Modeling Risk

How to Mitigate Risk and Improve Decision-Making via Probabilistic Thinking and Rare Events Modeling

Risk managers must acknowledge the role that chance plays – particularly in extremely unlikely events – to reduce risks and to make better, more profitable decisions. What tools and techniques can they use to ensure that their organizations focus on the most impactful set of priorities, rather than chase outliers and seek patterns where they do not exist?

Friday, June 7, 2024

By Cristian deRitis


Many Americans now believe the economy is in recession, the stock market is faltering and unemployment is at its highest level in 50 years, according to a recent Harris poll that highlighted the significant gap between public perception and the actual state of the U.S. economy. The truth is that the unemployment rate is under 4% and the S&P 500 is performing robustly, while the U.S. gross domestic product is growing.

This disconnect is at least partly the result of human biases. It also demonstrates how the average person thinks about chance and underscores a broader challenge facing risk practitioners: accurately assessing probabilities and risks, particularly in the context of rare events.

cristian-deritisCristian deRitis

Given inherent biases, what can risk managers do to ensure their organizations are making correct assessments and decisions? And what techniques should risk modelers consider to properly estimate the likelihood of risks in their portfolios – especially for rare events?

What Are the Chances?

Probability, the likelihood of an event occurring, is a fundamental concept underpinning many aspects of life. From weather forecasts to investment decisions, understanding probability is crucial for making informed choices. Yet, despite its importance, many people struggle to grasp probabilistic concepts.

Our aversion to randomness is a key reason. We inherently seek patterns, even in random events. This can lead to misconceptions like the gambler's fallacy – the belief that chance needs to "balance out," making an unlikely event more probable after a string of opposing outcomes.

Spend any amount of time in a casino and you are bound to find someone at a roulette table convinced that black is "due" after a long run of red. In reality, each spin is an independent event with the same exact odds.

Cognitive biases further complicate our understanding of probabilities. We tend to fixate on initial information (anchoring) and judge probabilities based on how easily we recall similar events (availability). A news story about a plane crash makes us think flying is dangerous, even though the actual risk is small once we consider the millions of miles flown each day by hundreds of thousands of airline passengers around the globe.

Our brains also struggle with very small probabilities. Hearing about a shark attack can spark a primal fear, inflating the perceived risk. Statistically, we are much more likely to be struck by lightning or injured on our way to the beach than to be attacked by a shark. Swimmers, however, tend to stay away at the first report of a shark attack – even if it took place days ago at a distant location.

Technical language can cloud our understanding of probabilities. Terms like "may" and "likely" can be misinterpreted. For instance, a weather forecast of a 20% chance that it may rain might be understood as rain being unlikely, when it actually means there's a one-in-five chance of getting wet somewhere within a specified region.

Increases in small probabilities may also lead us to overstate risks. For example, a new pharmaceutical may report a 400% increase in a negative side effect. While alarming, closer inspection may reveal that the absolute probability went from 0.01% to 0.05%. Though notable, the benefits of the drug may far exceed the increased downside risk.

Advice for Risk Managers

To counter these challenges, risk managers should foster a culture of probabilistic thinking within their organizations. This can be achieved by adhering to the following:

  • Focus on relatable examples. Translate complex probabilities into real-world scenarios employees can understand. Consider what probabilities mean in terms of number of units or dollars to make them relevant.
  • Visualize the data. Charts and graphs can help translate abstract probabilities into a clearer picture, making them easier to digest.
  • Be aware of cognitive biases. Acknowledge the influence of experience or emotions on risk perception and strive for objectivity.
  • Concentrate on long-term averages and trends. Avoid overreacting to a single data point. Reinforce an understanding of randomness and noise.
  • Promote clarity and critical questioning. Encourage colleagues to ask, "What does this probability really mean?"

By fostering a culture of probabilistic thinking, risk managers can make more informed decisions, leading to lower risks and improved profitability.

Modeling Probabilities and Rare Events

Risk modelers have a host of tools in their toolkit to assist with the estimation of probabilities. Discrete outcome models, such as a probit or logit, are the workhorses of risk analysts looking to assign probabilities based on historical relationships. For example, studying the connection between an event (like a loan default) and its covariates can help a risk modeler understand how the state of the economy and changes to individual financial conditions influence probabilities.

Survival or duration analysis techniques take this one step further by permitting modelers to estimate probabilities occurring within a specified time frame – based on information about dynamic covariates, such as the unemployment rate or a company’s current debt service coverage ratio.

Although these are powerful tools, some care is needed when using and interpreting the results of these models. One of their main assumptions is that the outcomes are fairly well populated. If the outcomes are rare in our sample, however, with relatively few observed events, the sparsity of the data can make it difficult to estimate a robust model.

Oversampling the rare outcomes can help improve the quality of our estimates. Other techniques, such as exact logistic regression or the Firth method, can help you build a more robust model.

AI: Pros and Cons

Researchers now also have access to advanced computing power and artificial intelligence (AI) techniques, but caution is required. The power to examine thousands if not millions of data points quickly may allow us to identify patterns and advanced correlations that we weren’t able to before. However, these techniques may also be fooled by randomness, mistaking idiosyncratic patterns based on a few observations for causal factors.

Risk modelers play an important role in educating the end users of their models about suitability, strengths and weaknesses. Documentation, presentations and a customer service focus can minimize the risk that models are misused, misinterpreted or abused.

Modelers should embrace the opportunity to leverage the additional resources that AI tools can bring to test a wider range of specifications – or to segment their data to a greater degree than they were able to previously. AI can also assist with more mundane and repetitive tasks such as model documentation, monitoring and tracking.

Discovering issues long before they metastasize can enable modelers to mitigate model risk quickly, thereby reducing their workloads.

Parting Thoughts

Embracing probabilistic thinking doesn’t mean that we must become human calculators. Rather, it involves making better decisions by acknowledging the role that chance plays. By recognizing our biases, moreover, we can move beyond innate confusion and navigate the world of probabilities with greater confidence.

This requires taking actions to train our minds to think differently. Recognizing our inherent biases is a good first step. Beyond that, we can actively practice probabilistic thinking when interpreting reports that require additional context.

We can, moreover, figure out how to communicate and prioritize risks, while carefully considering what it means for odds ratios to increase when we are dealing with rare events in our lines of business.

Extending this type of training to our organizations will ensure that managers are focused on the most impactful set of priorities, rather than chasing outliers. By embracing probabilistic thinking and analysis of rare events, risk professionals can make better decisions and avoid the temptation to find patterns where they don’t exist.


Cristian deRitis is Managing Director and Deputy Chief Economist at Moody's Analytics. As the head of econometric model research and development, he specializes in the analysis of current and future economic conditions, scenario design, consumer credit markets and housing. In addition to his published research, Cristian is a co-host on the popular Inside Economics Podcast. He can be reached at


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