Fixed Income Zvi Wiener 02-588-3049 Fixed Income 4.
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Transcript of Fixed Income Zvi Wiener 02-588-3049 Fixed Income 4.
http://www.tfii.org FI - 4 slide 2
Japanese Government Bonds JGB
• short term Treasury bills
• medium term bonds
• long term bonds
• super long term bonds (20 years)
http://www.tfii.org FI - 4 slide 3
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
http://www.tfii.org FI - 4 slide 4
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)
http://www.tfii.org FI - 4 slide 5
Brady Bonds
Argentina, Brazil, Costa Rica, Dominican Republic, Ecuador, Mexico, Uruguay, Venezuela, Bulgaria, Jordan, Nigeria, Philippines, Poland.
Partially collateralized by US government securities
http://www.tfii.org FI - 4 slide 6
Fixed Income 4
• Mortgage loans
• Pass-through securities
• Prepayments
• Agencies
• MBS
• CMO
• ABS
http://www.tfii.org FI - 4 slide 7
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.
http://www.tfii.org FI - 4 slide 8
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.
http://www.tfii.org FI - 4 slide 9
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.
http://www.tfii.org FI - 4 slide 10
Fixed Rate Mortgage
A series of equal payments with PV=loan.
Example: 100,000 for 20 years with 6% and equal monthly payments.
20*12
1
1206.0
1
000,100i
i
x
http://www.tfii.org FI - 4 slide 11
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.
http://www.tfii.org FI - 4 slide 12
Balloon Mortgage
One payment at the end.
Sometimes they have renegotiation points.
http://www.tfii.org FI - 4 slide 13
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.
http://www.tfii.org FI - 4 slide 14
Risk in Mortgages
Default risk
Liquidity risk
Interest rate risk
Prepayment risk
http://www.tfii.org FI - 4 slide 15
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.
http://www.tfii.org FI - 4 slide 16
Prepayment Risk in Mortgages
Sale of home
Better interest rates
Irrational factors
http://www.tfii.org FI - 4 slide 17
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
http://www.tfii.org FI - 4 slide 18
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.
http://www.tfii.org FI - 4 slide 19
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.
http://www.tfii.org FI - 4 slide 20
Non-Agency Pass-ThroughCredit enhancement to AA or AAA.OvercollateralizationSenior/subordinated structure
shifting interest structuremonths % of prepayment to senior1-60 7061-72 6073-84 4085-96 2097-108 12
http://www.tfii.org FI - 4 slide 21
Prepayments
Prepayment speed, conditional prepayment rate CPR (prepayment rate assumed for a pool).
Single-Monthly mortality rate SMM.
SMM = 1 - (1-CPR)1/12
http://www.tfii.org FI - 4 slide 22
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.
http://www.tfii.org FI - 4 slide 23
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
http://www.tfii.org FI - 4 slide 24
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.
http://www.tfii.org FI - 4 slide 25
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.
http://www.tfii.org FI - 4 slide 26
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.
http://www.tfii.org FI - 4 slide 27
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.
http://www.tfii.org FI - 4 slide 29
PSA standard default assumptions
0 30 60 120 Age in months
Annual default rate (SDA) in %
0.3
0.6Month 1 - 0.02%increases by 0.02% till 30mstable at 0.6% 30-60mdeclines by 0.01% 61-120mremains at 0.03% after 120m
0.02
http://www.tfii.org FI - 4 slide 30
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.
http://www.tfii.org FI - 4 slide 31
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.
http://www.tfii.org FI - 4 slide 32
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.
http://www.tfii.org FI - 4 slide 33
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.
http://www.tfii.org FI - 4 slide 34
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.
http://www.tfii.org FI - 4 slide 35
Other CMOs
PAC = Planned Amortization Class,
IO = interest only,
PO = principal only,
IO, PO strips.
http://www.tfii.org FI - 4 slide 36
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)
http://www.tfii.org FI - 4 slide 37
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.
http://www.tfii.org FI - 4 slide 38
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
http://www.tfii.org FI - 4 slide 39
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
http://www.tfii.org FI - 4 slide 40
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
http://www.tfii.org FI - 4 slide 44
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.
http://www.tfii.org FI - 4 slide 45
Example
bond coupon maturity yield duration convex.
A 8.5% 5 8.5 4.005 19.81 B 9.5% 20 9.5 8.882 124.17 C 9.25% 10 9.25 6.434 55.45
Bullet portfolio: 100% bond C
Barbell portfolio: 50.2% bond A, 49.8% bond B
http://www.tfii.org FI - 4 slide 46
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?