Quiz: CDS

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6 questions to check your understanding of the chapter “CDS”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.

1. Question 1

   As a hypothetical example, a bank buys protection through a credit default swap (CDS) with a notional amount of 5 billion yen, a spread of 80bp (0.8% a year), and a term of 5 years, and pays the premium every three months. After the premium payment at 1 year, a credit event occurs on the reference entity, and cash settlement sets the price of the debt at 40% of face value. What is the bank's profit or loss on the CDS?

   1. A.A profit of 1.96 billion yen
   2. B.A profit of 2.99 billion yen
   3. C.A profit of 2.96 billion yen
   4. D.A profit of 3.04 billion yen
   Answer and explanation

   Answer: C

   The bank makes a profit of 2.96 billion yen on the CDS. Each premium payment is 5 billion yen × 0.8% ÷ 4 = 10 million yen. The bank pays four times in the year, so the premiums paid total 40 million yen. In cash settlement, the protection seller pays the difference between face value and the price of the debt. The bank receives 5 billion yen × (100% − 40%) = 3 billion yen. The profit is 3 billion yen − 40 million yen = 2.96 billion yen. Premium payments stop once the event has occurred.

   A profit of 1.96 billion yen mistakes the 40% price of the debt for the amount received. It takes the amount received to be 5 billion yen × 40% = 2 billion yen. Subtracting the premiums gives 2 billion yen − 40 million yen = 1.96 billion yen. The seller pays the difference from face value, not the price. A profit of 2.99 billion yen subtracts only one premium payment: 3 billion yen − 10 million yen = 2.99 billion yen. A profit of 3.04 billion yen treats the premiums as received and adds them: 3 billion yen + 40 million yen = 3.04 billion yen. The protection buyer pays the premium to the seller.

   If no credit event occurs in the 5 years, the bank receives nothing from the seller. The premiums it paid, 5 billion yen × 0.8% × 5 years = 200 million yen, become its loss on the CDS.

   Learn more: Credit Default Swaps (CDS)

2. Question 2

   Which statement about CDS is incorrect?

   1. A.When the reference entity's credit quality falls and the spread rises, a CDS entered into earlier gains value for the buyer and loses value for the seller
   2. B.The credit risk a protection seller bears does not include the risk that its counterparty defaults
   3. C.Both the buyer and the seller can trade without holding the reference entity's debt
   4. D.Even when a loan incurs a loss, the CDS may make no payment if the credit event conditions are not met
   Answer and explanation

   Answer: B

   The incorrect statement is that the credit risk a protection seller bears does not include the risk that its counterparty defaults. In addition to the reference entity's credit risk, the seller bears the risk that its counterparty defaults.

   The other statements are correct. When the spread rises, a buyer who holds protection at a low spread that would now cost a higher spread gains, and a seller who took on the same risk at the low spread loses. Protection can be bought or sold without holding the reference entity's debt. The credit event conditions of a CDS are generally not the same as the conditions that count as a default under a bond or loan contract, so a loan you thought you had hedged can incur a loss without the CDS paying.

   Learn more: Credit Default Swaps (CDS)

3. Question 3

   As a hypothetical example, in an auction for a reference entity's debt, the first-stage midpoint was 30 and the open interest was 15 billion yen to sell. The second-stage buy limit orders, from the highest price down, were 4 billion yen at 32, 5 billion yen at 31, 8 billion yen at 29, and 10 billion yen at 27. Prices are per 100 of face value, and assume the final price stays within the cap on its distance from the midpoint. What is the final price?

   1. A.32
   2. B.31
   3. C.30
   4. D.29
   Answer and explanation

   Answer: D

   The final price is 29. When the open interest is to sell, buy orders are matched from the highest price down, and the price of the last order used to fill the full amount becomes the final price. Adding from the top gives 4 billion yen through 32, 9 billion yen through 31, and 17 billion yen through 29. The order at 29 is the one that reaches 15 billion yen, so the final price is 29. This final price becomes the recovery rate used to settle the CDS. The protection seller pays (100 − 29) ÷ 100 = 71% of the notional amount.

   32 is the price of the highest buy order. The first order alone is 4 billion yen, which falls short of 15 billion yen. 31 is the price of the last order before the total reaches 15 billion yen. 30 is the first-stage midpoint, which becomes the final price only when the open interest is zero.

   Learn more: Credit Events and Settlement

4. Question 4

   Which statement about physical settlement of a CDS is correct?

