council announced that it would no longer allow state-owned enterprises (SOEs) to allocate

welfare housing to their employees after December 31, 1999. Since then, residential mortgage

lending began to accelerate. By the end of 2005 the outstanding balance of residential mortgages

exceeded two trillion RMB Yuan (USD $198 billion), an increase of 40% compared to the 2003

balance, and almost 89 times the1997 balance. Residential mortgages play an increasingly more

important role in Chinese banks' lending activities. The outstanding mortgage balance constitutes

2The Cambridge History of China Volume 1, The Chin and Han Empires P666, Edited by Denis Twitchett andMichael Loewe.

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more than 12% of total loans made by financial institutions in the same period in 2005, compared

to less than 0.4% in 1997.

[Insert fig. 1]

Although mortgage lending currently constitutes about 85% of total consumer lending(no credit card loans and very few automobile loans are issued by banks in China), the ratio of

mortgage loans to total loans is 7.5% lower than most developed countries (e.g. the ratio of

mortgage to total loan is 39% in U.S. and 59% in U.K.), and even lower than other countries in

the Asian-Pacific region (e.g. the ratio in Hong Kong, Taiwan, Singapore, Malaysia and Korea

was 34%, 30%, 27%, 26% and 23%, respectively) . Therefore there is much room for continuing

growth in China' mortgage lending.

[Insert fig. 2]

[Insert fig. 3]

[Insert fig. 4]

The Institutional Background of Residential Mortgage Lending in China

The current residential mortgage market in China is dominated by four major state-owned

banks. They account for more than 90% of the total outstanding mortgage balance. Of these four

banks, Industrial and Commercial Bank of China (ICBC), and China Construction Bank (CCB)

are the two leading mortgage lenders, representing about 70% of total outstanding mortgage loans.

Currently there are four categories of residential mortgages in China: (1) individual

account housing loans, (2) individual provident fund housing loans, (3) combined housing loans,

and (4) second-hand housing loans. Individual account housing loans is the most common form

of individual household mortgage loans. CCB Individual provident fund housing loans are

housing loans using provident funds that bank operate on half of institutions that manage the

funds. Usually individual provident fund housing loans enjoy a lower mortgage rate than

individual account housing loans. The current spread is 44 basis points. Combined housing loans

refer to loans granted to individual home buyers, using both bank's funds and provident fund as a

source of funding. Second-hand housing loans are loans that facilitate individual purchases in the

secondary housing market.

Mortgage application requirements

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The loan amount shall not exceed 80% of the purchase price or the appraisal value,

whichever is lower. That is 20% of the purchase or maintenance price, is reserved for the down

payment. The applicant should provide acceptable statements of stable income and payment to

income ratio should not exceed 70%. The mortgage term shall not exceed 30 years. Other

required documentations include personal identification, purchasing contract, title to the property,

appraisal report, housing (pre-)sale permit, banking statement, proof of stock and bond

investments, etc.

Payment methods

If the loan term is one year or shorter, both principal and interest must be repaid as a

lump sum at maturity; if the loan term is longer than one year, the loan may be repaid in equal

installments of the principal plus interest, or in equal installments of principal. The borrower may

choose either method, but there may be only one payment method for each loan, and after the

method is specified in the contract, it may not be changed.

Mortgage Interest Rates and Adjustment

The mortgage rates that banks charge to customers are regulated by Peoples Bank of

China (PBC), the central bank of China. All banks follow the same lending rules. Currently the

mortgage interest rates is 4.77% for individual account housing loans with a term of five years or

below; for loans with a term above five years, the interest rate is 5.04%. The spread between the

long term (more than 5 years) and short term (5 years or less) is 27 basis points. The individual

provident fund housing loans is 3.6% and 4.04% for term below 5 years and above 5 years

respectively. All residential mortgages in China are adjustable rate mortgages (ARMs). During

the loan term, the interest rate may change according to what is set by the People's Bank of China

(PBC). Once the new mortgage rate is announced, the rate will be applied to all mortgages.

Default Risk Management

Currently Chinese banks use a five-category system to manage default risks of mortgageportfolio. The five default risk categories areNormal, Alert, Irregular, Distress, and Default.

Before approval of a loan, the bank investigates the credit worthiness of each individual

applicant. The bank will approve a mortgage to an applicant according some borrower

characteristics like family income, occupation, etc. Therefore there are only two pre-lending

classes: Normal for better credit loans and Alert for good credit loans. The bank watches the

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borrowers' payment behaviors very carefully and makes frequent adjustments to the borrowers'

risk level if they see any warning signal. Specifically, if the number of delinquencies is between 3

and 6, mortgage borrower's risk level becomes Irregular; if the number of delinquencies is above

6 then borrower's risk level becomes Distress. The last category in the five-category risk level is

Default. The headquarter of any mortgage lending bank also actively monitors its branches and

subsidiaries. An early warning is given to the branches with 1% to 3% delinquency rate in their

mortgage loan portfolio; the headquarter requires a reorganization of mortgage operations at

branches whose delinquency rate falls between 3% to 5%; the mortgage lending license would be

revoked if a branch has more than 5% delinquency rate.

Real Estate Developers and Strong Secular Growth Trend in Housing Demand

Real estate development was a highly regulated industry in China before 1992. With the

privatization of state owned housing and the fast growth of mortgage lending, real estate

developers in china begin to flourish. There are currently more than four thousands active real

estate developers in Beijing. Before 1992 there were only 37 state-owned real estate developers in

Beijing. With an average increase of 50 developers a year, the total number of developers until

1997 was 335. The total number of developers doubled in 1999 and structure of developer

became diversified. With the stimulation of mortgage lending activities, the average annual

growth rate jump to 96%, the total number was 548 in year 1998, 1023 in year 2000 and 1979 in

year 2002 respectively. In addition to the housing reform, China's capital market begin to grow,

with the recent reform such as apparition of Chinese currency Yuan and further opening of

financial market to foreign banks as required by the WTO. Moreover the most recent financial

innovations such as real estate investment trusts (REITs) and mortgage backed securities (MBS)

all start from the real estate finance sector, the emerging and fast-growth capital market in China.

The on-going process of these reforms has translated into a booming domestic property sector and

acceleration in residential housing investments in recent years. As a consequence, the share of

residential housing investment as a percentage of GDP has risen to 5.6% in 2003, up from less

than 1% before the 1990s.

Notwithstanding fast industrialization, the degree of urbanization, as measured by the

ratio of urban residents to total population, is exceptionally low in China. Industrialization

without urbanization is a unique Chinese phenomenon, owning to decades of government policies

that segregated urban and rural labor markets. The pent-up urbanization demand, evident from the

acceleration of rural migration, has also coincided with the unleashing of pent-up demand for

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improving housing conditions nationwide. The average per capita housing area in square meters

for both urban and rural residents has jumped from7-8 sq. m. in 1978 to above 20 sq. m. in recent

years. We believe the evolution of consumer demand is heavily influenced by income distribution

and the emergence of the middle class, because at a different income levels, different projects

become affordable and available. Experiences in other economies have shown that as annual

income crosses US$ 3,000 per capita; there is a period of rapid expansion in the size of the

middle class and acceleration in consumer demand. Figure 5 shows the decreasing nationwide

trend of supply to demand ratio indicating the strong secular growth trend in China's housing

demand.

