Effect of Default correlation on CDO's_Sep 10, 6

[Edwin]

The examiner's report says that the value of senior tranches falls while the value of junior ones increases.

I think this means the prices of Senior tranches will rise because they are most attractive hence the most hard hit and prices of equity will decrease because the investors will lose the interest to buy the equity tranch if they certainly know their money will be gone.

Am I right?

 

[Edwin]

Playing around with a simple excel sheet confirmed otherwise.

 

[Oxymoron]

This paper is up for me next, and this thread could serve as a nice prelude.

Edwin,
I'm not sure about the directness of the answer. If I see it right, (assuming only two contracts in the CDO) lesser the default correlation, higher the chance of "A or B" defaulting - and hence, more the probability that the junior tranche will lose out. There is also a higher probability that the senior tranche will lose out but only a lower value, since P(A&B) is low.

As probability increases, "A or B" converges to "A & B", reducing the probability the junior tranche (and the senior) loses out, but increasing the value lost to the senior tranche, since if A defaults, B will also default.

The net difference to the senior tranche will depend upon how much it loses in case A vs B, don't you think?

Edit:
OK - I got it. A few defaults would just have an impact on the junior tranche - but a lot of defaults would creep into the value of the senior tranche as well - thus reducing their value.

 

[Edwin]

This paper is up for me next, and this thread could serve as a nice prelude.

Edwin,
I'm not sure about the directness of the answer. If I see it right, (assuming only two contracts in the CDO) lesser the default correlation, higher the chance of "A or B" defaulting - and hence, more the probability that the junior tranche will lose out. There is also a higher probability that the senior tranche will lose out but only a lower value, since P(A&B) is low.

As probability increases, "A or B" converges to "A & B", reducing the probability the junior tranche (and the senior) loses out, but increasing the value lost to the senior tranche, since if A defaults, B will also default.

The net difference to the senior tranche will depend upon how much it loses in case A vs B, don't you think?

Edit:
OK - I got it. A few defaults would just have an impact on the junior tranche - but a lot of defaults would creep into the value of the senior tranche as well - thus reducing their value.

Actually I thought about it as a basket CDS or a CDO, with 10th to default basket = senior tranche. And same thing for lower tranches,

Let probability of default = 1% for each of 10 baskets. If default correlation = 0, P[>=1 default] = 1-0.99^10 = 0.096. This is the probability of triggering the junior tranche.

If default correlation is exactly 1, P[>=1 default] =0.01. Hence probability of triggering first default decreases making the 1st to default basket or 'CDO junior tranche' expensive.

The opposite can be shown for 10th to default baskets or Senior Tranches.

I.E if default correlation = 0. P[10 defaults] = 0.10 ^10 ~ 0%. If default correlation = 1. P[10 defaults] = 0.01. Thus probability of triggering Senior trance increases with default correlation. Hence the price of 10 th to default basket or Senior tranche decreases. This would have been my answer. Saying value alone perhaps should be explained further e.g examiner report and ASET speak about equity tranche increasing in value but do not explain 'value to who?'