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Describe credit derivatives in general along with three specific instruments: the CDS (credit default swap), the total return swap and the CDO (collateralized debt obligation).

FRM® Part II · Credit Risk Measurement and Management · Credit Derivatives · FRM2.CR.13.a

The idea

A credit derivative is a contract whose payoff depends on the creditworthiness of a reference entity, so credit risk can be moved without selling the underlying loan or bond. In a credit default swap (CDS) the protection buyer pays a periodic spread. If a credit event occurs, the buyer receives notional less the post-default value of the reference obligation. With R the post-default value as a fraction of face, the payout is: Payout = (1 − R) × notional. A total return swap (TRS) passes the full return of an asset, coupons plus price gains and losses, from the payer to the receiver in exchange for a funding rate plus a spread. It therefore transfers market risk as well as default risk. A collateralized debt obligation (CDO) slices portfolio losses into tranches, equity first, then mezzanine, then senior. The common error is to think a CDS pays on any price fall. It pays on a credit event, not on a price fall.

Formulas

CDS payout on a credit event

payout = (1 − R) × notional

R
the recovery rate, the post-default value of the cheapest deliverable as a share of par
notional
the CDS notional

Paid only after a credit event. Paying R × notional or the full notional are the two classic errors.

Net settlement to a total return receiver

net = coupon + price change − funding

coupon
the coupons on the reference asset
price change
the change in the asset's price over the period, negative for a fall
funding
the funding rate plus spread applied to the notional

The receiver has the economics of owning the asset. Leaving out the coupon, or adding a price fall, are the usual slips.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a total return swap on a corporate bond, which party bears the loss if the bond's price falls with no default?

  1. The total return payer, who keeps the bond and still receives the funding payments whatever the price does.Why not: Reverses the roles: the payer passes the bond's return to the receiver, so a price fall is an amount the receiver owes.
  2. Neither party, because a total return swap settles only when the issuer suffers a credit event.Why not: Confuses the TRS with a CDS: a TRS passes all price changes, not only default losses.
  3. The total return receiver, who pays the price decline to the payer as part of the swap settlement. - correct
  4. Both parties equally, because the swap settles at the average of the bond return and the funding rate.Why not: Invents a sharing rule; the receiver bears the whole price change and the payer bears none of it.

The TRS receiver gets coupons and price appreciation and pays price depreciation plus a funding cost, so it has the economic exposure of owning the bond. A TRS transfers market risk as well as credit risk.

A harder one

A bank bought five-year protection on USD 20 million notional of a company's debt through a CDS with a spread of 120 bp per annum paid quarterly. The company defaults just after a premium date, and the cheapest-to-deliver bond is worth 35 percent of face. What does the protection seller pay?

  1. USD 7.00 millionWhy not: Pays the recovery value (R x notional) instead of the loss given default (1 - R) x notional.
  2. USD 13.00 million - correct
  3. USD 20.00 millionWhy not: Pays the full notional, ignoring the 35 percent value the bank can recover on the defaulted bond.
  4. USD 13.24 millionWhy not: Adds a full year of premium (120 bp x notional) to the payoff; the premium is the buyer's payment, not part of the seller's payout.

Payout = (1 - R) x notional = 0.65 x 20 = USD 13.00 million. Because default came right after a premium date, there is essentially no accrued premium to net.

The hardest tier

A synthetic CDO references 80 names with USD 12.5 million notional each (USD 1,000 million in total) and a recovery rate of 25 percent on every name. The equity tranche covers 0 to 5 percent of the portfolio and the mezzanine tranche covers 5 to 15 percent. After 11 names default, what loss is allocated to the mezzanine tranche?

  1. USD 87.5 millionWhy not: Ignores recovery: uses the full notional of the defaulted names as the loss.
  2. USD 103.1 millionWhy not: Allocates the whole portfolio loss to the mezzanine tranche without first letting the equity tranche absorb its 50 million.
  3. USD 53.1 million - correct
  4. USD 34.4 millionWhy not: Applies the 25 percent recovery rate as the loss rate and ignores the first-loss equity tranche.

Loss per default = 12.5 x 0.75 = 9.375; total loss = 11 x 9.375 = 103.125. Equity absorbs the first 50, so mezzanine loses 103.125 - 50 = 53.125, below its USD 100 million size.

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