Credit Risk Transfer Mechanisms: formula sheet

Key formulas

Net exposure after credit protection (simple)

Net loss = EAD × LGD − Protected notional × LGD = (EAD − Protected notional) × LGD (assuming the protection seller pays in full)

Use for partial hedges. A CDS pays notional minus recovery, so the protected loss is the protected notional × LGD. Protection only covers the amount stated in the contract. If the protection seller defaults, the hedge payout falls by the unpaid amount.

Loss on a defaulted loan

Loss = EAD × LGD = EAD × (1 − Recovery rate)

Use to size what a transfer is worth. EAD is exposure at default, LGD is loss given default.

Retained first-loss exposure (securitization)

Retained loss = min(Pool loss, Retained tranche size)

If the originator keeps the equity tranche, it absorbs losses first up to that tranche size.

Capital relief (simple illustration)

Capital freed = Risk-weighted assets removed × Capital ratio

Illustrative only. Actual relief depends on the regulatory rules and on whether significant risk is truly transferred.

Protection leg payout

Payout = Notional × (1 − R)

R is the recovery rate (or final auction price as a fraction). Paid only on a credit event.

Annual premium

Annual premium = CDS spread × Notional

Spread in decimals: 120 bp = 0.0120. Quarterly payment ≈ annual premium ÷ 4 (actual/360 conventions may adjust slightly).

Spread approximation (credit triangle)

s ≈ λ × (1 − R)

λ is the annual hazard rate (default intensity). Approximation; assumes a flat hazard rate.

Implied hazard rate

λ ≈ s ÷ (1 − R)

Rearranged form. Used to back out default probability from a quoted spread.

Approximate default probability

P(default within T years) ≈ 1 − e^(−λT)

Use with constant hazard rate. Survival probability = e^(−λT).

Accrued premium on default

Accrual = Spread × Notional × (days since last payment ÷ 360)

Check the day count in the question; the convention is typically actual/360.

Physical settlement

Buyer delivers bonds with face = Notional and receives Notional

Buyer's net loss recovered = Notional − market value of delivered bond.

Tranche loss allocation

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

Attachment and detachment points are in the same units as the loss (₹, $ or % of pool). Equity attaches at 0.

Tranche thickness

Thickness = Detachment point − Attachment point

Thin tranches are more sensitive to pool losses. Their loss given default is often very high.

Subordination (credit enhancement) of a tranche

Subordination = Attachment point = total size of all junior tranches

Loss absorbed by junior tranches before this tranche is touched.

Overcollateralization

OC ratio = Pool principal ÷ Total notes outstanding

A ratio above 1 means the pool exceeds the notes. The excess is a loss buffer.

Excess spread

Excess spread = Pool interest income − Note interest − Servicing and other fees (before losses)

Simple form: pool coupon minus weighted note coupon minus fees, usually measured per year. It is an income flow, not a fixed capital layer. It is used to cover current-period losses before they reduce tranche principal. Any unused excess spread is released to the equity holder or retained in a reserve account, depending on the deal.

Tranche loss as % of its size

Loss % = Tranche loss ÷ (Detachment − Attachment)

Use this to compare tranche losses across structures.

CLN investor cash flows

Coupon ≈ risk-free rate + CDS spread, paid until default; on default, coupons stop and the investor receives par × recovery rate

Approximation. The investor pays par upfront, so the CLN is funded. The investor's principal loss is Notional × (1 − Recovery rate), and no further coupons are paid after default.

CDS payout on credit event

Payout = Notional × (1 − Recovery rate)

The CLN investor's principal loss equals this same amount, Notional × (1 − Recovery rate). The difference is that CLN coupons stop at default.

TRS periodic net payment to receiver

Net = Notional × (Coupon rate + Price % change − (Floating rate + spread))

Price % change is signed: it is negative for a price fall, so a fall reduces the net amount. Do not subtract it a second time. The receiver pays the funding leg and receives the asset's coupon (assuming the asset pays it). A price rise adds to the net amount. Scale the coupon and floating rates by the day-count fraction of the period.

Basic TRS cash flow check

Receiver gains if asset total return > funding rate paid

Total return = coupon yield plus price change over the period.

