Legends of Quantitative Trading: The Masters Who Changed the Market

In the previous articleWhy Choose Quantitative Tradingwe discussed the differences between humans and machines when executing strategies. Although calm and emotionless machines perform better in trading, don't forget that these genius machines were built by humans. Behind the rise of quantitative trading lies the wisdom and hard work of generations of financial pioneers. This time, let's get to know the legendary figures in the history of quantitative trading and pay tribute to these industry leaders who changed the rules of the game!

1. Jules Regnault

Based on the surviving records, the earliest person known to have used quantitative methods to analyze changes in data and uncover patterns in market price fluctuations was Jules Regnault, born in Bethune, France, in 1834.

Regnault came from a poor family. As an adult, he went to the Paris Stock Exchange to become a stockbroker's assistant. His daily work running errands and delivering messages exposed him to stock price fluctuations, strongly inspiring his dream of uncovering the underlying patterns and making a fortune in the stock market.

Regnault was highly hands-on. After work, he did not sit idle; instead, he manually compiled stock and government bond price data from 1825 to 1862. Gradually, he discovered an interesting phenomenon:

• If the holding period for a stock or government bond doubles, the price deviation increases by 1.41 times;
• If the period increases by 3 times, the price deviation increases by 1.73 times;
• An increase of 4 times means an increase of 2 times.

These numbers are all square roots!

Regnart was incredibly excited, feeling that he had uncovered the natural laws governing stock market rises and falls. He even discovered mispricing in government bonds and devised a strategy similar to statistical arbitrage.

For example, at the time there was a 3% perpetual government bond that paid interest every six months but never repaid the principal (face value of 100 francs), with its price fluctuating between 32.50 and 86.65 francs for a long time. He calculated precisely that the fair price was 73.4 francs, so he bought whenever the price was below that level, buying more the cheaper it was; whenever the price was above that level, he sold, selling more the higher it was.

That’s how, although he sometimes suffered small losses, he persevered for several years. By the age of 47，he finally achieved financial freedom! He bought an estate, hired a coachman and a gardener, and even had 3 carriages, reaching the pinnacle of life.

When Regnault died in 1894, he left a fortune of 3 million francs, including bonds, stocks, and real estate. His published work, “The Calculation of Probabilities and the Philosophy of Stock Trading,” is also regarded as an early foundation of quantitative trading.

However, it was ultimately a group of “top students” who were “not focusing on their proper careers” that later brought quantitative trading into the public eye.

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2. Edward Thorp (Edward Thorp)

Edward Thorp showed a great passion for numbers from a young age. Because his family was poor, Thorp began looking for ways to make money early on (the standard opening for a big shot 😂).

Once, Thorp and a grocery store owner bet on who could calculate the bill total the fastest. Thorp used his brain, while the grocery store owner used a calculator. In the end, Edward Thorp won and received an ice cream cone as his prize.

Sometimes, Thorp would spend five cents to buy a box of drinks, add some water to it, and sell it to thirsty workers at one cent per box, earning one cent on each box of drinks.

In 1955, while Thorp was a graduate student at UCLA, he discussed ways to make money with his classmates. Most saw gambling as a dead end, but Thorp believed that finding its mathematical structure could make it possible to beat the house.

He initially tried using a computer to predict roulette numbers, but found that the machine's accuracy was truly unimpressive, so he eventually gave up. Later, he came across a paper on blackjack strategy and decided to verify it in person at a casino, only to suffer a crushing loss.

It was not until he became a mathematics professor at MIT that Thorp worked out the winning formula for blackjack and wrote a paper he wanted to publish. But under the rules at the time, a paper had to be recommended by a member of the National Academy of Sciences before it could appear in the prestigious journal Proceedings of the National Academy of Sciences.

So Thorp sought out the renowned Claude Shannon—yes, the same Shannon who invented information theory.

The two soon became partners. Shannon suggested that he title the paper "The Winning Secrets of Blackjack."

Once the paper was published, letters poured in like a flood, and Thorp's blackjack secrets nearly became a taboo subject at MIT. Because there were so many letters, the university had no choice but to restrict him from discussing the topic any further.

But Thorp and Shannon did not stop at theory. They pooled some money and went to Las Vegas themselves to test it out. The result was naturally a resounding success. After returning, Thorp wrote a book—Beat the Dealer. This book, filled with mathematical theories, attracted a large number of readers because of its title and became a bestseller.

Although Thorp won a considerable amount of money, he also had to disguise himself in the casinos to avoid being recognized by security. However, the casinos were not willing to let it go.

