taleb

Taleb is a former trader who wrote a textbook on option and market making, and then became more philosophical in his best seller Fooled by Randomness, and now in The Black Swan. He considers his current occupation to be an “essayist & epistemologist of randomness”. Taleb’s general point is that we are generally prejudiced, biased and overconfident. True enough, but these observations at a general level are rather banal. I suppose many are hesitant to dismiss Taleb as a crank because he claims such a broad scope of expertise (he asserts he is not so much an expert on finance, but rather on “French literature, ancient & medieval Mediterranean history & languages, probability theory, and medieval Judeo-Arabic philosophy”), and most careful researchers are hesitant to make assertions outside their fields. Taleb’s confident assertions in these varied areas are compelling to many because of their unapologetic nature, as only a fool or a genius would make such bold statements. How could Taleb be a fool if he so specifically emphasizes the foolishness of ‘experts’;- clearly his self-actualization would suggest this is improbable. Like a researcher who highlights the bias of others, how could he be biased?

Easy. Many times, writers embody their main criticisms, as in the famous aphorism: “if he says it’s not about the money, it’s about the money.” Prominent stylists, such as Freud, Ayn Rand, L Ron Hubbard who have cowed their audience into appreciation with implacable self-esteem, have often been seen as geniuses by adoring intellectuals (at least briefly). There is something compelling about sureness, and Taleb's criticisms are funny because they are most appropriate in describing himself.

Taleb’s style is to criticize experts of all sorts severely, while implying that both he and his reader or listener are exempt from their many biases. He does this with a thinly disguised false modesty, and tolerance for faulty grammar and even spelling as if this highlights that he only cares about truth, not style. Lambasting ‘experts’ in this way is a popular tactic. Reading someone deflating puffed-up egos, criticizing the insular world of academics, and suggesting the experts have a huge blind spot on something important, can be fun reading. But it has to be making points that are true if new, or important if true, and here he fails to deliver.

For someone advocating doubt and criticizing expert and 'regular' people’s overconfidence and arrogance, Taleb’s writings are filled with certainty and immodesty, having the Godelian impossibility of someone shouting 'I am the most humble!' While people are generally overconfident about their diving ability or common sense, does that same overconfidence lead people to underestimate the probability of market crashes, and thus the price of insurance (eg, put options?) The data suggest the opposite is true, that is, that people overpay for such improbabilities based on hope. A psychological observation is not necessarily economically important, because markets tend to elicit results not from unmotivated an ignorant masses, but from a highly motivated and informed subset. People willing to offer ‘a side’ to such a bet tend not merely to be unbiased, but also pad their bets with a considerable safety margin so that their errors are not catastrophic, which in practice means you obtain much lower odds for improbable events than what simple surveys would imply.

Many of Taleb's assertions are riffs on the themes of chaos and uncertainty, interesting but not very fruitful.

Benoit Mandelbrot has been trying to sell the world on a big idea for several decades. James Gleick’s Chaos outlined the essence of Benoit Mandelbrot’s fractals, which takes a simple few lines of inputs to create graphics of insane complexity yet also beautiful recursive symmetry, in many cases eerily similar to nature (eg, ferns, snowflakes). In dynamic systems, you have chaotic systems that are purely deterministic though sufficiently complex that they appear random. These systems have large jumps, or phase shifts, reminiscent of market crashes or sudden bankruptcies; they have butterfly effects where small changes produce big differences in outcomes. Mandelbrot and others have been trying to apply these ideas to financial markets for many decades now, and the effort has not gained any traction. Mandelbrot’s big idea applied to finance is that it relies on flawed assumptions. The main error is that market prices are normally distributed. Mandelbrot argues market prices have much fatter distributions described by Cauchy distributions. This means that catastrophic drops in market prices happen more frequently than a normal distribution suggests.

The result of these mistaken assumptions is to understate risk, according to Mandelbrot, and so overprice stocks and underprice options, and also understate the capital cushion financial institutions need to withstand market risk. Mandelbrot’s alternative approach is based on new parameters that would replace the mean return and volatility of return or standard deviation. His first parameter is Alpha, derived from Pareto's Law, is an exponent that measures how wildly prices vary. It defines how fat the tails of the price change curve are. The second one, the H Coefficient, is an exponent that measures the dependence of price changes upon past changes.

