Antifragile: Things That Gain from Disorder

by Taleb, Nassim Nicholas

  Next, let us apply this very simple technique to the detection of fragility and position in the Triad.

  TRAFFIC IN NEW YORK

  Let us apply “convexity effects” to things around us. Traffic is highly nonlinear. When I take the day flight from New York to London, and I leave my residence around five in the morning (yes, I know), it takes me around 26 minutes to reach the British Air terminal at JFK airport. At that time, New York is empty, eerily non–New York. When I leave my place at six o’clock for the later flight, there is almost no difference in travel time, although traffic is a bit denser. One can add more and more cars on the highway, with no or minimal impact on time spent in traffic.

  Then, a mystery—increase the number of cars by 10 percent and watch the travel time jump by 50 percent (I am using approximate numbers). Look at the convexity effect at work: the average number of cars on the road does not matter at all for traffic speed. If you have 90,000 cars for one hour, then 110,000 cars for another hour, traffic would be much slower than if you had 100,000 cars for two hours. Note that travel time is a negative, so I count it as a cost, like an expense, and a rise is a bad thing.

  So travel cost is fragile to the volatility of the number of cars on the highway; it does not depend so much on their average number. Every additional car increases travel time more than the previous one.

  This is a hint to a central problem of the world today, that of the misunderstanding of nonlinear response by those involved in creating “efficiencies” and “optimization” of systems. For instance, European airports and railroads are stretched, seeming overly efficient. They operate at close to maximal capacity, with minimal redundancies and idle capacity, hence acceptable costs; but a small increase in congestion, say 5 percent more planes in the sky owing to a tiny backlog, can give rise to chaos in airports and cause scenes of unhappy travelers camping on floors, their only solace some bearded fellow playing French folk songs on his guitar.

  We can see applications of the point across economic domains: central banks can print money; they print and print with no effect (and claim the “safety” of such a measure), then, “unexpectedly,” the printing causes a jump in inflation. Many economic results are completely canceled by convexity effects—and the happy news is that we know why. Alas, the tools (and culture) of policy makers are based on the overly linear, ignoring these hidden effects. They call it “approximation.” When you hear of a “second-order” effect, it means convexity is causing the failure of approximation to represent the real story.

  I have put a (very hypothetical) graph of the response of traffic to cars on the road in Figure 14. Note for now the curved shape of the graph. It curves inward.

  FIGURE 14. The graph shows how the author’s travel time (and travel costs) to JFK depend, beyond a certain point, nonlinearly on the number of cars on the road. We show travel costs as curving inward—concave, not a good thing.

  Someone Call New York City Officials

  An apt illustration of how convexity effects affect an overoptimized system, along with misforecasting large deviations, is this simple story of an underestimation made by New York City officials of the effect of a line closure on traffic congestion. This error is remarkably general: a small modification with compounded results in a system that is extremely stretched, hence fragile.

  One Saturday evening in November 2011, I drove to New York City to meet the philosopher Paul Boghossian for dinner in the Village—typically a forty-minute trip. Ironically, I was meeting him to talk about my book, this book, and more particularly, my ideas on redundancy in systems. I have been advocating the injection of redundancy into people’s lives and had been boasting to him and others that, since my New Year’s resolution of 2007, I have never been late to anything, not even by a minute (well, almost). Recall in Chapter 2 my advocacy of redundancies as an aggressive stance. Such personal discipline forces me to build buffers, and, as I carry a notebook, it allowed me to write an entire book of aphorisms. Not counting long visits to bookstores. Or I can sit in a café and read hate mail. With, of course, no stress, as I have no fear of being late. But the greatest benefit of such discipline is that it prevents me from cramming my day with appointments (typically, appointments are neither useful nor pleasant). Actually, by another rule of personal discipline I do not make appointments (other than lectures) except the very same morning, as a date on the calendar makes me feel like a prisoner, but that’s another story.

  As I hit Midtown, around six o’clock, traffic stopped. Completely. By eight I had moved hardly a few blocks. So even my “redundancy buffer” failed to let me keep the so-far-unbroken resolution. Then, after relearning to operate the noisy cacophonic thing called the radio, I started figuring out what had happened: New York City had authorized a film company to use the Fifty-ninth Street Bridge, blocking part of it, assuming that it would be no problem on a Saturday. And the small traffic problem turned into mayhem, owing to the multiplicative effects. What they felt would be at the worst a few minutes’ delays was multiplied by two orders of magnitude; minutes became hours. Simply, the authorities running New York City did not understand nonlinearities.

  This is the central problem of efficiency: these types of errors compound, multiply, swell, with an effect that only goes in one direction—the wrong direction.

  WHERE MORE IS DIFFERENT

  Another intuitive way to look at convexity effects: consider the scaling property. If you double the exposure to something, do you more than double the harm it will cause? If so, then this is a situation of fragility. Otherwise, you are robust.

