Download Set 1 - NYU Stern

B40.3312 Policymaking in
Financial Institutions
Professor A. Sinan Cebenoyan
NYU-Stern-Finance
Copyright 1999-A. S. Cebenoyan
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Credit Risk
• “ …we are moving into a financial world
where credit has no guardian.” Henry
Kaufman, Stern Opportunity, 11/9/98
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•Measurement of credit Risk:
•Pricing of loans
•credit rationing
•Japanese FI’s overconcentration in real estate and in
Asia
•bad loans of 20 trillion yen in 1998
•Japanese Life insurers exposed to these banks by
about 14 trillion Yen in loans
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• C & I Loans
•Different size and maturities
•Secured or unsecured
•Fixed or floating
•Spot Loans or Loan Commitments
•Commercial paper (large corporations, directly or via
investment banker, sidestepping banks, lower rates)
•Real Estate Loans
•various features
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•Individual (Consumer) Loans
•Revolving loans
•High default rates (3-7 %, update the book)
•Return on a Loan
•Interest rate
•fees
•credit risk premium
•collateral
•nonprice terms (compensating balances, reserve
requirements)
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•Prime Rate most commonly used for longer-term loans,
fed-funds for shorter term
•LIBOR
The gross return on loan, k, per dollar lent is
f  ( L  m)
1 k  1
1  [b(1  R)]
Numerator is fees plus interest…promised cash flows
Denominator is net outflow from the bank
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•Expected return on the Loan
•Default risk
E (r )  p(1  k )
Retail versus Wholesale Credit decisions
•Retail
•Accept-Reject decisions
•credit rationing…….quantity restrictions rather
than price or interest rate differences
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•Wholesale
•Interest rate and credit quantity used to control credit
risk
•Prime plus a markup for riskier borrowers, BUT
•Higher rates don’t necessarily imply higher return
Measurement of Credit Risk
•Need to measure probability of default
•Information
•Covenants
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Default Risk Models
Three Broad Groups, Qualitative, Credit-Scoring, Newer Models
•Qualitative Models (Expert systems)
•Lack of public information leads to assembly of :
•Borrower Specific information
•Reputation, Long-term relationship, implicit contract
•Leverage, or capital structure (D/E), threshold beyond
which probability of default increases
•Volatility of earnings (stable v.s. high-tech)
•Collateral
•Market Specific Factors (Business cycle, Interest rates)
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•Credit Scoring Models
either calculate default probabilities or sort borrowers into
different risk classes, Thus:
•Numerically establish the factors that explain default risk
•Evaluate the relative importance of these factors
•Improve pricing of default risk
•Better screening of bad loan applicants
•better position to calculate reserves needed to meet expected
future loan losses
•Linear Probability Model
n
Z
i


j
X ij  error
j 1
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Example:
Suppose there were two factors influencing the past default
behavior of borrowers: the leverage or D/E and the sales/assets
ratio (S/A). Based on past default (repayment) experience, the
linear probability model is estimated as:
Z i  .5( D / E ) i  .1( S / A) i
Assume a prospective borrower has a D/E=.3, and a S/A=2.0, its
expected probability of default (Zi ) can then be estimated as:
Z i  .5(.3)  .1(2.0)  .35
Also,
E ( Z i )  (1  pi )
P is repayment probability
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Problem is probabilities can lie outside of 0 to 1. Logit Model
fixes this by:
1
F (Z i ) 
1  e Zi
The left hand side is the logistically transformed value of Zi
The Probit Model is an extension of Logit which considers a
cumulative normal distribution rather than a logistic function.
•Linear Discriminant Models
•Altman’s (of NYU) Z-score, uses various financial ratios in
classifying borrowers into high and low default risk classes:
Z  1.2 X 1  1.4 X 2  3.3 X 3  0.6 X 4  1.0 X 5
Where, X1=WC/TA, X2=RE/TA, X3=EBIT/TA,
X4=MVEq./BVLtd, and X5=Sales/TA, Low Z means high risk
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Altman’s Z has a switching point at 1.81.