Unfortunately, people looking at the same data will generally estimate different parameters as Alpha and H. Using one method, you could derive Alpha and H coefficients that suggest a stock is not risky; using another method, you would reach the opposite conclusion (remember, in these environments, small differences in initial values have big impacts). If the important parameters cannot reasonably pin down important differences in the ultimate output, application is relegated to hindsight, which is not a compelling alternative to the status quo. The output 'looks like' a financial time series, but it could be any time series, so is merely thematically suggestive because you can't parameterize it to fit any particular time series. It's like someone discovering another pseudo-random number generating algorithm, and then thinking they have discovered a great insight. Thus fractals remain a fringe approach to finance, decades after trying to apply it.

Frank Knight, meanwhile, in his classic Risk, Uncertainty, and Profit in 1921, outlined the basic idea that it is uncertainty, in the form of non-quantifiable dispersion, that is at the root of profits. The basic idea is that risk, once quantified, is diversifiable, and thus becomes risk-free. If you know that your champagne bottle could burst while fermenting with probability p, that number becomes very manageable the larger your operation via the law of large numbers. Economists have been intrigued by this notion ever since, but by definition it is unquantifiable so when you write down a random process, it is no longer Knight-like, making it rather elusive. The best we can do is assert areas where it is reasonable to assume Knightian uncertainty is more operative, but no one has found an area where high amounts of such uncertainty generate higher returns. Nonetheless, it first articulated the common practitioner complaint that uncertainty is not like a roulette wheel, but something quite different.

These are intriguing ideas, but they have been around a while, and no one has been able to do much with them.

Taleb’s career as a talking head started in 1996 when, as the author of a niche derivatives text, his outrageous claim in Derivatives Strategy magazine that the new Value-at-Risk phenomenon was worse than useless, made for great debate in risk management circles. I was leading a Value-at-Risk project at the time, so of course I found his criticisms of interest. JPMorgan had just introduced this method of aggregating risks in a highly popular practitioner brief, Riskmetrics. RiskMetrics outlined in detail the methods of estimating volatility when you had a portfolio of currencies, bonds, equities, and even options. Previously, financial books that contained bonds, currencies, equities, etc., each had little silos of risk reports, but this showed how they could be combined, basically by putting everything into a factor approach, in which every asset has a sensitivity to a factor, and every factor has a certain correlation and volatility. This was not new—factor analysis had been around for a while—but its clear application to a tangible problem was insightful, and created a lot of buzz.

It was not a panacea, but it was an improvement. Taleb’s criticisms of VAR then are similar to his criticisms now: that a metric is not flawless, and those who believe it is flawless are fools. In a trivial sense he is right, but in the case of VAR, or specific parametric statistics, or expectations in general, there are many users who understand that tools need to be supplemented by judgment. It is a cliché on the risk management lecture circuit that you need not just technical knowledge, but judgment, mainly by senior executives who don’t have any technical knowledge. Of course, Taleb was dead wrong on VAR, in that in spite of his criticisms it became ubiquitous as a framework for amalgamating risks from different instruments into a single metric, but ‘experts’ aren’t judged by prognostication (a theme Taleb mentions when discussing experts in other domains).

If you were to list all the financial bankruptcies, the one common thread would be that they blindsided investors with their exposures. Who knew Orange County had such a position against interest rates ex ante? Who knew Barings had such an exposure to a trader in Singapore ? These were not properly calculated risks that went awry, nor were they outright fraud where an unauthorized intraday position blew up. They were the result of investors or management not fully understanding the risks that were being taken, which often a correctly calculated VAR number, correctly communicated, would have easily shown. The errors were essentially combinations of VAR mistakes and breakdowns in incentives communication.

If operating risk is the primary reason why trading operations fail, emphasis on refining VAR seemingly misses the point. Operating risk is neglected for good reason, however, in that it is extremely difficult to quantify existing operating risks, which in turn makes it nearly impossible to evaluate methods of monitoring and reducing these risks. Yet just as Eisenhower stated it is essential to plan prior to battle even though once a battle has commenced the plan is useless, VAR is essential in planning the allocation of capital, yet in risky situations becomes useless. This is not a paradox, but merely the fact that when we train for competition, we practice tactics and strategies. Inevitably competition, especially competitions we ‘lose’, will bring forth new situations we have not prepared for, but the best preparation for such an occurrence is not nihilism, but more practice. And indeed many new situations are avoided by practice.