[Insert fig. 5]

The Forward (Pre-Sale) Housing Market in China

The majority of residential housing units in urban China are condominiums, and most

condo purchases are transacted on the forward market. A forward sale is also called pre-sale. In

2003, more than 80% of projects initiated a pre-sale according to a survey. Condo developers

usually sell their projects well before completion, usually two to three years,3 in order to hedge

the housing price and get additional funding. On the transaction date, home buyers (mortgage

borrowers) have to pay purchase price in full on a development that is not completed. To share

the risk of developer default, home buyers (mortgage borrowers) usually fund the housing

purchase by putting a down payment of 10% to 30% and borrow a 20 year mortgage4 from a bank

that charges the same adjustable mortgage rate. The mortgage provides the borrower embedded

options to default and prepay the loan at any point before loan maturity. Even though banks pool

forward and spot contracts in real estate market by charging the same rate, one should realize that

the market structure leads to very different option exercise behaviors for the two types of

borrowers. The collateralized borrowing based on the presale units introduces additional risk for

mortgage default and prepayment. The developer asks for the full purchase price at presale day,

the mortgage loan serves partially as consumption insurance. If the developer defaults on the

forward contract, the borrower defaults on her loan. (The loan is non-recourse in China).

Presale does not only exist in China, it is a popular practice in other markets as well. In

most Asian markets: Hong Kong, Taiwan, Singapore, Japan and in some European countries, like

Russia, Italy, Span forward housing sales are very active. The presale practice is also active in the

3The presale period used to be around 4 years, but now decreased to one to two years.4 Sometimes shorter maturity of 15, 10 years mortgages is borrowed with different rate.

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U.S. condominium market, especially in large cities. In United States, pre-selling of buildings and

resort condominiums (Miami, Hawaii, for example) has become a standard process, and virtually

every condominium is pre-sold today.5 The procedures of forward presale contract can vary from

country to country, and from developer to developer in the following dimensions: length of

presale period, size of down-payment/deposit, payment schedule, refund policy in case of the

developer default, and eligibility of mortgage loan and mortgage rate. In Hong Kong, the

common practice is that the developer must complete a certain percentage of the development

before the government gives the presale consent. In the U.S., China and Singapore for example,

the forward sale can take place after developer getting construction permit and before

construction starts, thus the name pre-construction. For example in Florida developers need pre-

construction sales of 50% to 90% of the units before they can borrow funds to begin construction.

While in Singapore and China the entire purchase price is required to be paid at the time of

presale contract is signed; a sequential payment schedule is contracted in U.S. For most Florida

condominium developments, investors need only deposit 10% of the presale price at contract time,

a second 10% after 3-6 months or when developer breaks ground. For most condo presales in

U.S., the deposits are held in escrow. The investors can get full refund in the case of developer

defaults.

Despite the differences in the contractual details of forward presales, there is a common

risk that associated with all forward contracts: the counterparty default risk. On the forward

housing market, all investors are well informed of the possible failure of delivery on the

contracted houses. Because the investors are buying something that does not yet exist, there is a

greater potential for unforeseen problems and setbacks to occur before the investor move into her

home. The need not be built disclaimer gives the developer protection from suits of

nonperformance if the developer does not proceed with the construction. However there may be a

significant social loss in the sense of incomplete structures that arise from developer default.

When the presale was first used in China around 1998, majority of developers are state-owned

and completion of the development was perceived by forward contract purchasers as guaranteed

by government. As the housing demand is so high and real estate development is such a profitable

industry, more and more private companies came into the market. With uncertain construction

cost, the developers then have incentives to exercise their default option. This introduces

inefficiency for there would be social waste resulting from uncompleted projects. The Chinese

5Sample of pre-sale contract can be found in Miami real estate website. www.miamirealestatetrends.com

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government has realized the problem incentive-compatible mechanisms are under consideration

beyond reputation and regulation rules.

The convoluted relationship among the developer, home buyer and mortgage lenders can

help to explain two paradoxes in China mortgage market: why the prepayment rate is high in the

adjustable rate mortgages where there is no incentive to refinance? Why the default rate is also

high in a period of a booming housing market? We will explore the phenomenon and

explanations in more detail in the empirical modeling session.

3.THE DATA

Micro Mortgage Loan Data

The unique micro mortgage dataset collected by the largest residential mortgage lender in

Beijing, China was first used by Deng, Zheng and Ling (2005). In this paper we enriched the

dataset in several dimensions. We updated the mortgage loan data to the end of 2003.

Furthermore we extended the loan information to include the property information and developer

characteristics. This second extension is crucial because those variables enable us to merge

borrowers characteristics of loan with the collateral information from developers in Beijing. The

loan dataset includes 103,462 individual mortgage loans issued between 1998 and 2003. The

mortgages are 5 year, 10 year, 15 years and 20 years adjustable rate loans with level payment. For

each loan, the available information include the year and month of origination and termination (if

it has been closed), indicators of prepayment or default, original loan amount, down payment rate,

initial loan-to-value ratio, maturity, remaining term, repayment method, mortgage contract rate,

the purchase price of the property, size of the house, location of property, sale type, appraisal

value of property at time of sale, unit price, etc. Other borrower characteristics include borrower

name, education, gender, monthly income, occupation and position, number of dependents in the

household and income from spouse. The dataset also has geographical information of the property

and its developer. This micro loan data is well suited for the study of mortgage default and

prepayment, since Beijing is the capital city of China and the real estate sector is steadily

increasing without speculative bubble. Among the 103,462 mortgage loans, 1,384 loans were

defaulted and 10,055 loans were fully prepaid during the sampling period, and 92,023 loans were

censored at end of year 2003. This data is best for survival analysis because the data avoid the

truncation and censoring problems. The sample started from 1998; which is the first year the bank

issue mortgage loans. There is no left truncation problem as most research has in sample selection

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process. The data collection cutoff date is December 31, 2003. Therefore the right censoring is

non-informative6.

Tables 1-5 provide the descriptive statistics of the mortgage loans. Among 103,462

residential mortgage loans originated in Beijing, more than 74% are based on forward contracts.

Among 1,384 defaulted loans, and among 10,055 prepaid loans, more than 90% are from forward

market. The borrowers behavior in default and prepayment vary by loan characteristics like LTV,

original loan amount, and borrowers income, occupation and other household characteristics. In

addition, borrowers behavior in default and prepayment vary by developer characteristics like

type, size, quality, history, etc. For example, about 45% defaulted loans are originated on the

properties built or to be built by joint developers with partners in Hong Kong, Macau or Taiwan

(HMT thereafter); while only 5% from joint developers with partners in foreign countries. Within

all prepaid mortgages, 47% are based on properties built or to be built by limited companies;

while only 2.5% are by joint venture with HMT. Among the 103,462 mortgages, more than 63%

loans are originated on a property which is the first project by its developer. Only 34% are by

developers who have built more than one project in the past. The detailed descriptions can be

found in table 1-4.

[Insert Table 1]

[Insert Table 2]

[Insert Table 3]

[Insert Table 4]

[Insert Table 5]

Developers Credit Risk Data

Another dataset used in this paper is credit rating data of real estate developer in Beijing

from Beijing Urban Construction Development Office (BUCD thereafter). BUCD is a

government agency regulating real estate industry in Beijing. In 2004 BUCD begins to annually

review all real estate developers in Beijing and publish the results on its official website. With

growing concern about information disclosure of developer credit record, BUCD also has built a

6An alternative sampling method, namely stratified sampling mechanism can be used for a large dataset. To correctthe possible sample selection bias, a weighing scheme which is assumed to be independent of error distribution can beused in the maximum likelihood estimation. Specifically, the weight addresses the stratified choice-based sampling ofmortgage .les across loan status cells. The weight is commonly defined as the inverse of the probability that the loan is

being selected from a cell where was sampled.

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credit database of real estate developer for public inquiry. This dataset include 3,088 developers

and 3,938 real estate development projects in total.

Among all developers, about 87 percent of developers only have one property in Beijing;

only 3% of the developers have 4 properties or more. The earliest developer in our sample, a state

owned enterprises (SOE), started its real estate business in 1966. There was no big growth in real

estate sector since then. In 1992 the total number of developers was only 90, the number

Quadrupled in 1997 to 335. Since then real estate development industry has experienced a

significant growth. By the end of 2003 the total number of developers was almost ten times the

number in 1997.