  The point has been aptly expressed by P. W. Anderson in the title of his paper “More Is Different.” And what scientists involved in complexity call “emerging properties” is the nonlinear result of adding units, as the sum becomes increasingly different from the parts. Just look at how different the large stone is from the pebbles: the latter have the same weight and the same general shape, but that’s about it. Likewise, we saw in Chapter 5 that a city is not a large village; a corporation is not a larger small business. We also saw how randomness changes in nature from Mediocristan to Extremistan, how a state is not a large village, and many alterations that come from size—and speed. All these show nonlinearity in action.

  A “Balanced Meal”

  Another example of missing the hidden dimension, that is, variability: we are currently told by the Soviet-Harvard U.S. health authorities to eat set quantities of nutrients (total calories, protein, vitamins, etc.) every day, in some recommended amounts of each. Every food item has a “percentage daily allowance.” Aside from the total lack of empirical rigor in the way these recommendations are currently derived (more on that in the medical chapters), there is another sloppiness in the edict: an insistence in the discourse on the regularity. Those recommending the nutritional policies fail to understand that “steadily” getting your calories and nutrients throughout the day, with “balanced” composition and metronomic regularity, does not necessarily have the same effect as consuming them unevenly or randomly, say by having a lot of proteins one day, fasting completely another, feasting the third, etc.

  This is a denial of hormesis, the slight stressor of episodic deprivation. For a long time, nobody even bothered to try to figure out whether variability in distribution—the second-order effect—mattered as much as long-term composition. Now research is starting to catch up to such a very, very simple point. It turns out that the effect of variability in food sources and the nonlinearity in the physiological response is central to biological systems. Consuming no protein at all on Monday and catching up on Wednesday seemingly causes a different—better—physiological response, possibly because the deprivation, as a stressor, activates some pathways that facilitate the subsequent absorption of the nutrients (or something similar). And, until a few recent (and disconnected) empirical studies, this convexity effect has been totally missed by science—though not by religions, ancestral heuristics, and traditions. And if scientists get
some convexity effects (as we said about domain dependence, doctors, just like weight lifters, understand here and there nonlinearities in dose response), the notion of convexity effects itself appears to be completely missing from their language and methods.

  Run, Don’t Walk

  Another illustration, this time a situation that benefits from variation—positive convexity effects. Take two brothers, Castor and Polydeuces, who need to travel a mile. Castor walks the mile at a leisurely pace and arrives at the destination in twenty minutes. Polydeuces spends fourteen minutes playing with his handheld device getting updates on the gossip, then runs the same mile in six minutes, arriving at the same time as Castor.

  So both persons have covered the exact same distance, in exactly the same time—same average. Castor, who walked all the way, presumably will not get the same health benefits and gains in strength as Polydeuces, who sprinted. Health benefits are convex to speed (up to a point, of course).

  The very idea of exercise is to gain from antifragility to workout stressors—as we saw, all kinds of exercise are just exploitations of convexity effects.

  SMALL MAY BE UGLY, IT IS CERTAINLY LESS FRAGILE

  We often hear the expression “small is beautiful.” It is potent and appealing; many ideas have been offered in its support—almost all of them anecdotal, romantic, or existential. Let us present it within our approach of fragility equals concavity equals dislike of randomness and see how we can measure such an effect.

  How to Be Squeezed

  A squeeze occurs when people have no choice but to do something, and do it right away, regardless of the costs.

  Your other half is to defend a doctoral thesis in the history of German dance and you need to fly to Marburg to be present at such an important moment, meet the parents, and get formally engaged. You live in New York and manage to buy an economy ticket to Frankfurt for $400 and you are excited about how cheap it is. But you need to go through London. Upon getting to New York’s Kennedy airport, you are apprised by the airline agent that the flights to London are canceled, sorry, delays due to backlog due to weather problems, that type of thing. Something about Heathrow’s fragility. You can get a last-minute flight to Frankfurt, but now you need to pay $4,000, close to ten times the price, and hurry, as there are very few seats left. You fume, shout, curse, blame yourself, your upbringing and parents who taught you to save, then shell out the $4,000. That’s a squeeze.

  Squeezes are exacerbated by size. When one is large, one becomes vulnerable to some errors, particularly horrendous squeezes. The squeezes become nonlinearly costlier as size increases.

  To see how size becomes a handicap, consider the reasons one should not own an elephant as a pet, regardless of what emotional attachment you may have to the animal. Say you can afford an elephant as part of your postpromotion household budget and have one delivered to your backyard. Should there be a water shortage—hence a squeeze, since you have no choice but to shell out the money for water—you would have to pay a higher and higher price for each additional gallon of water. That’s fragility, right there, a negative convexity effect coming from getting too big. The unexpected cost, as a percentage of the total, would be monstrous. Owning, say, a cat or a dog would not bring about such high unexpected additional costs at times of squeeze—the overruns taken as a percentage of the total costs would be very low.

  In spite of what is studied in business schools concerning “economies of scale,” size hurts you at times of stress; it is not a good idea to be large during difficult times. Some economists have been wondering why mergers of corporations do not appear to play out. The combined unit is now much larger, hence more powerful, and according to the theories of economies of scale, it should be more “efficient.” But the numbers show, at best, no gain from such increase in size—that was already true in 1978, when Richard Roll voiced the “hubris hypothesis,” finding it irrational for companies to engage in mergers given their poor historical record. Recent data, more than three decades later, still confirm both the poor record of mergers and the same hubris as managers seem to ignore the bad economic aspect of the transaction. There appears to be something about size that is harmful to corporations.

