At first glance, this brightly decorated room is no different from that of any other elementary school. Shelves are filled with storybooks; on the chalkboard, a vertical line of words reads ”prudence,” ”pretzel,” ”prairie,” ”purple.” But the nervous agitation of the boys’ hands, punctuated by occasional odd flapping gestures, betrays the fact that something is off kilter. There is also a curious poster on one of the walls with a circle of human faces annotated with words like ”sad,” ”proud” and ”lonely.” When I ask Cacciabaudo about it, she explains that her students do not know how to read the basic expressions of the human face. Instead, they must learn them by rote.
“It’s not necessarily about money, it’s about winning,” he told a visiting group of American college students. He told them that to understand trading, they needed to forget everything they learned in economics class and envision the amoral, take-no-prisoners world of “The Hunger Games.”
“The only time when people cooperate is to prolong their own lives,” he said. When rivals are no longer useful, “you stab them in the back.”
He told students he had accepted the fact that he was a rogue trader—but in his telling, it didn’t sound all that sinister.
A rogue trader, he said, “is a risk taker. It’s not a crime. It’s violating the mores established by the institution that you work for. It’s a rebellion against institutional controls that deny individuals opportunities for self-actualization.”
Vervet monkeys are known for their alarm calls. A monkey will scream to warn its neighbors when a predator is nearby. But in doing so, it draws dangerous attention to itself. Scientists going back to Darwin have struggled to explain how this kind of altruistic behavior evolved. If a high enough percentage of screaming monkeys gets picked off by predators, natural selection would be expected to snuff out the screamers in the gene pool. Yet it does not, and speculation as to why has led to decades of (sometimes heated) debate.
Researchers have proposed different possible mechanisms to explain cooperation. Kin selection suggests that helping family members ultimately helps the individual. Group selection proposes that cooperative groups may be more likely to survive than uncooperative ones. And direct reciprocity posits that individuals benefit from helping someone who has helped them in the past.
In “The Psychology of Invention in the Mathematical Field,” published in 1945, Jacques Hadamard quotes a mathematician who says, “It often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.” In the back yard, Zhang had a similar experience. “I see numbers, equations, and something even—it’s hard to say what it is,” Zhang said. “Something very special. Maybe numbers, maybe equations—a mystery, maybe a vision. I knew that, even though there were many details to fill in, we should have a proof. Then I went back to the house.”
To illustrate the phenomenon, consider the S&P’s daily percentage returns in terms of quantiles, which divides the performance record into equal-sized portions. The graph below plots the sample return of the S&P (black circles) against the theoretical quantiles (red line), defined here by a random distribution. If the S&P’s daily returns were perfectly random, the black circles would match the red line.
Normal distributions are still useful for analyzing markets and designing portfolios. Indeed, even in the daily return plot above it’s clear that the distribution looks quite normal for a fair amount of the sample. We can’t rely on normality alone for modeling markets. Factoring in fat-tails risk is essential. But letting a fat-tail worldview dominate your analysis is every bit as flawed as assuming that normal distributions will prevail. Asset pricing doesn’t neatly fit into one theoretical box, which means that our analytical tool kit shouldn’t be in a conceptual straightjacket either.