【2002 年中華民國住宅學會第十一屆年會論文集】
場次：B1-2
The Structural Design of Asset Securitization Taiwan, and the
Price and Prepayment Risk Analysis of Asset-Backed Securities
－Mortgage Securitization as an Example
我國資產證券化之架構設計與
相關證券價格及提前清償風險之分析研究
---以不動產抵押權證券化為例
Tsoyu Calvin Lin*
（林左裕）
Abstract
Key Words: Mortgage Securitization, Mortgage-Backed Security (MBS), Capital Adequacy Ratio
(CAR), Prepayment Risk, Stripped MBS, Convexity
This study firstly explores the effect of mortgage securitization on capital
adequacy ratio and current ratio of the banking industry in Taiwan. Secondly, the
price movement of mortgage securities in relation to prepayment speed is studied
through numerical simulation.
Finally, the structural design of mortgage
securitization system and different schemes for issuing MBSs are proposed. Results
show that mortgage securitization can significantly reduce the operation risks of the
banking industry in Taiwan. Further, as the interest rate declines, the price
movement of the MBS is different from that of callable bonds, due to the partial
prepayment of mortgagors. The higher the prepayment speed is, the closer the MBS
pricing behavior to callable bonds.
*
Assc. Professor, Dept. of Finance, ChaoYang University of Technology,
朝陽科技大學財金所副教授。
Add.: #168, Gi-Feng E. Rd., Wu-Feng, Taichung, Taiwan, 中縣霧峰鄉吉峰東路 168 號
Tel: 886-4-2332-3000 x 4212 or 7092, Fax: 886-4-2374-2333
E-mail: tcalvin@cyut.edu.tw
The author is grateful for the assistance provided by Mr. Ta-Chun Lin for the data collection of the
banking industries, and Mr. Tseng-Chi Tseng for the simulation analysis.
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【2002 年中華民國住宅學會第十一屆年會論文集】
The Structural Design of Asset Securitization Taiwan, and the
Price and Prepayment Risk Analysis of Asset-Backed Securities
---Mortgage Securitization as an Example
1. Introduction
As the real estate market in Taiwan slumped since 1992, banks’ non-performing
loan (NPL) ratio rose accordingly. The stability of financial system has encountered
unprecedented challenge.
Banks’ average NPL ratio in Taiwan has dramatically
risen from 1% in 1993 to 7% in 20011. As the expectation toward overall economic
growth still remains pessimistic, the banking industry in Taiwan has started to harshly
scrutinize lending process in order to avoid any risky loan and keep up the capital
adequacy ratio (CAR) required by the Bank for International Settlement (BIS).
However, harsh scrutiny of the loan requisites has not only blocked the capital inflow
of normally operated companies, causing them bankruptcy, but also put the decreasing
pressure to the current low interest rates due to over supply of the capital.
This
might eventually lead to the similar “liquidity trap” situation encountered in Japan
during the 1990s.
The financial disorder encountered in Taiwan is like Japan, called “domestic
financial debacle”, which is caused by the previous high economic growth and the
resulting asset price inflation. As the asset price bubble burst, the banking industry
which originated the loans and facilitated the inflation of the bubble has contracted
the lending activities to prevent the decline of the capital adequacy ratio.
The
contracting behavior has inevitably jeopardized the overall economy growth and
financial stability.
The decrease of investment and the resulting slow economy
growth in the long term might cause economic recession that has happened in Japan.
One of the solutions to prevent the lending contraction and the consequential
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【2002 年中華民國住宅學會第十一屆年會論文集】
recession is asset securitization. As the banking industry is able to sell the loans in
the form of securities to the capital markets, banks can thus transfer the risks of
lending to the securities investors, and consequently alleviate the pressure of the
lending contraction behavior.
Normally-run companies will then be able to operate
through the planned capital structuring without unexpected disturbance.
economy can thus continue to grow with the liquidity of capital.
The
As the example of
the United States, the mortgage securitization in the 1960s had successfully bailed out
the troubled S&Ls.
By the end of 2001, over 80% of the single-family mortgages
securitized and sold to the capital markets, and the outstanding traded volume of MBS
have outnumbered 2500 billions.
700 billions.
Other asset-backed securities (ABSs) were over
The total amount of MBSs and other ABSs have accounted for over
20% of the overall bond markets (Coles, 1999; Kuhn, 1990).
On the contrary,
Japan’s banking industry has been trapped by the NPLs since early 1990s. The
speed of financial innovation system in Japan was much slower than the slowdown of
the economy, missing the golden opportunity of financial innovation and
consequently leading to liquidity trap and long-run recession.