  As with the idea of having elephants as pets, squeezes are much, much more expensive (relative to size) for large corporations. The gains from size are visible but the risks are hidden, and some concealed risks seem to bring frailties into the companies.

  Large animals, such as elephants, boa constrictors, mammoths, and other animals of size tend to become rapidly extinct. Aside from the squeeze when resources are tight, there are mechanical considerations. Large animals are more fragile to shocks than small ones—again, stone and pebbles. Jared Diamond, always ahead of others, figured out such vulnerability in a paper called “Why Cats Have Nine Lives.” If you throw a cat or a mouse from an elevation of several times their height, they will typically manage to survive. Elephants, by comparison, break limbs very easily.

  Kerviel and Micro-Kerviel

  Let us look at a case study from vulgar finance, a field in which participants are very good at making mistakes. On January 21, 2008, the Parisian bank Societé Générale rushed to sell in the market close to seventy billion dollars’ worth of stocks, a very large amount for any single “fire sale.” Markets were not very active (called “thin”), as it was Martin Luther King Day in the United States, and markets worldwide dropped precipitously, close to 10 percent, costing the company close to six billion dollars in losses just from their fire sale. The entire point of the squeeze is that they couldn’t wait, and they had no option but to turn a sale into a fire sale. For they had, over the weekend, uncovered a fraud. Jerome Kerviel, a rogue back office employee, was playing with humongous sums in the market and hiding these exposures from the main computer system. They had no choice but to sell, immediately, these stocks they didn’t know they owned.

  Now, to see the effect of fragility from size, look at Figure 15 showing losses as a function of quantity sold. A fire sale of $70 billion worth of stocks leads to a loss of $6 billion. But a fire sale a tenth of the size, $7 billion would result in no loss at all, as markets would absorb the quantities without panic, maybe without even noticing. So this tells us that if, instead of having one very large bank, with Monsieur Kerviel as a rogue trader, we had ten smaller banks, each with a proportional Monsieur Micro-Kerviel, and each conducted his rogue trading independently and at random times, the total losses for the ten banks would be close to nothing.

  FIGURE 15. Small may be beautiful; it is certainly less fragile. The graph shows transaction costs as a function of the size of the error: they increase nonlinearly, and we can see the megafragility.

  About a few weeks before the Kerviel episode, a French business school hired me to present to the board of executives of the Societé Générale meeting in Prague my ideas of Black Swan risks. In the eyes of the bankers, I was like a Jesuit preacher visiting Mecca in the middle of the annual Hajj—their “quants” and risk people hated me with passion, and I regretted not having insisted on speaking in Arabic given that they had simultaneous translation. My talk was about pseudo risk techniques à la Triffat—methods commonly used, as I said, to measure and predict events, methods that have never worked before—and how we needed to focus on fragility and barbells. During the talk I was heckled relentlessly by Kerviel’s boss and his colleague, the head of risk management. After my talk, everyone ignored me, as if I were a Martian, with a “who brought this guy here” awkward situation (I had been selected by the school, not the bank). The only person who was nice to me was the chairman, as he mistook me for someone else and had no clue about what I was discussing.

  So the reader can imagine my state of mind when, shortly after my return to New York, the Kerviel trading scandal broke. It was also tantalizing that I had to keep my mouth shut (which I did, except for a few slips) for legal reasons.

  Clearly, the postmortem analyses were mistaken, attributing the problem to bad controls b
y the bad capitalistic system, and lack of vigilance on the part of the bank. It was not. Nor was it “greed,” as we commonly assume. The problem is primarily size, and the fragility that comes from size.

  Always keep in mind the difference between a stone and its weight in pebbles. The Kerviel story is illustrative, so we can generalize and look at evidence across domains.

  In project management, Bent Flyvbjerg has shown firm evidence that an increase in the size of projects maps to poor outcomes and higher and higher costs of delays as a proportion of the total budget. But there is a nuance: it is the size per segment of the project that matters, not the entire project—some projects can be divided into pieces, not others. Bridge and tunnel projects involve monolithic planning, as these cannot be broken up into small portions; their percentage costs overruns increase markedly with size. Same with dams. For roads, built by small segments, there is no serious size effect, as the project managers incur only small errors and can adapt to them. Small segments go one small error at the time, with no serious role for squeezes.

  Another aspect of size: large corporations also end up endangering neighborhoods. I’ve used the following argument against large superstore chains in spite of the advertised benefits. A large super-megastore wanted to acquire an entire neighborhood near where I live, causing uproar owing to the change it would bring to the character of the neighborhood. The argument in favor was the revitalization of the area, that type of story. I fought the proposal on the following grounds: should the company go bust (and the statistical elephant in the room is that it eventually will), we would end up with a massive war zone. This is the type of argument the British advisors Rohan Silva and Steve Hilton have used in favor of small merchants, along the poetic “small is beautiful.” It is completely wrong to use the calculus of benefits without including the probability of failure.2