Fixed Income 4
Zvi Wiener
02-588-3049
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Fixed Income
Japanese Government Bonds JGB
• short term Treasury bills
• medium term bonds
• long term bonds
• super long term bonds (20 years)
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German Government Bonds
• U-Schatze discount paper up to 2 years
• Kassens = federal government notes (2-6 y.)
• OBLEs = 5 year federal government notes
• Bunds = federal government bonds (6-30 y.)
all coupon payments are annual
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UK Government Bonds Gilts
• straights = bullet bonds (some callable)
• convertibles (option to holder to convert to
longer gilts)
• index linked low coupon 2-2.5%
• irredeemable (perpetual)
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Brady Bonds
Argentina, Brazil, Costa Rica, Dominican
Republic, Ecuador, Mexico, Uruguay,
Venezuela, Bulgaria, Jordan, Nigeria,
Philippines, Poland.
Partially collateralized by US government
securities
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Fixed Income 4
• Mortgage loans
• Pass-through securities
• Prepayments
• Agencies
• MBS
• CMO
• ABS
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Mortgage Loans
Mortgage is a loan secured by a specified real
estate property.
Conventional mortgage - credit of the
borrower and collateral.
Mortgage insurance - FHA, VA, FmHA
guaranteed by US government, there are
some private insurers as well.
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Mortgage Market
Mortgage originator - thrifts, banks
origination fee (in points = %)
PTI = payment to income ratio (include tax)
LTV = loan to value ratio
later on mortgages are securitized.
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Mortgage Services
Collecting payments, maintaining records
Servicing fee - % of outstanding plus some
other benefits.
Mortgage insurer required when LTV>80%.
Credit life - voluntary life insurance.
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Fixed Rate Mortgage
A series of equal payments with PV=loan.
Example: 100,000 for 20 years with 6% and
equal monthly payments.
100,000 
12*20