Taleb argues that the unpredictability of important events implies we should basically forget about all that is predictable, because that’s not where the real money or importance is. So from a risk management perspective, we should ignore Value at Risk, which measures anticipated fluctuations. Further, we should ‘go long’ on these unanticipated events by engaging in quirky activities on the off-chance that we randomly find something, or someone, really valuable.

Success in markets, like life, is a combination of ability, effort, and chance. Much of intelligent thought is distinguishing between what is predictable v. what is unpredictable; it is to any organism's advantage to find out what we can figure out and change, and what is forever mysterious and unalterable (eg, the Serenity Prayer). The brain is constantly predicting the environment, trying to figure out cause and effect so it can better understand the world. Most of what humans process is predictable, but because we take predictable things for granted, they are uninteresting. We can't predict some things, but instead of resorting to nihilism, we merely buy insurance or manage our portfolios--in the broad sense of the term--to have an appropriate robustness. Discovering certain things are basically unpredictable does not diminish our constant focus on trying to predict more and more things. People will disagree on which risks at the margin are predictable, but that's to be expected, and we all hope to be making the right choices that optimize our serenity at the margin of our predictable prowess.

Of course, in the face of being totally wrong in his evaluation of the usefulness of VAR as a tool — it’s ubiquitous in practical management of diverse trading books — Taleb now says he merely warned against naive usage of VAR. However, it was only his absurdly strong statement that VAR was for charlatans that got him mentioned in the Derivatives Strategy article that propelled him into public discourse (conveniently removed from his website, but you can read it online here). Then, as now, he points to anecdotes of imperfection to "prove" his points.

From Taleb's Wikipedia entry circa July 2006, we see where Black Swan thinking goes when applied to an investment strategy:

When he was primarily a trader, he developed an investment method which sought to profit from unusual and unpredictable random events, which he called "black swans." His reasoning was that traders lose much more money from a market crash than they gain from even years of steady gains, and so he did not worry if his portfolio lost money steadily, as long as that portfolio positioned him to profit greatly from an extremely large deviation (either a crash or an unexpected jump upwards).

In fact, Mandelbrot also argues for this strategy. Taleb co-authored a paper arguing that most people systematically underestimate volatility. Furthermore, he argues there exists not only a lack of appreciation of fat tails, but a preference for positive skew, in that people prefer assets that jump up, not down, which would imply the superiority of buying out-of-the-money puts as opposed to calls because those negative tails that increase the price of puts are unappreciated.

These assertions present some straightforward tests, which a Popperian like Taleb should embrace. Specifically, buying out-of-the-money options, especially puts (because of negative skew), should, on average, make money. But insurance companies, which basically are selling out-of-the-money options, tend to do as well as any industry (Warren Buffet has always favored insurance companies, especially re-insurers, as equity investments). Studies by Shumway and Coval (2001) and Bondarenko (2003) have documented that selling puts is where all the extranormal profit seems to be. Of all the option strategies, selling, not buying, out-of-the-money puts has been the best performer historically.

Famed New Yorker writer Malcom Gladwell in a 2002 New Yorker article contrasts the thoughtful, pensive Taleb versus the brash cowboy Victor Neiderhoffer: Taleb buys out-of-the-money puts, Neiderhoffer sells them. Taleb is betting on the big blow up, Niederhoffer on the idea that people overpay for insurance. Who was right? Well, Neiderhoffer still ran his flagship fund until September 2007 from a chalet-style mansion in Weston Connecticut . Taleb shut down his Empirica Kurtosis fund at the end of 2004, and the only public data on it suggest a rather anemic Sharpe ratio, below that of the S&P500 (60% in 2000, about zero for the next 4 years, see here), which is consistent with shutting it down, and trying to redescribe it as a hedge or laboratory, and then move into the more profitable business of teaching how to invest. While neither strategy was great, Niederhoffer's was better, if you just look at their lifetimes (management, in this case Taleb, always likes to say that people left positions of power due to desires to be with family or other opportunities, but the bottom line is, selling puts remained immune to family considerations longer than buying puts).