Retention (skin in the game)

Retained risk = Retained tranche amount ÷ Total securitized pool

Higher retention aligns originator incentives and reduces moral hazard. It is a ratio, not a rule with a fixed required value in the syllabus.

CDS protection buyer's counterparty loss

Loss ≈ max(0, Notional × (1 − Recovery on reference) − Collateral held) if the seller defaults after a reference credit event

Simplified. The buyer is exposed to the replacement cost of protection, not the full notional, unless the credit event has already occurred.

Tranche loss

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

Losses hit the equity tranche first, then mezzanine, then senior. Express attachment and detachment as amounts or percentages of the pool.

Risk-to-cause matching

Hidden information after the deal → moral hazard. Hidden information before the deal → adverse selection.

Use this timing test to separate the two on exam questions.

Quick revision

• A protection buyer pays a periodic premium and receives a payout if a credit event occurs.
• CDS payout on a cash-settled event = notional × (1 − recovery rate).
• Annual CDS premium = spread × notional; 100 basis points = 1%.
• Buying CDS protection on a bond you hold reduces credit risk but adds counterparty risk to the seller.
• Basis risk arises when the reference obligation or terms differ from the exposure being hedged.
• Securitization pools assets and issues tranches with different seniority.
• Losses are absorbed first by equity, then mezzanine, then senior tranches.
• Subordination below a tranche acts as its credit enhancement.
• Credit-linked notes are funded: the investor pays cash upfront and bears the reference credit risk.
• A loan sale transfers the exposure outright; a guarantee transfers risk but may leave the loan on the books.
• Originate-to-distribute models can weaken lending standards through moral hazard.
• Opacity and concentrated protection sellers can turn transferred risk into systemic risk.

Common mistakes

• Saying CRT eliminates credit risk. Fix: Remember risk is moved, not destroyed. The bank often keeps counterparty risk, a retained tranche or reputational exposure.
• Treating a CDS as a loan sale. Fix: A CDS leaves the loan on the balance sheet and moves only the default loss. A loan sale moves the asset.
• Paying out the full notional instead of notional × (1 − R). Fix: Ask what the seller truly loses: par paid minus the value of the bond received. That equals notional × (1 − R).
• Treating a spread in basis points as a percentage. Fix: Divide basis points by 10,000 every time. 150 bp = 0.0150.
• Applying the pool loss rate directly to every tranche. Fix: Losses are allocated bottom-up. Compare the loss in ₹ or $ to attachment and detachment points.
• Using default rate as the loss rate. Fix: Pool loss = pool × default rate × (1 − recovery rate), unless the question gives a loss rate directly.
• Saying a TRS pays only on default, like a CDS. Fix: A TRS passes total return, so it pays on price falls even with no default. A CDS pays only on a credit event.
• Treating a CLN as unfunded. Fix: The CLN investor pays par upfront. That makes it funded and reduces the protection buyer's counterparty risk.
• Mixing up moral hazard and adverse selection Fix: Use timing. Adverse selection is hidden information before the deal (selling the worst loans). Moral hazard is changed behaviour after the deal (weaker screening because risk was passed on).
• Saying CRT removes risk from the financial system Fix: Risk is transferred, not destroyed. It may return through counterparty failure, liquidity strain, or holdings of the same securities by other institutions.

Exam tips

• Questions often test the contrast between benefits (capital, concentration, funding) and risks (counterparty, moral hazard, opacity). Know both lists.
• Be exact on what moves in each tool. A CDS moves risk without moving the asset.
• Watch for absolute words like always or eliminates. They usually mark a wrong option.
• For numbers, compute LGD first, then apply the hedge to the protected amount only.
• Link CRT to the 2007-2009 crisis when an option mentions systemic risk or hidden concentration.
• Always convert basis points to decimals before any calculation, and state which party the question asks about.
• Memorise the pair: payout = notional × (1 − R), and s ≈ λ(1 − R). Most numeric CDS questions reduce to one of them.
• For settlement questions, remember that physical and cash settlement should give the seller the same economic loss, notional × (1 − R), if the delivered bond is worth R × par.