For each developer in the sample, we have information of credit ratings from real estate

administration office and commercial banks, type of developer, equity value of firm at

registration, location of properties and business address of developer, name of CEO and legal

person, total number of employees and detailed number of certified professionals in the

management. We also have the issuance and expiration date of license, starting date in real estate

business.

4.THE EMPIRICAL MODEL AND ESTIMATION METHODOLOGY

4.1 AN ECONOMIC MODEL OF MORTGAGE PREPAYMENT AND DEFAULT WITH EMBEDDED

FORWARD CONTRACT RISKS

A Simple Model for Forward Housing Market

The presale practice, adapted from Hong Kong and other Asian markets created a

forward market in Chinese residential housing market. Similar to financial instruments, investors

can buy real estate either on a spot market or on a forward market. On the spot market, investors

and developers transact on existing housing units - housing stock; while on the forward real estate

market, the investors and developers agree on the price at the date of sale but the underlying

property, which is not completed yet, is transferred to the buyer only at a certain period later,

usually at the date of completion. Because the unit is sold well before completion and occupation,

the forward contract is often called a pre-sale or pre-construction.

[Insert fig. 6]

Figure 6 uses a simple timetable to illustrate the interrelationship between the home

buyer (mortgage borrower), the developer and the bank on the forward housing market.

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Following Liu (2007), we set up a three period model, the agents only make decisions at discrete

time at T = 0, 1, 2, 3. T=1 is completion / delivery date of housing units. Home buyer (mortgage

borrower) can enter the housing market either at time T=0 (spot market) or at T=1 (forward

market). Therefore the transaction date can be either at T=0 or at T=1. At the transaction date, the

home buyer has to pay the developer the full purchase price on the housing unit and the home

buyer is eligible to borrower an adjustable rate mortgage from the Bank. The mortgage loan is

usually less than 80% of the housing value, which means that the purchaser only put down

payment of 20%. The mortgage matures at T=3, but the borrower can terminate the loan at any

time. For simplicity, we assume the borrower only terminate the loan at T=1, 2, 3. The developer

and the bank have an agreement so that the developer deposits the proceeds into the bank at

transaction date. Between time 0 and time 1, there is a pre-sale period, in which the developer

sells housing units forward before completion of the project. At T=1 of the forward market, there

is a probability of developers failure of delivery of the unit, which results in default of the

mortgage. In the case of default, the bank takes the collateral residuals, which typically have very

low recovery rate currently in China. If the housing unit is delivered in good quality, the home

buyer (mortgage borrower) starts to consume the housing consumption. T=2 is the option

exercise date for a home buyer (mortgage borrower) who is consuming a housing service and

pays a monthly interest and principal of mortgage. She would default if the value of the house is

lower than the value of the debt borrower from the Bank. She would prepay if the financing cost,

i.e. the mortgage interest cost, exceeds the alternative investment return. The borrower may not

optimally prepay the mortgage if she is financially constrained, either due to liquidity constrain

(the borrower does not have enough cash to pay off the loan) or she does not participate the stock

market investment. Therefore if the home buyer (mortgage borrower) does not terminate the

mortgage, at T=3 she makes the last payment and obtained the title of the house.

There are at least two main advantages for home-buyers to lock into a pre-sale contract

before the construction of the property is completed. First the housing price in the pre-sale market

is typically lower than that on the spot market. Second there may be richer menu of choices:

location, size, view, etc. For developers, there are two benefits associated with pre sale contract.

First, by locking in the selling price, the developer can hedge the project pipe line risk and share

the risk with buyers. The uncertainty about future demand and inventory risk is significantly

reduced. Secondly the developer can access additional zero cost financing in addition to

construction loan which is typically very difficult for private developer to apply from the banks.

For new developers, presale funding may be the only source of capital for construction.

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In China and other emerging markets, home buyers typically lose all the down-payments

in the case of developer defaults. However currently Chinese home buyers can borrow a certain

amount of mortgage loans from banks, and furthermore they benefit the same mortgage rate as

spot market investors. A condo purchaser can default the mortgage loan, if developer fails to

deliver the unit according to the presale contract. Because of the popularity of the forward

housing market and the practice of the risk sharing mechanism adopted by the home buyers

(mortgage borrowers) in China, the risks in the forward real estate market have been embedded

into the mortgage contract default risks, which makes the valuation of the mortgage default and

prepayment option value becomes more complicated than those in other countries.

Default Option with Embedded Forward Contract Risks

The option theory (Black and Scholes, 1973 and Merton, 1973) has been widely applied

to estimate the mortgage default and prepayment probability. Early examples include Findley and

Capozza (1977), Buser and Hendershott (1984), Brennan and Schwartz (1985) among others.

Recent applications include more sophisticated modeling techniques (see, for example, Schwartz

and Torous, 1989, Stanton, 1995, Deng, Quigley and Van Order, 2000) and more realistic

assumptions (see, for example, Quigley, 1987, Quigley and Van Order, 1995, Archer, Ling and

McGill, 1996, Calhoun and Deng, 2002). However this method was developed and first used in

developed mortgage market in which spot housing contracts are predominant. Understanding of

forward housing market and its option structures are necessary in order to apply the option theory

to the mortgage pricing in which the forward selling is active. Under the forward contract when

buyers borrow mortgages from bank and start to pay back amortized loan amount, they have not

seen their house yet. With astonishing growth in real estate market, many private developers enter

the residential housing market. There is increasing default risk among developers that fail to

deliver the house. Many Chinese borrowers use the mortgage as a consumption insurance

instrument to share the credit risk of developer with banks. In case the borrower did not get the

desired home, i.e. the developer defaults or fails to satisfy the home buyer on the date of delivery,

the borrower defaults. On the other hand, if the borrower gets a house of good quality, she will

not default, and will consider prepaying according to borrower's liquidity constraint and other

investment opportunities. For example, if borrower can earn a higher return from other

investment portfolio (from stock market or bond market), even though the borrower has cash on

hand - not liquidity constrained, she rather not prepay the mortgage. However if other investment

opportunities give her lower return then mortgage rate and If the investor is not constrained, she

will pay off the loan. Although in reality investor has to evaluate the option value of waiting, the

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prepayment option basically reflects the trade-off between financing cost (mortgage rate) and

alternative return, as well as liquidity constraint of the borrower.

This forward-selling practice is quite common in other developing countries or

transitional economies as well, where there is high demand in residential housing and the

governments encourage consumer lending to stimulate real estate construction. The increased

leverage via pre-sale then increases credit risk of developer which will be eventually transferred

to house buyers. It is rational for the buyer to borrow mortgage loan from a bank, thus sharing the

housing-consumption risk. On the demand side, since the commercial housing market is relatively

new, there may simply not enough desirable housing on the secondary housing market. Besides,

recognizing that the banks charge the same mortgage rate, pre-sale mortgage borrowers implicitly

get a cross subsidy from spot market borrowers.

The Default and Prepayment Option Analysis on the Forward Market

Due to the pre-sale feature, the mortgage options are different from the ones in the spot

market. Because all the current mortgage contracts in China are Adjustable Rate Mortgages

(ARMs)7 and the mortgage rates are not indexed to any rate, but imposed by the central bank. We

found that pre-sale practice in China's housing market plays a crucial role in mortgage defaults

and prepayments. An important reason why people want to borrow money from a bank is to

facilitate a housing consumption. Since they face tremendous risks when developers fail to

deliver properties on the contracted delivery date or fail to meet the quality requirements

specified in the pre-sale contracts. Here house refers to all kinds of housing units in China's

residential housing market, most of them are condominium, and some are not. In our sample

period, every year there are more than five hundred of new properties in Beijing. (Note: most

housing units are condos in which one property could have tens of thousands units). The

sophisticated borrowers use the mortgage as a consumption insurance instrument to share the

credit risk with banks. If the borrower had a bad draw, i.e. the developer defaults, the borrower

also defaults. On the other hand, if the borrower has a house of good quality, she will not default,

and will consider prepaying according to borrower's liquidity constraint and other investment

opportunities. There are two important institutional issues that permit such a risk sharing behavior.