Problems:
•Only two extreme cases discussed
•Are the coefficients stable over time?
•Are the ratios relevant over time?
•Qualitative factors ignored
•Lack of data
Newer Models
•Term Structure Derivation
We extract implied default probabilities on loans or bonds using the
spreads between risk-free discount Treasury bonds and discount bonds
issued by corporations of different risks
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Probability of default on one-period Debt Instrument
Assume risk-neutrality, and that the FI would be indifferent between
the corporate and the Treasury of same maturity discount bonds:
p(1+k) = (1+i)
p = (1+i) / (1+k) with i = 10% and k = 15.8%
p = (1.1) / (1.158) = .95 probability of repayment
thus, 5% is the implied probability of default given the market rates, a
5.8% risk premium ( F ) goes along with it.
F = k - i = 5.8%
If all is not lost at default, if g is the proportion of the loan that can
be collected, then
g(1+k)(1-p) + p(1+k) = 1 + i
the first term is the payoff to the FI if default occurs.
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The fact that there will be partial recovery reduces F
(1  i )
k i  F 
 (1  i )
(g  p  pg )
or
1 i
g
p  1 k
1 g
With i= 10%, and p=.95, and g=.9, risk premium F = 0.6
Mortality rate derivation of credit risk
Focus on historic default risk experience. Substitute mortality rates
for default rates.
MMR1= Ratio of total value of bonds of a certain grade defaulting in
year 1 of issue TO total value of same bonds outstanding in year1 of
issue
MMR2= Ratio of year 2 defaults TO total value of survivors in year2
Problems : backward-looking, period-sensitive, volume and size
sensitive.
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RAROC Models
Risk-adjusted return on capital, RAROC, is the ratio of loan income to
loan risk. A loan is approved if RAROC exceeds a FI established
benchmark rate (cost of capital)
Estimating loan risk is possible using a Duration-type approach
L
R
  DL
L
1 R
L   D L  L 
R
(1  R )
Replacing interest-rate shocks with credit quality shocks
R  Max[( Ri  RG )  0]
Do example in book, pages 207-209.
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Credit Risk Continued
• Option Models of Default Risk
• Borrower always holds a valuable default or
repayment option. If things go well repayment takes
place, borrower pays interest and principal keeps the
remaining upside, If things go bad, limited liability
allows the borrower to default and walk away losing
his/her equity.
• KMV corporation (www.kmv.com) has developed a
model called Expected Default risk Frequency EDF
used now by largest US banks.
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Payoff to
stockholders
0
Assets
A1
B
A2
-S
This is the borrower’s payoff function, s is the size of the initial
equity investment, B is the value of Bonds, and A is the market
value of the assets of the firm.
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Payoff to
debt holders
A1
B
A2
Assets
The payoffs to the bond holders are limited to the amount lent B
at best.
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Merton’s model:
F ( )  Be i [(1 / d ) N (h1 )  N (h2 )]
where
  T t
 i
d  borrower' s leverage ratio ( Be / A)
2
h1  [1 / 2   ln( d )] /  
2
h2  [1 / 2   ln( d )] /  
N (h)  probability of deviation exceeding h
2
  asset risk of borrower
We can get the equilibriu m default risk premium
k ( )  i  (1 /  ) ln[ N (h2 )  (1 / d ) N (h1 )]
k ( )  Required yield on risky debt
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On the last equation variance and leverage ratio would affect the risk
premium. But NOTICE that the key variables are A, market value of
assets, and asset risk  2 Neither of which are directly observable.
An Option Model Example is given on page 212.
The KMV model uses the OPM to extract the implied market value of
assets (A), and the asset volatility of a given firm. This is done by
viewing equity as a call-option on the firm’s assets and the volatility
of a firm’s equity value will reflect the leverage adjusted volatility of
its underlying assets. We have in general form:
E  f ( A,  , B , i , )
and
 E  g ( )
Where, the bars (-) denote variables that are directly observable.
