University of Amsterdam
Faculty of Economics and Business
Amsterdam Business School
The Study of RMBS Business in China
——Mode, Pricing, Risk and Case Introduction
Master Thesis
Version: Finalized Version
Program: Master in International Finance Student: Han Jiang
Student Number: 10874496 Thesis Supervisor: Dennis Jullens Date: 27th August 2015
Abstract
Residential Mortgage-Backed Securitization (RMBS) originated in the US is one of the greatest financial innovations in the 20th century. In recent years, it has a vigorous development all over the world. In 2005, the first RMBS product was launched by China Construction Bank.
For China, the development of RMBS brings many benefits. Thus, an overall study of RMBS business in China with international finance perspective will be quite meaningful and stimulating. However, as differed from traditional western countries, China has its own special characteristics in housing mortgages and RMBS. So a study of RMBS from Chinese angle is quite necessary. The master thesis is divided into 7 chapters. The first part and the second part are general introduction and literature review about RMBS. From the third part to the seventh part, I talk about the following topics:
1) The main modes of RMBS in developed countries/areas. The mode in the US is the most typical and mature one in the western world. Some other modes discussed are the modes in the UK, Australia, Canada and Hong Kong. Basically, the mode in the US, Canada and Hong Kong are more government-oriented and the others are more market-oriented.
2) The most suitable issue mode of RMBS in China. In China, the most issue suitable RMBS mode is Special Purpose Trust (SPT) mode which could perfectly realize true sale and bankruptcy-remote.
3) The risks of RMBS in Chinese market. There are credit risk, interest rate risk, prepayment risk and other risks in Chinese RMBS and some regression analysis is made by SPSS 19.0 to search for linear relationship between prepayment rate and several economic indices as well as the relationship between default rate and the same economic indices respectively.
4) The pricing of a RMBS product. Static Cash Flow Yield, Static Spread and Option-Adjusted Spread are introduced and Static Spread is suitable in China.
5) A brief introduction of “Jianyuan 2005-1 MBS”. The transaction structure and cash flow systems are introduced.
Content
Chapter 1. Introduction………1
Chapter 2. Literature Review………..5
2.1 The main modes of RMBS in developed countries/areas………..5
2.2 The most suitable issue mode of RMBS in China……….5
2.3 The risks of RMBS in Chinese market………..6
2.4 The pricing of a RMBS product………....7
Chapter 3. The Main Modes of RMBS in Developed Countries/Areas………8
3.1 The RMBS mode in the US………..8
3.2 The RMBS mode in the UK………...10
3.3 The RMBS mode in Australia………..11
3.4 The RMBS mode in Canada………....12
3.5 The RMBS mode in Hong Kong……….12
Chapter 4. The Most Suitable Issue Mode of RMBS in China………....14
Chapter 5.The Risks of RMBS in Chinese market………...17
5.1 Credit risk………....17
5.2 Interest rate risk………...18
5.3 Prepayment risk………...18
5.4 Other risks………....………...19
5.5 RMBS risk measurements in China………....………19
5.6 Empirical research of prepayment risk based on multiple regression……….21
5.7 Empirical research of credit risk based on multiple regression………...30
Chapter 6.The Pricing of A RMBS Product……….36
6.1 Static Cash Flow Yield………36
6.2 Static Spread………37
6.3 Option-Adjusted Spread………..39
6.4 The pricing method of RMBS in Chinese market………...41
Chapter 7.A Brief Introduction of “Jianyuan 2005-1 MBS”………...43
7.1 Basic procedures of Jianyuan 2005-1 MBS………43
7.2 The transaction structure of Jianyuan 2005-1 MBS………44
7.3 Cash flow structure of Jianyuan 2005-1 MBS………....45
1 Chapter 1. Introduction
Fixed income securities that are backed, or collateralized, by a pool (collection) of assets such as loans or receivables are referred to as Assets-backed Securities (ABS) (CFA Institute, 2014). A Mortgage-backed Security (MBS) is a type of ABS that is secured by a mortgage, or more commonly a pool of mortgages (CFA Institute, 2014). And Residential MBS (RMBS) are the bonds created from the securitization of mortgage loans for the purchase of residential properties (CFA Institute, 2014). Usually, a financial institution (such as a commercial bank) puts together its mortgages which have low liquidity but have steady cash flows in the future, restructures them into different groups, and sells them to a Special Purpose Vehicle (SPV). After several credit enhancements, such as financial hypothecation, these mortgage groups are sold to investors as securities from the SPV. RMBS, created in 1970s in the US, is the first type of securitization in the history of ABS. Due to its special characteristics and advantages, the market of RMBS expanded substantially in the past years.
Figure 1: The basic procedures of RMBS (Li Yan, 2007)
SPV Investors Launch RMBS RMBS Income Credit Enhancement Institutions Credit Enhanceme nt Trustee RMBS Principle and Interest Payment Services Institutions Principle and Interest Payment Original Debtor Principle and Interest Payment Original Initiator Debt Assets Transfer Transfer Income Credit Rating
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In China, the first practice of securitization started from the end of 1980s, and it was quite tentative. In the February of 2003, The People's Bank of China (PBC) first pointed out it would “actively promote the securitization of residential mortgages”; in the January of 2004, the central government said it would “proactively explore and develop securitization products” to carry forward the reform and openness in capital markets; in the March of 2005, the central government authorized pilot programs of China Construction Bank (CCB) and China Development Bank (CDB); in the April of 2005, PBC and China Banking Regulatory Commission (CBRC) launched Regulations for Credit Securitization Pilot Programs; in the December of 2005, CCB created the first RMBS business in China, introducing its “Jianyuan 2005-1 MBS” product (total amount of 3.016 billion CNY) to the market.
Right now, RMBS is still a hot topic in China. 10 years have passed since CCB’s first practice, and many other have also launched various RMBS products. However, compared with the RMBS business in the developed countries, China’s RMBS operation is still immature. What is immature in the present will be promising in the future.
For China, the development of RMBS has the following benefits:
1) The development of RMBS is propitious for commercial banks to expand their financing channel. By RMBS, commercial banks are able to transfer the mortgage loans they held into securities available for sale to the investors, thus obtaining funding. Also, these funding could be used to launch new mortgage loans which will be the basis sources for new RMBS. In this way, commercial banks strengthen their capital expansibility.
2) The development of RMBS is helpful for commercial banks to decrease the operational risks. Generally, the mortgage loan, which is a major part of bank’s assets, has a maturity of 20 to 30 years. However, for the liability side, the deposits are almost current deposits and term deposits with less than 5 years maturities. So, there is a mismatch in terms of the maturities of assets and liabilities. With RMBS, banks are able
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to transfer the illiquid mortgage loans into highly liquid securities, relieving the conflict between maturities of assets and liabilities. Also, a bank can set up a SPV to buy assets, removing them from the bank’s balance sheet and may increase their value by removing the risks that financial trouble at the bank will give other investors a claim to the assets’ cash flows.
