Understanding Rare Risks: A Simulation Approach

Navigating the complexities of risk management can be daunting, especially when dealing with rare but potentially disastrous risks. While traditional statistical methods provide a mathematical way of understanding these risks, many find the abstract numbers hard to grasp. This is where simulation models, like those built in Analytica , come into play, offering a more intuitive and visual way of understanding risk.

In an insightful piece on #RiskManagement, Stefan Hunziker, PhD recently shared a compelling example to emphasize the importance of not underestimating rare risks.

He presents a scenario to illustrate this concept: imagine a portfolio of 20 risks, each with a seemingly negligible 1% chance of occurring annually. While individually dismissible, these risks, when aggregated, possess a substantial probability of affecting the portfolio over a span of five years. The implications of this example are profound for risk management professionals, emphasizing that even the most infrequent threats can't be overlooked in a comprehensive risk strategy.

From my experience, many people find numerical statistical calculations challenging to comprehend. This is one of the key reasons I favor constructing simulation models in Analytica, which often provide a more accessible and intuitive understanding of complex data.

The simulation model uses a Bernoulli distribution—a common way to model two-outcome scenarios, like a risk occurring or not—to calculate the outcomes over multiple trials.

The model consists of two main variables (actually Indexes in this case): "Risk" and "Year." "Risk occurrence" is defined using a Bernoulli distribution, with each risk having an independent 1% chance of occurring each year. To determine the probability of at least one risk occurring within a given timeframe, the model uses a cumulative function to add up the occurrences year over year.

The results from the simulation model are enlightening. The probability mass function over the years shows that the likelihood of no risks occurring decreases over time, as one might expect. Conversely, the probability of experiencing at least one risk occurrence increases with each passing year.

But the real takeaway from the simulation is visualized in the last graph, where the lines representing the truth of at least one risk occurring cross the 50% threshold before 5 years. This provides a stark visual representation of the cumulative effect of rare risks over time, underscoring the importance of not underestimating them in risk management.

Simulation models like this serve a critical role in risk analysis. They transform abstract statistics into understandable visuals, making the implications of risk management strategies more accessible to all stakeholders. As the world becomes increasingly complex, such tools will only grow more essential in helping us navigate the uncertain waters of risk.