[ 2009 FRM Sample Exam ] Quantitative Analysis Q18 individual, references, corporate, following, default

lalamei

 

18. A standard synthetic CDO (basket credit default swap) references a portfolio of ten (10) individual corporate names. Assume the following:

The total reference notional (basket notional) is X, and the term is Y years

The reference notional per individual reference credit name is X/10 (i.e. equal weight per name)

The default correlations between the individual reference credit names are all equal to one (1.0)

The single-name credit default swap (CDS) spread for each individual reference credit name is 100 basis points, for a term of Y years

The assumed recovery rate on default for all individual reference credits is zero in all cases

The synthetic CDO comprises two tranches, a 50% junior tranche priced at a spread J, and a 50% senior tranche priced at spread S

All else held constant, if the default correlations between the individual reference credit names are reduced from 1.0 to 0.7, what is the effect on the relationship between the junior tranche spread J and the senior tranche spread S?

A. The relationship remains the same

B. S increases relative to J

C. J increases relative to S

D. The effect cannot be determined given the data supplied

lalamei

 

Correct answer is Cfficeffice" />

If the default correlations are initially all 1.0, then the only possible outcomes are that all issuers default at once, or no issuers default.  Given the zero recovery assumption, a default would then affect the junior and senior tranches equally.  Therefore the spreads on the junior and senior tranches would be identical (50bps and 50bps, since the total spread across the entire basket must be equal to the 100bps spread of all individual reference credits). 

If the correlation is reduced below 1.0 to 0.70, there are some outcomes where only some issuers default; these cases will impact the junior tranche more than the senior tranche.  However, the overall average default rate remains the same.  This means that at a correlation less than 1.0, the junior tranche bears more of the risk than the senior tranche.  Therefore, the spread on the junior tranche will increase relative to that of the senior tranche, because the total spread across the entire basket must remain 100bps.  The correct choice is C.

lumi

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wuna

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vory

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