# Framing probabilities of new normal patterns

Jul 10th, 2019

Framing probabilities of new normal patterns is oftentimes necessary. For example when geopolitical changes, climate change, etc., alter long term “normal” patterns. Oftentimes that occurs with seemingly repeated extreme events. The probabilities in the “New normal” may significantly alter the risk landscape around a project or a corporation. They may transform tolerable risks into intolerable ones, tactical risks into strategic ones (see figure below).

To ensure decision-makers and management can keep optimizing tactical and strategic planning a rational, emotionless update of the probabilities is paramount.

## An example of long term vs. “new” normal

Let’s suppose the price of a key material has varied monotonously over the last 30 years. In other words, business-like-usual evolution and “noise”.

In the last couple years, however, the price has skyrocketed due to some stochastic reasons. It is too early to say if the variation is here to stay. Perhaps it was a “fluke”? Perhaps the tweets that created the panic will be reversed tomorrow? Or perhaps the policy change may even “permanently” change the future price of the commodity.

The uncertainty has to be “solved” somehow. Indeed Managers and decision-makers need to update their ERM. They have to act rationally, while avoiding knee-jerk over-reactions. Also, they have to use available information.

Below is a simple yet powerful approach we propose to our clients. Because the extreme events are stochastic, very fresh, there is no “single magic number”. Thus we need to work by framing ranges, i.e with a min-max probability range.

## Framing probabilities of new normal patterns

After 30 years of business-like-usual and one extreme event, one can say the frequency of such an event is 1/31= 0.032 (3.2%). At the second occurrence it becomes 2/32=0.063 (6.3%). If the extreme event keeps occurring year after year, after another 30 years the frequency would be 30/60=0.5. In that case, if the extremes occurrences obey to a Poisson process (see explanations below), then the associated probability of at least one event next year would be roughly only 40%. Indeed, probability and frequency are not linearly related.

Obviously, no one has the time to wait or possesses a crystal ball despite claims by software sellers. ERM has to propose predictive values of the risks as soon as analyst detects an anomaly. Understanding the underlying assumptions, including maybe a few scenarios if the anomaly is too recent to know what type of change is occurring.  The three subheadings below discuss first the possible use of the Poisson process. Then they show a Poisson example, then a probability of exceedance example.

Results of stochastic events are a bit counter intuitive to say the least. Thus, the Poisson process commands some comments.

• The constant rate (frequency) needs to be known, however no one will ever understand it perfectly; and

• Events occur independently of the time since the last event.

As a result, the nature of the change dictates if one can or cannot use the Poisson approach.

• If a “fluke” occurs we can assume that our constant rate was initially incorrect. But with the correction we can then use Poisson.

•  Following a thread of panic-creating tweets, the events are not independent since the last event. However, if the author reverses the tweet later on, we can still use the long-term frequency number ignoring the blip. Finally,

• in case of policy change we do not know the constant rate and the independence of the time, and therefore we cannot use Poisson with the last 60 years of data (however we might with the last 30).

## Using Poisson processes

If one can assume that the extreme event follows a Poisson process and that its return is one year, then one can calculate the probability of seeing one or more next year at 0.63 (63%) using the Poisson process formula linking frequency to probability of occurrence. Also, if we look to a gap of two years, one with normal, the other with extreme event, then we have again an estimate of 40%. If we look to a gap of three years, one year normal and two years extreme, then the probability is roughly 50%.

## Using Exceedance probabilities

Another interesting approach is based on the probability of exceedance evaluation. Considering the last two years and the occurrence of the extreme “last year” the Exceedance probability of the extreme is 0.33 or 33%. Considering the last three years the same probability is worth 25%. If the whole thirty years of records is considered, the probability of exceedance is 1/31=3.2%.

## What do we do with the numbers?

Now it is where management needs some coaching in the final selection.

We have two sets of values:

• Historic data (including the last couple years of extremes) lead to an estimate of probability of occurrence of 3% to 7%. Probability of exceedance based on historic data is say 3%.
• Predictive data based on the last few years show a raise of the probability of occurrence to 40% to 60% and a probability of exceedance at 33%. The graph first displays an example with consequence at C1. Despite the increase of the probability the risk remains tolerable even in the “new normal”. However, management should be aware that there is a 33% chance the event will be exceeded, and thus it could become intolerable, when the consequences shift to the right following the exceedance arrow.

If the consequence is C2, then the initially tolerable risk becomes intolerable due to the probability increase. If exceeded it could also become strategic by “right shifting” of the consequences, again, following the exceedance arrow.

With these conditions mapped out in graphic format, management will be well armed to take the “best possible decision” based on the data at hand.

## Riskope Blog latests posts

• New achievements in risk assessment and management
• 2-05-2023
• New achievements in risk assessment and management will be attained thanks to SRK Consulting merging with Riskope. Indeed, we are…
• Open letter to the organizer of the tailings dam round robin exercise
• 29-03-2023
• Dear Ryan, please receive this open letter to the organizer of the tailings dam round robin exercise. It explains our…