Since we have 2 equations with 2 unknowns (A,), we can solve..
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The following is a graph that depicts the superior accuracy of
KMV-EDF over agency ratings in capturing expected
default probabilities.
Source KMV Corp.
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Loan Portfolio Risk
• We move beyond default risk measurements to
more aggregate contexts, i.e. portfolios.
• I will focus on two models that are not treated in
detail in the current edition of the Saunders book.
– A simple model : Migration Analysis
– A more sophisticated model: KMV Corporation’s
“Portfolio Manager Model”
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Migration Analysis
• A Loan Migration Matrix measures the probability of a
loan being upgraded, downgraded, or defaulting over some
period. Historic data is used, as such it can be used as a
benchmark against which the credit migration patterns of
any new pool of loans can be compared.
• In a Loan migration matrix the cells are made up of
transition probabilities.
• The number of grades are generally around 10 for most
FI’s.
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A Hypothetical Rating Transition Matrix:
Risk Grade
at beginning
of year
Risk Grade at end of year
1
2
3 D=Default
1
0.85
0.1
0.04
0.01
2
0.12
0.83
0.03
0.02
3
0.03
0.13
0.8
0.04
If the FI is evaluating the credit risk of of grade 2 rated borrowers,
and observes that over the last few years a much higher %, say 5%,
have been downgraded to3, and 3.5% have defaulted, the FI may
then seek to restrict its supply of lower quality loans (grades 2 and
3), concentrating more on grade 1. At the very least it should seek
higher credit risk premiums on lower quality loans. Migration analysis is used on commercial, credit card, and consumer loan portfolios.
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KMV Portfolio Manager Model
• KMV Portfolio Manager is a model that applies
Modern Portfolio Theory to the loan portfolio.
To estimate an efficient frontier for loans as in the above figure, and
the proportions (Xi), we need to measure :
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•Expected return on a loan to borrower i, (Ri)
•The risk of a loan to borrower i, (i)
•The correlation of default risks between loans to borrowers i and j
KMV measures each of the above as follows:
Return on the Loan:
Ri  AIS i  E ( Li )  AIS i  [ EDFi  LGDi ]
Where,
AIS = annual ‘all-in-spread’ on a loan =
(Annual Fees earned) + (Loan rate - Cost of Funds)
E(L) = expected loss on the loan
EDF = expected default frequency
LGD = loss given default
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Risk of the Loan:
 i  ULi   Di  LGD i  EDFi (1  EDFi )  LGD i
The Unexpected Loss (UL) is a measure of loan risk, i. It reflects the
volatility of the loan’s default rate, Di, times LGD. To measure Di
we assume loans either default or repay (no default), then defaults are
binomially distributed, then the  of the default rate for the ith borrower
Di, is equal to the square root of the probability of default times one
minus the probability of default, as above with EDF, (1-EDF).
Correlation :  ij
Correlation between the systematic return
components of the equity returns of borrower i and j. Generally low.
A number of large banks are using this model or variants to actively
manage their loan portfolios. Some are reluctant especially if involving
long-term customers. Diversification versus Reputation.
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Sovereign Risk
• Large Exposure
Japan
US
Britain
France
Germany
Other
Foreign banks’ share of total Asian debt at the end of June
1997 (excluding Singapore and Hong Kong. Source BIS)
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•Prior to July 97 Thai crisis, Foreign banks had $389 billion in loans
and other debt outstanding. See slide on page 29.
•This crisis is still unfolding
•Bailouts and loan restructuring packages (South Korea $57 billion
IMF organized loan package)
•Credit Risk
•Sovereign Risk
should dominate
•Repudiation (common before WWII) bonds
•Rescheduling (common since WWII) bank loans
•Relatively small number of banks (1/98 South Korea loans
just over 100 banks involved)
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•Same group of banks involved
•Cross-default provisions
•Governments view social costs of default on international
bonds less worrisome than on loans. Possible incentive
problems? Read Handout.
