The High Likelihood of Low Probability Events

This article discusses how good risk decisions can be taken when the level of uncertainty is well beyond that considered in traditional models of finance. Many of the risk decisions considered here are one-time only, implying that past data will be a poor guide. Though making good risk decisions are the ultimate interest, the focus of the article is how to deal with the unknown and unknowable, hereafter abbreviated UU. Hence, I will sometimes discuss salient problems outside of finance, such as geopolitical events, which are also unknown and unknowable.

This article will make no use of derivatives, nor run regressions, or make VaR calculations and neither look at the real options theory. In short, it eschews the normal tools of my financial risk management profession. It represents a blend of insights derived from reading academic works and from trying to teach their insights to others, and from lessons learned from direct and at-a-distance experiences with a number of successful risk managers in the UU world. 

At the end of the day, the essence of effective risk management is to select assets and business lines that will fare well when future states of the world become known. When the probabilities of future states of assets are known, as the efficient markets hypothesis posits, wise investing involves solving a sophisticated optimization problem. Of course, such probabilities are often unknown, banishing us from the world of the capital asset pricing model (CAPM), and thrusting us into the world of uncertainty.

Were the financial world predominantly one of mere uncertainty, the greatest financial successes would come to those individuals and firms best able to assess probabilities. That skill, often claimed as the domain of Bayesian decision theory, would swamp sophisticated optimization as the promoter of substantial returns.

The real world of risk management often ratchets the level of non-knowledge into still another dimension, where even the identity and nature of possible future states are not known. This is the world of ignorance. In it, there is no way that one can sensibly assign probabilities to the unknown states of the world. Just as traditional finance theory hits the wall when it encounters uncertainty, modern decision theory hits the wall when addressing the world of ignorance.

I shall employ the acronym UU for unknown unknowable to refer to situations where both the identity of possible future states of the world as well as their probabilities are unknown and unknowable. The table below outlines the three escalating categories:

Whether we like it or not, unknowable situations are widespread and inevitable. Consider the consequences for financial markets of global warming, future terrorist activities, or the most promising future technologies. These outcomes are as unknowable today as were the 1997 Asian meltdown, the 9/11 attacks, or 2008 GFC, shortly before they were experienced. These were all aggregate unknowables, affecting a broad swath of financial firms. But many unknowables are idiosyncratic or personal, affecting only firms or handfuls of firms.

Most risk managers – whose training, if any, fits a world where states and probabilities are assumed known – have little idea of how to deal with the unknowable. When they recognize its presence, they tend to steer clear, often to protect themselves from sniping by others. But for all but the simplest risk management decisions, entanglement is inevitable – and when risk managers do get entangled they tend to make significant errors. Many of the events that we classify as unknowable arrive in an unanticipated thunderclap, giving us little or no time to anticipate or prepare. But once they happen, they do not appear that strange.

You know, the human mind has an incredible ability to find a rationalization for why it should have been able to conjecture the terror attack of 9/11; or the Asian tsunamis of 1997 and 2005, respectively caused by currency collapse and underwater earthquake; or the recent Global Financial Crisis fueled by greed, excess-leveraging, and poor regulatory overview. This propensity to incorporate hindsight into our memories – and to do so particularly when Monday morning quarterbacks may attack us – hinders our ability to anticipate extreme events in the future. We learn insufficiently from our misestimates and mistaken decisions.

Other unknowable events occur over a period of time, as did the collapse of the Soviet Union. Consider most stock market swings. Starting in January 1996, the NASDAQ rose five-fold in four years. Then it reversed field and fell by two thirds in three years. Such developments are hardly thunderclaps. They are more like blowing up a balloon and then dribbling out the air. In retrospect, these remarkable swings have lost the flavor of an unknowable event, even though financial markets are not supposed to work that way. If securities prices at any moment incorporate all relevant information, a property that is usually posited, long-term movements in one direction are hardly possible, since strong runs of unanticipated good news or bad news will be exceedingly rare. 

