CDS on the Senior tranche of the CDO with tranche correlation

[xZhan3765]

A financial firm has sold default protection on the most senior tranche of a CDO. If the default correlation between assets held in the CDO decreases sharply from the correlation used in pricing the CDO tranches, assuming everything else is unchanged, how will the position of the financial firm be impacted?
A. It will either increase or decrease, depending on the pricing model used and the market conditions.
B. It will gain significant value, since the probability of exercising the protection falls.
C. It will lose significant value, since the protection will gain value.
D. It will neither gain nor lose value, since only expected default losses matter and correlation does not affect expected default losses.

Correct Answer:
B

B is correct. The senior tranche will gain value if the default correlation decreases. High correlation implies that if one name defaults, a large number of other names in the CDO will also default. Low correlation implies that if one name defaults, there would be little impact on the default probability of the other names. Therefore, as the correlation decreases, the cumulative probability of enough defaults occurring to exceed the credit enhancement on the senior tranche will also decrease. Hence the investor who has sold protection on the senior tranche will see a gain.

Not sure if I understand this exam sample question. If the correlation is decrease, the senior tranche will have a low probability of default driven by the low tranche correlation. The CDS on the senior tranche will have a tighter spread, and become cheap. The seller should lose money? I am not sure why the seller will gain value.

Thanks and it is my first time post the question, hope that is in the right section.

 

[David Harper CFA FRM]

Hi @xZhan3765 Welcome! I don't think you are alone, this is a question that bugs me because I think it's possible that it might possibly be a harder puzzle to those who are better prepared. The problem, to me, is the first sentence "A financial firm has sold default protection on the most senior tranche of a CDO" because its open to possible misinterpretation. We can infer exactly what is meant, by the answer:

• There exists a cash CDO that has a senior tranche. These are notes and we can think of them as bonds issued by the CDO vehicle except they are protected by subordination; i.e., the Mezz and Junior tranches. In fact, let us think of the senior tranche as a relatively safe cash bond issued by the CDO's SPE.
• The financial firm is a third-party who requires no relationship to the CDO. This firm writes a CDS (sells default protection) on the CDO's senior tranche. Per viewing the senior tranche as a single cash bond, the FI effectively is writing/selling a CDS on a relatively safe bond. This is the essential setup.
• As you correctly note (yay!), when default correlation decreases, the senior tranche (of the CDO, and I am now only referring to this senior cash bond) becomes "safer" such that its spread decreases and the value of this bond increases. As a bond, lower spread --> higher price.
• Separately--and I really do mean separately because when it comes to CDS, the FI requires no involvement in the CDO--the FI has written a CDS on this senior bond that just itself became safer and more expensive. The sold CDS is synthetically long the bond: its value increases just as a long position in the bond in the bond increases when the spread decreases. The price of a CDS moves in the opposite direction of the price of the underlying bond (see my point here at https://forum.bionicturtle.com/thre...atives-1td-cds-trs-cln-crouhy.9311/post-91072). When correlation decreases, this senior tranche becomes safer and more valuable, and the short CDS increases in value along with it (just like a long CDS on the same tranche will drop in value when correlation decreases, because it has a synthetically short position in the underlying).

Hence the problem with the question. If you think too much, the setup lends to possible confusion. Whereas the solution is correct:
"B. It will gain significant value, since the probability of exercising the protection falls."

In my words: when the default correlation drops, the senior CDO tranche (a relatively safe underlying cash bond) is less likely to default, its spread decreases and its value increases. Just as a long CDS (purchased credit protection) on that cash bond decreases in value (two ways to think about this: 1. the cost of new insurance is less; or 2. the long CDS is synthetically short the cash bond), the FI's short CDS (which is synthetically long the cash bond) also increases in value because it is less likely that it will be required to make the contingent payoff (the new spread "insurance" is lower than the old spread). I hope that's helpful,