Financial Risk Management

CHAPTER 13A Forward‐Looking Evaluation of Risk: Stress Testing

THE RETURN PERIOD

The concept of a rare or extreme event is at the core of stress testing. As we mentioned previously, the probability of occurrence is very low but still higher than expected in a Gaussian framework. The problem with this definition of an extreme event is its lack of precision. What does a “low probability” mean exactly? What is the threshold for considering a probability as low? Answering these two questions is of crucial importance for risk management, specifically to compare two events.

The statistician Emil Julius Gumbel offered an interesting alternative to cope with extreme events: the return period (Gumbel, 1958). Initially developed outside the field of risk management (e.g., hydrology and flood prediction), the return period is commonly used nowadays in stress‐testing programmes to express the frequency of occurrence of an event. The return period is defined as the average wait time between the exceedance of a specified extreme threshold. It is denoted as , where stands for the threshold.

Because an extreme loss may threaten the strength of a bank, the return period of such a rare event might be 100 years, corresponding to a probability of occurrence of 1% in any year. A common misinterpretation ...