Over the past several decades, risk analytics have emerged as essential tools in such diverse fields as finance, healthcare, engineering, and government monetary policy. In Part 3 of our serial on Risk, we will take a look at risk analytics from 30,000 ft. Our purpose with this high-altitude examination is to build a practical appreciation (and sometimes skepticism) for the science beneath the number crunching.
Using AI to parse Big Data dominates today’s social and news medias. Hyped as rapidly emerging and mysterious technology that will forever change global society, AI is nothing short of glamorous. But, the “science” behind this technology is neither glamorous nor new. When we pull back the curtain, we find a plethora of algorithms churning away at synthesizing information. The truth is, well-established risk analytics provide AI’s DNA.
The connections between AI and risk analytics are not as esoteric as they might first seem. All we really need to connect the dots is an intuitive understanding risk. From there you simply follow your nose. So … this post is not really about AI. AI does however, offer an interesting segue to understanding a little more about risk analytics. This said, anyone who has tinkered with Chat GPT-4o appreciates the practical usefulness of AI; it’s amazing. With incredible speed, AI can synthesize information and use this information to execute often complex tasks. How does this work?
Without getting too far into the weeds, the algorithms behind Chat GPT4o must do two things: (1) gather information, (2) choose and execute a best course of action … something humans do many times daily. So, viewed from a high altitude, AI is a collection of computer-codes that mimic human decision making. Human decision making is pretty straightforward. (To be clear, a decision is a situation where one presently chooses to execute one from among two or more alternatives; at least one of the alternatives has consequences that cannot be predicted with certainty.
Because of the uncertain consequences, all decisions are risk encumbered. (If you were certain about how all the alternatives are going to pan out, there is really nothing to decide.) So, decision making boils down to executing the alternative that has the most preferred risk. To do this we need first to rank-order the decision alternatives according to the amount risk involved. Then we simply execute the alternative at the top of the ordering. Of course, the devil is in the details of how we go about rank-ordering risk … this is where the algorithms coded into AI systems rely on “risk analytics”.
At the core of risk analytics, one must understand what risk is and how to quantitatively measure it. There is a very long history of how to do this, going all the way back to Daniel Bernoulli in 1738. Suffice it to say that quantitatively measuring risk is a very mature subject matter in the fields philosophy, mathematics, economics, and statistics. Thus, the development of risk analytics predates AI algorithms by nearly 250 years. So, what is risk … really?
Risk is how one characterizes their uncertainty about the value of a decision alternative, over the range of possible values the alternative might take.
The risk associated with choosing a particular alternative is actually a function where: You specify a range of possible values (in units of dollars), and the risk function returns a (unit-less) number between 0 and 1 that gauges your certainty that the “true value” will lie within the range you specified. The important idea here is:
Risk is a function that assigns a number between 0 and 1 to any possible range of values you care to discuss. (And, in science under“risk analytics” that the assignment of numbers must follow the rules of probability.
Relax. We’re not going to get into a detailed discussion of probability; it is not needed, here. The thing we do need is some intuition about how to measure “how big” a risk function is. Why do we need sound intuition about measuring risk functions?
Returning to human decision making, rational people are rightly anxious anytime their decisions involve a lot of money. Obviously, we should always choose the decision alternative having the smallest risk … whatever “smallest” means. But, numerically gauging the relative sizes of various functions is not an activity that humans are good at … which forces us to rely computer-codes performing risk analytics that can rank-order decision alternatives. And, anxious rational people making decision that involve a lot of money need a reliable intuition about what’s going on under the hood of the software informing their decisions. To this end, let’s appeal to a thought exercise.
Begin: Risk Function Thought Exercise
Legend has it that the pirate Jean Lafitte buried a treasure worth $1,000,000 somewhere on Galveston Island, Texas. Sixty two years after Lafitte’s death, Galveston was completely destroyed by fire. You can be certain that the as yet undiscovered treasure is somewhere beneath bare land. The treasure would surely have been discovered during post-fire construction of anything … houses, commercial buildings, roadways, pipelines, etc. Moreover, no one really believes that rumored $1,000,000 figure. More realistically, the treasure’s value is likely between $10,000 and $500,000 in today’s dollars. Further, one should suspect Lafitte to have judiciously chosen a hiding place … hiding his treasure more obscurely the higher its value.
Let’s suppose that the cost of treasure hunting is $1,000 per acre and you have $10,000 to spend. Galveston is a laid-back community. You can search for treasure on any parcel of bare land without fear of hassle from the local constabulary.
Like most treasure hunters, you are too lazy to craft more than nine search-pattern alternatives. Thus, you face a decision with 10 alternatives (since one of your alternatives is not to search and keep your $10,000). Actually, this is a pretty complicated decision scenario, and we’re not going to solve it in this thought exercise. Remember, we’re simply going after some intuition about risk functions and how they are ‘‘measured’’.
Obviously, if Lafitte’s treasure remains in Galveston, you are 100% certain that it lies under bare land somewhere on the island. Historical 2-D maps of the Galveston reveal all remaining bare land that could possible hold the treasure. So, you can easily construct an up-to-date 2-D map of Galveston Island that shows shows all bare land that could possibly hold the treasure.
Now, let’s craft a new map of that reflects your “certainty” about the location and value of potentially buried treasure. When your done, it will look sort of like one of those cool 3-D United States Geographic Survey relief maps of Galveston Island … except, here, the map height above sea level indicates your relative certainty about the value treasure that might lie beneath that location.
Making this “certainty of value” 3-D map is going to be sort of like making a bumpy cake with a pan in the shape of Galveston Island. First, let’s look at the bottom of the Island-shaped cake pan … which, of course, is a 2-D map of the island. On this 2-D map, each location point carries a number indicating the dollar value you think the treasure will hold if it were actually buried at that location. (Remember, Lafitte likely chose his treasure burial location judiciously … so different locations carry different dollar values).