3) The development of RMBS is beneficial for improving the profitability of commercial banks. First of all, banks can still provide services to the already securitized mortgage loans, and charge some fees. Secondly, banks can act as the underwriter of RMBS, and gain some commission. Thirdly, if the mortgage payments exceed the principle and interests payments of RMBS, banks have the right to enjoy the allocation of the remaining cash flows.
4) The development of RMBS assists commercial banks to reinforce the capital management. Basel Agreements have regulated the capital adequacy ratio of commercial banks. The relatively low capital adequacy ratio is one obvious problem that is faced by every bank in China. By RMBS, banks remove these risk-bearing assets (mortgage loans) from their balance sheets, thus enhancing capital adequacy ratios.
5) The development of RMBS can be used by the central bank to conduct macro financial control. Control in public market in one of the basic tools of central bank to adjust the currency supply. Transaction in bonds market is a major part of that control. Central bank could purchase or sell RMBS to regulate the monetary supply.
6) The development of RMBS promotes the maturity of capital market. RMBS business is an important low-risk financial innovation which combines capital market, currency market, and real economy. A lot of market players, such as commercial banks, SPV, rating institutions, securities companies, assets management companies, will participate in this business. Moreover, a new financial product will require government regulators to study and launch new laws and regulations.
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Thus, an overall study of RMBS business in China with international finance perspective will be quite meaningful and stimulating.
5 Chapter 2. Literature Review
2.1 The main modes of RMBS in developed countries/areas
From the practice of RMBS, it started and developed maturely in the US. In The Handbook of Mortgage-Backed Securities, Frank J. Fabozzi (2006) systematically introduced the various kinds of RMBS in the US, including their operation modes, pricing, and trading strategies. Also, he introduced the American RMBS system in detail, including original initiator, SPV, guarantee institutions, credit rating systems and trading and settlement procedures. Chaoying Zhang (2002) pointed out the basic reasons for the development of RMBS in the US, and the reasons are the specialization of real estate financing, the involvement of guarantee market into capital market, the standardization of contract, and the normalization of RMBS evaluation.
Yongping Liang (1999) introduced the methods of RMBS in Canada, the UK, France and Denmark. The RMBS team in CCB wrote a report about start, legislation, and government support of the RMBS in Canada and Hong Kong.
2.2 The most suitable mode of RMBS in China
Huazheng Wang and Junqi Tan (2005) divided RMBS into 3 groups according to the different functions of government. The groups were led RMBS, government-supported RMBS and market-oriented RMBS. The analysis of the three groups was helpful for finding the suitable RMBS mode in China. They believed that the development and maturity of financial market is the foundation of RMBS, the effective promotion from the government was an important external factor, and modern financial supervises system was the necessary assurance of RMBS business. Jianping Wei (2006) probed into the realistic barriers of RMBS: the unclearness in poverty right, the immaturity of prime guarantee market, the lack of experienced intermediaries, and the barbarism of legislations. Yongmei Li and Shuyin Fan (2006) considered RMBS as the typical kind of MBS. They gave some suggestions about Chinese RMBS based on the study of the RMBS in the US, Canada, and Australia.
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Wenxian Wu, FanrongZeng (2005) thought that the business of RMBS in China should be split into 2 steps. The first period was the pilot program of in-balance sheet securitization of mortgage, and the second period was the off-balance sheet securitization of mortgage. SiqiZheng, Wendan Li and Hongyu Liu (2003) listed the main factors affecting the selection of in or off-balance sheet securitization, and the factor were the scale of RMBS market, the regulations, the capital adequacy of commercial banks, and the historical factors.
In the choice of securities types, Rong Bin (2002) deemed that in the beginning and pilot period, the subsidiaries of state-owned banks should only launch MPS (Mortgage Pass-through Securities).
2.3 The risks of RMBS in Chinese market
Chao Liu, Youhua Li, and Ting Zhang (2003) believed that the main risks of RMBS came from credit risk, market risk and operation risk. Jianghong Zeng (2004) thought that RMBS were the breakthrough point of launching MBS and banking assets reorganization, and there would be interest risks, liquidity risk, and prepayment risk. Xiaorong Lv (2005) presented the risks during the process of RMBS and the measurement of risks. Yan Wang and Yan Wang and Xuexi Huo (2006) considered prepayment risk as the special derivate from RMBS, and gave some suggestions.
Jianhua Jiang (2001) researched the risks in every segment in RMBS, and pointed out that in the section of purchasing, there would be true sale risk, loan quality risk, scale risk; in the section of issuing and trading, there would be issue risk, liquidity risk, match risk; in the section of operating, there would be return risk, capital risk, investment risk and technical risk; in the section of assets managing, there would be management risk and default risk. Qing Wu (2005) analyzed the credit risk, liquidity risk and prepayment risk of RMBS investors. Minkang Liu (2007) said that when the macro-economy was on the upward way, financial institutions would be less risk-aware, and financial innovation required higher effectiveness of the financial market.
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For the present, the study of RMBS in China is mainly about the exploration of the mode. The risks during RMBS, especially the prepayment risk, are attracting increasing attention. The research of risks now is basically based on the western traditional theories and practice about RMBS. However, there must be some elements with Chinese characters.
2.4 The pricing of a RMBS product
For the pricing of RMBS, the tradition methods are discounted cash flow method, the reinvestment methods, holding period return method, and prepayment prediction method. Actually, they are all based on discounted cash flows. Another way is using interest rate model to forecast the route of interest rate changes, and price RMBS. US finance academics Black and Scholes (1972) proposed Black-Scholes model (which involved the study of the effect of interest rate on option price) in the book The Pricing of Options and Corporate Liabilities. McConnell and Muller (1988) pointed out that the prepayment rate in the interest model determined the difference between market interest and coupon rate. Schwartz and Torous (1989) pricing model assumed that all the information about interest rate term structure could be expressed in two variables: risk-free interest rate and default-free bonds return. Both two variables comply with Geometrical Brownian Motion.
From 1998, Chinese academic circle began to study RMBS systematically. However, most academic books are about the general and comprehensive introduction of MBS. Rong Bin (2002) wrote a book about RMBS. Still, it just covered the mode of RMBS in China. In short, in the pricing part, Chinese scholars mainly use the traditional methods.
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Chapter 3. The Main Modes of RMBS in Developed Countries/Areas 3.1 The RMBS mode in the US
The US is the birthplace of RMBS, and it has the most developed market of RMBS. From 1960s till now, the US has built a complete system for RMBS. Since the US is the creator of RMBS, the development of RMBS in America is the miniature of the development of RMBS in the world.
The biggest distinguishing feature of RMBS in the US is the combination of governmental involvement and market operation. Let us first have a look at the history of American RMBS.
In 1934, the US Congress passed National Housing Act (NHA). Under this act, the US government established Federal Housing Administration (FHA), providing mortgage insurance to low and medium income families. In 1938, under the authorization of NHA, FHA founded Fannie Mae (FNMA). At the beginning of establishment, FNMA brought mortgage from commercial banks and injected capital to the market when the economy was in depression; also, FNMA would withdraw money via sales activities when the economy was in prosperity. This operation encouraged the banks to supply mortgage. In 1944, Veterans Administration (VA) began to offer mortgage guarantee to veterans for free. These policies released the consumption demand of the people who had the housing need but lacked of payment capability, which in turn promoted the development of prime market.