Country Risk Evaluation
•Outside Evaluation Models
•Euromoney Index
•Institutional Investor Index
•Internal Evaluation Models
•Similar to our Credit-risk scoring models based on explaining
probability of a country rescheduling, like Z-scores
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Common variables in CRA:
•Debt Service ratio=(interest+amortization on debt)/Exports
positive relation with probability of rescheduling
•Import Ratio=(Total imports/Total FX reserves)
positive relation
•Investment Ratio= Real Investment/GNP
+/- relation, arguments on both sides
2
•Variance of Export Revenue=  ER
+ relation
•Domestic Money Supply Growth= M / M
+ relation
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Problems
•Measurement
•Population groups (a finer distinction than rescheduler or not)
•Political risk factors
•Portfolio aspects (systematic risk more important)
•Incentive Aspects (Benefits and Costs) Read section
•Stability (of variables)
Use of Secondary market for LDC Debt to measure risk
•The structure of the market
•Brady Bonds ($ loans exchanged for $ bonds-US Treasury bonds
are used to collateralize the bonds).
•Sovereign Bonds. No US-Tbonds used as collateral
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•Performing Loans
•Non-performing loans
LDC Market Prices and CRA
Regression analysis of price changes to key variables. LHS= periodic
changes in prices of LDC debt in the secondary markets, RHS= set of
key variables.
Once the parameters are estimated, FI can combine these with
forecasts of key variables to estimate price changes.
Has problems but hopefully reduces errors.
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Dealing with Sovereign Risk Exposure
•Debt-Equity Swaps (Industries like motor, tourism, chemicals
have been desirable fo outside investors.)
FI may sell $100 million loan to a company for $93, Company
negotiates with foreign gov. And swaps $100 million for $95
million worth equity in local currency. Company has $2million
buffer, country gets rid of US$ debt, company has to invest in
local markets in local currency.
•MYRA (Multiyear Restructuring Agreements)
•concessionality: The amount the bank gives up in present value
terms as a result of a MYRA.
example:From appandix of chapter.
•Loan sales
•Debt for Debt Swaps (Brady Bonds)
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Capital Adequacy
• Functions of capital
– To absorb unanticipated losses with enough margin to
inspire confidence and enable the FI to continue as a
going concern
– To protect uninsured depositors, bondholders, and
creditors in the event of insolvency and liquidation
– To protect the FI insurance funds and the taxpayers
– To acquire the plant and other real investments
necessary to provide financial services
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The Cost of Equity Capital
D1
D2
D
P0 

 ... 
2
(1  k )
(1  k )
(1  k ) 
If dividends are assumed to grow at a known and constant
rate g, then
D0 (1  g )
P0 
kg
The above can be extended to P/E and D/E ratios
Capital and Insolvency Risk
•Capital
•Net Worth a market value accounting
concept
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The market value of capital and credit risk
Simple examples on declines on Loan values and its effects on Net
worth can be easily constructed.
The larger the FIs net worth, the more protection
The market value of capital and Interest Rate risk
Example in Table 20-4
FASB Statement No.115, requires securities classified as ‘available for
sale’ to be marked to market. Regulators in 12/94 exempted banks.
The Book value of capital
•Par value of shares
•Surplus value of shares
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•Retained Earnings
•Loan Loss Reserve
BV=Par value+Surplus value+Retained Earnings+Loss reserves
•Book Value of Capital and Credit Risk (reluctance to recognize
losses)
•Table 20-6, recognizes partial loss
•Book value of capital and Interest rate risk : No change
•Discrepancy between MV/BV
•Arguments Against MV Accounting
•difficult to implement
(dubious)
•Introduces excessive variability to Net Worth (not all is held to
maturity)
•Credit Crunch
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Actual Capital Rules
Two different capital requirements since 1987
•The Capital-Assets ratio (Leverage ratio)
•L = (Primary or Core Capital) / Assets
Core capital=BV of Common + qualifying cumulative
preferred stock + minority interests in equity of consolidated
subsidiaries
Table 20-7
•Problems:
•Market Value (could be massively insolvent)
•Asset Risk (not all assets have same credit+int.rate risks)
•Off-balance-sheet activities (no capital required)
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Risk Based Capital Ratios (to improve on the previous)
The following may be changed in the next couple of years. BIS has
proposed to remove the 8% requirement and implement capital
adequacy guidelines based on ratings (S&P, Moody’s, etc.)
