Default probability of a bond portfolio

[nudiekap]

Hi There,

I was hoping that someone would be able to explain how I can calculate a default probability.

I have a portfolio containing 10 bonds, all with a default probability of 10% (for simplicity the LGD and correlation is assumed to be zero). I know that the probability of 0 defaults is (1-0,1)^10 = 0,3487 and that the probability of all bonds defaults is 0,1^10 = infinite small number, but I can't figure out how to calculate the probability of 5 bonds will default. I know that the result is 0,00148803 but how do I get that?

Thanks in advance!

 

[ShaktiRathore]

nudiekap u should know binomial distribution right,
Total combinations for 5 bonds default is 10C5=10.9.8.7.6/120=28*9=252
Now Acc toBinomial distribution, prob. for 5 bonds to default=10C5*.1^5*.9^5=252*.09^5=.0014880348

 

[nudiekap]

Thanks for your explanation Really appreciate it!