CFA Level II · CFA Level II Exam

Credit Default Swaps: formula sheet

Full chapter guide

Key formulas

Protection buyer's periodic premium: Premium per period = Coupon × Notional × (days in period ÷ 360); Standard coupon is quoted annually. Quarterly payment is roughly coupon ÷ 4 of notional, though the day-count convention is actual/360. Check what the question tells you.
Index CDS notional after a default: Remaining notional = Original notional × (n − defaults) ÷ n; For an equally weighted index of n names. Each name carries notional ÷ n.
Payout on a credit event (single name): Payout = Notional × (1 − Recovery rate); Equals Notional × loss given default. Recovery rate is a fraction of par.
Direction of exposure: Buyer = short credit risk; Seller = long credit risk; Spread widening benefits the buyer and hurts the seller.
Cash settlement payout: Payout = Notional × (1 − Recovery rate); Recovery rate is the auction final price as a percent of par. Equivalent form: Notional × (Par − Auction price) ÷ Par.
Payout using loss given default: Payout = Notional × LGD, where LGD = 1 − Recovery rate; Loss given default is the same figure as the payout percentage.
Physical settlement net result for buyer: Net = Notional (cash received) − Market value of delivered bond (at purchase); Buyer delivers bonds with face value equal to notional and receives par in cash. Economic gain relative to market value of the bond is Notional × (1 − recovery rate).
Credit events (rule list): Bankruptcy, Failure to pay, Restructuring; Restructuring must be a forced change in terms due to deteriorating credit. Not always covered in the contract.
Spread approximation: CDS spread ≈ PD × LGD; PD is the annual probability of default. It is an approximation, so use it when the question says so.
Loss given default: LGD = 1 − recovery rate; Recovery rate is a % of notional recovered after default.
Upfront premium (%): Upfront premium % ≈ (CDS spread − CDS coupon) × effective spread duration; Positive means the protection buyer pays. Negative means the buyer receives.
CDS price: CDS price ≈ 100 − upfront premium %; Quoted per 100 of notional.
Upfront payment: Upfront payment = upfront premium % × notional; Convert the % to a decimal first.
Survival probability: Survival to year n = (1 − h₁)(1 − h₂)…(1 − hₙ); h is the hazard rate, the conditional default probability each year.
Cumulative default probability: PD over n years = 1 − survival to year n; Use this for multi-year default probability.
Implied PD from spread: PD ≈ CDS spread ÷ LGD; Rearranged from the spread approximation.
Change in CDS value since inception (approximation): ΔCDS value ≈ Δspread × risk duration × notional; Use the buyer's view. A positive result means a gain for the protection buyer and a loss for the seller. Δspread is the change in market spread since inception.
Spread change since inception: Δspread = current market spread − market spread at inception; Use the spread for the remaining maturity of the contract, not the original tenor. Do not use the coupon here.
Total MTM relative to the coupon: Total MTM ≈ (current spread − coupon) × risk duration × notional; Uses the fixed coupon (100 or 500 bps), not the original market spread. Positive means value to the protection buyer.
Upfront premium (percent of notional): Upfront premium ≈ (CDS spread − CDS coupon) × risk duration; Positive means the buyer pays the seller. Negative means the seller pays the buyer.
CDS price (per 100 notional): CDS price ≈ 100 − upfront premium (%); Quoted from the protection seller's point of view. A higher spread means a lower price.
Payout at a credit event: Payout = (1 − recovery rate) × notional; This is the loss given default, paid to the protection buyer.
CDS basis: Basis = CDS spread − bond credit spread; Use the bond's Z-spread or similar spread for matching issuer and maturity. Negative: CDS below bond spread. Positive: CDS above bond spread.
Negative basis trade: Buy bond + buy CDS protection; Net carry ≈ bond spread − CDS spread, with credit risk largely hedged. Profit if the basis converges toward zero.
Positive basis trade: Short bond + sell CDS protection; Net carry ≈ CDS spread − bond spread. Bond shorting is hard, so this is less common.
Curve steepener: Sell short-tenor protection + buy long-tenor protection; Profits if long-tenor spreads rise relative to short-tenor. Flattener is the reverse.
Approximate CDS value change: ΔValue ≈ ΔSpread × duration × notional; Protection buyer gains when spreads widen; seller loses. Use the CDS risky duration.