i 1
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x
 0.06 
1 

12 

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i
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Adjustable-Rate Mortgage (ARM)
The contract rate is reset periodically, based
on a short term interest rate.
Adjustment from one month to several years.
Spread is fixed, some have caps or floors.
Market based rates.
Rates based on cost of funds for thrifts.
Initially low rate is often offered = teaser rate.
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Balloon Mortgage
One payment at the end.
Sometimes they have renegotiation points.
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Two-Step Mortgages
A loan carries a fixed rate for some period
(usually 7 years) and then reset rates.
For example: 250 basis points plus average of
10-years Treasuries.
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Risk in Mortgages
Default risk
Liquidity risk
Interest rate risk
Prepayment risk
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Risk in Mortgages
Default risk is highly affected by LTV.
LTV>80% in 40% of loans
LTV>90% in 15% of loans
different state laws give different
rights to lenders.
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Prepayment Risk in Mortgages
Sale of home
Better interest rates
Irrational factors
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Mortgage Pass-Through Securities
A group of mortgages form a pool which is
securitized.
Payments are pooled, service fee deducted
and the rest divided.
WAC = weighted average coupon rate
WAM = weighted average maturity
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Mortgage Pass-Through Securities
Ginnie Mae = Government National Mortgage
Association, MBS - guaranteed by GNMA.
Freddie Mac = Federal Home Loan Mortgage
Corporation, PC = participation certificate.
Fannie Mae = Federal National Mortgage
Association, MBS.
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Role of Agencies
guarantee timely payments
1. Coupon only
2. Both coupon and principal
Ginnie Mae is guaranteed by the US
government. Securities guaranteed by Ginnie
Mae are called MBS = Mortgage Backed
Securities.
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Non-Agency Pass-Through
Credit enhancement to AA or AAA.
Overcollateralization
Senior/subordinated structure
shifting interest structure
months
% of prepayment to senior
1-60
70
61-72
60
73-84
40
85-96
20
97-108
12
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Prepayments
Prepayment speed, conditional prepayment rate
CPR (prepayment rate assumed for a pool).
Single-Monthly mortality rate SMM.
SMM = 1 - (1-CPR)1/12
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Example of prepayments
Example: let CPR=6%, then
SMM = 1-(1-0.06)1/12 = 0.005143.
An SMM of 0.5143% means that approximately
0.5% of the mortgage balance will be prepaid
this month.
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Example of prepayments
If the balance at the beginning of a month is
$290M, SMM = 0.5143% and the scheduled
principal payment is $3M, then the estimated
repayment for this month is
0.005143 (290,000,000-3,000,000)=$1,476,041
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Prepayments
A general model should be based on a dynamic
transition matrix, very similar to credit
migration.
But note the difference of a pool of not
completely rational customers and a single firm.
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Prepayments
Prevailing mortgage rate relative to original.
Path of mortgage rates.
Level of mortgage rates.
Seasonal factors (home buying is high in
spring summer and low in fall, winter).
General economic activity.
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Bond Equivalent Yield
Bond equivalent yield = 2[ (1+yM)6 - 1]
Yield is based on prepayment assumptions
and must be checked!
PSA benchmark = Public Securities
Association. Assumes low prepayment rates
for new mortgages, and higher rates for
seasoned loans.
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PSA prepayment benchmark
The Public Securities Association benchmark
is expressed as monthly series of annual
prepayment rates.
Low prepayment rates of new loans and
higher for old ones.
Assumes CPR increasing 0.2% to 6% with
life of a loan.
Actual rate is expressed as % of PSA.
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100 PSA
Annual CPR in %
6
0.2
0
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30
Age in months
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PSA standard default assumptions
Annual default rate (SDA) in %
0.6
Month 1 - 0.02%
increases by 0.02% till 30m
stable at 0.6% 30-60m
declines by 0.01% 61-120m
remains at 0.03% after 120m
0.3
0.02
0
30
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60 120
Age in months
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Special Properties
Negative convexity - if interest rates go up
the price of a pass through security will
decline more than a government bond due to
lower prepayment rate.
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CMO and stripped MBS (ch. 12)
Collateralized Mortgage Obligations - are
bond classes created by redirecting the cash
flows of mortgage related products so as to
mitigate prepayment risk.
CMO is backed by a pool of pass-throughs,
whole loans, or strips, structured in order to
serve different types of clients.
The bond classes are called tranches.
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CMO Example
Since 1983 - sequential-pay CMO. Each class
is retired sequentially.
Example: collateral is a pass-through with
• par of $400M
• pass-through coupon rate 7.5%
• WAC weighted average coupon 8.125%
• WAM weighted average maturity 357 mo.
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CMO Example
4 tranches A,B,C,D divide the whole nominal,
coupons will be distributed proportionally, but
principals first go to A, until repaid, then to B,
etc.
Another example is an accrual CMO when
one of the tranches does not get receive
current interest. It is accrued and added to the
principal.
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CMO Example
Some tranches are floaters, others inverse
floaters.
Floater: Variable Rate + spread
Inverse Floater: Spread - Variable Rate
Often LIBOR is used as variable rate.
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Other CMOs
PAC = Planned Amortization Class,
IO = interest only,
PO = principal only,
IO, PO strips.
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ABS Asset-Backed Securities (13)
Collateral,
credit enhancement,
Payment structure (priorities),
legal structure (SPV=special purpose vehicle)
Auto loan backed securities
Credit Card backed securities
Home Equity loans (second lien)
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Bonds with Embedded Options (14)
Traditional yield analysis compares yields of
bonds with yield of on-the-run similar
Treasuries.
The static spread is a measure of the spread
that should be added to the zero curve
(Treasuries) to get the market value of a bond.
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Active Bond Portfolio Management (17)
Basic steps of investment management
Active versus passive strategies
Market consensus
Different types of active strategies
Bullet, barbell and ladder strategies
Limitations of duration and convexity
How to use leveraging and repo market
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Investment Management
• Setting goals, idea of ALM or benchmark
• GAAP, FAS 133, AIMR - reporting
standards
• passive or active strategy - views, not
transactions
• available indexes
• mixed strategies
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Major risk factors
• level of interest rates
• shape of the yield curve
• changes in spreads
• changes in OAS
• performance of a specific sector/asset
• currency/linkage
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Parallel shift
r
upward move
Current TS
Downward move
T
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Twist
r
flattening
T
steepening
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r
Butterfly
T
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Yield curve strategies
Bullet strategy: Maturities of securities are
concentrated at some point on the yield curve.
Barbel strategy: Maturities of securities are
concentrated at two extreme maturities.
Ladder strategy: Maturities of securities are
distributed uniformly on the yield curve.
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Example
bond
coupon
maturity
yield duration
convex.
A
B
C
8.5%
9.5%
9.25%
5
20
10
8.5 4.005
9.5 8.882
9.25 6.434
19.81
124.17
55.45
Bullet portfolio: 100% bond C
Barbell portfolio: 50.2% bond A, 49.8% bond B
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Dollar duration of barbell portfolio =
0.502*4.005 + 0.498*8.882 = 6.434
it has the same duration as bullet portfolio.
Dollar convexity of barbell portfolio =
0.502*19.81 + 0.498*124.17 = 71.78
the convexity here is higher!
Is this an arbitrage?
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The yield of the bullet portfolio is 9.25%
The yield of the barbell portfolio is 8.998%
This is the cost of convexity!
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