In this ongoing series, we provide our readers with two distinct perspectives on the same topic — one from an academic, the other from a practicing financial advisor. In “The Advisor and The Quant,” we will pose one specific question to the advisor and the quant. You will see their responses here on ThinkAdvisor.

If you have a question or two, please send them to us using the form at the end of this article.

Check out the previous column here.

Learn more about The Advisor, Joe Elsasser, CFP, and The Quant, Ron Piccinini, Ph.D.

QUESTION: What is fat-tailed modeling and why does it matter?


In order to understand “fat tails” we have to start with “tails.” The standard bell curve graph that we see used for everything from test scores to potential returns is fat in the middle and very narrow at the edges, which are also known as the “tails.”

Bell curve 

The bell curve is a representation of how often something happens (or should happen if used to project into the future). Its ranges are based on standard deviations, which is a measure of how often something that is not the mean should happen. One standard deviation is about 68% of the time, two standard deviations is about 95% of the time and three standard deviations is about 99.5% of the time.

The problem with using this model of returns is that in finance, it simply isn’t true. Extreme events happen far more often than a normal distribution would predict. Nicholas Nassim Taleb first popularized this idea after the Great Recession with his book “The Black Swan,” though it had been written about extensively by other academics prior.

Using the visual above, “fat tails” is simply a recognition that events that should happen very rarely, actually happen with quite a bit more frequency. So, a “fat tailed” model that more effectively represents the reality of financial market returns, looks narrower in the middle, but fatter in the tails like this example of the returns distribution of a 60/40 portfolio:

"Fat tail" model

The existence of heavy tails in market returns is what makes the advisor’s role as behavioral coach is so important. Big swings in both directions — up and down — happen regularly. As a result, we, as advisors, need to ensure that we are setting reasonable expectations as to the magnitude of those swings. If we fail to do so, we play directly into a client’s impulse, which is to buy when markets are hot and sell during times of panic. Recognizing that the range of what is normal for a given portfolio is considerably broader than is modeled by the old bell curve highlights the importance of using a more reasonable process for setting client expectations. 

Keep reading for The Quant’s answer:

Ron Piccinini, director of product, Covisum


For the last 4,000 years, ever since the first grain merchants, farmers, and traders of Assyria and Sumeria engaged in lending activities, financial operators deploying capital have been preoccupied with estimating risk. Over time, the concept of risk has evolved to denote the reasoned probability of incurring a permanent loss of capital (to paraphrase Warren Buffett). In today’s world, with high-speed computers and databases, financial operators create probabilistic models to estimate risk. These models are used in lending, trading, investing, insurance, retirement planning, etc.

One of the early models of the modern era (when computers where in their infancy), postulated that market returns could be modelled using a “Gaussian distribution,” an elegant probabilistic model successfully applied in the natural science domain. While a considerable leap forward at the time, the Gaussian model quickly showed its limits in risk modeling, because it vastly underestimates the probability of larger price movements in asset prices (which is precisely what a good risk model ought to do).

For example, the probability of the 1987 Black Monday according to the Gaussian model was so minuscule, it should have happened once every 100,000 times the age of the universe. To palliate this problem, sophisticated financial operators started using ‘fat-tail’ risk models, which do a vastly better job at assigning a reasoned probability to the large price movements so often observed in the past. These models are colloquially called ‘fat-tails,’ because if you compare their density function to that of the Gaussian, the areas away from the middle, aka the tails, are much more pronounced. If you want to impress your friends, the technical term is “leptokurtic.”

Applications of fat-tail modeling are pervasive in the financial world. Banks and insurance companies use it to size their capital reserves and lending requirements. Broker-dealers use it to manage margin lending. Traders use it to estimate the fair price of assets and derivatives. Portfolio managers use it for portfolio construction. If you’d like to understand how volatile your retirement portfolio could get, you should ask your advisor for a fat-tail risk analysis.

A basic tenant of finance is that risk and reward are two sides of the same coin. Misestimating risk can lead to outcomes ranging from suboptimal allocations to outright disaster (e.g. the 2007-2008 crisis). Fat-tail models represent the next evolution in the estimation of risk.