In the late of 1960s, America met economic recession with great volatility in interest rate. Due to the limitation of Term Q in 1933 Banking Act, saving and lending institutions had serious liquidity risk. Under this circumstance, Ginnie Mae (GNMA), which separated from FNMA, launched RMBS with government credit pledge. This was the mark of securitization. In 1968, FNMA became public company with government supervise. In 1970, Freddie Mac (FHLMC), a secondary market company for saving and lending institutions, was established. Subsequently, FHLMC and FNMA launched standardized RMBS in 1971 and 1980 respectively.
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The procedures of RMBS in the US could be divided into several steps. Firstly, commercial banks make loans to the applicants. Secondly, FNMA/GNMA/FHLMC buys the mortgage assets from the banks, putting them together to form an asset collection. Thirdly, the asset pool would generate different types of RMBS released by a SPV. And the SPV is the connection between prime market and secondary market.
The successful RMBS in the secondary market profits from the rigorous risk control. Resolving function is the core of RMBS in the US. In detail, the risk control could be presented in the following aspects:
1. Loan guarantee and insurance in prime market. In mortgage prime market, mature loan guarantee and insurance provides excellent credit protect, which reduces the risk in secondary market. The protection includes the loan vouching by FHA to low and medium income families, warranted by VA to veterans, etc. Also, loan institutions may require applicants to provide other private insurance or guarantee.
2. The bankruptcy-remote mechanism of SPV. SPV was created for securitization purpose with main function of mortgage assets bankruptcy-remote. Through true sale, loan institutions could transfer mortgage assets to SPV, removing these assets from the balance sheet and realizing off-balance sheet operation. When the institutions are bankrupted, the securitized assets cannot be included in the liquidation assets. In this way, the investors’ benefits are protected.
3. Return pledge in secondary market. In the RMBS market in the US, the securities issued by the 3 largest institutions (FNMA, GNMA, FHLMC) have taken up 85% market share. These institutions provide full or implicit governmental credit, enhancing RMBS credit rating. Moreover, by using external insurance or guarantee, SPV could further improve the credit quality of RMBS. Besides, in order to satisfy various demands from different types of investors, the security issuers could make some smart product design. The products have been increasing specialized: RMBS has developed from the initial
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pass-through securities to pay-through securities and from Collateralized Mortgage Obligation (CMO) to principle only and interest only securities. Investors in all kinds of risk preferences would find the exact right RMBS for themselves.
According to the history and mode of RMBS in the US, we can generalize its features. Firstly, the US government plays a very essential role in RMBS prime and secondary market. In the late stage of the Great Recession, it was the US government who legislated the mortgage to low and medium income families, boosting the housing consumption. When the financial institutions felt that the liquidity risk was becoming more and more severe, again, the US government founded FNMA, purchasing mortgage loan assets. In 1970s, when the interest rate kept going upward, disintermediation arose in loan institutions, GNMA, which founded by the US government, launched the first RMBS. After that, the big 3 RMBS institutions with full governmental credit and semi-governmental credit became the hard cores of the market. Secondly, the linkage between the prime market and secondary market brings out the best in each other. On one side, the full cultivation of primary market laid the foundation of secondary market. On the other side, the development of secondary market promoted the regulation of prime market. Thirdly, the system was improved and perfected gradually with the consideration of reality. At the beginning of RMBS history, the US government established FNMA to just make mortgage purchase, instead of securitization, to increase the liquidity of saving and lending institutions, because the prime market was so immature. Until 1970s to 1980s, the big 3 RMBS institutions began to launch RMBS under the fact that the mortgage scale was large enough and the liquidity risk as well as interest risk was serious enough. Hereafter, RMBS companies designed different products to meet various demands from the investors.
3.2 The RMBS mode in the UK
At the start of 1980s, the UK mortgage finance market was funded through a “specialist circuit of housing finance” dominated by building societies that depended on retail saving and instruments for their finance (Michael Prykeet al.,1994). In the financial innovation in 1980s, the development of RMBS has influenced the European area, and the UK is a
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leading country. In 1985, the first RMBS was launched in Britain, and since then the mortgage market of UK boomed.
Unlike the US RMBS, the British RMBS business is not driven by the government, instead, private sectors and institution investors are more important. Without government guarantee, the credit rating is low and the risk is relatively high. In order to keep investors interested, the RMBS system must include external or internal credit enhancements.
We can say that the British mode is a business-oriented mode. The mortgage market is completely developed as a private sector without any official government institution establishment. In the system, a SPV must be founded to realize true sale, bankruptcy-remote, and credit enhancements.
3.3 The RMBS mode in Australia
The RMBS is highly developed in Australia and largely driven by the market instead of the government. Macquarie Group a major player in Australian market, and its Commodity and Financial Market Division is responsible for securitization business (Jianfeng Lin, 2007).
Macquarie Group RMBS business has unified lending standards with the combination of entrusted loan and direct loan, so Macquarie Group is the direct generator of RMBS assets. Usually, Macquarie Group would set up a trust SPV to enhance the credit level. From 1996, Australia implemented consumer credit code nationwide, which made the credit judgment of lending institutions much easier.
In general, marketization is a marked feature of Australian RMBS. In the process of securitization, the company is the director producer of mortgage assets. In the meantime, due to lack of governmental credit assurance, credit enhancements from multiple perspectives would be necessary.
12 3.4 The RMBS mode in Canada
The mode of Canada is a “half-government and half-business” one. The core of this system is Canada Mortgage and Housing Corporation (CMHC). CMHC, founded in 1944 and belonged to the federal government, is the guarantee institution in Canadian mortgage market. CMHC functioned as the FHA in the US at the start, providing houses to veterans and lending to social housing construction. In 1954, in order to lower interest rate of down payment and increase the payment capacity of low and medium income families, Parliament of Canada modified the National Housing Act (Canada), authorizing CMHC to provide 100% warranty to low down payment housing and encouraging financial institutions to issue mortgage with small down payment. In 1986, CMHC carried out RMBS and launched NHA-MBS for attracting more investors to enter the market and stabilizing the mortgage loan supply. Later in 1992, Canadian government promoted the guarantee scheme for the first housing purchase, improving the insurance mechanism of NHA-MBS.
Macroscopic adjustment and control of the government and perfection of secondary housing market are the key successful drivers of Canadian RMBS business. In every period, Canadian government guided the development of RMBS through CMHC. The basic procedures of RMBS are like the followings: firstly, the banks strip out the mortgage from the balance sheet, and establish the assets pool; secondly, CMHC vouches the assets and invited credit rating institutions to evaluate the mortgage loans; thirdly, the issuing banks sign the underwriting agreement with investment banks for future underwriting.