Once, while Thorp was playing cards, he ordered a cup of coffee. After drinking it, his vision suddenly became blurry, and he could only stagger away from the table. The next day, he returned to the same casino, ordered only plain water, and dared to take just a small sip each time. The water tasted very strange, as if a large amount of baking soda had been added. Clearly, the casino owner hated him to the bone.

Shaken by this drugging incident, Thorp decided to turn to the stock market, which he believed was the real big casino.

Thorp's first subject of study was stock warrants. These warrants were similar to call options, granting holders the right to purchase stocks at a predetermined price in the future. Warrants were traded mainly through market makers and were a popular choice among investors at the time.

When analyzing stock warrants, Thorp discovered that by applying the law of large numbers, although it was impossible to accurately predict whether a particular stock would rise or fall in the future, it was possible to calculate the probability that it would rise or fall by a specific amount within a given period. If a stock's volatility was random, then it could be quantified. This discovery laid the foundation for later quantitative trading.

By precisely estimating the volatility of these stock warrants, it is possible to identify which warrants in the market are mispriced.

For example, suppose you buy a warrant on Kweichow Moutai. The current stock price is 100 yuan, and the stock price needs to reach 120 yuan after 6 months for you to make a profit. You would then need to calculate the probability that the stock price will rise to 120 yuan during this period and use this probability to estimate the warrant's actual value.

Thorp was able to accurately estimate the fair prices of these warrants by using a random walk model and introducing a factor representing the probability that a stock would rise or fall relative to the broader market.

To further validate his theory, Thorp collaborated with financial scholar Sheen Kassouf (Sheen Kassouf) and began systematically testing all the stock warrants available on the market.

The results delighted them, because according to their model, most warrants on the market were incorrectly priced.

Taking advantage of these mispricing opportunities, they shorted overpriced warrants while using the stock as a hedge. If the stock price unexpectedly rose, the gain in the stock would offset their losses on the warrants, and their formula precisely indicated how many shares to buy for the hedge.

This model became an early practical version of the later-famous Black-Scholes option pricing model, advancing the development of option pricing theory in modern finance.

Thorp was a very generous person, and he did not keep this system to himself. He told Sheen that this risk-free hedging system should be presented to the entire world. Thus, Beat the Market: A Scientific Stock Market System (Beat the Market:A Scientific Stock Market System) was born, and the book became a foundational work in the field of quantitative investing. The book described a very simple warrant hedging system for small retail investors. At that time, ordinary households did not yet have computers and could only draw tables on paper to identify overpriced warrants.

In 1969, Thorp founded his own hedge fund, Princeton-Newport Partners.

During the fund’s first few years, the market fell 5%, while his fund gained 3%. Its average annual returns remained in the double digits over the following years. By 1985, the fund had grown to $130 million.

Even during the 1987 stock market crash "Black Monday," Thorp's fund miraculously escaped unscathed and achieved profits of 27%. Through his flexible contrarian strategies, he not only mitigated the risks but also suffered virtually no losses. All of this made Thorp a legendary figure in the quantitative investment world.

3. Thomas Peterffy (Thomas Peterffy)

People who frequently engage in quantitative trading of U.S. stocks should have heard ofInteractive Brokers, and the person we are introducing next is Thomas Peterffy, the founder of Interactive Brokers.

Thomas Peterffy was born in 1944, during World War II, in the basement of a hospital in Budapest, Hungary. His childhood was marked by hunger and frequent moves caused by his parents’ debts.

In 1965, Peterffy escaped Hungary and arrived in New York with almost no money, beginning his life in the United States. As a Hungarian immigrant who barely spoke English, he started his legendary Wall Street career.

When he first arrived in New York, Peterffy found a job as a draftsman at an engineering company with the help of his Hungarian landlord.

The company purchased its first computer, but since no one knew how to operate it, Peterffy volunteered to learn programming. He discovered that learning computer languages was much easier than learning English. Before long, he developed a simple Pythagorean theorem algorithm that helped engineers calculate the radii and slopes of roads using sine or cosine functions.

He also designed a database system, becoming one of the few people at the company with computer expertise. His salary rose to 65 dollars per week, making him one of the few programmers at the time.

In 1967, Peterffy joined Aranyi, a company that developed computer systems for Wall Street clients. There, he wrote algorithmic trading software that helped investors quickly compare the characteristics and value of different stocks. The three-year experience deepened his understanding of financial markets and made him one of the few Wall Street professionals with programming expertise.