Firstly residential mortgages in China are non-recourse; and secondly, so far there is no personal

credit system in China, and banks dont share mortgage borrowers information. These features

are especially common in transitional economies or developing countries.

7See Stanton and Wallace (1999) for a discussion of application of option theory to the adjustable rate mortgages.

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Before the discussion on how to calculate the value of default and prepayment options,

further understanding the details of those options and how they differ from their U.S. counterparts

are needed. In China, a housing unit can be purchased on either the spot market, where the house

has been built, or on forward market (pre-sale), where the building has not been completed yet.

Although fundamentally different, (a specific housing unit cannot be simultaneously on both the

spot market and on forward market at the same time), the purchase and financing procedures are

exactly the same. Consumers have to pay in full using either own equity or mortgage or a

combination of both on the transaction date instead of forward delivery date. Mortgage lenders

charge the same rate to the borrowers. For the pre-sale house, the borrower can default on a

mortgage loan at delivery day. It is essentially a European put option. On delivery day, there is a

probability of developer default, hence failure of delivery of a contracted house. Mortgage default

can be of two reasons during pre-sale period. The first is from the credit risks of developer. These

risks include market risk (via a channel of construction cost) and the idiosyncratic risk of the

individual developer. The second risk is from the borrower. An individual borrower can have a

negative income shock or other unplanned event (e.g. a big expenditure on medical care). Since

during the pre-sale period, the borrower cannot borrow from other places and cannot re-sale the

house (due to its adverse selection problem), they will lose the house and payments made earlier

plus the down payment if they default before the maturity. Knowing this, a rational borrower will

keep enough funds for the mortgage payment beyond the down-payment during pre-sale period.

For simplicity, we assume the borrower only exercises the put option on the delivery date.

Therefore the mortgage partially serves as consumption insurance instrument. A borrower wants

the protection from the credit risk of developer or qualifies of house.

At the delivery date, the mortgage options for pre-sale and non- presale becomes identical.

After the pre-sale period, the borrower can default or prepay on the mortgage. Mortgage default

option can be regarded as a financial put option. If the current market value of the house, which

serves as collateral on the mortgage debt, drops below the current value of the remaining

mortgage balance, a borrower has an incentive to default. In a boom market, the default option is

usually out of the money. Borrowers would be better off by selling the house, rather than default,

if they have to move. On the other hand, the prepayment option is a real option (call) with strike

price updating every year (depending on bank ARM rate). This call option is does not depend on

interest rate, but is closely related to the borrower's alternative investment set. One can think of

mortgage debt as a consumption smoothing instrument. In the current Chinese capital market,

there are very few investment opportunities, and very few borrowing vehicles. For example there

are no credit card loans and other consumer loans are very limited. The mortgage market is a

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major and steady growing sector in Chinese debt market; while the stock market is the major

investment sector. Therefore borrowers will make prepayment decisions based on cost of capital

and stock market return. They will prepay when the cost of capital (mortgage rate), exceeds

investment return. Figures 7-8 show the mortgage rate dynamics and stock index return in China

during period of 1998 2005. The optimal stopping time of prepayment depends on borrower's

income and her judgment about stock market return and interest rate in the future. If borrowers

are the same, i.e. they have same income flow, same information, same perception of macro

economy, and same risk aversion, they will prepay at the same time.

[Insert fig. 7]

[Insert fig. 8]

In most developed economies, researchers model mortgage contract in a contingent claim

framework. The borrower's option to prepay the mortgage is an embedded call option at a strike

price of par while the default option is a put option at a strike price equal to the market value of

the collateral property. The prepayment option gives a mortgage borrower the right to repay the

mortgage balance when its market value equals or exceeds par, i.e. the market rate drops below

the mortgage coupon rate. Exercise of the call option results from two primary motivations: (1) to

refinance the existing debt at a lower rate of interest; and (2) to terminate the debt through sale of

the underlying asset house, due to relocation for example. However China's mortgage

prepayment behavior contradicts to the conventional wisdom in the existing literature which

considers the financial call option value of prepayment as an important factor. Because all the

current mortgage contracts are ARMs (see Cunningham and Capone, 1990, and Stanton and

Wallace, 1999, for a discussion of modeling the termination risks of ARMs). Furthermore, the

mortgage rates are not indexed to any rate, but extraneously imposed by the central bank.

An analog to prepayment, in U.S., mortgage default is regarded as a financial put option.

If the current market value of the house, which serves as collateral of the mortgage debt, drops

below the current value of the remaining mortgage balance, a borrower has an incentive to default.

Therefore the default may be viewed as a put option that gives the borrower the right to sell the

house to the lender at a price equal to the value of the mortgage. In the absence of transaction

costs, a rational borrower can maximize her welfare by exercising the options when they are in

the money. From a quick glance at China's housing prices, one can easily conclude that the

housing market is booming and the financial put option is far out of the money. Then what makes

the Chinese borrowers default or prepay their mortgage loans is puzzling.

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In this paper, we rationalize borrowers' behavior by realizing that the motivation of

mortgage borrowing is partly because of risk-sharing and partly due to liquidity constraints. We

found that the prepayment and default are closely related to the quality of the underlying property

or the credit risk of the developer. Since in our study all the defaulted loans involved a developer

with only one property for sale on the market; therefore, determining the default risk of mortgage

borrower is equivalent to predicting the credit risk of the developer company.

We also find that pre-sale practice in China's housing market play a crucial role in

mortgage defaults and prepayments. An important reason why people want to borrow money

from a bank to facilitate a housing consumption is that they are facing tremendous risks in the

case that developers fail to deliver the properties on the contracted delivery date or fail to meet

the quality requirements specified in the pre-sale contracts. However the house buyers have to

take the risk, since there are simply not enough existing houses on the market. In our sample

period, every year there are about 555 new development offered in Beijing. (Note: most housing

units are condos in which one property could have tens to thousands of units) on the market.

There are two important institutional issues that permit such a risk sharing behavior. The

residential mortgages in China are non-recourse; so far there is no personal credit system in China,

and banks don't share mortgage borrowers' information.

4.2 THE COMPETING RISKS HAZARD MODEL OF PREPAYMENT AND DEFAULT

The default and prepayment are options of borrowers embedded in any mortgage loans.

Recent research on mortgage markets indicates that exercise behaviors of those two options are

distinct but not independent. For example, exercising the default option, the borrower gives up

the option to prepay the loan in the future. We apply the Cox proportional hazard model to assess

the competing risks of mortgage termination by simultaneously modeling the prepayment risk and

default risk.

Since the early work of Dunn and McConnell (1981), Green and Shoven (1986),

researchers have modeled mortgage contracts in a contingent claims framework. The borrowers

option to prepay the mortgage is an embedded call option at a strike price of par while the default

option is a put option at a strike price equal to the market value of the collateral property. The

prepayment option gives a mortgage borrower the right to repay the mortgage balance when its

market value equals or exceeds par, i.e. the market rate drops below the mortgage coupon rate.

