An Introduction to Securitisation: formula sheet

Key formulas

Securitisation flow

Originator → (true sale) → SPV → issues tranched securities → investors; borrower payments → servicer → SPV → investors

Cash flows pass through the SPV to investors by the priority of the waterfall.

Pool cash flow identity

Cash available to investors = interest collected + principal collected − servicing and other senior fees

The waterfall pays senior tranches first, then lower tranches, with equity last.

Securitisation vs covered bond

Securitisation: investor recourse to the pool only; Covered bond: recourse to the issuer and the cover pool (dual recourse)

Covered bond assets typically stay on the issuer's balance sheet.

OTD incentive rule

Less retained risk ⇒ weaker incentive to screen and monitor

This is a moral hazard problem. Risk retention requirements aim to reduce it.

Waterfall priority (cash)

Fees and expenses → senior interest → mezzanine interest → principal by seniority → equity residual

Exact order depends on the deal documents. Sequential and pro-rata principal payment both exist; read the question.

Loss allocation (losses)

Equity first → mezzanine → senior

Losses are the reverse of the payment order. A tranche loses only when losses exceed the subordination below it.

Subordination (credit enhancement) for a tranche

Subordination = sum of the sizes of all tranches junior to it ÷ total pool balance

Example: ₹ pool of 100 with junior tranches totalling 15 gives 15% subordination to the senior tranche.

Tranche loss

Tranche loss = min(tranche size, max(0, pool loss − attachment point)) in pool-balance terms

Attachment point is the total size of tranches below. Detachment point = attachment point + tranche size.

Excess spread

Excess spread = pool interest income − (note interest + fees and expenses)

Excess spread is available to cover losses. Any remainder can be released to the equity holder or trapped in the SPV.

Tranche thickness

Thickness = Detachment point − Attachment point

Expressed as a percentage of total pool notional.

Tranche loss

Tranche loss = min[ max(Pool loss − Attachment, 0), Detachment − Attachment ]

Work in currency or in percent of pool consistently. Tranche loss rate = Tranche loss ÷ Thickness.

Overcollateralisation

OC amount = Pool principal − Notes issued; OC ratio = Pool principal ÷ Notes issued

The OC amount sits below all note holders and absorbs losses first.

Excess spread

Excess spread = Pool interest income − (Tranche coupons + Fees + Servicing costs)

Often shown as an annualised percentage of pool balance. It is not guaranteed.

Subordination level

Credit enhancement for a tranche = Sum of all tranches below it ÷ Pool size

Equals the tranche's attachment point when the equity piece is included.

Product by collateral

ABS = non-mortgage loans; MBS = mortgages; CDO = bonds, loans or tranches; CLO = corporate loans

Name the collateral first. It sets the main risk.

Re-securitisation

CDO-squared = CDO whose collateral is tranches of other CDOs

Adds a second layer of tranching and raises correlation and model risk.

Tranche loss allocation

Tranche loss = min(max(pool loss − attachment point, 0), detachment point − attachment point)

Losses hit equity first, then mezzanine, then senior. Expressed in same units as pool loss (₹ or %).

Tranche size

Tranche width = detachment point − attachment point

Thin tranches lose their whole value over a small range of pool losses.

CDS premium payment

Annual premium = CDS spread × notional

Paid by the protection buyer, usually quarterly. Example: 100 bps on $50 million = $500,000 per year.

CDS protection payout (cash settlement)

Payout = notional × (1 − recovery rate)

Paid on a credit event. Physical settlement delivers the defaulted bond for par instead.

Tranche loss

Tranche loss = min(max(L − A, 0), D − A)

L is portfolio loss, A is attachment point, D is detachment point. All in the same units (money or % of portfolio).

Tranche thickness

Thickness = D − A

Thin tranches are highly sensitive to a small change in portfolio loss.

Credit triangle (approximation)

Spread ≈ PD (hazard rate) × (1 − recovery rate)

Rough link between a CDS spread and annual default intensity. It is an approximation, not an exact rule.

Tranche loss allocation

Tranche loss = min(max(Pool loss − Attachment point, 0), Detachment point − Attachment point)

Losses hit the lowest tranche first. Express pool loss and the points in the same units, as a percentage of pool or in currency.

Tranche thickness

Thickness = Detachment point − Attachment point

A thin tranche can lose its whole principal on a small change in pool loss.

Correlation effect on tranches

Higher default correlation → equity tranche risk falls; senior tranche risk rises

A general result for typical pools. Mezzanine tranches can move either way depending on structure.

Retained-interest principle

Originator retains part of the credit risk → stronger incentive to screen

This is the logic behind risk retention rules. It reduces moral hazard but does not remove it.

