The Money Formula. Wilmott Paul

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СКАЧАТЬ men.” While Newton may not have tried to calculate the markets, and preferred chemical alchemy to the financial kind, he probably did more to shape the world of mathematical finance than any other scientist. His law of gravity, coupled with his three laws of motion, provided an archetype for a successful mathematical model that would influence not just areas such as physics and chemistry, but also social sciences including economics, and serve as an inspiration for quants to the present day.

      One person who appreciated the power of Newton's approach was Adam Smith. He is of course best known for his book The Wealth of Nations,10 which was the first to present economics as an objective, rational science, separate from areas such as ethics and political science. Some insight into his motivations is provided, however, by an earlier work on astronomy, written around 1758 but not published until after his death, in which his examination of “all the different systems of nature” culminates in a celebration of “The superior genius and sagacity of Sir Isaac Newton.” He was less impressed by John Law. As he wrote in The Wealth of Nations, “The idea of the possibility of multiplying paper to almost any extent was the real foundation of what is called the Mississippi scheme, the most extravagant project both of banking and stock-jobbing that, perhaps, the world ever saw.” (Smith would no doubt have been surprised to learn that we now organize our economies around Law's idea of a fiat currency, which was ahead of its time, rather than Newton's gold standard.)

      Smith saw philosophy as a kind of calming device for making sense of the world, with its random events and its John Laws, its “chaos of jarring and discordant appearances.” The beauty of Newton's method was the way in which it took a simple idea, such as gravity, and showed how “all the appearances, which he joins together by it, necessarily follow.”

      In the same book, Smith makes his first mention of the invisible hand. However, the passage was about the tendency for polytheistic religions to interpret events as being caused by gods: “the invisible hand of Jupiter.” It was only later that he attributed this miraculous power to the markets. In The Theory of Moral Sentiments, he used the term in the context of wealth distribution: the rich “divide with the poor the produce of all their improvements. They are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society.” (We wonder if he asked the poor.) Finally, and most famously, the phrase pops up again in The Wealth of Nations, in which – in a section on trade policy – an individual is again “led by an invisible hand to promote an end which was no part of his intention.”

      No one paid any attention to the metaphor until 1948, when Chicago School economist Paul Samuelson published his textbook Economics, which would go on to become the best-selling economics textbook of all time, translated into over 40 languages.11 As he paraphrased: “Every individual, in pursuing only his own selfish good, was led, as if by an invisible hand, to achieve the best good for all, so that any interference with free competition by government was almost certain to be injurious.” Which is when widespread use of the term, both in academic papers and general use, suddenly took off.12

      Box 1.1 On the Couch

      As mentioned above, it's unreliable to psychoanalyze people who aren't around to lie down on the couch, and sometimes it's annoying – as in the 2014 film The Imitation Game, in which Benedict Cumberbatch, the actor playing mathematician Alan Turing, might as well have worn a button saying “Hi, I have Asperger's!” Also, we're not psychologists and have no idea what we're talking about. But Adam Smith does seem worth a look.

      From our case notes, it seems that tales abound of Smith's bizarre character. Friendly and good-tempered, he was also, according to one friend, “the most absent man in Company that I ever saw, Moving his Lips and talking to himself, and Smiling.”13 He did things like absentmindedly walk into a tanning pit, from which he needed to be rescued, or go for a stroll in his nightgown and end up 15 miles outside town. He was frequently ill and his doctors diagnosed him as a hypochondriac. He had no known serious romantic relationships, and lived with his mother (his father died two months after he was born) until she died at the age of 90, just six years before his own death in 1790. As his biographer Dugald Stewart noted, Smith was “certainly not fitted for the general commerce of the world, or for the business of active life.”14

      Usually these quirks are presented as the harmless foibles of a genius – but there does seem to be a connection with this invisible hand business.

      As UCLA's Şule Özler wrote in the journal Psychoanalytic Review, Smith was financially dependent first on family income, and then on “rich businessmen, gentry, intellectuals, and aristocrats for teaching positions and his pension.”15 And there is a striking contrast between his life and his economic theories. “Denying his reality of lifelong dependence on his mother and benefactors, Smith appears to have idealized independence,” according to Özler. The invisible hand, after all, only works if everyone acts independently to further their own interests, without collusion. There is no room for things like money, power, or the fact that we can be financially dependent on one another.

      Smith found solace and refuge in Newtonian laws, which treated people as independent atoms, and he turned the market into a kind of parental figure that always knows what is right. Rather like a lot of modern economics then (whose practitioners often have about as much experience as Smith of “the general commerce of the world”).

Rational Mechanics

      Smith's work was influential on the USA at the time of its formation – the Founders were early readers of his work – and remains so today. Economist George Akerlof describes the “central ideology” of the United States as conforming to “the fundamental view of Adam Smith,” which even today “drives huge amounts of policy” (he should know, being married to Federal Reserve Chair Janet Yellen).16 According to this picture, the market is made up of firms and individuals acting to further their self-interest by buying and selling. If a good or service is too expensive, then more suppliers enter the market, supply increases, and competition drives the price down to its “natural” level, which serves as a “center of repose.” If instead the price is too low, then suppliers go broke or leave the market, and the price goes up: “The natural price, therefore, is, as it were, the central price, to which the prices of all commodities are continually gravitating.” The invisible hand is the market version of gravity.

      This view of society as a collection of atomistic individuals, each pursuing their economic self-interest, was modeled directly after Newton's view of nature as a mechanistic, law-bound system.17 Just as Newton had showed that a wide range of phenomena were all explained by the law of gravity, Smith had shown that market behavior could be explained by what was later known as the law of supply and demand. However, there was an important difference, for the theory lacked what Smith had so admired in Newton's work, namely the ability to make accurate predictions. It was qualitative rather than quantitative; descriptive rather than predictive. This problem would be addressed by a new generation of “neoclassical” economists in the late 19th century, including William Stanley Jevons in England and Léon Walras in France, who aimed to put the field on a solid mathematical footing, and turn it into a kind of “rational mechanics” for society. Their work would pave the way for the development of quantitative finance.

      Any model is a simplification of reality, and the neoclassical economists had to make some rather sweeping assumptions in order to make progress. The most basic of these was that people act to optimize their own utility – defined rather hazily as whatever makes them happy СКАЧАТЬ