3.5 The RMBS mode in Hong Kong
In 1997, the economy of Hong Kong was seriously beaten in Asian Financial Crisis, and the property market bubble broke. Many people turned into “negative net assets persons”. In order to boost the confidence for the market, Hong Kong government accelerated the progress of securitization. In March 1997, Hong Kong government set up The Hong Kong Mortgage Corporation Limited (HKMC).
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Basically, HKMC would issue debenture for purchasing mortgages, and build loan combinations. Then, HKMC turns the loan combinations into RMBS. HKMC uses off-balance sheet mode and a SPV is necessary for separate the bonds risk and business risk. HKMC provides guarantee for the RMBS with government credit, so a lot of expenses for credit rating and credit enhancement would be saved.
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Chapter 4. The Most Suitable Issue Mode of RMBS in China
For every country, the choice of RMBS has to be consistent with the trend of economic system reform. Currently, commercial banks in China cannot establish special institutions which are just for issuing RMBS. So the in-balance sheet mode is not that possible in China, since commercial banks have no qualification to do so. It would make no legal sense for banks to use its own mortgage as the guarantee of the liabilities. Also, in-balance sheet mode would make true sale and bankruptcy-remote impossible, which could not enhance capital adequacy ratio of banks. Moreover, in-balance sheet mode goes against the formation of a uniform and regulated prime market for mortgage loans. All in all, in-balance sheet mode is not suitable for China.
Now, let us consider off-balance sheet mode. This mode could perfectly realize true sale, bankruptcy-remote, and transformation to financing based on specific assets’ credits. Only in this way, the innovation of securitization is truly completed. Theoretically speaking, the nature of RMBS requires bankruptcy-remote instead of true sale. However, true sale is the method for bankruptcy-remote. In China, state-owned banks basically will never go bankrupted, so the key points of RMBS design is to avoid banks, as the issuers of RMBS, damaging the benefits of investors. From this perspective, off-balance sheet mode is the most suitable issue mode for China to prevent moral hazard.
The purpose of assets securitization is to financing backed by specific assets, and the core problem is what method should be used to realize fundamental assets risk separation. Establish a SPV is a necessary part in this mechanism. There are two different forms of a SPV: Special Purpose Corporation (SPC) and Special Purpose Trust (SPT). For SPC, the real assets will be sold to a SPC, as the issuer of RMBS. The function of a SPV is just the same as what we have talked about in the above, to protect the interest of the investors. A SPT is just like a SPV, however, the difference is that the original initiator would found a trust for special purpose, and put the assets into the trust. The Trust Law in China states that the trust assets have independency. This means that, bailee and bailor, no matter which part is bankrupted, the trust assets of bailee will never be affected. In fact, the character of the trust would separate the fundamental assets apart from the assets of
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trustees. In the present period, the formation of a SPC requires special legislation support. However, China has no specific law attending this problem. So both the establishment of a SPC and release of ABS from a SPC have some realistic barriers.
In China, currently trust institutions serve as a SPV to conduct off-balance sheet mode. The choice of trust companies stem from two reasons: bankruptcy-remote and state transition of property right. For a securitization plan, in order to separate the securitized assets and the unsecuritized assets, the scheme must include a special vehicle to load the securitized assets. Trust Law endows trust assets unique risk separation character, making trust institutions possible to become the SPV of ABS. In trust mechanism, the fundamental assets which have been put into the vehicle cannot be treated as the warranty of obligatory right, if the owner of the fundamental assets runs into debt. Meantime, the loaded assets must be separately managed with the inherent assets of trust institutions. The creditors of trust corporations have no rights to conduct compulsory execution. All of these features suggest that trust plan is very suitable for being a SPV to realize bankruptcy separation. The function to transit property right state makes trust, as a vehicle, transfer object assets into a new form, i.e. beneficial right of the trust. When a trust is designed as a special purpose one, it could issue negotiable securities with beneficial right backed by object assets, namely beneficial securities. In the process of trust issuing, all these functions of a trust achieve the true sale and bankruptcy-remote of mortgage assets, as sort of special purpose assets. So by establishing an independent trust institution away from the initiator as the trustee of the fundamental assets in securitization, the business could avoid the insider dealing and moral hazard of the initiator.
Actually, China has tried several rounds of this kind of credit ABS from 2005.With the development and conduction of RMBS, China has primarily build a suitable mode for RMBS where the fundamental assets are the mortgage loans, and a trust institution is necessary to found a SPT to release the securities.
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More information will be discussed in Chapter 7 (A brief introduction of “Jianyuan 2005-1 MBS”) where a specific example will be given.
17 Chapter 5.The risks of RMBS in Chinese market
The nature of RMBS is to split and restructure the tradable securities, making financial institutions be able to collect money before the maturity of the mortgage loans and lend new mortgage loans. The turnover rate of mortgage loan is accelerated and liquidity is improved. So the nature of RMBS involves the transition of return and risk from financial institutions to investors. The main risks in RMBS business are as the followings.
5.1 Credit risk
Credit risk means the failure of principle and interest payment of the borrowers, causing the issuers cannot pay the principle and interest to investors. When the default risk becomes higher, the expected return required by investors (cost of capital) is increased, leading difficulties in RMBS implementation and promotion.
So far, the fully covered credit rating system has not been established in China. Usually, there is some non-currency income and “gray income” in residents’ earnings and state-owned enterprises tend to launch low-salary proof of earnings while private companies do the opposite. So banks cannot clearly calculate and verify the real income level of the borrowers with their own credit investigation team, especially when the borrowers are business entities and major supervisors. Due to the lack of nationwide individual credit system as well as accompanied individual credit evaluation, credit investigation, and personal bankruptcy systems, banks feel impossible to truly judge whether the borrowers have liabilities and poor credit record or not. The shortage of credit systems will inevitably place commercial banks into a dilemma: the banks have to either give up the credit lending policies or make passive decisions under the uncontrolled credit risks. On the other hand, the housing guarantee system in China is not perfect either. When issuing mortgage loans, banks usually get the apartments/houses that to be brought as the assurance assets, requiring borrowers buy insurance for the apartments/houses or ask a third party to provide the collateral.
18 5.2 Interest rate risk
Interest rate risk (also called market risk) means the risk of loss from the interest rate floating. There are two layers of meaning: firstly, the price RMBS vary inversely with the interest rate, so interest rate change will affect the return of investors; secondly, the change of interest rate will cause the change of interest payment reinvestment return. Thus, interest rate risk is the least avoidable and manageable risk in RMBS. For the moment, China has no fully marketized interest rate system, and only inter-bank rate is determined by the market. Basic deposit and loan interest rates are decided by PBC. The control of interest rate twists the demand and supply mechanism of credit capital market, leading to interest rates which cannot reflect the market price of capital and deprival of saving and lending pricing rights from commercial banks. The nature of RMBS is to discount the cash flows from the mortgage assets collection according to some certain discount factor, namely the market rate. If we try to price RMBS product under the controlled interest rates, we may not be able to reflect its true investment value. Moreover, in principle, the return of a bank issued security is higher than the rate of government bonds, so return of investors cannot be lower than the government bonds rate with same duration. Therefore, under the current interest rate system, the profit margin of RMBS is limited.
