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Correlation in Senior and Subordinated Basket CDS

Vikas31

New Member
Hi,
In case of high default correlation, it is stated that Senior tranches become riskier and junior tranches become less riskier.
I am not clear as to why junior tranches would become less risky, because the risk they carry would still be the same as in case of lower correlation and they would be first to be affected. Though the senior tranches would surely become riskier now.

If I am missing something please let me know.

regards,
Vikas
 

ShaktiRathore

Well-Known Member
Subscriber
Its better to take risk of junior tranche relative to some benchmark.Due to low correlation the junior tranche is more riskier than senior tranche while with high correlation the the junior tranche has become less riskier than senior tranche relatively. So relative to senior tranche the risk of equity tranche has increased.
If senior tranche has risk x in two portfolios of tranches then in high correlation portfolio of tranche the risk of junior tranche is y almost equal to x or we may say approx. x=y ,in other portfolio of low correlation the risk of junior tranche z>x. From above it is clear z>y that means junior tranche is less riskier now in high correlation portfolio than the low correlation portfolio.
In case of high default correlation also as well as low default correlation the senior tranches have very high ratings so there probability of default is usually lower. In case of low correlation the junior tranche will suffer the loss first and the senior tranche will not be affected very much due to low correlation however in case of high correlation if the junior tranche suffers a loss the chances of senior tranche suffering the losses increases significantly thus the risk of the senior tranche increases as the risk of senior tranche approaches that of junior tranche similarly the risk of junior tranche becomes less as the default probability of senior tranche is less that means probability of default for junior tranche is also less due to high correlation that means the probability of default of junior tranche has decreased if not increased as compared to if there was low correlation.
I hope u understood it.
thanks
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Vikas,

To put number's on Shakti's statement, the classic example is: assume (n) credits each with the same (eg) pd = 1%.
  • If default correlation is zero, PD[1st-to-default; i.e., one default | rho =0 ] = 1-99%^n;
  • but if default correlation increases to 1.0, PD[1st-to-default; i.e., one default | rho = 1.0] = 1%, which is lower if not much lower.
  • For example, if n = 20, PD[1TD | rho = 0] = 1-99%^20 = 18%, up from 1% if rho=1.0
More here http://www.bionicturtle.com/forum/threads/basket-tranches-value-and-risk.5901/#post-17330

hope that helps, thanks,
 
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