Suppose now that you poured one kilogram of very stiff batter into the Galveston Island cake pan. The batter is so stiff that it will retain any hills and valleys that you care to create … thus, you can create a 3-D map of the island made with 1kg of homogeneous stiff batter. Suppose that you shape the hills and valleys of your 3-D map reflect your certainty that the treasure might by found a given location … relatively greater heights imply greater certainty, while relatively lower heights mean lower certainty. This bumpy cake in the shape of Galveston Island is a visualization risk … capturing your certainty about the monetary value of finding treasure anywhere on the island.
You might immediately ask, “How will this bumpy cake help me decide where to spend money searching for Lafitte’s treasure?” The answer is neither complicated nor counterintuitive. Here is how it works. Recall that lazy treasure hunters identify only a handful (here 10) of alternative searches, each of which being within your $10,000 budget. You will simply compare the alternatives and choose the one having the smallest risk. Actually, you can use the bumpy Galveston cake to “measure” the risk of the various search alternatives. A search-pattern alternative is nothing more than specifying an area (made of shapes on the 2-D map) that you would explore … under the proviso that your total search cost of $1,000/acre for the alternative doesn’t bust your $10,000 budget. The risk for any particular search alternative is visualized as follow:
Remove all cake from the pan that is not above the search area. This leaves you with a 3-D certainty-relief map of the search area.
Find the point on the bottom of cake pan where remaining bumpy cake will be perfectly balanced if you sat it on a sharp nail.
Read the dollar value of the balance point from the 2-D map on the bottom of the pan, and then subtract the alternative’s search cost. This gives you a dollar value measuring the size of the risk function.
There you have it. Real risk analytics. We just “measured” a risk function, and we did it without using esoteric math. But, if you want to impress a quant by throwing around some snappy mathematics terminology, you are measuring the risk function of a decision alternative with its probability mass-centroid (i.e., the probabilistic expected monetary value of choosing that alternative). Actually, choosing the decision alternative having the least risk is the exactly the same thing as choosing the alternative with the greatest expected monetary value. This equivalence is intuitively obvious and is easily shown using integration by parts … if you happen to remember freshman calculus.
End Thought Exercise
What are key take-aways from this high-altitude thought exercise about risk analytics? (We’ll get to that list in just a minute, but first let’s nail down some perspective.) At a glance, the word “analytics” might seem to cover a lot of different topics in the general space of data science and computational statistics. Further, using the word “risk” as a proper adjective modifying the noun “analytics” gives an impression that “risk analytics” is an impenetrable subject understandable only by quants holding Ph.D.’s in computer science or theoretical physics. But, the truth is, almost all “analytics” are focused on quantifying “risk”. So, having an intuitive grasp of “risk” removes a much of the mystery that surrounds “analytics” in general and “risk analytics” in particular. That said, a “qualitative risk-intuition” is easily developed … you don’t need to be an uber-mathematical quant to get it. And, once acquired, risk-intuition is an especially durable bull shit filter. So, here is a bullet list of take-aways about risk analytics
Risk analytics are simply algorithms that attempt to quantify risk using data.
Risk is a type of information that describes your certainty about a range of dollar values that something might have. As a matter of convenience and convention, uncertainty is typically gauged on a scale of zero to one.
“Uncertainty” in not a physical property … it’s a unit-less personal perception that may or may not agree with the perceptions of others
Risk is unfailingly associated with decision making. (Unless you are faced with choosing between alternatives of uncertain value, why would you bother to gauge risk?)
Risk is not a single number! Suppose, for example, that I am considering selling my car. The risk of selling my car is the likelihood that there is a buyer willing to pay at least $p, if I were to offer the car at price $p. In other words, risk is a function where I input a potential range of sale prices (between p and infinity) and the function returns a value between zero and one expressing the likelihood that there will be a willing buyer for that price range.
Risk does not necessarily characterize likelihoods of an economic loss. For example, selling my car results in loss only if I sell it for fewer dollars than it is actually worth to me. Potential gain and loss is often distinguished with the terminology up-side risk vs down-side risk.
Making a decision is nothing more than choosing and executing one of your alternatives. All decision alternatives carry monetary risk. That is, each alternative has its own risk function.
You should always choose the decision alternative with the smallest risk. The trick is figuring out how to measure the size of risk functions so that we can compare them.
Measuring risk is never anything more than finding the center point of your certainty about the dollar value of a decision alternative. (This center point goes by other names including expected value and probability mass centroid.)
Even the most sophisticated (utility-weighted) risk functions are measured for the purposes of rank ordering by finding their expected value (i.e., their mass centroid … like when we found the balance point of Galveston Island search-area risk-cakes). Greater expected value is another way of saying lower measure of risk.
All of risk analytics boils down to data-crunching computer algorithms attempting to create risk functions and finding their centroids.
The old computer programming aphorism-acronym GIGO (garbage in, garbage out) most certainly applies to risk analytics. Often your QRI (qualitative risk intuition) is all you need to sniff out garbage in risk analytics … even garbage that has been deodorized using Artificial Intelligence.
Final thought: The word intelligence is often used to describe the human capability to acquire and understand information for the purpose of making decisions. AI (which served as our segue into a discussion risk analytics) is nothing more than a collection of computer codes build on (very mature) principles of risk and decision making. Hence, the moniker “Artificial” Intelligence is a good one. And, like any good computer code, the output should agree with sound human intuition. So, “the better your QRI” the “better your prospects of benefiting from” AI chatbots.