Continuing on the topic of risk management for models. After building a model, how do you make sure the model remains robust under working conditions? More importantly, make sure it works well under extreme conditions? We discussed the importance of independent validation for empirical models in a previous post. In my experience, model failures have been frequent when the validation process has been superficial.
Now, I want to move on to sensitivity analysis. Sensitivity analysis involves understanding the variability of the model output as the inputs to the model are varied. The inputs are changed by + or - 10 to 50% and the output is recorded. The range of outputs gives a sense of the various outcomes that can be anticipated and one needs to prepare for. Sensitivity analysis can also be used to stress test the other components of the system which the model drives. For example, let's say the output of the model is a financial forecast that goes into a system that is used to drive, deposit generation. The sensitivity analysis output gives an opportunity to check the robustness of the downstream system. By knowing that one might require occasionally to generate deposits at 4-5 times the usual monthly volumes, one can prepare accordingly.
Now, sensitivity analysis is one piece of stress testing that has usually been misdirected and incomplete. Good sensitivity analysis looks at both the structural components of the model as well as the inputs to the model. Most sensitivity analysis I have encountered stress only the structural components. What is the difference between the two?
Let's say, you have a model to project the performance of the balance sheet of a bank. One of the typical stresses that one would apply is to the expected level of losses on the loan portfolio of the bank. A stress of 20-50% and sometimes even 100% increase in losses is applied and the model outputs are assessed. When this is done consistently with all the other components of the balance sheet, you can get a sense of the sensitivity of the model to various components.
But that's not the same as the sensitivity to inputs. Because inputs are based in real-world phenomena, their impact is usually spread out to multiple components in the model. For example, if the 100% increase in losses were driven by a recession in the economy, there would be other impacts that one would need to worry about. Now, a recession is usually accompanied by a flight to quality from investors. So if there is a recessionary outlook, the value of equity holdings could crash as well due to equity investors moving out from equities (selling) and into more stable instruments. A third impact could be the impact of higher capital requirements on the value of traded securities . As other banks face the same recessionary environment, their losses could increase to such an extent that a call to increase capital becomes inevitable. How does one increase capital? The easiest route is to liquidate existing holdings. Driving a greater fall in the market prices of traded securities. Thus, putting further stresses on the balance sheet.
So, the scenario of running a 50% increase in loan losses is a purely illusory one. When loan losses increase, one has to contend with what the fundamental driver could be and how can that fundamental driver impact other portions of the balance sheet.
The other place where sensitivity analysis is often incomplete is by not looking at the impact of upstream and downstream processes and strategies. A model is never a stand-alone entity. It has upstream sources of data and down-stream uses of the model output. So if the model has to face situations where there are extreme values of inputs, what could be the implications on upstream and downstream strategies? These are the questions any serious model builder should be asking.
This discussion on sensitivity analysis has hopefully been eye-opening to modeling practitioners. Now, we will go on to a third technique, Monte Carlo simulation in another post. But before we go there, what are other examples of sensitivity analyses that you have seen in your work? How has this analysis been used effectively (or otherwise)? What are good graphical ways of sharing the output?