In 1969, Peterffy joined Mocatta, founded by prominent Wall Street figure Henry Jarecki. Jarecki gave him ample room to apply his talents. That same year, Peterffy developed Wall Street’s first “black box” system, which read market data, processed it through algorithms, and generated buy and sell orders. The system delivered substantial profits for Mocatta.

In the early 20 century 70s, Mokatta began venturing into options trading. At the time, options pricing was largely based on intuition because the Black-Scholes model had not yet been developed. Relying on traders' experience, Jerik and Peterffy gradually identified several key factors affecting options pricing:

1. Option strike price
2. Expiration date
3. Volatility
4. Risk-free interest rate

After more than a year of effort, Peterffy developed an options pricing algorithm based on these parameters. Mocatta used this algorithm for options trading and achieved good results. They later discovered that the algorithm was very similar to the Black-Scholes options pricing model published a year later.

By the end of the 70s of the 20 century, with the establishment of the Chicago trading market, Peterffy keenly realized that the stock options market was about to emerge and believed that it would have enormous potential and profit opportunities.

In 1977, Peterffy had saved $200,000 and used $36,000 of it to buy a trading seat on the American Stock Exchange, formally beginning his entrepreneurial journey.

However, his early options trading did not go smoothly. He relied on algorithms he had developed himself to price options and strictly adhered to his own profit range. If the price of an options contract fell outside his conservative range, he refused to trade. Even with such caution, mistakes were still unavoidable, and he once lost one hundred thousand dollars.

Although this devastating blow came suddenly and heavily, Peterffy was not defeated. He pulled himself together, gradually accumulated capital, and expanded his trading team and trading volume. However, because of the language barrier, he could not talk with the market makers as other traders did, making it difficult for his orders to be executed. The market makers were also unwilling to deal with this trader who had a strong Hungarian accent.

Peterffy came up with a unique and unexpected strategy: he hired several attractive blonde women as his traders 🤣. Although these female traders did not need trading experience or market intuition and only had to execute orders according to his algorithmic instructions, their presence immediately attracted the market makers' attention. As a result, the orders placed by these blondes were quickly accepted by the market makers, who did not realize that they were carrying out a series of trades unfavorable to themselves.

Peterffy realized that, with the support of his algorithms, greater trading volume could effectively diversify risk and increase profits. Therefore, he decided to join the ranks of market makers at the American Stock Exchange.

However, several months later, the market makers who traded with Peterffy gradually realized that they had almost never won against Peterffy's blonde traders. As market makers, they were theoretically required to continuously provide two-sided bid and ask quotes, while Peterffy chose to trade selectively, participating only in favorable contracts. This strategy caused strong dissatisfaction among the market makers, who threatened to revoke Peterffy's market-maker status unless he provided two-sided bid and ask quotes for all options simultaneously. However, Peterffy's team relied primarily on computer algorithms and could not manually monitor the market and provide quotes at all times, once again hindering his trading.

Peterffy conceived of an idea that had long been buried in his mind: a handheld computer. He began working to turn this concept into reality and collaborated with physicists at New York University to design a revolutionary touch-screen tablet computer.

This device is approximately 8 × 12 inches, 2 inches thick, contains transistors and integrated circuit boards inside, with the circuit boards connected by gold wires, and is equipped with a touchscreen on top. These tablet computers connect via telephone lines to Quotron market data machines, receive market data, process it through algorithms to generate trading instructions, and then transmit the instructions back to the tablets via shortwave radio. After receiving the instructions, the blonde female trader quickly quotes a price to the market maker.

In stark contrast, Peterffy's competitors still relied on “fair value pricing sheets” that could only be updated once or twice a day, while Peterffy's real-time trading system clearly held a major advantage.

From then on, Peterffy’s annual profits exceeded $1 million.

To expand the business, he planned to enter the Chicago Board Options Exchange (the largest options exchange in the United States), but was rejected because the exchange prohibited bringing in equipment such as computers. Ultimately, he turned to the New York Stock Exchange and expanded his stock options business.

To improve traders' efficiency, Peterffy designed colorful rods with lights that used different colors to indicate the trading instructions generated by the system, making them easier for floor traders to identify.

As trading volume increased, Peterffy’s profits rose sharply. By 1986, the exchange had become a major source of profit: the company’s capital grew from $1 million to $5 million by year-end, a 400% annual return. His stock-options positions also required hedging in the stock market, which substantially increased his stock-trading volume.

One day in 1987, a Nasdaq staff member went to Peterffy's office in the World Trade Center for a routine inspection. He expected to see bustling crowds, the clamor of ringing phones, and traders busy at Nasdaq trading terminals, but instead, all he saw was an IBM computer connected to a Nasdaq terminal.