Taleb's big problem is that he misinterprets the mode-mean trade. A mode-mean trade is where a trader finds a strategy with a positive mode, but zero or negative mean. He then uses someone else’s capital to make money off several years of good returns, making good money for creating or managing the strategy, then, when the strategy gives it all back, the investor bears all the loss. That’s a bad strategy for the investor, and the trader who manages it is either naïve or duplicitous. That is, selling extreme options or writing insurance on extreme events at any prices generates a good mode return, but if it underestimates the probability or severity of the bad times, it may generate a zero or negative average return. Buying High Yield debt is a good example. However, just because selling puts is a bad strategy, it doesn't mean buying puts is a good strategy. A Sharpe of 0.2 is a bad long position, but a worse short (because a - 0.2 Sharpe is worse than a 0.2).

The ‘Black Swan’ is something that is totally unexpected, and important (by that definition, the Black Swan is not a ‘Black Swan’ because Black Swans are not important. Such is the profundity of Taleb that his thematic icon itself is inconsistent). But we get the picture: people assumed all swans were white, but then, they saw a black swan, and every little guy who was so certain all swans were white was wrong! That’s a 'gotcha game' for people who really take seriously someone’s assertions on the color of birds. But when there’s a price involved, the payoff to such an insight is not obvious, if not totally absent. For example, London bookmakers offer ‘only’ 250-1 odds a perpetual motion machine will not be discovered, and 100-1 odds aliens won’t be contacted: longshots ignored in a casual context are overpriced in actual markets.

In option markets, there is a volatility smile, whereby out-of-the-money options have higher implied volatilities, especially on the downside. For example, in May 2006 when rumors of GM's woes were large and its stock price was around 32, GM options had a one-year at-the-money implied volatility of 60, but down at a strike price of 15 its volatility is a much higher 140. The fact that Black-Scholes assumes lognormal returns does not imply market participants think likewise, so it is really ignorant to assert that a market collapse of 23 standard deviations was totally unexpected, because that assumes someone was not only asserting stock prices are lognormally distributed, but willing to put money down on this assertion. You can't profit from the idea that market returns have fat tails because that's priced into the market via the volatility smile, and this volatility smile shows up in 'disaster' insurance of all types: People pay a lot to sleep easy. Many people have looked at option prices, and they all find that out-of-the-money puts are the most overpriced of all options—people are expecting ‘Black Swans’ too much.

Taleb responds by noting that the 1987 stock market crash changed everything, because if you bought puts then, you would have made enough money to make up for decades of otherwise weak performance. While Shumway and Coval do not include 1987 in their academic study, Bonderanko does, and gets the same results. Taleb points out several anecdotes of financial market crises as further evidence of the importance of financial debacles, such as the 1998 crisis related to Long Term Capital Management (implied vols, libor spreads, skyrocked), or the emerging markets blow up of 1997. These events made money for people with long volatility, or specifically short puts, but the plural of anecdote is not data, so he should have cited an empirical paper showing the positive abnormal returns to taking on fat-tailed or asymmetric risk. Though it is easy to recall big blowups, one has to put them in full context, against the cost of insuring against these events over long periods of time. The volatility smile, and large bid-ask spreads in the extremes as a function of price, imply you can’t make extranormal profits by going long ‘Black Swans’ - at least in the markets where Taleb has the most experience (though not, according to him, expertise, which is more philosophically oriented). Perhaps as a trader, where he did not have to cross the bid-ask spread, but instead received it, he bolstered his intuition that buying out-of-the-money options was a good strategy. Many good strategies for traders don’t work well when you have to pay the bid-ask spread as opposed to receive it.

The bottom line is that people tend to underappreciate low probability events when they are immaterial--because they are immaterial! So they underestimate the prevalence of Black Swans because if you find one, who cares? But hurricane insurance, a 3-delta put option? You will pay up for that. Improbable yet economically significant items are generally overpriced. Reading Taleb, you are encouraged to buy all improbable things, a transparently suboptimal strategy.

In the end, he promises to teach us how to take advantage of these Black Swans. His strategy is pretty simple. He argues for a barbell strategy of much safety, and a dollop of wild risks, which is, basically, an exposure to something totally unquantifiable, like Llama farms, or any of the myriad opportunities neighbors, spammers, and late-night paid-TV tout. In the context of Tobin’s two fund separation theorem, this means the ‘efficient’ risky portfolio is the most insanely unquantifiable and risky portfolio you can imagine, tempered by its modest allocation. Yet this implies the unquantifiable and risky portfolio has very good returns, which by definition (unquantifiable) is merely an assertion.