5.3 Prepayment risk
Under fully-amortized mortgage, a borrower would pay the same amount on monthly basis. So the shares of the unpaid principle and interest would change every month. Usually speaking, in the early stage of the mortgage loan, the interest would take up a larger part of the monthly payment, and later the principle would have more shares. Once the mortgagor chooses to make prepayment, the assets cash flows would be affected. The benefits of the originator from providing RMBS services would be less. Also, as the cash flows change, the valuation of the security would also be modified which influences the expected return of the RMBS investors.
19 5.4 Other risks
5.4.1 Compliance risk
The law systems for RMBS are not completed in China, which hinders the development of RMBS to some extent. In western countries, a general company, partnership or trust organization can act as the SPV with pure purpose of realizing bankruptcy-remote. Currently in China, the matter of SPV is usually solved by establishing a SPT by a trust. However, there is no specific law or regulation about a general company serving as SPV. If a company wants to be a SPV, then according to the Corporate Law, it should extract 10% of the after-tax profit as the legal sinking fund. Nevertheless, a SPV is just an institution for bankruptcy-remote instead of survival and development. Thus, the legal requirement of sinking fund conflicts with the purpose of a SPV. True sale is an essential part of successful RMBS. According to Trust Law, it is quite easy to achieve true sale when using trust to release securitized products. However, there are no detailed laws or regulations for true sale in the RMBS issue via a general company. The lack of laws and regulations increases the promotion cost and transaction risk of RMBS
5.4.2 Policy risk
Intervention from the government or some changes in policies would bring policy risk to RMBS business. As one of the major pillar industries, real estate industry is highly controlled by Chinese government. For example, from 15th January 2007 to 25th June 2008, the central bank has increased Required Reserve Rate for 16 times in order to stabilize housing price. These policies would increase the cost of capital of the borrowers, causing them make prepayments. In conclusion, real estate is the fundamental assets of RMBS, and changes in property policies would affect RMBS indirectly, especially in China.
5.5 RMBS risk measurements in China
5.5.1 The measurement of prepayment risk——Constant Prepayment Rate Model Constant Prepayment Rate (CPR) model is the most widely used model for prepayment. The main assumption of CPR model is that during the remaining payment period,
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repayment of principle would happen in every month. The major methods for measurements are Single Month Mortality (SMM) and Conditional Prepayment Rate (CPR).
SMM is the most basic index of prepayment as well as the foundation of other prepayment measurement models. Usually, SMM is a monthly rate with the following equation:
SMM = Prepayment for month
(Beginning mortgage balance for month − scheduled principle repyament for month)
Generally speaking, when the SMM becomes bigger, it menas borrowers would choose quicker speed to make prepayments and investors would have larger loss.
CPR is the annualized SMM, which is the assumed prepayment for a pool of residential mortgage loans:
CPR = 1 − (1 − SMM)12
5.5.2 The measurement of prepayment risk——Public Security Association Model An industrial standard in mortgage market is Public Security Association (PSA) prepayment model. It is a prepayment pattern or benchmark over the life of a mortgage pool reflects the prepayment rates described by market participant in the US. The PSA prepayment benchmark assumes the monthly prepayment rate for a mortgage pool increases as it ages, or becomes seasoned. The PSA benchmark is expressed as a monthly series of CPRs. For example, the PSA standard benchmark is 100% PSA is that CPR equals to 0.2% for the first month after origination, increasing by 0.2% per month up to 30 months, and CPR is 6% for months after 30.
5.5.3 The measurement of prepayment risk——Office Thrift Supervision Model Some past experience suggests that main influential factors of prepayment are Seasonality, Burnout, Aging and interest rate change. Seasonality means there is a seasonal trend in prepayment, which is related to housing purchase, work relocation, job hunting, etc. Burnout suggests prepayment ratio is also connected to route of interest rate
21
change, which mainly relies on fixed interest mortgage. Aging stands for the raise of prepayment ratio with the increase of mortgage duration. Interest rate change implies that the refinancing behavior of the borrowers if the mortgage rate is less than the contract rate or cost of refinancing.
All these factors can be multiplied to predict the prepayment ratio. One typical model is the OTS model from Schwartz and Torous (1989). The model uses interest rate gap, refinancing inclination, seasonality factor, and burnout event to explain related elements, and includes Log-logistic distribution as the basic function of prepayments.
5.5.4 The measurement of prepayment risk——Goldman Sachs Model
Researchers in Goldman Sachs applied some new elements in prepayment model: Refinance, Relocation, Assumption, and Curtailment. Refinance means the increase of prepayment due to the enlarging gap between mortgage contract rate and market interest rate. Relocation suggests new property purchase which inevitably raises prepayment ratio. Assumption stands for the inheritance of mortgage loan from the seller to the buyer during a real estate transaction. The seller does not have to prepay the mortgage himself/herself. Curtailment represents small share in total payments in the beginning, however, the cumulative influence from it would be quite significant (Qiangzhi Liu et al., 2008). The calculation of this model is that
Monthly Prepayment Ratio = Relocation − Assumption + Refinance + Curtailment
5.6 Empirical research of prepayment risk based on multiple regression 5.6.1 Data sources and measurement criteria
1) Data sources
The article selected SMM and several economic indices from May 2012 to May 2015 as the object of this study. For some lost data in the original data, assumptions had to be made in order to make the data set complete.
2) Calculation of SMM
22
SMM =(Beginning mortgage balance for month − scheduled principle repyament for month)Prepayment for month
So after rearrangement and calculation of the 37 months’ data, we could see the SMM for every month during the period (See Appendix 1 and Figure 1).
Figure 1
From the figure, we could see that SMM in every month basically maintained in a certain level with some fluctuations. In December 2013, it reached the peak.
3) Calculation of CPR
From the above, we could also know that
CPR = 1 − (1 − SMM)12
So, since we now have all the SMM, we could easily calculate the monthly CPR (See Appendix 1 and Figure 2).
-0.50 1.00 1.50 2.00 2.50 M ay -12 Jul -12 S ep -12 No v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 Sep -14 No v -14 Ja n -15 M ar -15 M ay -15 SMM (%)
23 Figure 2
5.6.2 Data selection
1) Dependent variables selection
Of course, from the above equation, we clearly choose SMM as the dependent variable and measurement criterion of prepayment. We selected data from the trust report of “Jianyuan 2005-1 MBS”, and the data is shown in Appendix 2.
2) Independent variables selection
From the above theoretical study, we could see that during the process of RMBS, there are several affecting factors. This article selected 4 variables from the perspective of interest rate market, capital market and real industry market. They are Mortgage rate for 5 years or longer (X1), Shanghai Stock Exchange Composite Index (X2), Real estate
climate index (X3) and Residential price index (X4). The time sequence charts are as the
followings (Appendix 3): -5.00 10.00 15.00 20.00 25.00 M ay -12 Jul -12 S ep -12 No v -12 Ja n -13 M ar -13 M ay -13 Jul -13 Sep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 No v -14 Ja n -15 M ar -15 M ay -15 CPR (%)
24 Figure 3
From the figure, we could find that there was a staged decreasing trend in the past 3 years. And from July 2012 to October 2014, the mortgage rate stayed in 6.55%.