Risk-retention minimum

Retained interest ≥ 5% of securitised exposures (EU and generally US)

Retention may be vertical, first-loss or other permitted forms. The retained piece cannot generally be hedged or sold.

Basel approach hierarchy

SEC-IRBA → SEC-SA → SEC-ERBA → 1,250% risk weight

Use the first approach the bank is permitted and able to apply. Jurisdictions may restrict ERBA use.

Fallback risk weight

RWA = 1,250% × exposure

Equivalent to a full deduction at 8% capital. Applies when no approach can be used.

Capital from RWA

Capital requirement = RWA × minimum capital ratio

At an 8% ratio, a 1,250% weight gives capital equal to 100% of exposure (1,250% × 8% = 100%).

Risk-weight floors

Non-STS: 15%; senior STS: 10%

Floors apply to securitisation exposures under the Basel framework. Check the question for the specific category.

Quick revision

• Securitisation pools assets and sells tranches of notes backed by the pool's cash flows.
• Originate-to-distribute weakens the originator's incentive to screen borrowers if risk is fully sold.
• The SPV is legally separate from the originator, so assets are isolated if the originator fails (bankruptcy remoteness).
• Losses are absorbed from the most junior tranche upward; payments flow from the most senior downward.
• Subordination, overcollateralisation and excess spread are forms of credit enhancement.
• The equity (first-loss) tranche is the most sensitive to defaults; senior tranches are most sensitive to systemic losses.
• Higher asset default correlation raises risk in senior tranches and lowers it in equity tranches.
• A CLO is backed by leveraged loans; a CDO is backed by bonds or other debt, sometimes ABS tranches.
• Synthetic securitisation transfers credit risk with credit derivatives, without selling the assets.
• Ratings reflect default probability or expected loss and can fail when correlation or models are wrong.
• Rating agency conflicts and over-reliance on ratings were major lessons from the subprime crisis.
• Regulation responded with risk retention by originators and tougher capital for securitisation exposures.

Common mistakes

• Treating securitisation and covered bonds as the same thing. Fix: Remember the recourse: covered bonds have dual recourse to the issuer and a cover pool, which usually stays on the balance sheet.
• Saying the SPV is owned and controlled by the originator for bankruptcy purposes. Fix: The point of a true sale is legal isolation (bankruptcy remoteness) of the assets from the originator.
• Assuming that because the originator may consolidate the SPV for accounting purposes, the originator is always liable for the pool's losses. Fix: Remember the point of the SPV is legal isolation. An SPV may be consolidated for accounting purposes but remains legally separate. In a true sale, investors have recourse to the pool, not to the originator's other assets. So the originator is not liable for the pool's losses beyond any retained or contractual exposure. That exposure can be real. A retained first-loss piece, or other contractual support such as representations and warranties or implicit support, does expose the originator to losses.
• Treating synthetic securitisation as moving the loans to an SPV. Fix: In synthetic deals the loans stay on the originator's balance sheet. Credit risk is transferred by credit derivatives or guarantees.
• Allocating losses pro rata across tranches. Fix: Losses go bottom-up in strict order. Senior loses only after all junior tranches are exhausted.
• Measuring tranche loss rate against the whole pool instead of the tranche. Fix: Tranche loss rate = loss in the tranche ÷ tranche size. A 2% pool loss can wipe out a 2% equity tranche entirely.
• Treating MBS as separate from ABS in every context. Fix: Read the question's convention. MBS are asset-backed in a broad sense, but exams usually treat ABS as non-mortgage.
• Saying a CLO is backed by bonds. Fix: A CLO is backed mainly by corporate loans, often leveraged loans. A CDO is the broader term.
• Saying a synthetic securitisation sells the assets to an SPV. Fix: In synthetic deals the originator keeps the assets. Only the credit risk is transferred through a CDS or similar.
• Treating unfunded protection as free of counterparty risk. Fix: Unfunded protection depends on the seller's ability to pay. Funded notes reduce this because cash collateral is held.

Exam tips

• Look for the keyword recourse. It separates securitisation from covered bonds.
• Questions often link OTD to the subprime crisis. Answer with incentives and asymmetric information.
• Watch for absolute words such as always or never. Capital relief and risk transfer depend on conditions.
• Know each participant's role: originator, SPV, servicer, arranger, rating agency.
• Expect applied questions on who does what. Learn one-line roles for originator, SPV, servicer, trustee and rating agency, and use elimination.
• Always draw the tranche stack before any loss or cash calculation. Cash flows down, losses come up.
• Be able to state true sale versus synthetic in one sentence each, including where the assets sit and how risk moves.
• Watch for incentive questions. Originate-to-distribute weakens screening, and the answer often links to retention of a first-loss piece.