Asset-Backed Security (ABS) Instrument and Market Features: formula sheet

Key formulas

Securitization flow of assets

Borrowers → Seller/Depositor (originates loans) → SPE/SPV (true sale of pool) → ABS investors

Loans move one way to the SPE; cash from investors moves back to the seller as the purchase price.

Source of ABS payments

Investor payments = cash flows from the pooled receivables (interest + principal), net of servicing and trustee fees

Payments depend on the collateral and structure, not on the seller's credit standing.

Role map

Seller = originates and sells | SPE = holds pool, issues ABS | Servicer = collects and administers | Trustee = protects investors | Rating agency = rates tranches

Most exam items test which party performs which role.

Bankruptcy remoteness

True sale of assets to SPE → assets not part of seller's bankruptcy estate

This allows the ABS to be rated on the collateral rather than the seller's own rating.

True sale test (concept)

True sale = legal transfer of ownership of assets to the SPE, so assets are outside the originator's estate

If a court treats the transfer as a secured loan instead, the assets may be pulled back into the originator's bankruptcy.

Credit risk source in ABS

ABS credit risk depends on: collateral pool quality + credit enhancement + SPE structure, not the originator's credit

This is why an ABS can be rated higher than the originator.

SPE features

SPE = separate legal entity + limited purpose + restricted activities and debt

These features make the SPE bankruptcy remote in its own right.

Cash flow chain

Borrowers → servicer → SPE → ABS investors

The originator sells assets to the SPE and receives cash raised from investors.

Overcollateralization amount

Overcollateralization = Collateral value − Face value of securities issued

A positive amount is first-loss protection. Express as a percentage of collateral or of securities, as the question states.

Excess spread

Excess spread = Interest earned on collateral − Interest paid on securities − Fees and servicing costs

Positive excess spread can absorb losses or be trapped in a reserve account.

Loss allocation rule

Losses: junior tranche first, senior tranche last. Cash flows: senior tranche first, junior last.

Losses and payments run in opposite order of priority.

Senior tranche loss threshold

Senior tranche loses only when pool losses exceed (junior tranches + overcollateralization + reserves + trapped excess spread)

Use this to judge how much protection a tranche has.

Internal vs external

Internal: subordination, overcollateralization, excess spread, reserve accounts. External: guarantees, bond insurance, letters of credit.

External enhancement adds the guarantor's credit risk.

Pass-through rate

Pass-through rate = WAC − servicing fee − other fees (such as guarantee fee)

Investors receive less than the borrowers pay. The WAC is the balance-weighted average of loan rates.

Single monthly mortality rate

SMM = Prepayment in month ÷ (Beginning balance − Scheduled principal payment)

Monthly prepayment rate. Do not forget to subtract scheduled principal in the denominator.

SMM to CPR

CPR = 1 − (1 − SMM)^12

Annualizes SMM with compounding. Use the keys y^x or ^ on your calculator.

CPR to SMM

SMM = 1 − (1 − CPR)^(1/12)

Reverse conversion. CPR is an annual rate; SMM is monthly.

PSA benchmark (100 PSA)

CPR = 0.2% × months since origination, up to month 30; then 6% CPR

Month 30 gives 6%. A speed of 150 PSA means 1.5 times the benchmark CPR at each age.

Rate effect on prepayment

Rates fall → prepayments rise → contraction risk. Rates rise → prepayments fall → extension risk.

Negative convexity covers both: capped price gains when rates fall and larger price declines when rates rise.

Auto loan ABS cash flow

Cash flow = interest + scheduled principal + prepayments

Amortizing collateral, so principal is returned over the life of the security.

Credit card ABS cash flow, revolving period

Investor cash flow = interest only; principal collections are reinvested in new receivables

Applies during the lockout or revolving period.

Credit card ABS cash flow, amortization period

Investor cash flow = interest + principal collections

Starts at the scheduled end of revolving or on an early amortization event.