Basel Agreement implemented two new risk-based capital ratios
Total risk-based cap ratio= Total cap / Risk-adj.assets > 8%
where Total capital= Tier I plus Tier II
and
Tier I (core) cap ratio = Core cap / Risk-adj. Assets > 4%
Table 20-8 summarizes Prompt Corrective Action Provisions of
FDICIA of 1991.
Table 20-9 gives definitions of Tier I and Tier II capital
Copyright 1999-A. S. Cebenoyan
Calculations will be done
in class examples
41
Criticisms of the Risk-based Capital ratio
•Risk weights
•Balance sheet incentive problems
•Portfolio aspects
•Bank specialness
•All commercial loans have equal weight
•Other Risks
•Competition
Capital requirements for securities firms
Net Worth / Assets > 2%
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Capital Requirements for Life Insurance Firms
NAIC model
C1= Asset Risk (Table 19-15)
C2= Insurance Risk
C3= Interest rate Risk
C4= Business risk
RBC 
(C1  C 3) 2  C 2 2  C 4
(Total Surplus and capital) / RBC > 1
Capital requirements for Property-Casualty Insurance Firms
Tables 19-16 and 19-17 will be discussed in class examples
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Securitization
• In 1998 47% of all residential mortgages
securitized.
• Worldwide value of outstanding securitized issues
rapidly approaching $500 billion.
• Similar to loan sales, but with creation of
securities
• Three major types:
– Pass-through security
– Collateralized Mortgage Obligation (CMO)
– Asset-backed security
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•The Pass-Through Security
Securitization of residential mortgage loans:
•GNMA: Ginnie Mae, Government national Mortgage Assoc.,
split in 1968 from Fannie Mae, directly owned by government.
•Sponsors mortgage-backed securities programs of Fis
•Acts as guarantor to investors regarding the timely passthrough of principal and interest, i.e. provides timing insurance
•GNMA supports only FHA, VA, FMHA insured pools.
•FNMA: Fannie Mae 1938, now private , implicit government
•FNMA creates MBSs by purchasing mortgage packages from
FI’s. finances them thru sale of MBSs to Life insurers and
pension funds. Engages in swaps of MBSs with original
mortgages.
• Unlike GNMA, FNMA securitizes conventional mortgages.
•FHLMC: Freddie Mac similar to FNMA but primarily deals with
savings banks.
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The incentives and mechanics of Pass-through Security Creation
•The creation of a GNMA pass-through security
•Bank originates 1,000 new $100,000 mortgages, $100 million
total size . Each has 30 year maturity, 12 % coupon. FHA
insured. Financed by deposits and equity.
•Bank faces capital adequacy requirements. Risk adjusted value
of residential mortgages is 50% of face value, and the risk-based
capital requirement is 8%, bank capital needed to back the
mortgage portfolio:
Capital requirement= $100 mill. X .5 X .08 =$4 million
•Bank also faces reserve requirements of 10%. Needs $96
million in deposits after reserves, and the $4 million in equity
capital.