Exercise of the call option results from two primary motivations: (1) to refinance the existing debt

at a lower rate of interest; and (2) to terminate the debt through sale of the underlying asset, the

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house, due to relocation reason for example. In analogy to prepayment, mortgage default is a put

option. If the current market value of the house, which serves as collateral of the mortgage debt,

drops below the current value of the remaining mortgage balance, a borrower has an incentive to

default. Therefore the default option gives the borrower the right to sell the house to the lender at

a price equal to the value of the mortgage. In the absence of transaction costs, a rational borrower

can maximize her welfare by exercising the options when they are in the money.

As discussed in the section above, the special features of Chinas mortgage contract have

to be taken into account when calculating the option values. Specifically the collateral of pre-sale

house has to be carefully modeled for default option; while prepayment option is different in an

economy where there is essentially no interest risk. The prepayment option is at work, even

though there is no interest risk, because mortgage borrowers the will decide when to exercise

based on the trade-off between borrowers financing cost and alternative investment returns.

Furthermore, these two options compete against each other. Kau et al (1992, 1995) have

discussed the theoretical relationships among the options. Schwartz and Torous (1993) is among

the first to demonstrate the empirical importance.

The desired model outputs are explanatory variable effects on conditional probabilities of

mortgage default or prepayment. We estimate a proportional hazards model (PHM) which

estimates the effects of theses variables on the time to default. In particular, we estimate the

probability that a mortgage with certain characteristics will terminate in a given period where

there has been no default or prepayment experience up until that period.

Following Deng, Quigley, and Van Order (2000), this paper simultaneously estimates the

competing risks of mortgage defaults and prepayment. The joint survival function is given in the

following form:

}),,,(exp{)(

}),,,(exp{)(

where

}exp{

},,,,,,|,Pr{

),,,,,,|,(

2'

1'

0

2'

1'

0

11

ppBCpkppkpk

ddBCdkddkdk

t

k

pk

t

k

dk

pdBCppdd

pdBCpd

ZXXRHgthh

ZXXRHgthh

hh

ZXXRHtTtT

ZXXRHttS

pd

++=

++=

=

>>=

== (1)

The log integrated hazard function can be also written in the following form as:

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jBCjjjjjjBCjjjj XXRHgIIZXXRHglh +++++= ),,,(),,,( 432'

10 (2)

In this formulation, Sis cumulative survival probability conditional on housing priceH,

alternative investment returnR , vector of macro-economic variablesZ and vector of micro

variables ),,,( BC XXRHg . Both Z and g are time-varying, where Z measures the systematic

risk of the market and loan level information g measures the intrinsic values of the default and

prepayment options. Among g, BX represents borrower characteristic and cX stands for

collateral information. Ij is a dummy variable equal to unity if the loan is to finance a forward

house, and zero otherwise. dT , pT are discrete random variables representing the loan life of a

mortgage prior to default and prepayment respectively. hik ; i = d; p are hazard functions;

Unobserved error terms associated with the hazard functions for default and prepayment are

denoted by d , p respectively to represent heterogeneities. The Kaplan-Meier approach was

used to fit the empirical hazard rates of prepayment and default based on the entire sample.

However equation (2) assumes that the market effects of Z are the same for both forward

mortgage and spot market mortgage. It also assumes that the error structures are the same for all

mortgage loans. To accommodate this restriction, a more complete separation regression for

forward market and for spot market can be estimated similar to Blinder (1973) and Oaxaca (1973).

For Spot market without pre-sale

S

j

S

jj

SjjBC

Sjjj

Sj

G

ZXXRHglh

+=

+++=

),,,( 2'10(3)

For Forward market with pre-sale

F

j

F

jj

F

jjBC

F

jjj

F

j

G

ZXXRHglh

+=

+++=

),,,( 2'

10(4)

where ]'),,,([ ' ZXXRHgG BCji

j = is a column vector of repressors; j = d; p and i =

S; F ; jjj 2'

10 = , jjj 2'

10 = are regression coefficients.

The log Hazard Ratio, denoted by LHR between two groups of F and S can be

decomposed into two parts.

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)()(

+=

=

FSF

SF

j

GGG

GGLHR(5)

where the upper bar associated to a variable indicates the mean and estimated coefficients. The

first part of risk differential is due to differences in the typical loan characteristics of forward

versus spot )( FjF

j GG , assuming they are valued at the same spot market. The second part of

the risk differential reflects the portion of the higher risk on forward market loans that arises

because they are priced differently than otherwise identical mortgages for existing house

financing.

The default options in pre-sale period versus post-sale period are total different. In the

post-sale period the default option is related intensively to the housing price. However in the pre-

sale period, the default option is mainly depend on the probability of default of developer.

Following Deng, Quigley and Van Order (2000), the proxy values of exercising the put option

for mortgage borrower in post-sale period is measured by the probability of negative equity.

Typically one cannot estimate directly to which the default option is in the money without

knowing the entire path of individual house values. However, we can use the initial loan-to-value

ratio and the diffusion process of house prices to estimate the critical value for borrower exercise

of put option, known as the probability of negative equity. Specifically, the variable put_proxy

is defined as:

))loglog(Put_Proxy

Hr VVN = (6)

Where

= +

+

+=

kT

ii

k

kr

r

MV

1 )1(

(7)

)(

H

HPV kH

+= (8)

Vr is the market value of mortgage debt; M is monthly payment of mortgage principle

and interest, kr+ is adjustable mortgage rate for loan originated at time and after the seasoning

period of k. T is the mortgage term. VH is the market value of the house which is purchased at

with price P and valued at +k ; H is housing price index at time in the area. The term in

parentheses of equation (8) follows a log normal distribution. )(N is the cumulative standard

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normal distribution function, is housing index volatility8. The calculation of Vr is a little

complicated. It involves firstly calculate annually re-setting monthly payment of principle and

interest.

The intrinsic value of call option is defined as:

r

Rr

V

VV =Call_Proxy (9)

where Vr defined previously is the market value of mortgage, the cost of financing a

house purchase, and VR is the value of a hypothetical income, the return from alternative

investment.

Since stock market is a major investment alternative, the Shanghai stock price index is

used in return calculation. Specifically, VR is defined as:

=

++

+

+=

kT

ii

f

i

KkR

r

RMV

1 )1(

)1( (10)

In addition to intrinsic value of options, three sets of non-option related variables are

included in the regression. Those variables include time varying and time invariant determinants

of mortgage performance motivated by recent research. The first set of variables, denoted by XB,

describe the borrowers characteristics, including gender, age, education, log value of monthly

income from borrowers and their spouses, occupation, marital status, number of dependents in

borrowers household, etc. The second set of variables, denoted by XC, describes the collateral

information. The developer related information includes credit ratings, type of developer, age of

the developer, equity value of firm at registration, size of developer, ratio of certified

professionals to total employees, and number of projects, etc. Other loan related information

includes original loan amount, down payment rate, loan-to-value ratio at origination, year and

month, maturity, size of the house, location of property, sale type, appraisal value of property at

time of sale, unit price, etc.

5.EMPIRICAL RESULTS

The risks analyses are based on the full sample from the combined dataset of bank loans

and real estate developer credit database. The competing risks of default and prepayment are

8The housing price indices and their volatilities are estimated according to the three stage procedure originally createdby Case and Shiller (1989) and modified by Quigley and Van Order (1995).

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estimated jointly. Table 6 presents three variations of the competing risks model of loan

termination. All specifications incorporate both market variables and a rich set of loan

characteristics including borrowers characteristics and collateral information. The market

variables include time-varying proxies for local economic conditions, such as inflation,

unemployment rate, the slope of term structure of interest rate, stock market returns, etc. Each of

the three models contains separate flexible baseline functions for default and prepayment that

follow Han and Hausman (1990). Model 1 tests both default rate and prepayment rate equations

following equation (2) where the presale dummy is estimated in hazard regression framework and

the interaction term 4 is constrained to be zero. Further, the model does not control directly for

the intrinsic value of call and put options in the estimation. Model 1 provides a benchmark for the

competing risks specifications discussed below. Model 2 extends model 1 by including the

contemporaneous values of options in both default and prepayment equations. Model 3 further

extends model 2 by including interaction terms of presale with call option and put option in both

risk equations. Overall, the competing risks models are well-specified and control for

approximately 40 different characteristics of the loan, borrower and collateral characteristics and

market information.