The outstanding
mortgage loans by the end of 2001 in Taiwan was over NT 2600 billion dollars
(1USD = 33 NTD in 2001).
If 70% of the of the mortgages can be securitized and
sold to capital market from banks’ assets, around NT 1800 billion dollars will become
liquid in the banking system through securitization, equivalent to 20% of the GNP in
Taiwan in 2001. Therefore, asset securitization will be one of the major directions to
solve the malfunction of the financial markets in Taiwan.
Should the secondary mortgage markets be successfully developed, and the
liquidity and default risks of mortgages be reduced through government guarantee or
insurance companies, the capital supply of mortgage loans will consequently be
sufficient.
Lending risks originally assumed by the banking industry can thus be
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【2002 年中華民國住宅學會第十一屆年會論文集】
transferred to MBS investors. No more temporary subsidized low-rate mortgages
provided by the government will be necessary in order to bail out the banking industry
for the sake of financial stability, mostly due to the large amount of illiquid and
non-performing mortgage loans in the assets of the banking industry.
This study firstly explores the effect of mortgage securitization on capital
adequacy ratio and current ratio of the banking industry in Taiwan.
Seven
government-owned banks in Taiwan are sampled for the empirical analysis.
Secondly, the price and prepayment risk analysis of mortgage-backed securities (MBS)
and stripped securities are studied through numerical simulation.
The “implied
model” is employed as the prepayment assumption in the simulation simply to
observe the pattern of the price movement of mortgage securities.
Finally, the
structural design of mortgage securitization system and different schemes for issuing
mortgage securities are proposed for countries like Taiwan that opt to introduce the
system.
2. The Influence of Mortgage Securitization on the Risks of the Banking Industry
in Taiwan
In this section, we investigate the impact of mortgage securitization on the risks of
the banking industry in Taiwan. The risks of the banking industry are measured by
capital adequacy ratio, which is required by the Banks for the International Settlement
(BIS), and liquidity ratio.
We collected data in early 2000 regarding lending
activities from financial reports of seven government-owned banks in Taiwan
including the Bank of Taiwan, Taiwan Land Bank, Taiwan Corporative Bank,
Chang-Hwa Commercial Bank, the First Commercial Bank, Hwa-Nan Commercial
Bank, and Taiwan Business Bank.
It is expected that mortgage securitization can
significantly reduce the risks of lending activities, i.e., raise the capital adequacy ratio
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and the current ratio.
The calculation of capital adequacy ratio is shown in Table,
and the current ratio is shown in Table 2.
Table 1
The Capital Adequacy Ratio of Seven Government-Owned Banks in Taiwan
Unit: Million of New Taiwan Dollar
Equity
Risk-based
Housing
Housing
Capital
(A)
Assets
Mortgages
Mortgages ×
Adequacy Ratio
Risk Weighting
(CAR) = A/B
Bank
(B)
（50％）
Bank of Taiwan
166,401
879,343
179,062
89,531
18.9%
Taiwan Land Bank
82,393
738,575
475,327
237,663
11.2%
Taiwan Corporative Bank
77,923
785,535
479,029
239,514
9.9%
Chang-Hwa Bank
67,646
737,368
280,103
140,051
9.2%
First Commercial Bank
78,594
801,807
240,005
120,002
9.8%
Hwa-Nan Bank
73,015
685,933
351,159
175,579
10.6%
Taiwan Business Bank
51,856
574,246
277,895
138,947
9.0%
Sources：Various Government-Owned Banks in Taiwan, 2000.
Table 2
The Current Ratio of Seven Government-Owned Banks in Taiwan
Unit: Million of New Taiwan Dollar
Bank
Current
Current
Mid-Term
Long-Term
Current
Assets
Liability
Mortgages
Mortgages
Ratio (CR)
Bank of Taiwan
548,562
199,117
98,294
236,067
2.75
Taiwan Land Bank
307,565
73,978
133,894
498,634
4.16
Taiwan Cooperative Bank
425,766
244,019
143,648
461,080
1.74
Chang-Hwa Bank
229,607
175,081
66,561
183,517
1.31
First Commercial Bank
289,277
151,902
93,203
208,535
1.90
Hwa-Nan Bank
307,880
149,511
62,255
182,151
2.06
Taiwan Business Bank
178,626
63,178
97,952
213,176
2.83
Source：Taiwan Economic Journal, 2000.
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【2002 年中華民國住宅學會第十一屆年會論文集】
Herein we specify the definition of financial data as follows.