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Balance sheet may look like:
Assets
Liabilities
Cash Reserves
$10.66
Long-term mortgages 100.00
Demand Deposits
Capital
$106.66
4.00
Bank also has to pay insurance premium to FDIC (assuming 27
basis points)
$106.66 million X .0027 = $287,982
These amount to 3 levels of regulatory taxes (incentive enough?):
1. Capital requirements
2. Reserve Requirements
3. FDIC insurance premiums.
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Two more problems:
•Duration mismatch (core DD generally have a duration of less than 3
years, whereas mortgages depending on prepayment assumptions
normally have durations of at least 4.5 years)
•Illiquidity exposure. May lead mortgage asset fire sales if large
unexpected DD withdrawals happen.
•Bank can deal with the above by a variety of tools, lengthening
durations, swaps, etc.. BUT regulatory burden stays,
By contrast:
•creating GNMA pass-through securities can largely resolve the
duration, and illiquidity risk problems and reduce the burden of
regulatory taxes.
•Bank packages the loans and places them with a third party,
removing them from the B/S. Next gets the GNMA guarantee for a
fee, and arranges to service the mortgages for a fee.
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The GNMA pass-through securities are issued and sold in the capital
markets. These are desirable to investors as they are FHA/VA insured
against default by homeowners, and GNMA insured against default by
the originating bank or the trustee.
The relevant rates:
Mortgage coupon rate
minus
servicing fee
minus
GNMA insurance fee
equals
GNMA pass-through bond coupon
12%
0.44
0.06
11.50%
Barring prepayment, the investor receives a constant stream of
monthly payments.
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Post-securitization Balance Sheet of the FI:
Assets
Cash reserves
Cash proceeds from
mtge securitization
Liabilities
$10.66
Demand Deposits
100.00
Capital
$106.66
4.00
Dramatic change. Illiquid mortgages replaced by cash. Duration
mismatch has been reduced. Regulatory taxes reduced, e.g. capital
requirements reduced as cash has 0 risk-adjusted asset value. Reserve
requirements and insurance (FDIC) fees will also be reduced if FI
retires some DD. More importantly, The FI can generate new
mortgages with the new cash and securitize those.
Act like a broker. Fee income becomes more important.
BUT, prepayment risk may reduce demand for MBSs.
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Prepayment Risk
Most conventional mortgages are fully amortized:
An annuity problem.
Given:
Size of pool = $100,000,000
Maturity
= 30 years (n=30)
# of monthly
payments
= 12 (m=12)
r (annual mtge
coupon rate) = 12 %
R = constant monthly payment
To get the monthly payments, we need to solve the following equation
for R:
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r 1
r 360
100 ,000 ,000  R[(1  )  ...  (1  )
]
m
m
1

1 
r mn
(1  )

m
100 ,000 ,000  
r


m





  R  PVAF  R




With our numbers, r= 12%, m=12, n=30, we get
R= $1,028,613.00
This amount fully amortizes the loan, thus each R has a different
principal and a different interest component. Table 28-3, page 675.
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With a 1/2 percent fee (insurance and servicing), the R that is passed
through is
R = $990,291.00
this assumes no prepayment.
Prepayment has 2 major sources:
•Refinancing
•Housing Turnover
Prepayment is a function of the gap spread between mortgage pool
rates, and the current mortgage coupon rates.
Without prepayments:
R1=R2=R3=……….=R360
With prepayments
CF1<CF2<CF3…<CF60>CF61>……>CF360
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Prepayment has :
• Good News Effects: Lower rates increase present values
Lower rates lead to faster principal recovery
•Bad News effects: Fewer interest payments, and reinvestment risk
•Prepayment Models
•WSJ reports Bear Sterns prepayment model based data. Among
other thing Weighted Average Life WAL is reported:
WAL = [S(time x Expected Principal received)] / Total principal outsd.
E.g. Loan with 2 years maturity, $40 year 1, $60 year 2 principal pmts.
WAL = 160/100 = 1.6 years.
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PSA (public securities association) Model
•develops and average rate of prepayment based on past experience.
•PSA behavior assumes: 0.2% per annum in the first month, going up
by 0.2 % per month for the first 30 months, leveling off at 6%
annualized rate for the remaining life of the pool.
