”It’s not the bad ideas that do you in, it’s the good ideas. And you may say, ‘That can’t be so. That’s paradoxical. What he [Graham] meant was that if a thing is a bad idea, it’s hard to overdo. But where there is a good idea with a core of essential and important truth, you can’t ignore it. And then it’s so easy to overdo it. So the good ideas are a wonderful way to suffer terribly if you overdo them.”

― Charles T. Munger, Poor Charlie’s Almanack: The Wit and Wisdom of Charles T. Munger


“I do not mean to suggest that the Greeks gave no thought to the nature of probability. The ancient Greek word EIKOS (eikos), which meant plausible or probable, had the same sense as the modern concept of probability: “to be expected with some degree of certainty.” Socrates defines Elkos as “likeness to truth.”10 Socrates’ definition reveals a subtle point of great importance. Likeness to truth is not the same thing as truth. Truth to the Greeks was only what could be proved by logic and axioms. Their insistence on proof set truth in direct contrast to empirical experimentation. For example, in Phaedo, Simmias points out to Socrates that “the proposition that the soul is in harmony has not been demonstrated at all but rests only on probability.” Aristotle complains about philosophers who, “… while they speak plausibly,… do not speak what is true.” Elsewhere, Socrates anticipates Aristotle when he declares that a “mathematician who argues from probabilities in geometry is not worth an ace.”11 For another thousand years, thinking about games and playing them remained separate activities. Shmuel Sambursky, a distinguished Israeli historian and philosopher of science, provides the only convincing thesis I could find to explain why the Greeks failed to take the strategic step of developing a quantitative approach to probability 12 With their sharp distinction between truth and probability, Sambursky contends in a paper written in 1956, the Greeks could not conceive of any kind of solid structure or harmony in the messy nature of day-to-day existence. Although Aristotle suggested that people should make decisions on the basis of “desire and reasoning directed to some end,” he offered no guidance to the likelihood of a successful outcome. Greek dramas tell tale after tale of the helplessness of human beings in the grasp of impersonal fates.”

-Peter Bernstein, Against the Gods


“Greater knowledge of a danger permits greater safety. For centuries, shipbuilders have put care into the design of their hulls and sails. They know that, in most cases, the sea is moderate. But they also know that typhoons arise and hurricanes happen. They design not just for the 95 percent of sailing days when the weather is clement, but also for the other 5 percent, when storms blow and their skill is tested. The financiers and investors of the world are, at the moment, like mariners who heed no weather warnings.”

– Benoit Mandelbrot, The Misbehavior of Markets

Fat Tails

“First, price changes are not independent of each other. Research over the past few decades, by me and then by others, shows that many financial price series have a “memory,” of sorts. Today does, in fact, influence tomorrow. If prices take a big leap up or down now, there is a measurably greater likelihood that they will move just as violently the next day. It is not a well-behaved, predictable pattern of the kind economists prefer-not, say, the periodic up-and-down procession from boom to bust with which textbooks trace the standard business cycle.

Examples of such simple patterns, periodic correlations between prices past and present, have long been observed in marketsin, say, the seasonal fluctuations of wheat futures prices as the harvest matures, or the daily and weekly trends of foreign exchange volume as the trading day moves across the globe.

My heresy is a different, fractal kind of statistical relationship, a “long memory.” This is a delicate point to which a full chapter will be devoted later. For the moment, think about it by observing that different kinds of price series exhibit different degrees of mnemory. Some exhibit strong memory. Others have weak memory. Why this should be is not certain; but one can speculate. What a company does today–a merger, a spin-off, a critical product launch shapes what the company will look like a decade hence; in the same way, its stock-price movements today will influence movements tomorrow.

Others suggest that the market may take a long time to absorb and fully price information. When confronted by bad news, some quick-triggered investors react immediately while others, with different financial goals and longer time-horizons, may not react for another month or year.

Whatever the explanation, we can confirm the phenomenon exists-and it contradicts the randomn-walk model.

Second, contrary to orthodoxy, price changes are very far from following the bell curve. If they did, you should be able to run any market’s price records through a computer, analyze the changes, and watch them fall into the approximate “normality” assumed by Bachelier’s random walk. They should cluster about the mean, or average, of no change. In fact, the bell curve fits reality very poorly.

From 1916 to 2003, the daily index movements of the Dow Jones Industrial Average do not spread out on graph paper like a simple bell curve. The far edges flare too high: too many big changes. Theory suggests that over that time, there should be fifty-eight days when the Dow moved more than 3.4 percent; in fact, there were 1,001. Theory predicts six days of index swings beyond 4.5 percent; in fact, there were 366. And index swings of more than 7 percent should come once every 300,000 years; in fact, the twentieth century saw forty-eight such days. Truly, a calamitous era that insists on flaunting all predictions. Or, perhaps, our assumptions are wrong.”

– Benoit Mandelbrot, The Misbehavior of Markets

Financial Engineering

“We could be either too lax or too stringent in accepting past information as a prediction of the future. As a skeptic, I reject a sole time series of the past as an indication of future performance; I need a lot more than data. My major reason is the rare event, but I have plenty of others.

On the surface, my statement here may seem to contradict earlier discussions, where I blame people for not learning enough from history. The problem is that we read too much into shallow recent history, with statements like “this has never happened before,” but not from history in general (things that never happened before in one area tend eventually to happen). In other words, history teaches us that things that never happened before do happen. It can teach us a lot outside of the narrowly defined time series; the broader the look, the better the lesson. In other words, history teaches us to avoid the brand of naive empiricism that consists of learning from casual historical facts.

Somehow, what came to be known as the Lucas critique was not carried through by the “scientists.” It was confidently believed that the scientific successes of the industrial revolution could be carried through into the social sciences, particularly with such movements as Marxism. Pseudoscience came with a collection of idealistic nerds who tried to create a tailor-made society, the epitome of which is the central planner. Economics was the most likely candidate for such use of science; you can disguise charlatanism under the weight of equations, and nobody can catch you since there is no such thing as a controlled experiment. Now, the spirit of such methods, called scientism by its detractors (like myself), continued past Marxism, into the discipline of finance as a few technicians thought that their mathematical knowledge could lead them to understand markets.

The practice of “financial engineering” came along with massive doses of pseudoscience. Practitioners of these methods measure risks, using the tool of past history as an indication of the future. We will just say at this point that the mere possibility of the distributions not being stationary makes the entire concept seem like a costly (perhaps very costly) mistake. This leads us to a more fundamental question: the problem of induction.”

– Nassim Nicholas Taleb, FOOLED BY RANDOMNESS, The Hidden Role of Chance in Life and in the Markets