1. Capital Adequacy Ratio (CAR) = Equity / Risk-Based Assets
2. Capital Adequacy Ratio after Securitization (CARS)
= Equity / 〔Risked-Based Assets – (Mortgages * Risk Weight (50%) *Securitization Ratio)
3. Current Ratio (CR) = Current Assets / Current Liability
4. Current Ratio after Securitization (CRS)
=〔Current Assets + (Mid- and Long-term Mortgages) * Securitization Ratio〕/ Current Liability
Method
We employ the regression model for analysis and use Ordinary Least Squares
(OLS) to estimate parameters. The model is described as follows:
Model 1: MCASij  a j  b j Sij   ij
i  1,2,3100% ， j  1,27
where
MCARSij = (CARSij – CARj) / CARj, representing the change of capital adequacy
ratio of bank j after i% assets being securitized
CARSij：the capital adequacy ratio of bank j after i% assets being securitized
CARj：the capital adequacy ratio of bank j before securitization
Sij：the ratio of assets being securitized of bank j
εij：the error term of bank j
Model 2： MCRS ij  cij  dij Sij   ij
, i  1,2,3,100% , j  1,2,7
where
MCRSij＝(CRSij – CRj) / CRj, representing the change of current ratio of bank j
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【2002 年中華民國住宅學會第十一屆年會論文集】
after i% assets being securitized;
CRSij： the current ratio of bank j after i% assets being securitized;
CRj：the current ratio of bank j before securitization
Sij：the ratio of assets being securitized of bank j
εij： the error term of bank j
Analysis Result
As shown in Table 3, the ratio of asset securitization is positively correlated with
the change of capital adequacy ratio. That is, as the ratio of mortgage securitization
increases, the capital adequacy ratio will increase accordingly, especially for Taiwan
Land Bank and Taiwan Cooperative Bank. This is because that these two banks hold
more mortgages as assets than the others, the change of capital adequacy ratio is thus
more significant after securitization.
The change of current ratio also positively correlates with the ratio of
securitization, as shown in Table 4. As the ratio of mortgage securitization increases,
the current ratio increases correspondingly, especially for Taiwan Land Bank.
It may
be attributed to the fact that Taiwan Land Bank hold more mid- and long-term
mortgages than others.
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【2002 年中華民國住宅學會第十一屆年會論文集】
Table 3
The regression result of the change of capital adequacy ratio
and the ratio of asset securitization
Dependent Variable：MCARS
Bank
Taiwan Bank
Taiwan Land Bank
Taiwan Cooperative Bank
Chang-Hwa Bank
First Commercial Bank
Hwa-Nan Bank
Taiwan Business Bank
Independent Variable
Intercept
Ratio of Asset Securitization
-0.002
0.11
(-10.9515)***
(356.8792)***
-0.028
0.47
(-10.0544)***
(98.37309)***
-0.024
0.43
(-10.1294)***
(105.0612)***
-0.008
0.23
(-10.611)***
(181.7577)***
-0.005
0.18
(-10.7694)***
(236.262)***
-0.016
0.34
(-10.3402)***
(129.356)***
-0.014
0.32
(-10.3989)***
(138.097)***
Source: Analysis results partly from Lin and Lin (2001).
Note：Numbers in the parentheses are the T value,
***represents significance level of 1%.
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【2002 年中華民國住宅學會第十一屆年會論文集】
Table 4
The regression result of the change of current ratio and the ratio of asset
securitization
Dependent Variable：MCRS
Independent Variable
Bank
Ratio of Asset Securitization
Intercept
Bank of Taiwan
3.55E-17
0.61
(1.379931)
(1.38E+16)***
0
2.06
0
(2.63E+16)***
-1.7E-15
1.42
(-9.35277)***
(4.53E+15)***
-5E-16
1.09
(-7.37142)***
(9.39E+15)***
9.95E-16
1.04
(9.06985)***
(5.53E+15)***
-3.6E-16
0.79
(-7.284)***
(9.47E+15)***
-7.1E-16
1.74
(-8.38202)***
(1.2E+16)***
Taiwan Land Bank
Taiwan Cooperative Bank
Chang-Hwa Bank
First Commercial Bank
Hwa-Nan Bank
Taiwan Business Bank
Source: Analysis results partly from Lin and Lin (2001).
Note：Numbers in the parentheses are the T value,
***represents significance level of 1%.
From the analysis above, it is clear that mortgage securitization can
significantly raise the capital adequacy ratio as well as the current ratio of the banking
industry. Therefore, banks in Taiwan can thus reduce operation risks and increase
capital efficiency and asset liquidity through asset securitization.
In the following
sections, this paper further investigates the price movement of the mortgage securities
in relation to interest rate and prepayment risks, and proposes the structural design of
the securitization system.
