Fixed Income Zvi Wiener 02-588-3049 Fixed Income 4.

Fixed Income

Zvi Wiener

02-588-3049http://www.tfii.org

Fixed Income 4

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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.

20*12

1

1206.0

1

000,100i

i

x

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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-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

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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

0 30 Age in months

Annual CPR in %

0.2

6

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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

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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

T

r

Current TS

Downward move

upward move

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Twist

T

r

steepening

flattening

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Butterfly

T

r

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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 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

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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!