Fixed Income Securities and their Derivatives

Asset-Backed Securities

ABS derive their cash flows from a pool of underlying assets

MBS = mortgage backed securities

CARS = certificates for automobile receivables

CARDS = certificates for amortizing revolving debts

HELS = home equity loan securities

The underlying assets generate cash flows of principal and interest which can be repackaged and sold to investors.

Fixed income assets Principal Interest Asset-backed securities

In ABS, the underlying assets are collected into a pool .

Pool assets are standardized .

The asset pool is placed in trust.

Claims on the cash flows generated by the asset pool are structured:

Pass-through structures

Multi-class structures

Securities representing these claims are sold.

Securitization

By pooling and repackaging cash flows, ABS issuers can convert illiquid fixed income assets into marketable bonds.

Requires trust structure to hold underlying assets, and

Credit enhancement to achieve investment grade bond rating

External: guarantees

Internal: over-collateralization.

Issuers

Mortgage related agencies

Ginnie Mae (pass-thoughs)

Freddie Mac (PCs)

Fannie Mae (MBS)

Private label MBS

Citi, GE, Prudential

Private label ABS

GMAC and other auto companies

Finance companies

Credit card issuers

Investors

Insurance companies

Pension funds

Mutual funds

Wealthy individuals

MBS

Backed by mortgage loans.

A mortgage loan is a loan secured by real estate

The “mortgage” is a security agreement that gives the lender the right to seize by foreclosure the property securing the loan if the borrower defaults

Mortgage loans are originated by banks and other financial firms.

Once originated, a mortgage loan may be held, sold to an investor for cash, or pooled and securitized.

Mortgage Loan Types

Fixed-rate, level pay (“plain vanilla”)

Term of loan is fixed (30 years is common in US)

Contract rate of interest is fixed for the life of the loan.

Payments (usually monthly) are constant for the term of the loan

The payments fully amortize the loan.

FHA, conventional, conforming, nonconforming, jumbo

Mortgage Loan Types

Graduated payment loans (GPMs)

Low initial payments and period of negative amortization

Graduated equity loans (GEMs)

Fixed coupon with growing payments

Balloons

Adjustable rate mortgages (ARMs)

Various index rates

Caps and collars

Mortgage Loan Payments

The payments on a plain vanilla mortgage are determined by

Initial principal Contract rate of interest Mortgage term in years

For Example

The monthly payments on a $187,000 loan written at 10% for 15 years is

In Excel, you can use the financial function PMT(rate, nper, pv,fv,type)

Mortgage Loan Payments

Each payment consists of

interest equal to i /12 times the amount of principal owing at the time the payment is due, and

scheduled principal repayment

Payments are calculated such that the interest due is paid first and then the remainder of the payment is used to reduce the principal owed.

A table listing the payments and how they are divided between interest and principal is called an amortization schedule.

Amortization Schedule

For example, here are the first few lines of an amortization schedule for a 15-year, 10% fixed rate loan with an initial principal of $187,000

A better way to visualize the amortization process is to look at a graph of the payments

The principal balance remaining after any number of payments can be determined by constructing an amortization schedule or by employing the formula

The logic of this formula is that the principal balance remaining after s payments is always the present value of the remaining 12T-s payments discounted at the contract rate of interest

Graphically

Mortgage Servicing

Servicing

Collection and forwarding of payments

Administration of escrow accounts

Servicing fees

Typically 50 basis points

Right to service loan is sold by owner of mortgage loan

Mortgage Servicing

For example

This servicing annuity is worth about $5,450 at a 9.5% discount rate

Prepayments

Payments made by borrowers in excess of their scheduled loan payments.

Entire (as when the house is sold or refinanced)

Partial (accelerated principal repayment)

Most prepayments are optional to the borrower

put option

Borrower incentives when rates

Rise

Fall

For Example

Consider a mortgage that’s been outstanding for two years and rates have fallen 2%

Prepayments

To the extent that prepayments cannot be perfectly predicted, they create uncertainty about the term of mortgage loans.

This uncertainty is a disadvantage from the standpoint of an investor.

What’s worse: Prepayments are more likely when rates fall and less likely when they rise, so prepayment risk is positively correlated with interest rate risk

Pass-throughs

The simplest type of MBS

Similar mortgages are pooled and

Principal and interest payments are passed through to investors (pro rata)

Less servicing and insurance (credit enhancement) fees

Pass-through cash flows are uncertain because prepayments of mortgages within the pool are uncertain.

Prepayment models

To price a pass-through bond, an estimate of prepayments is needed.

Prepayments will affect the duration of the bonds (Can you see how?)

There are several “models” for estimating prepayments

However, none of these models is designed to describe borrower response to changes in interest rates.

CPR

The constant prepayment rate model assumes a constant percentage of the outstanding principal will prepay each month.

CPR is an annual rate that can be translated to a single monthly mortality rate (SMM) as

An SMM of z% means that z% of the principal remaining in the pool after all scheduled payments have been made will prepay during the month

CPR

For example, a CPR of 6%

Translates to an SMM of .514%

So if you owned a pass-through with a beginning of the month balance of $181,824.99 and $494.30 of scheduled principal payments, then prepayments would be predicted at

PSA