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【2002 年中華民國住宅學會第十一屆年會論文集】
3. Simulation Analysis of the Price Movement of Mortgage Securities in Relation
to Prepayment
Mortgages are usually prepayable, but some contracts may require prepayment
penalty.
Prepayment may be caused by economic or non-economic factors.
Economic prepayments include declining interest rates, disappeared tax shield, or
the appreciation of real estate value.
Non-economic factors comprise the
termination of partnership, housing turnover, divorce, or the growth of family size.
The prepayment behavior can be divided into full prepayment and partial
prepayment. The mortgage refinancing behavior and housing turnover are usually
full prepayment.
seasonality.
Partial prepayment behaviors mostly are correlated with
In Taiwan, most partial prepayments occur at the end of lunar year as
employees receive bonus from the companies they work. This is different from
the peak prepayment season in spring and summer in the United States.
Issuers of
MBSs should thus evaluate and apply appropriate prepayment models for pricing
mortgages or MBSs accurately.
The impact of declining interest rates on prepayment is more obvious for
fixed-rate mortgages (FRM).
As the market interest rate declines, borrowers tend to
take advantages of the lower cost of capital and refinance. As shown in Figure 1, the
prepayment volume of FNMA mortgages dramatically increased in 1998 as the
30-year mortgage rate fell below 7%.
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【2002 年中華民國住宅學會第十一屆年會論文集】
Source：Antczak (2000); Merrill Lynch, Fannie Mae, Bloomberg (2000),
Mortgage Pool #250060, Originated in June, 1994. Original Mortgage Amount
US$335,820,595。
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30-Year Market Mortgage Rate (%, Right Axis) -----
Prepayment Volume (Dollars, Left Axis)
Figure 1
The Relationship between the Market Mortgage Rate and
Prepayment Volume of FNMA Mortgages in the U.S.
(1994-2000)
與市場房貸利率之關係圖 (1994-2000)
【2002 年中華民國住宅學會第十一屆年會論文集】
There have been a great number of prepayment models developed and applied to
forecasting the prepayment behavior, including 12-year average maturity, a multiple
of FHA experience, PSA model, SMM model, and such conditional prepayment rate
(CPR) methods as simple regression model, logistic model (Navratil, 1985), and
proportional hazards model (Green and Shoven, 1986). Becketti (1989) indicates
that refinancing, relocation, and default are direct causes of MBS prepayments, and
the relative coupon is the most important factor in the decision to refinance.
If the
current mortgage rate begins to fall below the rate on the existing mortgage, the
borrower would be better off with a mortgage at the new rate.
Tuckman (1995) summarizes that mortgage prepayment models can be
categorized into three approaches. They are static cash flow model, implied model
and prepayment function model.
The static cash flow model assumes that the
prepayment is related to mortgage age. PSA and FHA models are typical examples
of this approach. The major advantage of the static cash flow model is that it allows
for a yield calculation.
However, it may provide misleading price-yield and
duration-yield curves due to the fixed cash flow assumption of this model.
The
implied model simply estimates mortgage durations, assuming that the duration of a
mortgage changes slowly over time as the interest rate changes.
The major
drawback of this model is that mortgage durations may change rapidly over time.
Taking into accounts of such variables as interest rate spread between mortgage and
market rates, age of mortgages, seasonings, yield curve, and burnout effect, the
prepayment function model is considered the most popular among sophisticated
practitioners.
Monte Carlo simulation is often employed for approaching the
mortgage price (Broadie et al., 1997; Bolye, 1977).
To MBS investors, borrowers’ prepayment is similar to the call option of
corporate bonds.
The relation between MBS prices and interest rates can be
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【2002 年中華民國住宅學會第十一屆年會論文集】
illustrated in the following simulation.
In the absence of empirical data of mortgage
prepayment experience in Taiwan, we simulate a amortization mortgage pool of
$1million, 9% coupon rate and 30-year maturity as an example.
The “implied
model” is employed as the prepayment assumption for the observation of the price
movement of mortgage securities.
We assume that the average maturity of the
mortgage pool is 13 years and the current mortgage rate is 10%.
As the spread of the
mortgage coupon rate over the market rate increases 1%, the average maturity of the
mortgage is assumed to decrease 2 years. The simulation result is shown in Figure 2.
As the market rates increase, the prices of the vanilla bond without any provision and
the mortgage pass-through securities (MPTS) both decline accordingly.
As the
market rates decline, the prices of the bonds rise. The relation between the bonds
and the interest rates is like a curve convex to the origin point, called convexity.