Figure 4 -1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 M ay -12 Jul -12 S ep -12 No v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 N o v -14 Ja n -15 M ar -15 M ay -15
Mortgage rate for 5 years or longer (%)
-500.00 1,000.00 1,500.00 2,000.00 2,500.00 3,000.00 3,500.00 4,000.00 4,500.00 5,000.00 M ay -12 Jul -12 S ep -12 N o v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 No v -14 Ja n -15 M ar -15 M ay -15
25
From the figure, we could know that before July 2014, the index maintained in a relatively low level (2000-2500), and after that, there was a upward trend all the way up to more than 4500 in May 2015.
Figure 5
From the figure, we could see that the index had a descending trend in overall, however, before February 2013, and it ascended and reached its peak at that time.
89.00 90.00 91.00 92.00 93.00 94.00 95.00 96.00 97.00 98.00 99.00 M ay -12 Jul -12 S ep -12 N o v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 Sep -14 No v -14 Ja n -15 M ar -15 M ay -15
26 Figure 6
From the figure, we could perceive that the residential prince index had a similar trend as the real estate climate index, and the largest number came at July 2013.
5.6.3 Establishment of the model
1) Introduction to multiple linear regression model
Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y (Yale University, 1997). Formally, the model for multiple linear regression, given n observations is yi=β0+β1xi1 +β2xi2 + ... βpxip + εi, for i = 1,2, ... n 99.00 99.50 100.00 100.50 101.00 101.50 102.00 102.50 103.00 103.50 M ay -12 Jul -12 S ep -12 No v-12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 No v -14 Ja n -15 M ar -15 M ay -15
27 2) Establishment of prepayment prediction model
This article applies multifactor regression model to make some research of prepayment in Chinese RMBS. The theoretical foundation is to test the influential effects of the independent variables by multiple regression. And index modification method would be used.
The equation for the regression model is
SMMt = ke βitXit+εt
n i=1
The equation could be turned into
LnSMMt = Lnk + βitXit + εt n
i=1
Set Lnk=β0, and we would have the finalized model for the study,
LnSMMt = β0 + β1X1t + β2X2t + β3X3t + β4X4t + εt
β0: intercept, usually means the Constant;
X1t: Mortgage rate for 5 years or longer at time t;
X2t: Shanghai Stock Exchange Composite Index at time t;
X3t: Real estate climate index at time t;
X4t: Residential price index at time t;
SMMt: Single Month Mortality at time t;
β1, β2, β3, β4: regression coefficient of each variable.
εt: stochastic disturbance.
5.6.4 Empirical analysis
In order to avoid a very small regression coefficient, we divide Shanghai Stock Exchange Composite Index by 1000, and then conduct multiple regression in SPSS 19.0 with the result in Table 1, Table 2 and Table 3:
28 Table 1
Model Summary
Model R R Square Adjusted R Square Std. Error of the
Estimate
1 .516a .266 .174 .327786125817748
a. Predictors: (Constant), X4, X1, X3, X2
Table 2
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1 Regression 1.244 4 .311 2.895 .037a Residual 3.438 32 .107 Total 4.683 36 a. Predictors: (Constant), X4, X1, X3, X2 b. Dependent Variable: LNSMM Table 3 Coefficientsa Model
Unstandardized Coefficients Standardized
Coefficients t Sig. B Std. Error Beta 1 (Constant) -37.920 15.810 -2.398 .022 X1 .390 .457 .276 .853 .400 X2 .440 .228 .797 1.929 .063 X3 .057 .078 .241 .731 .470 X4 .282 .191 .609 1.473 .151 a. Dependent Variable: LNSMM
From the above tables, we could see that the P value of the whole regression model is 0.037, which is less than 0.05, meaning that the general regression model is significant. On the other side, we could also find that the R square is 0.266, representing that the model is not that explanatory for LnSMM. The concrete model is that
29
All the independent variables (X1 to X4) have positive correlation with dependent
variable (LnSMM). Under significant level of 0.1, the P value of the regression coefficient of Shanghai Stock Exchange Composite Index (X2) is 0.063, which means
Shanghai Stock Exchange Composite Index has significant influence on LnSMM. The regression coefficient β2=0.44 means that when Shanghai Stock Exchange Composite
Index increases by 1000 points, LnSMM will be 0.44 unit larger. From the model, we could at least analyze the effect on SMM from these economic factors:
1) Mortgage rate for 5 years or longer has positive correlation with SMM. Most borrowers in China are truly in need of money for buying a(n) house/apartment, and banks in Chine prohibit making profit through borrowing new debt with low interest rate to pay back old mortgage with high interest rate. So in the practice of RMBS, when the mortgage rate for 5 years or longer increases, the borrowers tend to make prepayment in order to avoid heavier burden, so SMM will rise.
2) Shanghai Stock Exchange Composite Index has positive correlation with SMM. In China, borrowers usually cannot have enough economic return in real industry, so many of them make investment in capital market. When the return from capital market and the disposable income raise, borrowers will most probably make repayment, therefore SMM will increase.
3) Real estate climate index has positive correlation with SMM. The index reflects comprehensively the development situation of real estate in China. When the industry is in prosperity, borrowers will choose to make prepayment and trade his/her properties in the secondary market, if possible. On the opposite, when Chinese government begins to regulate and control this industry (as the government usually does), the housing price will decrease, then borrowers will not make prepayment, and SMM will fall.
4) Residential price index has positive correlation with SMM. When this index ascends, it means the cost of housing for residents also increases. If the salary level keeps stable, then the actual mortgage load will augment, and borrowers will make prepayment.
30
From the above analysis, we could conclude that the prepayment risk of “Jianyuan 2005-1 MBS” is closely connected with Chinese interest rate market, capital market and real industry market. And it also verifies the applicability of multiple regression model in the study.
5.7 Empirical research of credit risk based on multiple regression 5.7.1 CPV model
Credit Portfolio View is a model with multiple factors which is used to feign the common conditional distribution of the default probability and migration for various groups of estimation and in different industries (Crouhy etal., 2000). This model was developed by Wilson within McKinsey. The approach developed by this author bases itself on the hypothesis that the probability of defect and migration are connected to macroeconomic factors such as the level of the long-term interest rate, the growth rate of the GDP, the global unemployment rate, the exchange rates, the public spending, the savings. Probability of default=f (GDP, Unemployment Rate, … , Exchange Rate). In the Credit Portfolio View model, the probabilities of default are modeled as being a Logit function. In this modeling the independent variable is a specific speculative index in every country and which depends on macroeconomic variables. The Logit function allows for values of probability of default are included between 0 and 1 (Crouhy et al., 2000; Hamisultane, 2008).
