Statistical credit models enable fast and quick assessment of many counterparties at once, and thus offer a great way of scaling credit risk analysis in an efficient way.
State-of-the-art models make use of a variety of inputs, including financial ratios, macro-economic and socio-economic indicators (such as country and industry risk), combined in a logistic regression and optimized to generate a credit score or a probability of default that best aligns with historical default experience.
With so many inputs and only one output, the question is: what is/are the main risk driver/s?
To identify the main risk drivers of a modelled Probability of Default (PD) or score, risk analysts often look at the input coefficients, to get an idea of the “input weight”, but usually get more and more baffled:
- Why is the input coefficient so high, but the model output changes only by a fraction, when I change the input?
- Why is the coefficient of “input A” so small compared to “input B”, and yet the model output seems more sensitive to “input A” than to “input B”?
- Which input contributes the most to the model output?
All these (legitimate) questions arise because statistical models based on logistic regressions are strongly non-linear: the relationship between model output and each model input does not look like a straight line, but can be rather approximated by an “S” shaped curve. Therefore, looking at the input coefficient can be quite confusing as the coefficient of an input is a fixed number, but the actual “weight”/effect of the model input depends on the position on the curve.
To help address these questions, S&P Global Market Intelligence offers two analytic features: sensitivity and absolute contribution.
Source: S&P Global Market Intelligence, Analytic Development Group. For illustrative purposes only.
Sensitivity is calculated by perturbing a model input by a small amount and by seeing how much the credit-worthiness changes. It all depends on which point of the “S” curve we start from and arrive to. For very small or very large initial values, we sit on the flat parts of the “S” curve, and the sensitivity will be small because a small change of the input has a tiny impact on the final credit-worthiness. For intermediate values of the model input, we are effectively “sitting” on the steep part of the “S” curve, and even a small change of the input will have a big impact on the creditworthiness, thus the sensitivity is high. Effectively, the sensitivity tells us the “slope” of the “S” curve, at a specific point of the curve.
Absolute Contribution is calculated by setting the input to its best possible value, effectively “switching off” the bad effect due to such input, and checking how much the model output improves by. This can be repeated for each model input, and the effects can be compared against each other and normalized to 100%, to understand which of the inputs mostly drives the model output.
In plain words, absolute contribution shows which input has gone further away from the best condition, while the sensitivity tells us what happens at the very next “little step”.An input can have at the same time large absolute contribution but very little sensitivity, when it is very far away from the optimal value (on one flat end of the “S”), or both small absolute contribution and small sensitivity if it is close to the ideal case (on the opposite flat side of the “S”). As a loose rule of thumb, the inputs with largest absolute contribution will tend to have smaller sensitivity. Why is that? In order to have large absolute contribution, the input needs to be very far from the ideal case, thus it will likely sit on the other flat part of the “S”, where the sensitivity is low.
In a non-linear model, both sensitivity and absolute contribution of the same input vary not only from company to company, but also for the same company, depending on the position on the “S”. Thus, the absolute contribution and sensitivity of a given input will change from quarter to quarter, when new company financials arrive.
At S&P Global Market Intelligence, we offer a wide variety of analytical models that enable clients to scale the assessment, monitoring and management of credit risk. Our models come equipped with analytic features, such as sensitivity and absolute contribution that help users make the most of our tools, and identify potential paths to recovery of credit strength.