[Insert Table 6]

As evidenced in model 1, estimation results indicate that economic conditions of the

market have important impacts to default and prepayment behaviors. As a proxy for overall

economy, the Shanghai Stock Index is negatively associated with default and prepayment. The

increase in local unemployment rates positively affects the exercise of the default option and

prepayment option. This result is highly significant across model specifications. Unemployment

rate is a macro variable indicating the strength of the macro economic environment. It also

reflects Chinese borrowers confidence about the job-stability and financial soundness. For most

Chinese households, housing is a basic consumption. When facing uncertainty about future

wealth, they will choose to invest in housing, rather than risky stocks and bonds. This is quite

different from US, where prepayment risk is negatively associated with unemployment rate. The

slope of term structure of interest rate, defined as the difference between the five year CD rate

and spot rate disclose the expectation of future interest rate. When the yield curve becomes fatter,

borrowers in China may prefer to prepay the mortgage debt. As show in model 1 while the

relationship between default behavior and slope of term structure is statistically insignificant, the

prepayment rate is negatively associated with the slope of term structure and statistically

significant.

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The estimates from model 1 suggest that the loan to value ratio at origination is positively

associated with default risk and negatively associated with prepayment risk. Higher LTV reflects

that the purchaser is more liquidity constrained and has less equity invested in the house. Model1

also shows that the likelihoods of default and prepayments vary positively with housing-expense

burdens proxied by mortgage expense to income ratio.

Model 1 also estimates the affects of borrowers characteristics, including borrowers age,

sex, marital status, education background, occupation and job positions, log monthly household

income and number of dependents in the household. Among these categorical or continuous

variables, household income is an important factor in determining default and prepayment risk.

High income borrowers are less likely to default and more likely to prepay. The log income is

highly significant across 3 models. Another continuous covariate that is statistically significant is

number of dependent in a household. The more the dependents in the household, the higher

burden of the mortgage borrower, thus the higher the default probability and the lower

prepayment risk. Among the categorical covariates, the sex is insignificant; age is significant

among these 3 models. Older borrowers have relatively lower default risk and higher prepayment

risk. As younger people in China are more liquidity constrained and also prefer to smooth

consumption by borrowing, reflecting a difference in lifestyle preference in China. Marital status

is another significant factor in determining default rate and prepayment rate. Married borrowers

have both lower default rate and prepayment rate reflecting that a family is a more stable and

responsible social unit than singles. Occupations and job positions are significantly associated

with prepayment risk. Business and Trade industry shows higher prepayment risk due to their

relatively volatile income streams, while research and education sector has lower risk of

prepayment because of the nature of relatively stable income streams. Managers exhibit relatively

higher prepayment risk than technicians and self-employee. On the other hand, none of them is

statistically significantly associated with defaults. Borrower with college degree has lower default

risk but higher prepayment risk.

In addition to borrowers characteristics, model 1 also finds significant impact of

collateral information to mortgage termination in China. Specifically, mortgages with underlying

property built by bigger or older developer exhibit lower default risk. There are two measures of

developer size, one is currency adjusted value of registered equity, and the other is total number

of employee in the firm. These two size variables are all statistically significantly associated with

default risk, while the association with prepayment risks is insignificant. New developers tend to

associated with higher default risk and higher prepayment risk of mortgage loans. In the sample

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period of the study, Chinese housing sector is experiencing tremendous development which

triggers more company enter into real estate business. While it is hard for the investors to monitor

and judge the quality of the property they are developing, established developers have operational

advantage in this market. Not only the developer quality affect property price, but also have

impact to financial market via the channel of mortgage termination. The developers who involved

in residential real estate development for more than 20 years are associated with lower default

risk and higher prepayment risk. The ratio of certified professionals to total employee of the

developer is also significantly associated with mortgage default and prepayment rates. The higher

the professional ratio is associated with lower default risk and higher prepayment risk. A strong

developer tends to have more certified professionals and have passed higher industry standard

(for example ISO9000) and also prefer to take long-term commitment. Since a developer with

good quality tends to have better cost management, quality control and reputation concern, its

presale house will have higher probability of failure of delivery. Therefore the mortgages

associated with good quality developers will have lower default risk and higher prepayment rates.

The type of developers also associates with different default risk and prepayment risk. The

foreign joint venture developer exhibits lower default risk and higher prepayment risk, while the

joint venture with Hong Kong, Macao and Taiwan developer are associated with higher default

risk. Comparing with State-Owned developers, the private developers and limited company have

both higher default risk and higher prepayment risks. The location of property is also associated

with different default and prepayment risks. In central city area, due to competition and tighter

regulation or monitoring, mortgages with underlying property in central city area tend to have

lower default risk and higher prepayment risk.

Model 2 extends model 1 through the introduction of the option-related time-varying

covariates into both the default and prepayment equations.9 The estimates confirm that the put

option, measured as the probability of negative equity, is positive and highly significant in the

exercise of the default option; the call option value is also positively and highly significant in the

exercise of the prepayment option. In other words, increase in the probability of negative equity,

the incidence of default increases dramatically. On the other hand, declines in returns from

alternative investment that bring the call option "in-the-money" will lead to a high prepayment

activities. Stock market in China is a fast growing investment vehicle beyond traditional deposit.

Investment in stock market has been attached more and more importance in Chinese peoples

financial decision. The intrinsic value the prepayment option basically reflects investors portfolio

9 Log Likelihood and Schwarz-Bayesian Criterion (SBC) reported at the bottom of the table provide comparison of thegoodness of .t among alternative models. Models with lower values are considered preferable.

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choice. Model 2 further indicates that a value of call option is negatively associated with default

risk. In a bull stock market, household may relocate their asset from housing to stock market by

stopping mortgage payment.

Model 3 further include the interaction term between presale and option values to test

whether the intrinsic value of options in forward market have different influence than on the spot

market. The default behavior is less sensitive to the put option and call option for mortgage loans

with pre-sale properties. For prepayment behavior, the call option and put option are less sensitive

to pre-sale mortgage loan borrowers. This means that the pre-sale in apparently an important

factor that highly correlated with default risk and prepayment risk. If the loan is associated with

forward housing purchase, it is such a bad news for default and prepayment risks that option

value (both call and put) do not add as much to the risks as in spot market. The significance in the

product terms indicate that the default risk and prepayment risks exhibit quite differently in

forward market for the pre-sale houses than on spot market.

In a similar fashion, product terms between presale and other borrower characteristics

and collateral information can be tested. Since mortgages on presale houses exhibit strikingly

different default and prepayment behaviors, a more complete separation of hazard regressions are

performed towards forward market and spot market respectively. Table 7 displays the regression

results for the two markets. On forward market, while intrinsic value of call option is significant

for exercises of default option and prepayment option, probability of negative equity is associated

with neither default option nor prepayment option in statistical sense. The value of mortgage

default option has totally different underlying among pre-sale houses, versus completed projects.

