As a hypothetical example, Company S has lent 2 billion yen each to five reference entities. Company S buys protection on a first-to-default (FTD) basket of these five, with a notional amount of 2 billion yen, a term of 5 years, and a spread of 7.8% a year (paid once a year). The recovery rate is 40%. Right after the payment at year 3, one entity defaults, and at year 4 another entity defaults. What is Company S's total result, counting the loan losses, the FTD compensation, and the spread it paid?
Quiz: Credit Exotics
Last reviewed: October 4, 2026
This is a draft, shown for review before publication.
4 questions to check your understanding of the chapter “Credit Exotics”. 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.
Question 1
Answer and explanation
Answer: B
Company S's total is a loss of 1.668 billion yen. One year of spread is 2 billion yen × 7.8% = 156 million yen. Company S pays it three times by year 3, so the spread paid is 468 million yen. The loan loss from one default is 2 billion yen × (1 − 40%) = 1.2 billion yen, so two defaults cost 2.4 billion yen. The FTD compensates only the first default, 1.2 billion yen, and the trade ends at the first default. The total is −2.4 billion yen + 1.2 billion yen − 468 million yen = −1.668 billion yen.
The loss of 468 million yen assumes the second loss is also compensated: −2.4 billion yen + 2.4 billion yen − 468 million yen = −468 million yen. FTD compensation stops at one entity. The loss of 1.824 billion yen assumes the spread is paid again at year 4: −2.4 billion yen + 1.2 billion yen − 624 million yen = −1.824 billion yen. The trade ended at year 3, so there is no payment at year 4. The loss of 2.868 billion yen assumes no compensation is received: −2.4 billion yen − 468 million yen = −2.868 billion yen.
Learn more: First-to-Default Baskets
Question 2
As a hypothetical example, the 5-year credit default swap (CDS) spreads of five reference entities are 100bp, 150bp, 200bp, 300bp, and 450bp. In what range does the spread of an FTD on these five entities fall?
Answer and explanation
Answer: C
The FTD spread is at least 450bp and at most 1,200bp. The lower bound is the largest CDS spread among the five entities (450bp). The upper bound is the sum of the five CDS spreads (1,200bp). When the default correlation of the five is 0, the spread equals the sum. When the five default together, the basket is effectively one entity, and the spread equals that of the largest one. An FTD is cheaper than buying a CDS on each entity.
The option starting at 100bp confuses the lower bound with the smallest spread. The option of 450bp to 900bp takes the upper bound as twice the largest spread (450bp × 2 = 900bp), but the sum is the upper bound. The option of 240bp to 450bp confuses the lower bound with the average of the five (1,200bp ÷ 5 = 240bp) and takes the largest single spread as the upper bound. It misses the sum as the upper bound.
Learn more: First-to-Default Baskets
Question 3
As a hypothetical example, a portfolio bundles the CDSs of 100 reference entities, with a notional amount of 1 billion yen each (100 billion yen in total). The recovery rate is 40%. This synthetic CDO is divided into tranches: equity (loss range 0 to 5%, notional 5 billion yen), mezzanine (5 to 15%, notional 10 billion yen), and senior (15 to 100%, notional 85 billion yen). When 20 entities default, what is the loss on the mezzanine tranche?
Answer and explanation
Answer: A
The mezzanine loss is 7 billion yen. When one entity defaults, the portfolio loss is 1 billion yen × (1 − 40%) = 600 million yen. 20 defaults give 12 billion yen, which is 12% of the portfolio. The portfolio loss level at which a tranche starts to bear losses is called the attachment point. The mezzanine attachment point is 5% (5 billion yen), and its detachment point, where the whole principal is lost, is 15% (15 billion yen). Of the 12 billion yen loss, the equity tranche bears the first 5 billion yen, and the mezzanine tranche bears the 12 billion yen − 5 billion yen = 7 billion yen above that. The senior tranche takes no loss.
2 billion yen subtracts the mezzanine notional amount of 10 billion yen from the 12 billion yen loss, instead of the equity part of 5 billion yen. What is subtracted is the attachment point of 5 billion yen. 3 billion yen is the distance left to the detachment point of 15 billion yen (15 billion yen − 12 billion yen). It is the room the mezzanine still has to absorb loss, not the amount it has already borne. 10 billion yen is the notional amount of the mezzanine tranche. It is the loss when the portfolio loss reaches 15 billion yen, and at 12 billion yen the mezzanine has not yet lost all its principal.
Learn more: Synthetic CDOs and Tranches
Question 4
In the tranches of a synthetic CDO, how does the value to the party that takes on the tranche (the protection seller) move for the equity and senior tranches when defaults become more likely to occur in the same period (when default correlation rises)?
Answer and explanation
Answer: D
For the party taking on the tranche, the equity value rises and the senior value falls. When correlation is high, both cases become more frequent: almost no defaults, and many defaults at the same time. The equity tranche bears only the first few defaults, so what it gains when almost no defaults occur outweighs what it loses when many default, and its value rises. The senior tranche takes losses only when many default, so its value falls as that probability rises. The mezzanine tranche has both effects, and they offset each other.
The option that equity falls reasons that bearing losses first makes high correlation more dangerous. The options that both rise or both fall assume the same direction of effect on both tranches. In fact, the way correlation skews how defaults occur works in different directions depending on the order in which a tranche bears losses.
Learn more: Synthetic CDOs and Tranches