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In 1754, the infamous scam artist, diarist, and womanizer Giacomo Girolamo Casanova reported that a certain type of high-stakes wager had come into vogue at the Ridotto. The bet was known as a martingale, which we would immediately recognize as a rather basic coin toss. In a matter of seconds, the martingale could deliver dizzying jackpots or, equally as often, ruination. In terms of duration, it was the equivalent of today’s high-speed trade. The only extraordinary fact about the otherwise simple martingale was that everybody knew the infallible strategy for winning: if a player were to put money on the same outcome every time, again and again ad infinitum, the laws of probability dictated that not only would he win back all he may have previously lost, he would double his money. The only catch was that he would have to double down each time, a strategy that could be sustained only as long as the gambler remained solvent. On numerous occasions, martingales left Casanova bankrupt.

In modern finance, the coin toss has come to represent a great deal more than heads or tails. The concept of the martingale is a bulwark of what economists call the efficient-market hypothesis, the meaning of which can be grasped by an oft-repeated saying on Wall Street: for every person who believes a stock will rise—the buyer—there will be some other equal and opposite person who believes the stock will fall—the seller. Even as markets go haywire, brokers and traders repeat the mantra: for every buyer, there is a seller. But the avowed aim of the hedge fund, like the fantasy of a coin-tosser on the brink of bankruptcy, was to evade the rigid fifty-fifty chances of the martingale. The dream was heads I win, tails you lose.

One premonition as to how such hedged bets could be constructed appeared in print around the time when gambling reached an apex at the Ridotto casino, when an eighteenth-century financial writer named Nicolas Magens published “An Essay on Insurances.” Magens was the first to specify the word “option” as a contractual term: “The Sum given is called Premium, and the Liberty that the Giver of the Premium has to have the Contract fulfilled or not, is called Option . . .” The option is presented as a defense against financial loss, a structure that would eventually make it an indispensable tool for hedge funds.

By the middle of the next century, large-scale betting on stocks and bonds was under way on the Paris Bourse. The exchange, located behind a panoply of Corinthian columns, along with its unofficial partner market, called the Coulisse, was clearing more than a hundred billion francs that could change volume, speed, and direction. One of the most widely traded financial instruments on the Bourse was a debt vehicle known as a rente, which usually guaranteed a three-per-cent return in annual interest. As the offering dates and interest rates of these rentes shifted, their prices fluctuated in relationship to one another.

Somewhere among the traders lurked a young man named Louis Bachelier. Although he was born into a well-to-do family—his father was a wine merchant and his maternal grandfather a banker—his parents died when he was a teen-ager, and he had to put his academic ambitions on hold until his adulthood. Though no one knows exactly where he worked, everyone agrees that Bachelier was well acquainted with the workings of the Bourse. His subsequent research suggests that he had noted the propensity of the best traders to take an array of diverse and even contradictory positions. Though one might expect that placing so many bets in so many different directions on so many due dates would guarantee chaos, these expert traders did it in such a way as to decrease their risk. At twenty-two, after his obligatory military service, Bachelier was able to enroll at the Sorbonne. In 1900, he submitted his doctoral dissertation on a subject that few had ever researched before: a mathematical analysis of option trading on rentes.

Bachelier’s dissertation, “The Theory of Speculation,” is recognized as the first to use calculus to analyze trading on the floor of an exchange, and it contained a startling claim: “I have in fact known for several years that it would be possible . . . to imagine transactions where one of the parties makes a profit at all prices.” The best traders on the Bourse knew how to establish an intricate set of positions designed to protect themselves no matter which way or at what speed the market might move. Bachelier’s process was to separate out each element that had gone into the complex of bets at different prices, and write equations for them. His committee, supervised by the renowned mathematician and theoretical physicist Henri Poincaré, was impressed, but it was an unusual thesis. “The subject chosen by M. Bachelier is rather far away from those usually treated by our candidates,” the report noted. For work that would unleash billion-dollar torrents into the capital pools of future hedge funds, Bachelier received a grade of honorable instead of très honorable. It was a B.

Needless to say, Bachelier’s views of math’s application to finance [published in 1900] were ahead of his time. The implications of his work were not appreciated, much less exploited, by Wall Street until the nineteen-seventies, after his dissertation was discovered by the Nobel Prize winner Paul Samuelson, the author of one of the best-selling economics textbooks of all time, who pushed for its translation into English. Two economists, Fischer Black and Myron Scholes, read the work and, in a 1973 issue of the Journal of Political Economy, published one of the most famous articles in the history of quantitative finance.

Based on Bachelier’s dissertation, the economists developed the eponymous Black-Scholes model for option pricing. They established that an option could be priced from a set-in-stone mathematical equation, which allowed the Chicago Board Options Exchange (C.B.O.E.), a new organization, to expand their business to a new universe of financial derivatives. Within a year, more than twenty thousand option contracts were changing hands each day. Four years after that, the C.B.O.E. introduced the “put” option—thus institutionalizing the bet that the thing you were betting on would lose. “Profit at all prices” had joined the mainstream of both economic theory and practice…

From the remarkable story of the French dissertation that inspired the strategies that guide many modern investors ad al that it has wrought: “A Brief History of the Hedge Fund.”

Spoiler alert: it hasn’t always worked out so well (c.f. Long-Term Capital Management)… at least for investors. As Janet M. Tavakoli observed in Structured Finance and Collateralized Debt Obligations: New Developments in Cash and Synthetic Securitization

Hedge funds have made massive leveraged credit bets, knowing that their upside is billions in fees and their downside is millions in fees.

* Benjamin Graham

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As we ruminate on risk, we might recall that it was on this date in 2020 that the Federal Reserve rode in to rescue financial markets to prevent their complete freezing up– which could have entered history books as another global mega-crash. The Dow Jones stock market index had hit an all-time record of 29,551 on February 12, 2020. Then, the coronavirus emerged in earnest in the U.S., unemployment soared, and on March 9 the DJIA took a dive of over 2,000 points; it continued to fall, down to 18,321 on March 23… at which point the Fed intervened, pouring vast sums of cash into the financial system, resulting in a stock market bonanza in the midst of the worst economic collapse since the Great Depression. The Dow stands at this writing at over 35,000.

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