There is good reason, however, to suspect one loses money on the wildest risks. Consider longshot odds at the racetrack and the highest payout (and thus riskiest) lottery tickets. Researchers have found a negative return premium for highly volatile stocks. Applied to ‘uncertainty’, this same pattern holds, as stocks with the most earnings forecast estimation error also have the most volatility, so it is no surprise they too have a negative premium. Truly improbable scenarios generally involve more hope than rational investment, as people will pay you to help them dream of the chance to become incredibly rich in the same way that the biggest lotteries, with 100 million to 1 odds, have the highest jackpots and the lowest mean returns. There are an infinite number of companies that directly target people wishing to make an end run around the rat race, and most of these companies are engaged in selling nothing more than hope (see Imergent). Whatever unexpectedly happens, Taleb will claim it was exactly what he meant by wild uncertainty. This is classic broker advice.

Black Swan argues that standard statistics is flawed because it is backward looking — it uses ‘historical’ data — and argues that standard measures of risk like the normal distribution are ‘frauds’. The Gaussian distribution is common in theory because it is so analytically tractable; it often creates closed form solutions that allow one to see how one variable affects another, and has nice properties, such as the fact that two Gaussian random variables added together is also a Gaussion random variable. In practice, no one actually believes in this view, and makes ad hoc adjustments, such as the volatility smile for option prices. The key is that from an expositional point of view, the Gaussian distribution usually gives one the gist of the true ‘fatter-tailed’ distribution, and allows easy exposition. Non-economists often giggle at the term ‘fat-tailed’ or homoskedasticity, but indeed most real world distributions are not ‘Normal’ or Gaussian, they simply have fatter tails than average. Does this imply statistics is a fraud? Well, if you mistake the map for the territory, indeed, this is news. For everyone with an IQ above 115 or some experience in the field, it’s an approximation or expositional device.

Taleb belittles predictions that have large or unmentioned error rates, yet any specific error metric (standard deviation, value-at-risk, correlation, R2, etc) is, in his mind, a fraud and useless because it relies on an assumption, one that is 'wrong'. He argues we reward those who imagine the impossible, but what does that mean in practice? That we encourage people to enumerate everything possible no matter how improbable? In finance, these risk reports are all too common because they reflect a lot of work, in that generating a list of unprioritized things that could happen is easy but practically useless, because you simply can’t address all the points and so must leave them as mere ‘I told you so’ observations. One can remember Richard Clarke’s vague warning about Al Qaeda prior to 9/11, which in no way suggested that changes to hijacking protocols or airline boarding should be made, but rather that something could happen, true but unhelpful.

Getting people to highlight wild risks comes easy, which I think is part of his book’s appeal. Legislators and personal-injury lawyers eagerly hype risks with negligible real impact, like secondhand smoke, or getting cancer from trace amounts of chemicals. Sometimes they create considerable public concern about risks that don't exist, like that of contracting anti-immune disease from breast implants, or cell phones causing cancer. Newsrooms are full of English majors who acknowledge that they are not good at Math, but still rush to make confident pronouncements about global-warming or some other complicated process, all in hopes of getting viewers or readers activated.

I could imagine Taleb teaching a statistics class to freshman and instead of starting with the arithmetic mean and standard deviation, asking 'what was the probability of an airplane taking down the World Trade Center on September 10, 2001?', and waxing poetic about how ‘we just don’t know!” Students might think such talk is much "cooler" than boring formulas, but such confused thinking leads nowhere in particular and can be indulged indefinitely without producing anything useful, as Taleb demonstrates. Of course one needs technical knowledge and common sense in anything, but while you can teach one, you can't teach the other. We teach statistics, calculus, etc., not because it solves every problem, but because it can help in many problems to delineate and potentially manage that which we can change from that which we can’t.