Yet as the interest rate declines, the rising trend of the MPTS price slows down due to
the increase of the prepayment.
The price compression of the MPTS is called
negative convexity, which is different from the pricing behavior of the vanilla bonds.
Thus, the MBS investors are like buying a callable bond and short for a call option.
The call option is mortgagors’ privilege of prepayment anytime. The MBS price can
therefore be shown as the following equation:
PMBS = P noncallable bond - P call option
The value of the callable option in the equation above is the prepayment value in
Figure 2, which can be obviously perceived as the price of the vanilla bond
subtracting the MPTS price. As the interest rate declines and the prepayment speed
increases accordingly, the rise of the MPTS price slows down due to prepayment.
On the contrary, the price of the MPTS declines, like the vanilla bond, as the interest
rates increase and prepayment rate declines.
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As a result, MBS investors are
【2002 年中華民國住宅學會第十一屆年會論文集】
rewarded as higher yield for the tradeoff of assuming the prepayment risks. Therefore,
the U.S. government guaranteed MBS---GNMA, has higher yield than T-bonds of
similar maturity.
Figure 2
The Relation of the Prices of Vanilla Bond, MPTS and Prepayment Option
versus Changing Interest Rate
1600000
MPTS
Vanilla Bond
Prepayment Option
1400000
1200000
1000000
800000
Price
600000
400000
200000
0
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
10.00%
11.00%
12.00%
13.00%
14.00%
15.00%
16.00%
-200000
Interest Rate
We further use the same example to simulate the relation between the negative
convexity of the MPTS and prepayment behavior in greater detail.
The relation
between MPTS prices of different prepayment rates (B, C, and D) and interest rates
can be shown in Figure 3. As the interest rate rises, the prices of MPTSs, callable
bonds and vanilla bonds without any provision all decline. As the interest rate
declines, the price of the vanilla bond (as the curve A in Figure 3) increases; the price
increasing trend of the callable bond (as the curve E in Figure 3) and MPTSs of
different prepayment speed (as the curve B, C, D in Figure 3) slow down as the
prepayment rate escalates. MPTSB、C、D are assumed that as the spread of mortgage
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coupon rate over the market interest rate increases 1%, the average maturity of the
mortgage pool will decrease 1, 2 and 3 years, respectively.
The different levels of
negative convexity of these three MPTSs can be obviously observed in Figure 3.
In
general, as the interest rate declines below the coupon rate of callable bonds, the
callable bonds may all be redeemed.
However, the slowdown of MPTS’ price
increasing trend (called realistic prepayment) is different from that of callable bonds
(called optimal prepayment) (Tuckman, 1995).
The reason can be attributed to the
factors that effect mortgage prepayment do not only include the change of interest
rates, but also housing value, mortgage balance, refinancing costs or penalty,
information costs and others. Further, the mortgage prepayment behavior can be
divided into full and partial prepayment.
Therefore, the realistic (partial)
prepayment of the mortgages keeps the MPTS price increasing, but the trend slows
down. As the interest rate continues to decline and causes prepayment to increase,
the MPTS price will eventually decline and approach callable bonds.
MPTS with
the greatest prepayment rate (D) has the greatest negative convexity and requires
highest yield, and vice versa.
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【2002 年中華民國住宅學會第十一屆年會論文集】
Figure 3
The Relation of prices of Bonds, MTRTs, P Os and I Os versus
Changing Interest rate and Prepayment Effect
IOb
1,600,000
1,500,000
POb
A
1,400,000
1,200,000
1,100,000
1,000,000
B: MPTSb
B
1,300,000
A: Vanilla
Bond
IOc
C
D
900,000
Price
800,000
700,000
PO
c
POd
E
POc
IOb
C: MPTSc
600,000
500,000
POb
IOd
400,000
300,000
200,000
POd
IOc
100,000
D: MPTSd
IOd
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
E: callable
bond
16.00%
Market Interest Rate
We further compare the price movement of stripped MBSs---Interest Only (IO)
and Principal Only (PO) of different prepayment rates as the interest rate changes.
The movement of PO prices (e.g., POb、c and d)can be observed in Figure 3.
As the
prepayment rate increases (e.g., POd), the volatility of PO price increases. On the
other hand, investors of IO do not receive repayments of principal.
receive interests of mortgage balance.
They only
As the interest rates decreases and the
prepayment rate increases, mortgage balance and the corresponding interests decrease
accordingly. The price of IO consequently decreases. Yet the declining interest
rate increases IO’s present value. The interest rate movement thus has different
impact on IO’s price. As shown in Figure 3, the prices of IOb、c and d all decline as
the interest rate surges or slumps.