We are all familiar with the Bell Curve (or Normal Distribution), which nicely describes the number of flips of a fair coin that will come up heads in a large number of trials. But such a mechanical and controlled problem is extremely rare. Heights are frequently described as falling on a Bell Curve. But in fact there are many too many people who are extremely tall or extremely short, due say to glandular disturbances or genetic abnormalities. The standard model often does not apply to observations in the tails. So too with most disturbances to investments. Whatever the explanation for the recent Global financial Crisis October, it was not due to the usual factors that are used to explain market movements.

More generally, movements in financial markets in general appear to have much thicker tails than would be predicted by Brownian motion, the instantaneous source of Bell Curve outcomes. That may be because the fundamental underlying factors produce thicker tails, or because there are rarely occurring anomalous or weird causes that produce extreme results, or both. The UU and UUU models would give great credence to the latter explanation, though both could apply.

Now, are UU events to be feared? At the end of the day, it is essential to remember that virtually all surprises are unpleasant, right? Most salient UU events seem to fall into the left tail of unfortunate occurrences. This may be more a matter of perception than reality. Often an upside unknowable event, say the diminution of terror attacks or recovery from a dread disease, is difficult to recognize. An attack on any single day was not likely anyway, and the patient still feels lousy on the road to recovery. Thus, the news just dribbles in, as in a financial market upswing.

B.F. Skinner, the great behavioral psychologist, taught us that behavior conditioned by variable interval reinforcement – engage in the behavior and from time-to-time the system will be primed to give you a payoff – was the most difficult to extinguish. Subjects could never be sure that another reward would not be forthcoming. Similarly, it is hard to discern when a string of inconsistently spaced episodic events has concluded. If the events are unpleasant, it is not clear when to celebrate their end.

An interesting field, usually ignored by risk managers, is behavioral decision-taking that has shaken the fields of economics and finance in recent decades. Basically, this work shows in area after area that individuals systematically deviate from making decisions in a normal 'rational' manner. Granted, that is hardly the path to prudent investment, but alas behavioral decision has strong descriptive validity. Behavioral decision has important implications for investing in UU situations. When considering our own behavior, we must be extremely careful not to fall prey to the biases and decision traps it chronicles. Almost by definition, UU situations are those where our experience is likely to be limited, where we will not encounter situations similar to other situations that have helped us hone our intuition.

When you think about it, the two critical components of decision problems are payoffs and probabilities. Effective decision requires that both be carefully calibrated. Not surprisingly, Prospect Theory, the most important single contribution to behavioral decision theory to date, finds that individuals’ responses to payoffs and probabilities are far from rational. To my knowledge, there is no tally of which contributes more to the loss of expected utility from the rational norm. (Some strong supporters of behavioral decision theory, however, think it is our norms that are misguided, and that the way the brain naturally perceives outcomes, not the prescriptions of decision theorists and economists, should be the guideline.)

Anyone will surely agree with the fact that generally speaking the more difficult a field is to investigate, the greater will be the unknown and unknowables associated with it, and the greater the expected profits to those who deal sensibly with them. Unknownables can’t be transmuted into sensible guesses -- but one can take one’s positions and array one’s claims so that unknowns and unknowables are mostly allies, not nemeses. And one can train to avoid one’s own behavioral decision tendencies, and to capitalize on those of others.

In the financial world at least, a key consideration in dealing with UU situations is assessing what others are likely to know or not know. You are unlikely to have mystical powers to foresee the unforeseeable, but you may be able to estimate your understanding relative to that of others. 

I reckon that the theory of UU is often tentative and implicit. But the question it seeks to answer is clear: How can one make good risk decisions rationally in UU situations? The question sounds almost like an oxymoron. Yet clear thinking about UU situations, which includes prior diagnosis of their elements, and relevant practice with simulated situations, may vastly improve risk management decisions where UU events are involved. If they do improve, such clear thinking will yield substantial benefits. For financial decisions at least, the benefits may be far greater than are available in run-of-the-mill contexts, since competition may be limited and prices well out of line.

How important are UU events in the great scheme of financial affairs? That itself is a UU question. But if we include only those that primarily affect individuals and firms alike, the magnitude is far greater than what our news accounts would suggest. Learning to make risk management decisions more wisely in a UU world may be the most promising way to significantly bolster your prosperity. Again, as already lauded to, central concepts in decision analysis, game theory, and behavioral decision are deployed along- side real risk management decisions to unearth successful business strategies.