Martin Gardner wrote a popular column for Scientific American, and in the process received a lot of mail from ‘cranks’ telling him about perpetual motion machines and the like. So he wrote a book called Fads and Fallacies. In the book he describes "cranks" as having five invariable characteristics:

On his personal website, Taleb once described himself as being "an essayist, belletrist, literary-philosophical-mathematical flâneur." The third-person is perfect pitch for describing himself, and the other, well, literary-philosophical-mathematical types,- especially flâneurs - tend to be 'full of themselves,' supporting Gardner ’s characteristic #1. He prides himself on not submitting articles to refereed journals (one can sense the rejection), considers most people who are indifferent to him as fools, and disdains editors, even spellcheckers (#2). He proudly notes that someone told him “in another time he would have been hanged [me: for what, inanity?].” Wilmott Magazine, a quant publication published by his colleague Paul Wilmott, wrote a fawning article about him in which they noted that he is “Wall Street’s principal dissident. Heretic! Calvin to finance’s Catholic Church” (#3). His website states his modest desire to understand chance from the viewpoint of “philosophy/epistemology, philosophy/ethics, mathematics, social science/finance, and cognitive science”, supporting #4. Lastly, for #5, he has gone so far as to print a glossary for his neologisms (eg, “epistemic arrogance” for “overconfidence”). In Martin Gardner’s taxonomy, Taleb is a classic crank.

Clearly his experience as an options trader gives him credibility, but let us look at this experience. Before he became a regular on the talking-head circuit and expert on Judeo-Arabic philosophy, he was primarily a trader for large market makers. These are not speculators investing their wealth based on insights, but more like brokers, making money off customer flow, only their buyers and sellers are the guys on the phones talking to retail clients. Such traders spend most of their time looking at a model such as Black-Scholes that tells them what price to buy and sell based on some underlying parameters. These models are more or less standard, and so the main thing the market maker has to do is keep his model inputs fresh, post prices to potential buyers and sellers, fill market orders, and pick off stale limit orders. Customers generally have access to older prices, and in a situation where the current price moves every second, this clearly puts a trader at an informational advantage, which is why it was such a lucrative field, especially in the days before the internet became big (ie, Taleb's time). The trader makes money irrespective of movements in the underlying model price, as in general he keeps his exposure to first-order (eg, delta) and second order (eg, vega) risks as close to zero as possible.

But such trading skill is quite distinct from what a speculator or investor does, which involves a directional bet on the first or second order risks that traders normally try to erase. Traders know as much about what makes prices move as plankton knows about what makes the tides move. Much of being a trader is encouraging trading activity from a hesitant broker, and so many traders are quite adept at presenting themselves as more than middlemen, but also men with an angle or a story. A good trader is probably truly delusional about his prognostic abilities because this allows him to appear sincere in his sales pitch for the latest trade idea; those who don't believe their own stories make weak sales pitches (see Robert Trivers, who Taleb mentions favorably in The Black Swan). Most of these traders are certain they could make money without their customer flow, because the same self-deception that serves them well chatting up brokers or impressing their boss generates delusions of strategic grandeur. Supreme self-assurance, even if undeserved, just as much as knowing your Greeks, makes for a good trader . Thus Taleb’s ‘narrative fallacy’ argument plays right into his own biases, that is, he has fooled himself into thinking he knows 'the big picture' because that delusion was helpful in his own career.

Rich investor or rich broker: Who is the more easily fooled about his alpha? Notice the relation to the theme of Fooled by Randomness? Taleb is consistently amusing because his criticisms of others apply so neatly to himself: he claims he is an empiricist yet supports his points with anecdotes. The Black Swan makes fun of ‘experts’ with credentials, but he states he does not deign to engage with anyone not sufficiently expert; he states he is not interested in being a speaker-bureau commodity , but routinely travels the rubber chicken circuit; he derides forecasters who don't give a full accounting of their prior forecasting history, yet delinks old remarks about Value-at-Risk, and recategorized his extinct Hedge Fund as a hedge, not a fund; he claims to prize humility, yet is most immodest; he argues against applying the law of large numbers, and also of inferring too much from small samples; people apply models to reality in biased manner, people naively extrapolate data without the appropriate theory; forward thinking is adaptive, forward thinking is error-laiden. Some people think inconsistency is a sign of genius; I think it just reflects confused thinking.

To be popular, it is helpful to make people think they are thinking, and a self-serving message makes this more attractive still. Taleb has managed to dress up some old and unwieldy ideas from Frank Knight and Benoit Mandelbrot, and suggest they are novel and important. They are interesting, to be sure, but they have remained curiosities because they don’t have any good, practical applications, and, in the case of embracing wild uncertainty, are simply foolhardy (invest in llama farms) or meaningless ('expect the unexpected'). The bumper sticker "shit happens" is kind of funny, kind of true, but hardly profound.

Nassim Taleb's Black Swan