Fixed-Income Securitization: formula sheet

Key formulas

Basic flow of securitization

Originator → sells loan pool → SPE → issues ABS → investors; investors' cash → SPE → originator

Loans move one way; cash for the loans moves the other way.

Source of payments to investors

Borrower payments → servicer → SPE (or trustee) → ABS holders

Investors depend on the pool's cash flows, not the originator's credit.

Benefits to the originator

Lower funding cost + new funding source + liquidity + balance sheet relief

Funding cost can fall because the securities' credit quality depends on the pool and credit enhancement, not the originator.

Benefits to investors

Access to new risk-return profiles + diversification + liquidity of tradable securities

Tranching lets investors pick the risk level they want.

Loan-to-value ratio

LTV = Loan amount ÷ Property value

Property value is usually the lower of purchase price and appraised value. Higher LTV means higher credit risk for the lender.

Level payment on a fully amortizing loan

Payment = PV × r ÷ [1 − (1 + r)^(−n)]

r is the periodic rate (annual rate ÷ 12 for monthly payments). n is the number of payments. On the calculator, set N, I/Y, PV, then CPT PMT.

Interest-only payment

Payment = Loan balance × periodic rate

The balance does not fall during the interest-only period, so the full principal is still owed afterwards or at maturity.

Adjustable-rate mortgage rate

New rate = Reference rate + Margin (subject to caps and floors)

The margin is fixed for the life of the loan. The reference rate changes at each reset date. An ARM shifts interest rate risk to the borrower, because the payment can rise.

Recourse vs non-recourse rule

Recourse: claim on property + borrower's other assets. Non-recourse: claim on property only.

Non-recourse lending gives the borrower a put-like default option and so increases lender credit risk.

Single monthly mortality (SMM)

SMM = prepayment in the month ÷ (beginning balance − scheduled principal payment)

The denominator is the balance after scheduled principal, not the beginning balance.

CPR from SMM

CPR = 1 − (1 − SMM)^12

Do not multiply SMM by 12. That overstates CPR.

SMM from CPR

SMM = 1 − (1 − CPR)^(1/12)

Use when the question gives an annual CPR and asks for monthly prepayment.

Weighted average coupon (WAC)

WAC = Σ (loan balance ÷ pool balance) × loan rate

Weights are outstanding balances.

Weighted average maturity (WAM)

WAM = Σ (loan balance ÷ pool balance) × remaining months

Remaining term, not original term.

Pass-through rate

Pass-through rate = WAC − servicing and other fees

Investors earn the pass-through rate, which is below WAC.

PSA benchmark

100 PSA: CPR = 0.2% × month for months 1 to 30; CPR = 6% after month 30. For x PSA, multiply by x ÷ 100

Example: at 150 PSA in month 10, CPR = 0.2% × 10 × 1.5 = 3.0%.

Sequential-pay principal rule

All principal → Tranche A until retired; then B; then C; interest paid on each tranche's outstanding balance

Short tranches have contraction risk; the longest tranche has extension risk.

Interest on a tranche

Interest = tranche coupon ÷ 12 × beginning-of-month balance

Use the balance outstanding at the start of the period. Monthly pay is typical.

PAC protection

PAC schedule holds if prepayment speed stays within the collar (lower PSA to upper PSA)

The support tranche absorbs variation. If support tranches are exhausted, PAC protection fails.

Floater and inverse floater coupons

Floater coupon = reference rate + spread; Inverse floater coupon = K − L × reference rate. With a zero spread: L = floater principal ÷ inverse floater principal, and K = C × (1 + L), where C is the fixed coupon of the underlying tranche.

K and L both depend on the principal split and on the fixed coupon C. With L set this way, the reference rate cancels out in the principal-weighted average, so the weighted average coupon of the floater and inverse floater equals C. Example: C = 6%, floater $40 million, inverse floater $20 million. L = 2 and K = 18%. Weighted average = (40 × R + 20 × (18% − 2R)) ÷ 60 = 6%.

Risk conservation

Total prepayment risk of the CMO = prepayment risk of the collateral

A CMO redistributes risk. It does not eliminate it.

Debt service coverage ratio (DSCR)

DSCR = Net operating income ÷ Debt service

Higher is safer. A DSCR below 1 means income does not cover the loan payments.

Loan-to-value ratio (LTV)

LTV = Loan amount ÷ Appraised property value

Lower is safer. Appraisals can be stale, so treat LTV with care.

Amortizing vs non-amortizing pools

Auto loans: amortizing. Credit cards: non-amortizing (revolving period, then amortization)

Credit card ABS investors receive interest only during the revolving period.

