FRE6571 – Mortgage Backed Securities
01/28/2016
Dr. Steve Mandel
Rogers Hall 216
Class Website http://www.busybeegroup.com/FRE6571.html
Text Book: Fixed Income Mathematics(4th Edition) – Frank J. Fabozzi – ISBN
007146073
Computer/Analytics Systems
 The Yield Book – Comprehensive FI individual security and portfolio analytics
GRADING
Homework: 10% of grade
Final Exam: In-class, closed book and notes, formula sheet provided, 2 hours.
Asset Backed Securities
1. Terminology
Securitization – The process of packaging financial promises (loans) and transforming
them into a form whereby they can be freely transferred among investors.
Structuring – Segmenting cash flows and risks to transform raw assets into a form that is
more desirable for investors.
Three Types of Instruments in Financial Markets
 Direct obligations of corporations and sovereigns – bonds, equities
 Derivatives – swaps, futures, options
 Securitized and structured assets.
Collateral – Raw loans that underlie securitized instruments.
Credit Enhancement – a process whereby securities may be protected from losses
associated with the underlying collateral.
2. The securitization structure
Borrower
Loan Originator
Credit
Agency
Special
Purpose Trust
Credit
Enhancer
Underwriter
Investor
3. Value Added Through Securitization
Loans
Illiquid
Collateral valuation subjective
And periodic
Originator assesses risk
Securities
Liquid/tradable
Market determines value
In some cases daily
Third parties – rating agencies and enhancers
– assess risk
Investor market local
Investor market national/global
Limited terms and rates offered Buffet of terms and rates offered borrowers
borrowers
4. Financial Assets securitized













Fixed rate mortgages
Adjustable rate mortgages
Second mortgages
Home equity loans
Auto loans
Commercial real estate loans
Credit card receivables
Equipment leases
Mobile loans
Student loans
Recreational vehicles
Junk Bonds
Aircraft leases
5. Basic Requirements for Securitization




Standardization of contracts, laws, and servicer qualities.
Database of historic statistics
Reliable supply of credit enhancers
Computers to handle complexity of analysis
6. Benefits of Securitization
Benefits to consumerborrowers
Lower cost of funds
Increased buffet of
credit forms
Competitive rates and
terms nationally and
locally
Funds available
consistently
Benefits to
originators
Ability to sell
assets readily
Profit on sales
Benefits to investors
High Yield on highly
rated securities
Liquidity
Increased
Enhanced diversification
servicing income and investment profiles
More efficient
use of capital
Potential Trading Profits
Benefits to
investment bankers
New Product Line
Continuous flow of
originations and fees
Trading volume and
profits
Potential for
innovation and market
expansion
7.Disadvantages to Securitization
Reduces Accountability. May result in reduced risk management and increased risk.
Mortgage Cash Flows
a. Underlying loan – No prepayments
Monthly Payment
P
Balance  Coupon / 1200
rem = remaining term in months
1  (1  coupon / 1200) (  rem)
Example:
Balance = $100,000
Coupon = 6%
Years = 30
rem =12 x 30 = 360
P
100,000  6 / 1200
 $599.55
1  (1  6 / 1200) ( 360)
% Balance
(1  Coupon / 1200) Age  1
% Balance  (1 
)  100
(1  Coupon / 1200) OriginalTerm  1
Age & Original term in months
Example
For Age = 0 %, Balance = 100%
For Age =1 (month)
(1  6 / 1200)1  1
% Balance  (1 
)  100  99.90045
(1  6 / 1200) 360  1
Amortized Principal = 100 – 99.90045 = .09955% = .09955 x 100,000/100 = $99.55
Coupon
 Starting Pr incipal  Amortized Pr incipal
1200
6
MonthlyPayment 
 100,000  99.55  500  99.55  599.55
1200
MonthlyPayment 
Price/Yield
Pr ice  i 1
W AM
CashFlowi
(1  Yield / 1200) Ti
(Monthly compounding)
Bond Equivalent Yield
BEY  200  ((1 
1
MEY 6
)  1)
1200
MEY  1200  ((1 
BEY 6
)  1)
200
Example
MEY = 6
6 6
)  1)  6.0755
1200
BEY  200  ((1 
Average Life
W AM
AverageLife 
 T  Pr incipal
i
i 1
W AM
 Pr incipal
i 1
i
(time in years and reflects delay)
i
Duration – Measures of Interest Rate Sensitivity
Macaulay Duration – Percentage change in Price for a percentage change in Yield.
(Average life of PV of Cash Flows)
W AM
MacaulayDu ration 
 T PV
i 1
W AM
i
i
 PV
Where, PVi 
i
i
Cashflowi
( Ti in Years)
BEY 2Ti
(1 
)
200
Modified Duration – Percentage change in Price for a 100 basis point change in Yield.
First derivative of Price/Yield Curve. Convexity is second derivative.
1
)CFi
12

Yield i  2
i 1
(1 
)
12

100
Convexity 
Full Pr ice  100
W AM
ModifiedDu ration 
MacaulayDu ration
Yield
1
200
Yi (Yi 
Mortgage Pools – with prepayments
b.
Partial Prepayments – curtailments.
Loan Paid Off – Due to refinancing, selling of house, or default. All measures re-weighted.
Measures of prepayments
SMM – Single Monthly Mortality (% of outstanding principal prepaid)
CPR - Conditional Prepayment Rate (annualized SMM)
PSA - Public Securities Association Model (30 month ramp to 6% CPR)
SMM  100 
( ScheduledBalance  ActualBala nce)
ScheduledBalance
CPR  100  (1  (1 
PSA  100 
SMM 12
) )
100
CPR
min( age,30)  0.2
1
SMM  100(1  (1 
CPR 
CPR 12
) )
100
PSA  min( age,30)  0.2
100
Example
Scheduled Balance = 99.0045
Actual Balance = 98.95
(99.0045  98.95)
SMM  100 
 .055
99.0045
PSA  100 
CPR  100  (1  (1 
.055 12
) )  .598
100
.598
 299%
min( 1,30)  0.2
Actual Balance
SMM t
)
100
Age
SMM t
ActualBala ncet  ScheduledBalancet   (1 
)
100
t 1
ActualBala ncet  ScheduledBalance t  (1 
Market Conventions
Day Count – 30/360
AccruedInterest  (
CouponRate
DaysAccrue d
)(
)  Pr incipalBal ance
100
360
Difference between Cash Flows of Mortgage Loan vs Mortgage Backed Securities
1. Prepayment Effect
2. Service Fee (Net vs Gross Coupon) Effect
3. Delay Effect