Quick revision

The protection buyer pays the premium; the seller pays if a credit event occurs.
The reference entity is the issuer whose credit risk is covered.
Credit events include bankruptcy, failure to pay and, in some contracts, restructuring.
Settlement can be by auction (cash) or physical delivery of the bond.
Approximate payout is notional × (1 − recovery rate).
Approximate credit spread ≈ annual probability of default (hazard rate) × loss given default.
Approximate upfront premium (% of notional) ≈ (CDS spread − CDS coupon) × effective spread duration. Multiply by notional for the amount. The protection buyer pays the upfront premium when the CDS spread is above the coupon and receives it when the spread is below the coupon. CDS price ≈ 100 − upfront premium %.
Change in CDS value ≈ change in spread × effective spread duration × notional. If the market spread rises above the contract spread, the protection buyer gains.
If the market spread falls, the protection seller gains.
A rising hazard rate means a higher default probability and a higher spread.
Basis = CDS spread − bond credit spread. A negative basis (CDS spread < bond spread) means the bond looks cheap relative to CDS, so buy the bond and buy CDS protection. A positive basis (CDS spread > bond spread) means the bond looks expensive relative to CDS, so sell or short the bond and sell CDS protection. Shorting the bond can be hard to implement in practice.
Buying protection on a bond you hold reduces credit risk but leaves other risks.

Common mistakes

Thinking the protection buyer must own the reference obligation. Fix: A CDS can be bought purely to take a view on credit or hedge another exposure. Ownership is not required.
Saying the protection seller is short credit risk. Fix: The seller is exposed to the loss if default occurs, like holding the bond. The seller is long credit risk.
Treating any missed payment as a credit event immediately. Fix: Check whether the grace period has passed and the missed amount exceeds the minimum in the contract.
Calling a voluntary debt exchange a restructuring credit event. Fix: A restructuring credit event requires terms worsened for creditors because of credit deterioration. Voluntary or market-driven changes do not trigger payout.
Using the full spread instead of spread minus coupon for the upfront premium. Fix: Only the gap between spread and coupon is settled upfront.
Using the recovery rate instead of LGD in spread = PD × LGD. Fix: Always compute LGD = 1 − recovery first.
Giving the gain to the protection seller when the spread widens. Fix: The seller's income is fixed at the old coupon. A wider market spread means the seller is underpaid for the risk, so the seller loses.
Using the original tenor's duration after time has passed. Fix: Use the duration for the remaining life. It falls as maturity approaches.
Mixing up which side of the CDS the basis trade uses. Fix: Negative basis means CDS spread is below the bond spread. The bond pays more, so buy it and buy cheap protection.
Computing basis as bond spread minus CDS spread. Fix: Basis is always CDS minus bond. Carry on a negative basis trade is the reverse, the positive number.

Exam tips

Always label buyer and seller first. Most wrong answers come from reversing the direction of risk.
In an index question, look for the number of names and defaults before doing any arithmetic.
If the vignette gives recovery as a percentage of par, convert it to a fraction and use 1 minus recovery.
Watch the wording on the reference obligation: the CDS covers the entity's credit risk, with the obligation used to define the claim.
Read which party the question asks about. The same event can gain for one side and cost the other.
Read the vignette for the exact event wording: forced versus voluntary, grace period passed or not, and whether the committee ruled.
Write payout as notional × (1 − auction price) before looking at the options. Distractors often show the recovery amount instead.
If the vignette does not state the settlement type, think auction-based cash settlement, but only say so if the question allows it.