Credit Portfolio analysis for Financial Instiitutions

Credit ratings form integral part in the analysis of credit portfolio held by Financial Institutions. Suppose if the hold only AA+ rated debts of companies. Then the credit issued to them has the same quality.

If a bond issued by a company is selling at 108, then,

100=1/108((Px100)+(1-P)50) from which the survival probability is calculated. Then default probability λ = - ln P

Now the Credit rating agencies like Moody’s publish a credit rating scores called the ‘Diversity scores’ for different types of debts. If we call D as the diversity score for a particular class of debt, then default rate can be calculated as for say ‘k’ defaults in the portfolio,

X=(D C k) λ^{k .}(1-λ)^D-k

This will be the default rate annually for a particular class of debt.

Now to see how many defaults occur in the firs two months,

Default rate for two weeks = e^X . ^2/12

This will give the value of how many debts in your portfolio is going to be at default in two weeks time for a particular default probability.

For example if you get a number like 0.06 means that 6 debts you hold in your portfolio out of 100 of particular quality analysed will default. 

Diversity scores are the prerogatives of the Credit rating agencies like Moodys or Standard and Poor. The way they calculate this is still unknown. It is assumed it is done from past data of similar debts.

Comment:

If one Nation has an Insurer who can be considered fail safe at any level then the above can be used to creae Credit Default Swaps(CDS). The 6% got above can be taken as the damages and the CDS premium will be equal to (price + damages). Caveat is the Insures must have unlimited insuring capability.