At the period of very low interest rate, the
prepayment effect is greater than the discounting effect, so that IO’s price declines.
The greater is the prepayment rate (IOd), the lower the IO price. During the period
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of very high interest rate, IO’s price also tends to decline due to the fact that the
discounting effect is greater than the prepayment effect.
Only during the period of
stable interest rate, IO’s price is relatively higher and remains stable.
Therefore, the
prices of strips, especially IO, are significantly influenced by the movement of interest
rates.
IO is thus suitable for investors of risk pursuing tendency or hedging purposes
since it assumes high risk and requires high yield.
It is clear from Figure 4 and the analysis above, as the higher is the prepayment
rate, the larger the price volatility of IO and PO. The direction of prepayment’s
impact on PO is consistent.
The higher is the prepayment rate, the sooner the
principal repayments to be received. The price of PO thus increases, and vice versa.
Therefore, the higher prepayment rate of the PO is (as the POd in Figure 4), the
steeper of the price curve and the longer the duration of PO. The direction of
prepayment’s impact on IO is also consistent. The higher is the prepayment rate, the
lower the IO price, and vice versa.
But as the interest rate increases to an extremely
high level, the prepayment rate will decline, and the IO price will decline due to the
discounting effect.
Therefore, the higher is the prepayment rate (e.g., IOd in Figure
4), the larger the amount of price decrease and the greater the convexity, as shown in
Figure 4.
We further compare the price movement of MPTSs of different mortgage coupons
(13% and 9%) as the interest rate changes under the same prepayment scenario.
In
Figure 5, as the interest rate declines below 13%, the increasing trend of the
13%-coupon MPTS price starts to slow down, and eventually approachs $1million
(i.e., the face value) as the interest rate keeps decreasing.
However, the price of 9%
MPTS still keep increasing as the interest rate descends, as long as the interest rate is
higher than 9%. The increasing trend of the 9%-coupon MPTS price does not stop
until the interest rate falls below 9%.
From this figure, it is clear that mortgages or
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【2002 年中華民國住宅學會第十一屆年會論文集】
MBSs of high coupon assume higher prepayment risks caused by interest rates than
those of low coupon.
In Figure 6, we compare the price movement of IOs and POs of different
mortgage coupons as the interest rate changes.
The prices of 13%-coupon
and9%-coupon POs are both negatively correlated with interest rates due to the early
receipt of principals.
Apparently, the 13%-coupon PO enjoys higher price
appreciation caused by prepayment.
As the interest rate is low enough to cause full
or optimal prepayment of all the mortgages, the price of 13%-coupon PO will
approach $1million (the face value). For IOs, the price of 13%-coupon may move
towards zero should full prepayment occur as the interest rate is low enough. This
also indicates that the prepayment risk is higher for the IOs with higher coupon.
The analysis above has shown that IOs and POs are risky investments since the
embedded option components are greater than in the underlying security, and their
returns are more dramatically affected by changes in the market rate volatility and the
sensitivity of prepayment rates to changes in interest rates. The value of mortgage
securities are thus more stable than its IO and PO components viewed in isolation
(Asay and Sears, 1989).
Due to the sophisticated behavior of IOs and POs, it is
suggested that mortgage strips should used as a useful hedging tool rather than an
investment vehicle (Carlson and Sears, 1998; Becketti, 1988).
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Figure 4
The Price Volatility of IOs and POs
at Different Prepayment Rates
(9% mortgage coupon, b: low prepayment rate, d: high prepayment rate)
Iob
1,000,000
900,000
Pob
800,000
700,000
600,000
Price
Iod
500,000
400,000
300,000
Pod
200,000
100,000
0%
2%
4%
6%
8%
10%
12%
14%
16%
Market Interest Rate
Figure 5
The Comparison of Price Volatility of MPTSs of Different Mortgage Coupons
1,400,000
MPTS--13%
1,200,000
1,000,000
800,000
MPTS--9%
Price
600,000
400,000
200,000
0
0%
2%
4%
6%
8%
10%
Interest Rate
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12%
14%
16%
【2002 年中華民國住宅學會第十一屆年會論文集】
Figure 6
The Comparison of Price Volatility of IOs and POs of Different Mortgage Coupons
1,200,000
1,000,000
800,000
Price
IO---13%
PO---13%
600,000
IO---9%
PO---9%
400,000
200,000
0
0%
2%
4%
6%
8%
10%
12%
14%
16%
Interest Rate
4. The Structural Design of Mortgage Securitization, and Various Issuance
Schemes According to Risk Segmentation
Figure 7 is the design of mortgage placement and securitization process for a
newly-developed secondary mortgage market.
