Risk of the complete portfolio, Financial Management

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(a) Presume we have a portfolio of n names with some default correlation ρ. The risk of the complete portfolio moves according to the change in default correlation. Alternatively if the portfolio is trenched according to the order of their defaults then a variety of tranches behave differently as ρ changes. For instance a high ρ indicates subsequent defaults occurring together where as a low ρ makes occurrence of subsequent defaults more or less independent.

(b) As default correlation raises the area under the middle part of the default density function decreases and the mass on the two extreme tranches increase. Therefore area under the subordinate tranche increases which means that the probability that the subordinate tranche loses all its money decreases. Therefore the risk for this tranche decreases along with the spread.

Alternatively the cushion for the senior tranches decreases as default correlation increases. Therefore it is more likely that the protection seller for the senior tranches will concede some losses.

Therefore the risk and hence the spread for this tranche increases.

(c) With a diminish in default correlation one should long on protection on the subordinate tranches and short on protection on the senior tranches.

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