•A Number of reasons why a specific pass-through may differ from
PSA, such as: Age of pool, coupon of pool relative to current
coupons, fully amortized R or not, Assumability, Size of pool,
Conventional or not, Geographic location, age and jobs of mortgagees.
•One approach would be to assume a fixed deviation from PSA, like
150% PSA, 50% PSA..
Other Empirical Models
•the better the prepayment model the more the FI makes. Variations
on PSA theme. Considering conditional probabilities, burn-out
factors.
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Option Models: Use Option Pricing theory to figure out the fair
yield spread of pass-throughs over securities (Option-adjusted spread,
OAS models).
PGNMA  PTBOND  PPREPAYMENTOPTION
•The value of a GNMA bond to an investor is equal to the value of a
standard noncallable Treasury bond of the same duration minus the
value of the mortgage holder’s prepayment call option.
•In yield terms:
YGNMA  YTBOND  YOPTION
•The investors’ required yield on a GNMA should equal the yield on a
similar duration T-bond plus an additional yield for writing the
valuable call option.
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•How to calculate the value of the OAS on GNMAs
•Assume:
> Refinancing only reason for prepayment
> T-Bond yield curve flat
> mortgage coupon rate 10%, principal balance $1 million
> mortgages have 3-year maturity, and annual payments
> mortgages fully amortized, no servicing fee.
> Prepayment only after 3% drop from mortgage coupon rate (10%)
> maximum yearly interest rate move is 1% up or down
> In any year, CF is either R ($402,114 here), R+repayment of any
outstanding principal, or zero if all paid off.
We start out with current yields at 9%, GNMA bond sells at a premium.
>Cash Flow at end of year 1 is R with certainty, as no prepayment
>Cash Flow at end of year 2 is tricky: rates now may have gone down
to 7% which is going to trigger prepayment. The probability of that is
25%. So, with 25% chance investor receives R plus Principal balance
remaining at end of year 2.
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Principal balance remaining at end of year 2 (after 2 payments have
been made) is going to be $1,000,000 minus principal paid with first
payment and minus principal paid with second payment:
principal1  402 ,114  (. 1)1,000 ,000  302 ,114
principal2  402 ,114  (. 1)697 ,886  332325 .4
balance  1,000 ,000  302 ,114  332 ,325 .4  365 ,560 .6
Cash Flow received by investor in year 2 with repayment :
$402 ,114  $365 ,560 .6  $767 ,674 .6
Thus expected cash flow at end of year 2 will be :
CF2  .25 ($ 767 ,674 .6)  .75 ($ 402 ,114 )
 $493 ,504 .15
Cash Flow at end of year 3 :
CF3  .25 (0)  .75 ($ 402 ,114 )  $301,585 .5
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Derivation of the option-adjusted spread:
E (CF3 )
E (CF1 )
E (CF2 )
P


2
(1  d1  Os ) (1  d 2  Os )
(1  d 3  Os ) 3
assuming
d1  d 2  d 3  8 %
solve for O s
1,017 ,869 
402 ,114
493 ,504
301,585 .5


(1  .08  Os ) (1  .08  Os ) 2 (1  .08  Os ) 3
Os  0.96 %
YGNMA  YBOND  Os
 8%  0.96 %  8.96 %
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Collateralized Mortgage Obligations (CMOs):
•Uncertainties about the maturities of mortgage pass-throughs make
them unattractive to market participants.
•CMOs reduce the uncertainty concerning maturity of mortgagebacked security, thereby provides a risk-return pattern not available
with typical mortgage pass-through securities.
•CMO is a mortgage backed bond issued in multiple classes or
tranches.
•GNMA bonds placed in a trust (REMIC) as collateral
•CMO with 3-17 classes created. Class A, B, C, thru Z.
•Value is created,
n
P
i ,CMO  PGNMA
i 1
Where n=3,…17.