Assuming that there are $10 million
mortgages in a bank’s asset and 10% of those are non-performing loans, banks can
repossess or auction these NPLs, or securitize them through issuing zero-coupon
bonds; or sell these NPLs together with normal performing loans to mortgage
brokerage companies.
The bank can sell the other 90% normally performing loans
to brokerage companies and then securitize them through issuing MBSs of different
risk levels.
In this example, the mortgage brokerage companies are assumed to
purchase $9 million mortgages from banks and then issue MBSs, receiving $7.38
million back in cash. Other revenues will come from the issuance of junior bonds
and notes, and servicing fees (Oldfield, 1997). Since the overcollateralization rate of
the AA-class MBSs is 167%, there should be no doubt in the marketability and
liquidity of the MBS trading.
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Besides issuing derivative MBSs like IOs, POs and CMOs, mortgages can be
securitized through dividing the cash flows into various securities of different risk
levels in order to increase marketability (Books and Najafi, 1989; Hu, 1988).
The
last section of this study tends to provide several structural schemes of issuing
mortgage securities according to risk segmentation for newly developed countries of
this system.
MBSs can usually be segmented as senior debts and junior debts
according to risk differential.
These designs are illustrated as follows.
(1). Issuing MBSs of Different Coupon Rates
Taking the mortgage pool of $100 million, 10% coupon rate as an example, we
can divide the $100 million principal into a senior debt of $70 million, 7% coupon,
and a junior debt of $30 million, 17%. Should default occur, the loss is firstly
absorbed by the junior debt.
As shown in Figure 8, the coupon reduction value of
the senior debt ($21 million) is transferred to the junior debt.
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【2002 年中華民國住宅學會第十一屆年會論文集】
rate (7%) is added to the original coupon 10%, equaling to 17%. The high return of
the junior debt is the tradeoff of its high risk. Thus, the junior debt can be viewed as
an investment vehicle of high return and risk.
Figure 8
The MBS Design as Senior and Junior Debt according to the Risk Level
(2). Issuing Vanilla Bonds and IO
The cash flow of mortgages can be divided into different mortgage securities
through splitting the interest and principal payments. At the current interest rate of
8%, for example, the 10-year, 10% coupon, $100 million non-amortization mortgage
pool can be divided into two bonds of different risks through splitting the interest
payments.
One is the senior bond of 10-year, 8% coupon, $100 million, and the
other is the junior bond of 2% IO strip.
The mortgage price is the present value
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【2002 年中華民國住宅學會第十一屆年會論文集】
through discounting the future cash flows, as shown in Figure 9.
Figure 9
The MBS Design as Vanilla Bond and IO Strip through Splitting Interest Payments
(3). Issuing Vanilla Bonds and PO
The mortgage payments can also be divided into two bonds of different risks
through splitting the principal repayments.
As an example of the aforementioned
10-year, 10% coupon, $100 million non-amortization mortgage pool, the payments
can be divided into a senior bond of 10-year, 10% coupon, 80 million mortgage and a
junior bond of 10-year, 20 million PO at the current rate of 12.5%. The mortgage
price is still the sum of the present value of the discounted future cash flows, as
shown in Figure 10.
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Figure 10
The MBS Design as Vanilla Bond and PO Strip through Splitting Principal Payments
5. Conclusion
As the prices of global assets remain sluggish, financial institutions will have to
keep assuming the real estate market risks, interest rate risks and default risks through
holding the long-term mortgages in assets. The increasing non-performing loan ratio
in Taiwan also jeopardizes the stability of the financial markets.
After the
establishment of asset management companies, mortgage securitization will be the
indispensable track besides the repossession and auction of the non-performing loans.
Asset securitization can not only reduce lenders’ risks through transferring the risks to
ABS or MBS investors, but also can increase lending institutions’ capital adequacy
ratio and current ratio.
The behavior of shrinking lending tendency of the financial
institutions can consequently be reduced.
This study investigates the effect of mortgage securitization on the operation
risks of the banking industry in Taiwan, analyzes the prices and risks of the mortgage
related securities in relation to prepayment risk, and proposes the structural design of
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【2002 年中華民國住宅學會第十一屆年會論文集】
mortgage securitization. Results of this study show that mortgage securitization can
significantly raise the capital adequacy ratio and current ratio, and that the higher the
prepayment speed is, the closer the MBSs to callable bonds and the higher the
prepayment risk.
However, the over-priced real estate value and under-estimated mortgage default
rate may reduce the marketability of MBSs, and thus endangering the mortgage
securitization system.