Pj,t = 1 1 + e−Yj,t
Yj,t = βj,0 + βj,1Xj,1,t+ βj,2Xj,2,t+ ⋯ + βj,mXj,m,t+ εj,t
Where Pj,t indicate the conditional probability of default for period t for the debtors of the
industry j and Yj,t represent an indication stemming from a model in m factors. βj,0, βj,1,…,
βj,m are coefficients to be estimated by the method the Ordinary Last Squares (OLS).
31
country j. εj,t represent a term of error which is normally distributed and independent of
Yjjt(A. Derbali et al., 2012).
5.7.2Empirical study of credit risk 1) Establishment of credit risk model
Since macro-economy factors have significant influence on RMBS, so this article uses the above-mentioned CPV model to make empirical study about the credit risk in “Jianyuan 2005-1 MBS”. The CPV model for its default rate is as the following:
Pj,t = 1 1 + e−Yj,t
Yj,t = βj,0 + βj,1Xj,1,t+ βj,2Xj,2,t+ ⋯ + βj,mXj,m,t+ εj,t
Yj,t is the various national economic status; βj is the estimated coefficient of the debtors;
Xj,t is macro-economic variable at time t; and εj,t is an independent error term.
2) Data selection and analysis
Besides the above-mentioned four independent variables as the Xj,t, this article selects
default rates from the trust report of “Jianyuan 2005-1 MBS” from May 2012 to May 2015. Some missing data are made up by reasonable assumptions. Figure 7 shows the default rate in the sample period.
32 Figure 7
From the figure, we could find that there was a staged increasing trend in the past 3 years. In April and May of 2015, the default rate reached its historical peak of 0.70%.
3) Empirical analysis
First of all, we used Excel to transfer monthly default rate Pj,t into Yj,t as shown in the
above equation (Figure 8). 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 M ay -12 Jul -12 Sep -12 No v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 N o v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 No v -14 Ja n -15 M ar -15 M ay -15 Default Rate (%)
33 Figure 8
Secondly, we make multiple regression with SPSS 19.0. The independent variables are Mortgage rate for 5 years or longer (X1), Shanghai Stock Exchange Composite Index
(X2), Real estate climate index (X3) and Residential price index (X4). The result is shown
in Table 4, Table 5 and Table 6. Table 4
Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate 1 .790a .624 .577 .019548439 a. Predictors: (Constant), X4, X1, X3, X2 -5.100000 -5.080000 -5.060000 -5.040000 -5.020000 -5.000000 -4.980000 -4.960000 -4.940000 -4.920000 -4.900000 -4.880000 M ay -12 Jul -12 S ep -12 No v -12 Ja n -13 M ar -13 M ay -13 Jul -13 S ep -13 No v -13 Ja n -14 M ar -14 M ay -14 Jul -14 S ep -14 No v -14 Ja n -15 M ar -15 M ay -15 Yjt
34 Table 5
ANOVAb
Model Sum of Squares df Mean Square F Sig.
1
Regression .020 4 .005 13.265 .000a
Residual .012 32 .000
Total .033 36
a. Predictors: (Constant), X4, X1, X3, X2 b. Dependent Variable: Yjt
Table 6 Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -3.088 .943 -3.275 .003 X1 -.112 .027 -.957 -4.129 .000 X2 -.015 .014 -.335 -1.132 .266 X3 .007 .005 .345 1.458 .155 X4 -.018 .011 -.460 -1.557 .129
a. Dependent Variable: Yjt
From the results, we could have the P value which is 0.000 of the regression model. Since the P value is less than significant level of 0.05, the general regression model is significant. On the other side, we could find that the R square is 0.624, meaning that the regression model is highly expositive. The detailed model is
Y = −0.3088 − 0.112X1− 0.015X2+ 0.007X3− 0.018X4
P = 1
1 + e−(−0.3088 −0.112 X1−0.015 X2+0.007X3−0.018 X4)
From the above regression model, we could perceive that real estate climate index (X3) has positive correlation with national economic status (Yj,t), and other factors have
35
direction as Yj,t increases, so we could know that real estate climate index has positive
correlation with credit risk and other factors have negative correlation. Under the significant level of 0.1, the P value of mortgage rate for 5 years or longer (X1) is 0.000,
which means this variable has significant influence on Yj,t. Its regression coefficient β1
=-0.112 represent that when other elements main the same, every increased 1% mortgage rate for 5 years or longer would lead to 0.112 unit decrease in Yj,t. From the model, we
could analyze the effect on credit risk from these economic factors:
1) Mortgage rate for 5 years or longer has negative correlation with credit risk. In China, people usually default when the cost of default is low. So if the mortgage rate for 5 years or longer increases, residents tend to make less default since the cost of default is larger.
2) Shanghai Stock Exchange Composite Index has negative correlation with credit risk. When the return from capital market arises, the disposable income of the borrowers will increase, and then the income for paying back mortgage loan will be added, leading a lower default risk.
3) Real estate climate index has positive correlation with credit risk. In China, when the real estate market is booming, some unqualified real estate developers will swarm into this industry. However, a flourishing real estate industry will always lead to rigid regulation and control from Chinese government, thus these unqualified developers will usually default and run away in order to avoid being caught by the government. So, the mortgagors will have to default.
4) Residential price index has negative correlation with the credit risk. Residential price index reflects the price of housing rent and purchase market. When the price of rent/purchase a house or an apartment is high, then the original borrowers will choose to rent out or sell their properties to gain some return, thus decreasing the default rate.
36 Chapter 6. The Pricing of A RMBS Product
Pricing is quite essential to RMBS, as a financial product, since it directly affects the benefits of the issuers and the acceptance of the investors.
6.1 Static Cash Flow Yield 6.1.1 Equations
Static Cash Flow Yield (SCFY) is an early pricing method for RMBS. This method basically uses cash flows discounted by a specific return to calculate the price of the security. The formula is as the following:
P = 𝐶𝐹1 1 + 𝑟+ 𝐶𝐹2 (1 + r)2+ ⋯ + 𝐶𝐹𝑛 1 + r 𝑛 = 𝐶𝐹𝑖 (1 + 𝑟)𝑖 𝑛 𝑖=1
In the equation, P is the price of RMBS security, CFi is the cash flow in time period i, and
r is the required return. When determining the future cash flows, we can set reasonable prepayment criteria according to the constituent parts of the mortgage assets collection as well as the trends of future interest rate, and calculate the cash flows.
In the market of securitization, SCFY method is the most basic and investor-friendly method with simple procedures and calculation. However, this method overlooks some important features of securitized products, such as interest rate volatility, interest rate term characteristic, and the influence of interest rate change on prepayment, so SCFY does have limitations. Although SCFY has obvious fault, its historical analysis result is a great inspection of other pricing methods.
