correlation是负的，为什么joint default frequency增加？

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136. You are considering an investment in the mezzanine tranche of a tranched basket default swap (TBDS) constructed from a basket of N assets. The TBDS is structured such that the junior tranche is exposed to the first four defaults, the mezzanine tranche to the fifth, sixth, seventh and eighth defaults, and the senior tranche to the ninth and higher defaults. The risk of this investment increases as:

a. The number of assets in the basket, N, increases and the default correlation of the assets becomes closer to zero.

b. The number of assets in the basket, N, increases and the default correlation of the assets becomes more negative.

c. The number of assets in the basket, N, decreases and the default correlation of the assets becomes closer to zero.

d. The number of assets in the basket, N, decreases and the default correlation of the assets approaches becomes negative.

Answer: b

我选的是a,不明白为什么default correlation of the assets becomes more negative的时候违约率增加

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关键词：correlation Frequency relation Default fault Default correlation joint Frequency

我是这样认为的，zero的时候发生多个default的风险是比较小的，negative的，我觉得可以负负得正，N的数目很多情况下就会出现很多asset的关联性是接近1的，很可能发生同时违约

default correlation非平时说的RETURN CORRELATION.

DEFAULT CORRELATION如果很大（接近+1），说明ASSETS同时default或者没有任何DEFAULT发生（发生5-8个assets 出现joint default的概率不大）。如果为负，则说明不管什么情况，部分ASSETS (一定）会发生DEFAULT的概率增加（即发生5-8个ASSETS 出现joint default的概率增加），所以这个时候mezzanine tranche 风险更大。

也可用数学公式表达，不过会很复杂应该不是考题的意图，所以从感觉上出发就可以了。

P(A+B) = P(A) + P(B) - P(AB) = P(A) + P(B) - P(A)*P(B) - rho*sigma(A)*sigma(B)

given A, B are binary r.v. It should clear your question.