Structured Credit Risk - Query

[Raj_S]

Hi David et al,
In Malz, Chapter 9: Structured Credit Risk - Page 108, it is said "the equity benefits from high correlation, while the senior bond is hurt by it".
I did not fully understand that.
Say if the defaults rates are high and correlation is high, equity will have more chances of loosing the complete value irrespective of correlation isn't it. Senior tranch is definitely at risk but how is that beneficial to equity tranch??

regards
Subin

 

[ShaktiRathore]

Hi there,
in a basket of bonds the correlation determines the default behavior of senior bond. That is a higher correlation means that when there is a default by junior bond than there is a high chance of default by the senior bond as well due to high correlation of the bonds in the debt structure. So a high correlation increases the default risk of the senior bond because since junior bond is risky a high correlation with it will make the senior bond also risky. So senior bond risk increases thereby hurting it. The equity tranche which gets paid after all the debt interest etc. is paid, as debt becomes more risky due to high correlation the equity investors demand a high return for that extra risk. you can visualize that the beta of equity increases due to more risk introduced with risky debt which increase the expected return that investors demand so equity benefits.

thanks

 

[David Harper CFA FRM]

Hi Subin

You are correct, in a broader sense, that the equity tranche is generally primarily a function of, a sensitivity to, the overall default probability: depending on the params, the equity tranche is significantly risky such that, while increases in default correlation --> decrease its spread (make is safer), it's spread generally dominates the upper tranches nevertheless. So, this statement about the impact of correlation is ceteris paribus, it simply means that, conditional on a holding PD and other params constant, increasing only default correlation will tend to lower the spread (e.g., lower the cost of first to default protection due to lower PD).

The reason equity benefits is that higher default correlation increases the probability that no defaults occur; i.e., higher correlation increases the density in both "tending toward extreme" tails, making both events more likely, that nothing defaults and everything defaults.

The classic use-case is binomial, if the credits all have a given PD = pd, then probability of zero defaults = (1 - pd)^n; e.g., if pd = 1%, n = 10, the p[0 defaults] = 99%^10 = 90.44%. But if correlation increases to 1.0, p[0 defaults] jumps up to 99%. By increasing correlation from zero to 1.0, we've basically made the extreme tail at "no defaults occur" fatter (and also the other tail is fatter, too, where "all default"). I hope that helps,

 

[privatepilot]

David - the above answer has been quite informative to me as well. So thank you for that.

If you don't mind, I can certainly use a quick clarification though.

Could you clarify the basis of the sentence ...But if correlation increases to 1.0, p[0 defaults] jumps up to 99%.

Thanks

 

[steff]

Hi all,

maybe I can help on that subject:

If correlation increases to 1.0, then the credits are perfectly correlated, i.e. if any credit defaults, all default. So in this case, there are only two possible scenarios: all credits default with a probability of pd = 1% or no default with a probability of 1 - pd = 99%.

Hope that helps, regards
Steff

 

[ShaktiRathore]

@privatepilot
also for more clarification try this link:
http://forum.bionicturtle.com/threads/basket-cds.6490/

thanks

 

[David Harper CFA FRM]

Under perfect correlation, 10 credits (n credits) act like a single credit. I think of it like, a single coin is 50/50 (default/no default; the p is too high here but still....). If you flip uncorrelated 10 coins, the ex ante odds of all tails are 50%^10. But if the correlation is 1.0, then the coins are effectively glued together in a stack of one 10-coin-tall coin (imagine them glued in a roll), that either flips heads or tails, with same probability as a single coin, thanks,

 

[privatepilot]

thanks Shakti and David. I get it now.