On the forward market, housing price index has little to do with default risk, since the collateral

for presale houses is on paper. Therefore the probability of negative equity is more closely

associated with houses on spot market, while houses on forward market depend more on

probability of house delivery. Another remarkable feature on the separate regressions is that

borrowers characteristics and developer information play different roles on spot market versus

forward market. The borrower characteristics (age, marital status, education, occupation and job

position) are only statistically significant on spot market, not significant on forward market. On

the other hand the developer characteristics (number of projects, size, type and history of the

developer) are only statistically significantly associated with mortgage termination for presale

loans, none of them is significant on spot market. For example, younger borrowers, singles,

elementary school education group and clerk, social service as well as self-employment group are

associated with higher default risk, while older borrowers, singles, college education and

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managers are associated with higher prepayment risk. However none of these borrower

characteristics is statistically associated with mortgage termination risks on forward market. On

the other hand, good credit quality of developer, e.g. completed more projects in the past, bigger

and experienced developers, higher ratio of certified professional to total employee, foreign joint

ventures, is associated with lower default risk and higher prepayment risk. None of these

developer characteristics is statistically significant in the spot market regression. Although the

sensitivities are different, some loan variables, location variable and market condition share the

same sign across the spot market and forward market. For instance, on both markets, the more

dependents in a household, the higher the default risk, the lower the prepayment risk due to

households liquidity constraints. Central city location enjoys lower default risk and higher

prepayment risk.

[Insert Table 7]

To demonstrate the mortgage prepayment and default risks with and without embedded

forward contract risks, we simulate 300 paths of house price appreciation rates and stock returns

according to a joint stochastic mean-reverting process. These 300 randomly sampled paths are

applied to the prepayment and default functions reported by Model 3 in table 6 to compute the

monthly prepayment and default risks associated with hypothetical 0.5 million RMB mortgage.

We compare two hypothetical mortgage pools characterized by two risk structures between spot

versus forward market mortgage borrowers. The present values of the cash flows from the two

groups allow us to calculate risk premium on the forward presale housing market. 10 Table 8

reports a simulated result on forward risk premium which is about 250 basis points per year. In

other worlds, there is a 2.5% risk premium on forward market relative to the spot market in China.

[Insert Table 8]

6. CONCLUSION

This paper is the first to realize the mortgage risks on forward presale housing market.

This finding indicates that borrower characteristics and collateral information are both important

to determine the mortgage termination risks. Currently most Chinese banks price the consumerloan based on borrower characteristics only. The results of this paper indicate a potential

improvement in banks mortgage risk modeling. In addition, the mortgage borrowers

prepayment and default behavior in the forward housing market is significantly different from

those in the spot housing market. The study found that the cross-subsidy between the forward and

10This is similar to Deng and Gabirel (2006).

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spot housing market in China can be as high as 250 basis points. The finding of this study will

provide valuable insight about emerging housing and mortgage markets in China as well as those

in other transition economy.

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Figure 1. Residential Mortgage Market in China

Residential Mortgage Market in China

( 98% AAGR since 1997)

19 43136

338

560

825

1,330

1,592

2,000

0.39%

1.07%

2.14%

5.07%

6.94%

8.59%

9.27%

11.27%

12.00%

0

500

1000

1500

2000

2500

1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

BillionRMBYuan

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

Total Mortgage Outstanding Ratio of Mortgage to Total Bank Loans

Source: Chinese Banking Regulation Committee.

Figure 2. International Comparison of Mortgage to Consumer Loan Ratio

International Comparison of Consumer Loans (2003)

9.1%

26.3%29.5%

34.3%27.3%

38.8%

22.6%

59.2%2.7%

3.3%

2.6%

1.3%

2.4%

2.5%

3.9%

3.7%

3.7%

6.7%4.9%

16.0%

8.7%

28.4%

12.0%

7.5%

0.0%

2.0%1.4%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

China Thailand Malaysia Taiwan HongKong Singapore U.S. Korea U.K.

PercentageofTotalLoans

mortgage credit-card loan other consumer loan

Source: Goldman Sachs

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Figure 3. International Comparison of Loan to GDP Ratio

International Comparison of Loan-GDP Ratio (2003)

11.4%

19.2%

26.1%

36.6% 34.7%

25.5%

50.0%

57.5%

3.4%

2.7%

4.0%1.5%

3.0%

4.0%

3.6%

3.0%

4.3%

3.7%

6.3%20.3%

32.6%

7.1%

11.7%

7.2%1.6%

0.0%

2.1%

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

Thailand China U.S. Malaysia Taiwan Singapore Korea HongKong U.K.

PercentageofGDP

mortgage credit-card loan other consumer loan

Source: Goldman Sachs

Figure 4. International Comparison of Mortgage to Income Ratio

International Comparison of Mortgage-Income Ratio (2002)

7%

17%

30%

55%

75%

89%94%

114%123% 123%

174%

0%

20%

40%

60%

80%

100%

120%

140%

160%

180%

200%

India Thailand China Taiwan Malaysia HongKong U.S. Korea Japan U.K. Singapore

PercentageofDisposableIncome

Source: Goldman Sachs

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Figure 5. Supply and Sales in the Residential Housing Market in China

Supply and Sales of Residential Housing in China

1.58

1.31 1.361.25 1.22 1.2

1.131.03

0

50

100

150

200

250

300

350

400

1997 1998 1999 2000 2001 2002 2003 2004

Year

MillionSquareMeters

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Housing Square Meters Completed Housing Square Meters Sold

Supply-Sales Ratio of Residential Housing

Source: Goldman Sachs

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Figure 6. Market Microstructure of Forward and Spot Housing Market in China

SimpleModelfor

Forwardv.s.SpotHousingM

arketinChina

1.Forward

HousingMarket

TimeLine

Customer

Developer

Bank

2.SpotHousingMarket

TimeLine

Customer

Developer

Bank

1.ReceiveLastMortgagePayment

1.ReceiveH

ousePriceinFull

2.Depositin

Bank

1.Mortgage

LendingBasedonBorrower

Characteristics

2.TakeDep

ositfromDeveloper

1.New

ARMRateAnnounced

2.PrepaymentRisk,ReceivePayment

atPar

3.ReceiveResidualValueofHousein

CaseofBorrowerDefault

4.ReceiveMortgagePaymentif

OptionnotExercised

T=3

MortgageMatu

rity

1.Purchase

HouseonSpotMarket

2.PayinfulltoDeveloperwith

Downpayme

nt+Mortgage

3.Consume

Housing

1.PrepayifFinan

cing

Cost>Investment

Return

2.DefaultifValue

ofHouseInvestment

Return

2.DefaultifValue

ofHouse= 30 55 3665 38875 42595

(0.13) (8.60) (91.27) (49.78)

Registered Equity

1268 2872 32497 36637

(3.46) (7.84) (88.70) (42.78)

57 4140 44805 49002

(0.12) (8.45) (91.44) (57.22)

Number of ProjectsSingle Property 1373 6592 57495 65460

(2.10) (10.07) (87.83) (63.42)

Multiple Properties 11 3417 34335 37763

(0.03) (9.05) (90.92) (36.58)

Equity < 30 Million RMB

Equity >=31 Million RMB

Table 4. Descriptive Statistics for Mortgage Loans

Frequency of Loans by Category and by Payoff Types(Continued)

(Currency Exchange adj. )

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Variable Defaulted Prepaid Other All Loans

Marital Status

Married 562 4277 41440 46279

(1.21) (9.24) (89.54) (44.73)

Single 822 5778 50583 57183

(1.44) (10.10) (88.46) (55.27)

Education

College 843 6432 57563 64838

(1.30) (9.92) (88.78) (62.67)

Secondary Sch. 482 3254 31195 34931

(1.38) (9.32) (89.30) (33.76)

Primary Sch. 59 369 3265 3693

(1.60) (9.99) (88.41) (3.57)

Age Cohort

Age < 40 1036 6574 72420 80030

(1.29) (8.21) (90.49) (77.35)

Age > 40 348 3481 19603 23432

(1.49) (14.86) (83.66) (22.65)