He found it unbelievable that this computer was handling Peterffy's enormous trading volume. The computer was running code that indicated the instruments, times, and quantities to trade.

The staff member had no idea that what he had just seen was the computer running the world's first fully automated algorithmic trading system.

Peterffy's system was more than just a simple trading signal; it could obtain real-time data directly from the Nasdaq terminal, automatically decide on and execute trades without human intervention.

By analyzing the constant stream of incoming market data, Peterffy's algorithm could effortlessly generate trading orders based on the bid-ask spread. This innovation marked the beginning of a new era on Wall Street. Subsequently, programmers, engineers, and mathematicians launched a 20-year assault on the financial markets using algorithms and automated trading technology. Algorithms became increasingly complex and intelligent, gradually replacing humans and becoming a major force in the market.

When the Nasdaq staff member learned that Peterffy had achieved automated trading by externally "stealing" market data, he immediately demanded that Peterffy stop, because Nasdaq's software was intended only for humans to view market data and enter trading orders, not for automated trading.

At Nasdaq's request, Peterffy and his engineers quickly made technical improvements and created a new machine hand for entering trading orders.

After a busy week, when Nasdaq personnel came to inspect again, the scene before them seemed to come straight from a science-fiction novel: trading orders poured in nonstop, the machine's noise drowned out human voices, and the handle struck the keyboard rapidly, producing a shocking level of noise. Whenever the machine paused, as if taking a moment of silence, it quickly resumed and sent out even more orders than before. The staff's minds were blown 🤣

Peterffy’s automated trading system astonished Wall Street and earned him $25 million that year. He later designed more systems and algorithms, introduced numerous technical innovations, and expanded into additional instruments and markets. He especially favored emerging markets because they offered more opportunities and less competition.

In 1990, Peterffy renamed the company Interactive Brokers, abbreviated as IB. At Interactive Brokers, engineers were regarded as the company's core, and 75% of the employees were programmers and engineers.

In 1993, Peterffy began offering his gradually refined trading system as a service to clients. Because the service was inexpensive, offered a wide range of trading instruments, and provided broad coverage, it was enthusiastically welcomed by professional trading firms and professional traders. Based on average daily revenue trade statistics, Interactive Brokers quickly became the largest online broker.

Interactive Brokers listed successfully on Nasdaq on May 4, 2007. At the opening bell, the company was valued at $12 billion, making it the second-largest U.S. IPO that year.

Although Interactive Brokers' minimum funding requirement of 10,000 dollars makes it unsuitable for small retail investors, it leads the industry in international trading and low-cost commissions sought by professional traders. In addition, Interactive Brokers offers a Universal Account, allowing clients to trade stocks, options, exchange-traded funds (ETFs), futures, forex, bonds, and at more than 100 market centers in 24 countriesContracts for Difference (CFD).

4. James Harris Simons

I’m sure everyone came across this six months agonews of this prominent figure’s death. James Simons, the founder of Renaissance Technologies, is an unavoidable name in the entire history of quantitative trading.

Unlike the previous three moguls who had disastrous starts, Simons had the script of a middle-class kid and prodigy.

James Harris Simons was born in 1938 in a Jewish family in a suburb of Boston, Massachusetts. Even as a child, Simons showed an intense interest in numbers and shapes that exceeded that of his peers; he said that he longed to study mathematics at the age of 3.

After completing his secondary education in the town of Newton near Boston, he entered the Massachusetts Institute of Technology to study mathematics. At the time, his mentor, Professor Singer, recalled: “Simons had exceptional insight and could understand mathematical principles intuitively. This ability was extremely rare.”

In 1958, at the age of 20, Simons transferred to the University of California, Berkeley, to pursue a doctorate in mathematics after completing his bachelor's degree in just three years. During this period, he married for the first time, and he invested all the cash gifts he received at the wedding. Whether in stocks or soybean futures, he made a profit. However, at that time, Simons did not show much interest in investing or trading.

Three years later, Simons successfully earned his doctorate and returned to the Massachusetts Institute of Technology to teach at the age of 23. His doctoral advisor described him this way: “Jim was an extremely creative person who enjoyed standing by his own views.”

His doctoral dissertation explored geometric problems in multidimensional curved spaces, which belonged to the field of topological geometry, as did the Chern-Simons theory later named after him and the Chinese-American mathematician Shiing-Shen Chern.