6.1.2 Calculation
Suppose the monthly payment is M, then 𝐴0 = 𝑀 1 +12𝑟 + 𝑀 (1 +12𝑟)2 + ⋯ + 𝑀 (1 +12𝑟 )𝑁 So we can have M =𝐴0× 𝑟 12× (1 + 𝑟 12)𝑁 (1 +12𝑟)𝑁− 1 = 𝐴0×12𝑟 1 − (1 +12𝑟)−𝑁
37 The mortgage balance after n months is
𝐴𝑛 = 𝑀 × (1 + 𝑟 12)𝑁−𝑛 − 1 𝑟 12× (1 + 𝑟 12)𝑁−𝑛 The interest payment in this month is
𝐼𝑛 = 𝐴𝑛−1× 𝑟 12 The principle payment in this month is
𝑃𝑛 = 𝑀 − 𝐼𝑛
According to the equations, we can analyze the supposed mortgage assets pool and have the cash flows. We could just make assumptions on interest rates in every year. According to the cash flows calculated above, we can calculate the discounted value of these cash flows. Add the discounted value together, and we can have the total discounted value of the RMBS.
6.2 Static Spread 6.2.1 Equations
The mean idea of Static Spread (SS) method is to find an appropriate discount rate which equals to a fixed spread plus the return of government bonds. The specific equation of RMBS price is as the following:
P =1 + 𝑟𝐶𝐹1 1+ 𝑆𝑆+ 𝐶𝐹2 (1 + 𝑟2+ 𝑆𝑆)2+ ⋯ + 𝐶𝐹𝑛 1 + 𝑟𝑛+𝑆𝑆 𝑛 = 𝐶𝐹𝑖 (1 + 𝑟𝑖+ 𝑆𝑆)𝑖 𝑛 𝑖=1
In the equation, ri is the return at time i on the yield curve of government bonds, such as
treasury bonds. SS is the static spread, reflecting the risk premium between RMBS and government bonds. The assumption in SS method is that there is a steady interest spread between the security with certain credit rating and government bonds. This method takes the difference among discount rates with various terms into consideration, i.e. the risk premium.
38
When the cash flows are relatively concentrated, there would not be many differences between SS method and SCFY method. However, when the situation is the opposite, things would be different. Generally speaking, the largest cash flow in corporate bonds comes at the last, so the results of SS method and SCFY method are not far away from each other. Nevertheless, for securitized product whose cash flows are distributed uniformly in every payment, SS method is more accurate.
In capital market, seldom do we see flat yield curve. Generally speaking, the curve is upward-sloping, reflecting the uncertainty of securities in long term, thus the risk premium arises. So we can conclude that SCFY method is only suitable for pricing short-term securitized products with concentrated cash flows in the last, whereas SS method is applicable to long-term securitized products with equally distributed cash flows. For both ways, the prerequisite for correct valuation is a mature government bonds market.
6.2.2 Calculation
As mentioned above, we could assume the mortgage assets collection with debt to be paid, the interest rate of mortgage, and the time period. In SS method, we also need to make assumption for prepayment, and the probability of prepayment is SMM. We suppose At-1 is the mortgage assets pool balance after (t-1) months, and the debt to be
paid in time t is Mt with Pt (principle to be paid) and It (interest to be paid), so
𝑀𝑛 = 𝐴𝑡−1× 𝑟 12 1 − (1 + 𝑟 12)𝑡−1−𝑇 𝐼𝑡 = 𝐴𝑡−1× 𝑟 12 𝑃𝑡 = 𝑀𝑡− 𝐼𝑡
Suppose the SMM at time t is SMMt, the prepayment is PPt, and the total cash flow is CFt,
then we have
𝑃𝑃𝑡 = 𝑆𝑀𝑀𝑡× (𝐴𝑡−1− 𝑃𝑡) 𝐶𝐹𝑡 = 𝐼𝑡 + 𝑃𝑡+ 𝑃𝑃𝑡 = 𝑀𝑡+ 𝑃𝑃𝑡
39
According to the equations, we can analyze the supposed mortgage assets pool and have the cash flows. In SS method, the discount rate equals to government bonds rate plus a fixed spread. Thus the first step towards the discount rate is to collect government bonds yield in every term. In this article, EViews could be used to statistically calculate the function of government bonds rate with its term. After OLS analysis, we can have a function of
Y = aX + b
X is the term, and Y is the return. We could assume the static spread, and then the future discounted cash flows can be calculated. Add the discounted cash flows up, and we can have the total discounted cash flow of the assets collection, which means the theoretical price of this kind of security.
6.3 Option-Adjusted Spread 6.3.1 Equations
In 1980s, with the expansion of option-embedded security market, a new method for pricing securities arose, and that was Option-Adjusted Spread (OAS). One of the above-mentioned concepts for valuation is static spread whose foundation is the right measurement and analysis of the interest rate. With correct measurement and analysis, the government bonds yield curve could be considered as the expectation of the future interest rates. The measurement of prepayment in SS method is based on statistical analysis of historical data, however, it does not represent the relationship between interest rate and prepayment. Actually, it is a zero volatility OAS.
The main idea of OAS method is to calculate the route of interest rate via the simulation of interest rate. This interest rate is the return of securitized product with risk premium above government bonds. The basic prerequisite of OAS method is the existence of prepayment in mortgage assets pool. In other words, the cash flows from the assets collection would be affected by interest rate or other factors, causing the uncertainty of future cash flows since the mortgage borrowers may make prepayments. In detail, firstly, we should simulate of the future possible market interest rate through a certain change
40
route. Secondly, prediction of prepayment could be conducted with the simulated interest rate, and then the cash flows on every interest route could be calculated. Thirdly, we would calculate the present value of these cash flows by the discount factors, and have the sum of weight average present value. In mathematical sense, OAS method could be written as the following equation:
P = 1 𝑁 𝐶𝐹(𝑡, 𝑛) (1 + 𝑟𝑘 𝑛 + 𝑂𝐴𝑆) 𝑡 𝐾=1 𝑇 𝑡 =1 𝑁 𝑛=1
In the formula, P is the market price of RMBS, N is the number of interest rate route, t is the number of payments, CF (t,n) is the cash flow on the NO.n interest rate route at time t, and rk(n) is the market interest rate on the NO.n interest rate route at time k. The result P
includes the premium of the risks, such as option risk, prepayment risk and credit risk that investors have to bear.
With the above valuation model, OAS could be a measurement of whether the RMBS price is high or low. If the OAS of RMBS calculated from the market price is 48 base points, whereas empirical data show that the OAS of this kind of security is 50 base points, then we could judge that the price is higher by 2 base points. And the investors could decide whether this product is worth investing or not.
The simulation of interest rate route of OAS method could be done in a computer, so there would be enough routes to guarantee the accuracy of interest rate simulation and express the interest rate volatility. However, OAS method still has some limitations: first of all, this method only takes prepayment situation into consideration with including default case; secondly, the computed OAS is an average number, so it is possible that the real interest rate spread does not equal to the calculated spread; thirdly, when calculating the OAS, if the interest rate model is not same as the prepayment model, there may be different results which could affect (negatively) the financial decision of investors. Therefore, even if we are using OAS method for pricing the security, we still need to exanimate the rationality of the models and parameters to judge the reliability.