Excess spread (simplified approximation)

Excess spread ≈ collateral yield − (coupon + servicing fee + charge-offs)

This is a simplified approximation. The exact definition varies by deal. Excess spread is a common first line of credit enhancement, and a falling excess spread can trigger early amortization if the deal documents say so.

Asset type and structure

Auto loans: amortizing, prepayment risk. Credit cards: non-amortizing, revolving period.

The core classification rule for the exam.

Cash flow waterfall (priority of payments)

Collateral cash flow → fees → senior interest → mezzanine interest → principal/tests → equity (residual)

Payment goes top down. Losses go bottom up, starting with equity.

Residual to equity

Equity cash flow = collateral cash flow − fees − interest on debt tranches (after tests are met)

Equity is a leveraged residual claim, so its return is the most volatile.

Leveraged equity return (approximate)

Equity return ≈ [Collateral income − fees − debt interest] ÷ Equity invested

A small equity share of capital magnifies gains and losses.

Quick revision

• Securitization turns a pool of loans or receivables into securities paid from the pool's cash flows.
• The originator sells assets to a special purpose entity; investors buy the securities the entity issues.
• The servicer collects payments from borrowers; the trustee protects the interests of investors.
• Bankruptcy remoteness means the assets are legally separate, so the originator's creditors cannot claim them.
• Subordination means junior tranches absorb losses before senior tranches.
• Overcollateralization means the pool's value exceeds the face value of the securities issued.
• Excess spread is the interest from the pool left after paying security interest and costs; it can cover losses.
• Internal credit enhancement is built into the structure; external enhancement comes from a third party.
• Prepayment risk is central in mortgage pools; falling rates usually speed prepayments.
• Credit card ABS have a revolving period during which principal is reinvested, followed by amortization.
• Auto loan ABS pools amortize, and losses relate to defaults and the value of repossessed vehicles.
• A CDO is backed by a pool of debt instruments and is divided into tranches, with equity absorbing losses first.

Common mistakes

• Saying the seller issues the ABS. Fix: The SPE issues the ABS. The seller only sells the receivables to the SPE and receives the proceeds.
• Confusing the servicer with the trustee. Fix: The servicer collects and administers payments from borrowers. The trustee is the fiduciary acting for investors and monitoring the deal terms.
• Thinking ABS investors depend on the originator's credit rating. Fix: Remember the true sale. The assets belong to the SPE, so risk comes from the pool and the credit enhancement.
• Confusing a true sale with a secured loan. Fix: A true sale transfers ownership. A secured loan leaves ownership with the borrower, so the assets stay in its bankruptcy estate.
• Saying senior tranches absorb losses first because they are bigger. Fix: Remember: senior is paid first and loses last. Junior is paid last and loses first.
• Classifying a guarantee as internal credit enhancement. Fix: Anything supplied by a third party outside the structure is external.
• Mixing up contraction and extension risk. Fix: Contraction means the investment life shortens when rates fall. Extension means the life lengthens when rates rise.
• Multiplying SMM by 12 to get CPR. Fix: Use CPR = 1 − (1 − SMM)^12. Multiplying overstates CPR.
• Saying credit card ABS pay principal to investors from day one. Fix: Remember the lockout period: principal collections buy new receivables, and investors get only interest.
• Calling credit card receivables amortizing. Fix: Card balances have no fixed payoff schedule. They are non-amortizing.

Exam tips

• Questions often list a task and ask which party performs it. Memorize one verb per party.
• Remember that the SPE is the issuer, not the seller.
• Link true sale to bankruptcy remoteness and to ratings that rest on the collateral.
• Note that the servicer is often the seller itself, which can be a point in an answer choice.
• Read benefit questions carefully for whose benefit is asked: seller, borrower or investor.
• Expect conceptual questions with no calculations. Read the stem for who is bankrupt: the originator or the SPE.
• Link the words true sale, SPE and bankruptcy remote together. Questions often test the chain of cause and effect.
• Eliminate any option that says investors rely on the originator's credit or that the originator guarantees the ABS.