   1. A.The seller delivers debt of the reference entity to the buyer, and the buyer pays the face value
   2. B.The buyer can deliver any debt of the reference entity, and the contract does not limit which debt
   3. C.The buyer delivers debt of the reference entity to the seller, and the seller pays the face value
   4. D.A buyer that bought protection without holding bonds can settle without obtaining any debt
   Answer and explanation

   Answer: C

   In physical settlement, the buyer delivers bonds, loan claims, or other debt of the reference entity to the seller, and the seller pays the face value. As a hypothetical example, take a CDS with a notional amount of 1 billion yen, where the price of the debt falls to 25 per 100 of face value. The seller pays 1 billion yen and receives bonds worth 250 million yen, so it bears a loss of 750 million yen.

   The choice in which the seller delivers the debt to the buyer has the direction of delivery reversed. It is the protection buyer that delivers the debt, and the seller pays the face value. The contract determines which debt can be delivered. A buyer that bought protection without holding bonds must also obtain bonds in the market to settle.

   Learn more: Credit Events and Settlement

5. Question 5

   As a hypothetical example, you value a CDS with a notional amount of 1 billion yen, a 5-year maturity, and quarterly premium payments in arrears (every period is treated as 0.25 years long). The hazard rate is 2% and the interest rate is 1% continuously compounded; both are constant until maturity and independent of each other and of the recovery rate. If the recovery rate is raised from 40% to 60%, what happens to the par spread and the RPV01 (the difference in the value of the premium leg when the premium differs by 1bp)?

   1. A.The par spread falls, and the RPV01 does not change
   2. B.The par spread falls, and the RPV01 falls
   3. C.The par spread rises, and the RPV01 does not change
   4. D.The par spread rises, and the RPV01 falls
   Answer and explanation

   Answer: A

   The par spread falls, and the RPV01 does not change. The protection leg covers the loss, which is face value minus the amount that can be recovered. The higher the recovery rate, the smaller the value of the protection leg. The par spread is roughly proportional to the hazard rate and to (1 − recovery rate). This relationship is called the credit triangle, and as a formula it is $S_p \approx \lambda (1 - R)$ (where $S_p$ is the par spread, $\lambda$ is the hazard rate, and $R$ is the recovery rate). Raising the recovery rate from 40% to 60% changes (1 − recovery rate) from 0.6 to 0.4, so the par spread becomes two-thirds of its value. Under these conditions, it falls from 120.15bp to 80.10bp.

   The RPV01 shows how much the value of the premium leg changes when the premium changes by 1bp. The value of the premium leg does not include the recovery rate, so the RPV01 stays at 463,727 yen. The choices in which the RPV01 falls confuse the recovery rate with the hazard rate. Raising the hazard rate lowers the survival probability, and the RPV01 falls. The choices in which the par spread rises get the direction of the effect of a higher recovery rate backward.

   If the recovery rate is lowered from 40% to 20%, (1 − recovery rate) becomes 0.8, and the par spread rises to 160.20bp.

   Learn more: Pricing a CDS

6. Question 6

   As a hypothetical example, you hold protection on a CDS index of 100 equally weighted names, with a notional amount of 5 billion yen and a coupon of 100bp (1% a year). A credit event occurs on one of the constituents. The event determination date falls on a payment date, and an auction that finishes before the next payment date sets the recovery rate at 40%. Which statement about the payment and later coupons is correct?

   1. A.The seller pays 50 million yen, and later coupons are calculated on a notional amount of 4.95 billion yen
   2. B.The seller pays 30 million yen, and later coupons are calculated on a notional amount of 4.95 billion yen
   3. C.The seller pays 30 million yen, and later coupons are calculated on a notional amount of 5 billion yen
   4. D.The seller pays 50 million yen, and later coupons are calculated on a notional amount of 5 billion yen
   Answer and explanation

   Answer: B

   The seller pays 30 million yen, and later coupons are calculated on a notional amount of 4.95 billion yen. When a credit event occurs on a constituent, the protection seller pays the loss for that name's weight. Each name has a weight of 1/100 (1%). The seller pays 5 billion yen × 1% × (1 − 40%) = 30 million yen. The index administrator publishes a new version in which that name's weight is set to 0, and the notional amount of the trade falls by that name's weight. The notional amount from then on is 5 billion yen − 5 billion yen × 1% = 4.95 billion yen. The coupon on the next payment date is 4.95 billion yen × 1% ÷ 4 = 12,375,000 yen.

   The choices in which the seller pays 50 million yen do not reduce the loss by (1 − recovery rate) and treat the notional amount for the one name's weight as paid in full: 5 billion yen × 1% = 50 million yen. The seller pays the loss net of the 40% that can be recovered. The choices that keep calculating on a notional amount of 5 billion yen overlook that the new version reduces the notional amount.

   Even without a credit event, the protection buyer takes a mark-to-market loss if views on the creditworthiness of the constituents improve and the spread tightens. If the spread widens, the buyer has a mark-to-market gain.

   Learn more: CDS Indices (iTraxx, CDX)