## Using a probability of default

In the last post, we had looked at credit risk models and, specifically, what a probability of default model does. But how does that apply to banks, and why should a financial institution trust a probability of default (PD) analysis.

The methodology for a PD—using identifiable variables to determine the probability of a particular event—is something we should all be familiar with, as we regularly rely on probability theory in many aspects of our everyday life. Take for example the weatherman on your ten o’clock news. The rain forecast was likely a “Probability of Precipitation” coefficient.

You might ask, “Why use a weatherman as an example to demonstrate the value of probability theory? Everyone knows their forecasts are often incorrect.” And while probability may not be a perfect predictor of an end result, it can still prove extremely valuable in improving predictability of a particular outcome and thus reducing the associated risk. Someone who had watched the weather report would feel more confident in their ability to predict rain than someone who just flips a coin.

For financial institutions, even the slightest improvement in default predictability offered by a PDM can prove highly valuable in reducing credit risk and thus increasing an institution’s earnings. Consider the following example:

Let’s suppose a bank has a C&I portfolio of 100 customers, each with an average credit balance of $100,000. For every customer that defaults, the bank stands to lose up to the full balance owed. Now let’s suppose that, using a PDM either at origination or early enough in the review process to cure a loan, the bank’s credit department is able to correctly identify a mere ten percent more default customers than they would have otherwise. The bank can either choose to not make the loan in the first place or put in place safeguards for collection on “likely” defaults that are already in the portfolio. The math is simple:

*Loan Volume x Average Loan Size x Percent Improvement = Savings*

100 x $100,000 x 0.10 = $1,000,000

Under these conservative assumptions, the bank would be looking at a substantial $1,000,000 savings in its losses. Of course, the higher the predictive power of the model, the more substantial of an impact it may have on earnings and losses. A probability of default can be a good indicator that can help analysts make better loan pricing and risk rating decisions. This will help improve the decision-making process and the amount of time a financial institution has to react to credit deterioration.