Let’s discuss a 3-class CMO :
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Investment bank buys $150 million GNMAs and places them in trust as
collateral. Issues CMO with A, B, C classes:
•Class A: Annual fixed 7% coupon, $50 million size
•Class B: ……………..8%………………………….
•Class C:………………9%…………………………
•The underlying GNMA may have had 9% coupon, and maybe 25 years
to maturity.
•The logistics of the CMO:
•Each month R is received by the trustee, which distributes Coupons
to all classes, and then principal to Class A first, once A is paid off
then Class B and so on… Example:
R= $2.5 million
A gets coupon of [(.07/12)x50 million]=$291,667.
B gets coupon of [(.08/12)x50 million]=$333,333.
C gets coupon of [(.09/12)x50 million]=$375,000.
Interest adds up to $1,000,000.
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•Principal payments:
•Only Class A gets the $1.5 million left after interest payments.
Thus class A now has $48.5 million outstanding.
•After Class A is retired B is paid off, and so on.
•Most times there is an additional Class Z, which is like a zero but
not quite. It starts paying interest and principal only after all
preceding classes have been paid off.
•There is also a residual R class. This gives the owner the right to
any collateral remaining in the trust after all other bond classes
have been retired PLUS any reinvestment income earned by the
trust. This is a high risk bond.
It is also a unique bond: as there is more left in the pool, more will
be reinvested, and less will be retired, Thus a higher value at end.
But this means negative duration! As interest rates rise value of
class R goes up.
Very attractive for hedging portfolios.
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Mortgage Backed Bond (MBB)
Mortgage-backed bonds stay on the Balance sheet.
•MBBs have no direct link to the CFs of underlying mortgages, the
relationship is one of collateralization .
•If the FI fails, MBB bondholders have a first claim to a segment of
the FI’s mortgage assets.
•FIs back most MBB issues with excess collateral, Thus receiving
AAA ratings for the MBB, even when the FI may be rated BBB or
lower. The cost is thus lower.
•Example:
•FI finances $20 million in mortgages with $10 million in
uninsured deposits (wholesale, over $100,000), and $10 million
in insured deposits (retail, less than$100,000).
•Duration of assets greater than leverage adjusted duration of
liabilities, and uninsured depositors are worried about interest
rate and default risk, requiring high risk premiums.
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•Insured depositors are not worried, and are charging next to risk free
rate.
•Genius strikes!: FI puts up $12 million of its mortgages as collateral
backing a $10 million long-term MBB issue. Because of the
overcollateralization, MBB will cost less than uninsured deposits. FI
uses the MBB to retire the uninsured deposits.
•Duration Gap improved, costs reduced.
•At the expense of FDIC! The insured depositors are only backed by
$8 million in unpledged assets. If FDIC were not there, these
depositors would have required high rates for compensation.
•FDIC discourages high risk institutions from excessive MBB sales.
•Other than regulatory interference, MBB are undesirable as they tie
up mortgages on the B/S, increasing the illiquidity of the assets.
•FI still liable for reserve requirements and capital adequacy taxes.
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IO Strips
•A bond whose cash flows reflect the monthly interest payments
received from a pool of mortgages.
PIO 
IO360
IO1
IO 2

 ... 
y
y 2
y 360
(1 
)
(1 
)
(1 
)
12
12
12
•Discount effect: As y falls price rises
•Prepayment effect: As y falls, more prepayments, value falls.
•As interest rates fall below coupon, prepayment starts to dominate and
value of the bond falls. Again negative duration.
•Thrifts have been buying Ios to hedge their portfolios.
•See graphs. Page 697.
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PO Strips
•A bond with cash flows that reflect the monthly principal payments
received from a pool of mortgages.
PPO 
PO360
PO1
PO2

 ... 
y
y 2
y 360
(1 
)
(1 
)
(1 
)
12
12
12
•Discount effect: As y falls, value rises
•Prepayment effect: As y falls, more early payoffs, value goes up.
•Most other assets can and have been securitized.
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