Therefore, such systems as mortgage insurance, real estate
appraisal, and the mortgage and MBS credit rating are crucial to reduce investors’
uncertainty and in turn increase the marketability.
As an example of the United
States, government mortgage insurance or guarantee serves as a critical element to the
success of the mortgage securitization system.
We suggest that the mortgage
guarantee or insurance system in Taiwan to be implemented, starting from such
groups as military servicemen, government employees and teachers with stable
income and low default rate.
Under the circumstances without government
guarantee, the mortgage brokerage companies may issue MBSs which volume is
lower than the original mortgage as overcollateralization in order to increase the credit
rating (Lederman, 1990).
With the mortgage guarantee system, the band of investors
can thus be expanded to the reserves of the posting system, insurance companies and
international funds.
Especially for the life insurance companies, long-term
mortgages and MBSs are good investment vehicles to match their long-term capital
structure.
Since the mortgage securitization has not yet been implemented in Taiwan,
experiences from other countries are thus very important. Besides the discussion of
related regulation and taxation, the technique of designing the system and pricing
MBSs in Taiwan has just initiated. This study tends to investigate the effect of
securitization system on the risks of banking industry, simulate the price movement of
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【2002 年中華民國住宅學會第十一屆年會論文集】
mortgage securities in relation to various prepayment levels, and propose a structural
design of mortgage securitization and various issuance schemes.
The following
researchers may further model domestic mortgage prepayment and default
experiences, and propose related models to predict the prepayment and default
behaviors for pricing mortgages and MBSs more accurately.
Note
1. The non-performing loan ratios are official figures cited from the “Financial
Statistics Monthly of the ROC in Taiwan”.
It is considered under-estimated by
the practitioners. However, the increasing trend is correct.
References
Antczak, S., Primer on Mortgage-Backed Securities, Fixed Income Strategy, May,
Merrill Lynch & Co., May, 2000, 10.
Asay, M. R. and T. D. Sears, Stripped Mortgage-Backed Securities---Basic Concepts
and Pricing Theory, Housing Finance Review, 1989, 8, 199-232.
Becketti, S., The Prepayment Risk of Mortgage-Backed Securities, Economic Review
of the Federal Reserve Bank of Kansas City, 1989, 74:2, 406-420.
Becketti, S., The Role of Stripped Securities in Portfolio Management, Economic
Review of the Federal Reserve Bank of Kansas City, May, 1988, 20-31.
Bolye, P. P., Options: A Monte Carlo Approach, Journal of Financial Economics,
1977, 4:3, 323-338.
Books, R. P. and J. Najafi, Elements of Design for a Commercial Mortgage
Security：An Issuer’s Primer, Housing Finance Review, 1989, 8, 3-29.
Broadie, M., P. Glasserman, and G. Jain, Enhanced Monte Carlo Estimates for
American Option Prices, The Journal of Derivatives, Fall, 1997, 25-44.
Carlson, J. H. and T. D. Sears, Stripped Mortgage Pass-Throughs: New Tools for
Investors, in F. J. Fabozzi (Ed)., The Handbook of Mortgage-Backed Securities,
Probus Publishing, Chicago, IL., 1998.
Coles, A., Securitization: What Is Different about the USA? Housing Finance
International, 1999, 13:3, 9-13.
Financial Statistics Monthly of the ROC in Taiwan (2001) April, Ch.14, “The Balance
- 86 -
【2002 年中華民國住宅學會第十一屆年會論文集】
of Consumer Loans and Housing Mortgages” (in Chinese), The Interior
Department of the Government of the ROC.
Green, J. and J. B. Shoven, The Effects of Interest Mortgage Prepayments, Journal of
Money, Credit, and Banking, Feb. 1986, 41-59.
Hu, J. C., Derivative Mortgage Securities: An Overview, Journal of Real Estate
Finance and Economics, 1988, 1, 95-115.
Kuhn, R. L., Mortgage and Asset Securitization, Volume V of the Library of
Investment Banking, Irwin, Homewood, IL., 1990.
Lin, T. C. and T.C. Lin, The Study on Mortgage Securitization in Taiwan---from the
Viewpoints of Banks’ Managers, and the Effects on the Operation Risks of the
Banking Industry, Unpublished Working Paper, 2001.
Navratil, F. J., The Estimation of Mortgage Prepayment Rates, Journal of Financial
Research, Summer, 1985, 107-117.
Oldfield, G. S., The Economics of Structured Finance, The Journal of Fixed Income,
1997, 7:2, 92-99.
Tuckman, B., Fixed Income Securities---Tools for Today’s Management, John Wiley
and Sons, N.Y., N.Y., 1995.
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