Balloon payment (concept)

Balloon payment = Remaining loan balance at maturity

Balloon risk is the chance the borrower cannot refinance it. This is extension risk.

CMBS call protection forms

Loan level: lockout, defeasance, yield maintenance, prepayment penalty. Structure level: sequential tranche priority

Lockout bars prepayment. Defeasance replaces the loan collateral with a portfolio of securities, usually government securities, whose cash flows cover the remaining payments.

Overcollateralization amount

Overcollateralization = Collateral value − Face value of securities issued

Example: ₹ or $ collateral of 110 backing 100 of bonds gives 10 of cushion; losses up to 10 hit the cushion first.

Overcollateralization ratio

Collateral value ÷ Face value of securities

A ratio above 1 (more than 100%) means the structure is overcollateralized.

Loss allocation in subordination

Losses hit the most junior tranche first, then the next, and the senior tranche last

Payments of interest and principal go in the opposite order: senior first.

Covered bond recourse

Dual recourse = claim on issuer + preferred claim on cover pool

Assets stay on the issuer's balance sheet; no SPE sale is needed.

Quick revision

• Securitization moves loans to an SPE, which issues securities backed by the pool's cash flows.
• The SPE is legally separate from the originator, which isolates the assets from the originator's bankruptcy.
• A fixed-rate mortgage pays level payments, with interest falling and principal rising over time.
• Recourse loans let the lender claim other assets of the borrower; non-recourse loans limit the claim to the collateral.
• Prepayments tend to rise when rates fall, which creates contraction risk.
• Prepayments tend to slow when rates rise, which creates extension risk.
• Pass-through securities pass interest, scheduled principal and prepayments to investors, net of fees.
• CMO tranches redistribute prepayment risk but do not remove it from the pool.
• CMBS loans are usually non-recourse and have call protection (prepayment penalties, defeasance, lockouts), whereas residential mortgages are typically prepayable without such protection; recourse varies by jurisdiction.
• Credit enhancement can be internal, such as subordination and overcollateralization, or external, such as a guarantee.
• Covered bonds are obligations of the issuer, backed by a cover pool that stays on its balance sheet. The cover pool is dynamic: the issuer must replace defaulted or prepaid assets. Investors also have recourse to the issuer.
• Read the question for who bears the risk and in which rate environment before choosing an option.

Common mistakes

• Saying the originator issues the ABS. Fix: The SPE issues the ABS after buying the pool. The originator only sells the loans.
• Thinking investors rely on the originator's credit. Fix: ABS investors rely on the pool's cash flows, the structure and credit enhancement, because the assets sit in the SPE.
• Saying the borrower carries interest rate risk on a fixed-rate mortgage. Fix: Ask who is hurt when market rates move. On a fixed-rate loan, the lender is stuck with a below-market rate when rates rise. On an ARM, the borrower's payment changes.
• Thinking an interest-only loan reduces the principal. Fix: During the interest-only period, the payment equals balance × periodic rate and the balance stays the same. Principal is repaid later or as a balloon.
• Multiplying SMM by 12 to get CPR Fix: CPR is compounded: CPR = 1 − (1 − SMM)^12. The answer is always a bit below 12 × SMM.
• Dividing prepayment by the beginning balance when computing SMM Fix: Subtract scheduled principal from the beginning balance first, then divide.
• Saying a CMO eliminates prepayment risk. Fix: Remember that the risk is redistributed. Whatever the PAC avoids, the support tranche bears.
• Thinking the support tranche is protected. Fix: Support means it supports the PAC by absorbing prepayment variation. It has the most risk and the highest yield.
• Saying credit card ABS pay principal from the start. Fix: Remember the revolving period: investors get interest only, and principal collected buys new receivables.
• Treating CMBS as having the same prepayment risk as residential MBS. Fix: CMBS have loan-level call protection and tranche priority, so prepayment risk is lower.

Exam tips

• Memorize the roles: originator, SPE, servicer, trustee, underwriter, rating agency. Many items are pure matching.
• When you see 'bankruptcy remote', link it to the true sale to the SPE.
• For benefit questions, first name the party, then choose the benefit that fits it.
• There are three options only, so discard any that reverse the cash flow direction or make the originator the issuer.
• Do not spend time on calculations here. This topic is mostly conceptual, so answer fast and save time for numerical items.
• Expect one-line conceptual items that ask who bears a risk. Learn the feature-to-risk pairs by heart.
• Questions on recourse often test the borrower's default option. Non-recourse makes default more attractive when the home is worth less than the loan.
• For LTV, read which value the stem tells you to use before dividing. Lower-of-two is a common trap.