Probability of default on loans

lindah · 2011-04-22 18:45:10

Hi guys,

May I confirm if my working is correct for this question:

In a portfolio of loans 70% are rated good with the probability of default of 0.001, 25% standard with the probability of default 0.01 and 5% stressed with the probability of default 0.1. If two loans are chosen at random what is the probability that exactly one of them will default?

I've calculated the probability of default as:
P(default) = P(default | Good) P(Good) + P(default | Standard) P(Standard)+ P(default |Stressed) P(Stressed)
= (0.001 x 0.7) + (0.01 x 0.25) + (0.1 x 0.05)
= 0.0082 or 41/5000
The probability of not defaulting is, per the complementary rule is:
1 - 0.0082 = 0.9918

Now this is where I am not sure of myself:
Is the P(exactly one default) simply:
1) 0.0082 x 0.9918 or is it
1) 41/5000 x 4959/4999 - because of no replacement?

Thanks in advance for any feedback
Lin

bobbym · 2011-04-22 20:36:11

Hi lindah;

I am doing it like this:

There are these combinations, where B stands for bad what you called Stressed. M stands for Standard. G is for good. The small d means that is the one that defaulted.

I get for that:

As the probability of exactly one defaulting.

lindah · 2011-04-23 12:25:37

Hi bobbym;

Thanks for setting it out that way, it makes it so much clearer than (0.0082 x 0.9918)!!!
As always I try to over-complicate probability questions

Thank you very much.
Lin

Last edited by lindah (2011-04-23 12:26:33)

bobbym · 2011-04-23 16:05:59

Your welcome! Glad to help.

Math Is Fun Forum

#1 2011-04-22 18:45:10

Probability of default on loans

#2 2011-04-22 20:36:11

Re: Probability of default on loans

#3 2011-04-23 12:25:37

Re: Probability of default on loans

#4 2011-04-23 16:05:59

Re: Probability of default on loans

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