Income GroupsMont y Income

< 8888RMB 1006 6623 69403 77032

(1.31) (8.60) (90.10) (74.45)Monthly Income

>8888RMB 378 3432 22620 26430

(1.43) (12.99) (85.58) (25.55)

OccupationBusiness/Trade 248 1854 20303 22405

(1.11) (8.27) (90.62) (21.66)

Social Service 130 849 8759 9738

(1.33) (8.72) (89.95) (9.41)

Self-Employment 602 4960 36746 42308

(1.42) (11.72) (86.85) (40.89)

R&D 80 773 9038 9891

(0.81) (7.82) (91.38) (9.56)

Others 324 1619 17177 19120

(1.69) (8.47) (89.84) (18.48)

Job PositionManager 768 6184 55766 62718

(1.22) (9.86) (88.92) (60.62)

Others 214 607 5457 6278

(10.77) (16.76) (172.48) (6.07)

Technician 168 1256 12482 13906

(1.21) (9.03) (89.76) (13.44)

Clerk 234 2008 18318 20560

(1.14) (9.77) (89.10) (19.87)

Table 5. Descriptive Statistics for Mortgage Loans

Frequency of Loans by Borrower Category and by Payoff Types

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Default Prepay Default Prepay Default Prepay

Fraction of Contract -2.616 2.722 -3.017 4.618Value (Call Option) (11.93) (30.49) (5.80) (21.45)

Probability of Negative 3.967 2.105 3.533 5.377

Equity (Put Option) (5.69) (13.13) (9.55) (10.04)

Presale 1.058 1.118 1.013 1.097 1.090 1.020

(dummy) (2.56) (28.10) (1.96) (27.56) (2.88) (12.74)

Interaction of Presale -1.937 -2.029

and Call Option (7.42) (8.86)

Interaction of Presale -3.103 -3.462

and Put Option (7.54) (6.45)

age > 40 -0.283 0.105 -0.280 0.111 -0.245 0.103

(dummy) (4.65) (4.73) (4.54) (4.96) (3.93) (4.61)

female -0.044 0.009 0.010 0.020 0.007 0.022

(dummy) (0.82) (0.44) (0.18) (1.02) (0.13) (1.12)

married -0.017 -0.057 -0.027 -0.064 -0.058 -0.067

(dummy) (1.29) (2.85) (1.42) (3.15) (1.97) (3.28)

occupation: -0.077 0.051 -0.095 0.050 -0.022 0.045

business and trade (dummy) (0.84) (1.96) (1.03) (2.33) (0.24) (1.94)

occupation: 0.070 0.013 0.943 0.018 0.054 0.013

social service (dummy) (0.70) (2.33) (0.44) (1.95) (0.53) (0.33)

occupation: -0.141 0.060 -0.180 0.047 -0.106 0.045

others (dummy) (1.78) (2.15) (0.23) (2.62) (1.32) (1.61)

occupation: 0.017 -0.033 0.040 -0.024 -0.136 -0.022

R&D (dummy) (0.15) (2.84) (0.34) (2.17) (1.15) 2.06

education: -0.102 -0.083 -0.110 -0.046 -0.056 0.044

secondary school (dummy) (0.78) (1.55) (0.83) (0.86) (0.42) (0.82)

education: -0.149 0.119 -0.158 0.108 -0.127 0.106

college (dummy) (2.63) (5.37) (2.78) (4.86) (2.23) (4.79)

job position: -0.021 0.045 -0.019 0.036 -0.025 0.036

manager (dummy) (0.24) (2.71) (0.22) (2.18) (0.29) (2.36)

job position: 0.994 -0.042 0.943 -0.041 0.836 -0.040

self-employment (dummy) (1.29) (1.92) (0.85) (2.82) (1.58) (1.88)

job position: 0.013 -0.063 0.031 -0.049 0.082 -0.051

technician (dummy) (0.12) (1.98) (0.29) (1.95) (1.76) (1.45)

number of dependents 0.229 -0.568 0.224 -0.550 0.213 -0.549(20.63) (50.02) (20.09) (48.49) (18.67) (48.40)

log monthly income -0.100 0.130 -0.103 0.123 -0.152 0.122

(2.60) (6.62) (1.63) (6.07) (2.40) (6.03)

Model 1 Model 2 Model 3

Table 6 Maximum Likelihood Estimates for Competing Risks

of Chinese Adjustable Rate Mortgage Prepayment and Default

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multiple project -1.829 0.077 -1.748 0.119 -1.868 0.116

(dummy) (10.68) (3.35) (10.08) (5.14) (2.40) (5.03)

size -0.104 0.000 -0.099 0.000 -0.099 0.000

(in 10mill. currency adj.) (6.31) (0.79) (5.96) (0.31) (6.44) (0.51)

number of employee -0.063 0.000 -0.060 0.000 -0.061 0.000(15.82) (1.58) (15.25) (1.43) (15.37) (1.00)

license longer than 20y -0.458 0.152 -0.426 0.105 -0.502 0.103

(dummy) (3.86) (6.89) (3.57) (4.72) (4.15) (4.64)

new developer 2.431 0.123 2.499 0.117 2.457 0.118

(dummy) (9.80) (5.13) (9.83) (4.89) (9.57) (4.94)

developer type: joint venture -0.936 0.056 -0.987 0.130 -0.934 0.128

with foreign developer (dummy) (7.16) (1.14) (7.37) (2.68) (6.96) (2.63)

developer type: joint venture 0.834 -0.059 0.844 -0.049 0.800 -0.039

with HK Macau, TW (dummy) (8.59) (0.87) (8.63) (0.72) (8.20) (0.58)

developer type: 0.196 0.158 0.295 0.157 0.299 0.150

private developer (dummy) (1.14) (2.68) (1.72) (2.66) (1.78) (2.55)

developer type 0.504 0.094 0.451 0.101 0.506 0.105

limited co.(dummy) (5.03) (2.36) (4.48) 2.56 (4.99) (2.65)

district 0.399 0.113 0.352 0.108 0.402 0.110

(6.24) 5.05 (5.45) (4.83) (6.17) (4.93)

central city location -1.306 0.086 -1.224 0.084 -1.271 0.085

(dummy) (9.55) (3.38) (8.93) (3.30) (9.18) (3.35)

ratio of certified professionals -4.501 0.256 -4.402 0.269 -4.470 0.271

(9.55) (5.38) (18.38) (5.67) (18.51) (5.71)

Loan To Value Ratio 0.068 -0.043 0.046 -0.073 -0.003 -0.074

(1.70) (3.25) (3.08) (4.11) (0.06) (4.12)

Housing Exp. To Income 0.578 -0.363 0.537 -0.352 0.360 -0.343

(9.95) (12.68) (9.08) (12.43) (5.89) (12.13)

log loan amount 0.129 -0.117 0.047 -0.190 -0.061 -0.191

(0.99) (1.87) (0.72) (1.36) (0.92) (1.53)

stock market 0.002 -0.005 0.002 -0.005 0.002 -0.005

(1.79) (39.45) (0.50) (39.50) (1.43) (39.36)

slope term structure -0.494 -1.549 -0.762 -1.512 -0.649 -1.511

(2.16) (48.74) (3.11) (47.30) (2.65) (47.28)

unemployment 0.059 0.081 0.046 0.077 0.053 0.076

(7.69) (48.20) (5.44) (46.21) (6.27) (46.01)

Log Likelihood

SBC

164107

164638

165089

165545

164254

164747

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Default Prepay Default Prepay

Fraction of Contract -0.278 4.048 -2.456 2.669

Value (Call Option) (1.45) (9.98) (9.52) (28.76)

Probability of Negative 9.064 2.781 2.762 2.075

Equity (Put Option) (2.35) (2.05) (0.88) (0.56)

age > 40 -0.454 0.127 -0.198