# Probability default calculation

I want to calculate default of probability of internal ratings for a particular bank. I have only the following data:

1. Liquidity Ratio
• short-term assets / short-term liabilities = 2.6
2. Profitability Ratios
• ROA - yearly net profit / average total assets = 26%
• Sales growth - (current sales − previous sales) / previous sales = 31%
• Projected debt service capacity - (Projected Operational Cash − Flow (stress tested for FX risk)) / Total payments toward the bank = 3
3. Solvency Ratios
• Debt/EBITDA = 0.4
• Total equity / total assets = 71%

Could you tell me can I calculate the probability default (PD) rate with this data? How to proceed?

Thanks

• Do you have at least a large data set you can regress against?
– will
Commented May 13, 2017 at 22:25

No, you cannot. If you had a pre-existing model that had been validated and used these variables, then yes you could, but you cannot calculate a probability from one data point and no other source of information.

Subjectively, the short run probability is small as there is massive coverage of short term debt. Unless there is a hidden liability, it is nearly zero. If the firm were sued tomorrow, lost in court and the judgment was devastating then it could become insolvent, but it is nearly zero. The exact value cannot be calculated without other information. Even for questions such as "will the sun rise tomorrow," there is a small, if trivial possibility some catastrophic and unknown event could happen. It is just so close to zero that we ignore it. This is the same for the above. It is nearly zero, in the very short term. We do not know if management will change its policies because it is doing so well.

• I need to map the bank's internal credit ratings to the ratings of S&P or some other external organization. I tried to implement the mapping based on default probability rates. Could you recommend me how can I do it, what model to use...?
– Sako
Commented Dec 14, 2016 at 16:05
• I cannot. I don't know your resources and skills. Additionally, bond ratinga are ordinal data, this isn't a trivial task. Without having extensive information, I am sorry, I cannot help. Commented Dec 14, 2016 at 20:29
• @Sako are you trying to do a validation study or find the default risk for one specific investment? Commented Dec 14, 2016 at 21:32
• I have Bank's internal ratings from 1-7 (1,2,3.....7), and each number has its qualitative and quantitative criteria (above-mentioned criteria and some qualitative criteria, like business activities & market position, management & organisation etc.) and I should map These numbers to S&P Ratings (AAA, BBB.....).
– Sako
Commented Dec 15, 2016 at 8:59
• Do any of your customers have external ratings? Commented Dec 15, 2016 at 15:02