In 1967, at the invitation of Stony Brook University president John Toll, Simons became chair of the university’s mathematics department. He recruited leading scholars from institutions including the University of Bonn, the University of Michigan, and Saint Petersburg State University.

During his eight years at Stony Brook University, he not only co-founded the renowned Chern-Simons theory with Shiing-Shen Chern, a leading scholar of differential geometry at the University of California, Berkeley, but also elevated the university's Department of Mathematics to a leading position nationwide in topological geometry research.

In 1974, after turning $600,000 into $6 million in the commodities market, Simons became interested in trading. Despite his strong academic record, he had grown frustrated with the slow pace of academic research and the role of luck in producing results.turning $600,000 into $6 million), Simons became interested in trading. Although his achievements in academia were already highly significant, he gradually grew tired of the field. He once said, "The pace of academia is too slow." In addition, achieving results in the area of mathematics that Simons studied usually required a long time and sometimes an element of luck.

In 1978, Simons left Stony Brook University to become a professional investor. He founded the Monemetrics fund, focusing especially on foreign exchange while also investing in small companies in a style similar to modern venture capital.

Over the following ten years, the Monemetrics Fund achieved investment returns of 25 times, equivalent to an average annual growth of approximately 38%.

In 1988, Simons closed the ten-year-old Monemetrics fund and founded Renaissance Technologies, which would manage the renowned Medallion Fund. Rather than locating on Wall Street, the company established itself near Stony Brook University.

During this period, Simons's investment strategy underwent a complete transformation from discretionary trading to quantitative trading.

The Medallion Fund and the Monemetrics Fund had two significant differences.

First, the Medallion Fund was no longer involved in venture capital investments.

Although Simmons’s initial success stemmed from investing in small companies, and he has always been passionate about directly investing in small companies, the Medallion Fund’s investment products had to meet three conditions: first, they had to be traded on public markets; second, they had to have sufficient liquidity; and third, they had to be suitable for trading using mathematical models.

Second, the Medallion Fund employed a purely quantitative investment approach, relying primarily on technical data, whereas the Limroy Fund relied mainly on fundamental data and subjective judgment. Regarding the reasons for this transition, Simmons said: “First, mathematical models reduced investment risk. Second, mathematical models eased the psychological pressure that had to be endured each day.” The latter was particularly important because investing based on subjective judgment required maintaining a high level of vigilance at all times to respond to constantly changing information and adjust investment positions.

In its first year of operation, the Medallion Fund achieved returns of 8.8%.

Beginning in 1989, the model encountered problems: the Medallion Fund lost 30% from the start of the year through April. After six months of review, Simons removed the model’s macroeconomic inputs, focused on technical data, and shifted toward short-term trading. The change became a milestone and remains a foundation of the fund’s success.

When the new company was first established, Simmons's team came mainly from three places: one was the mathematics department at Stony Brook University, where he had served as department chair; another was the Institute for Defense Analyses; and the third, rather unexpectedly, was IBM's speech recognition laboratory. There were rumors that Simmons had poached all the top talent from the entire speech recognition laboratory at the time.

Through the collective efforts of this diverse and elusive group of scientists, the company's mathematical models were constantly updated and refined, with many ideas emerging precisely from this kind of interdisciplinary collision. Simmons's Medallion Fund therefore quite naturally moved from one victory to the next.

In 1994, the Federal Reserve raised rates six times, from 3% to 5.5%, while government bonds yielded 6.7%. In that environment, the Medallion Fund returned 77%.

During the technology-stock downturn in 2000, the S&P 500 fell more than 10%, while the Medallion Fund posted an unprecedented net return of 98.5%.

It seems that whenever the stock or bond market is underperforming and market volatility increases, Medallion's performance becomes even stronger. Simons himself once said that his fund performs best amid a certain degree of volatility. He said, “To make money, the market has to move.”

The Medallion Fund's portfolio covers more than a thousand different stocks and other financial instruments, and it trades frequently and rapidly. Many people describe the Medallion Fund's trading style as being “like a machine gun”; in the past, its annual turnover ranged from more than ten times to several dozen times.

By the end of 2003, the Medallion Fund's stock investments had reached $8.2 billion across 1,387 stocks, while its stock holdings at the end of the previous year amounted to $12.3 billion. These were not obscure names, but highly traded companies in fields such as biochemistry, food, pharmaceuticals, mining, defense, and finance.

In 2005, Renaissance Technologies CFO Mark Silber disclosed that the Medallion Fund had reached its liquidity limit and would return outside investors’ capital. The fund had already been returning external capital for three years, and by the end of 2005 all outside capital had been repaid.

Beginning in 2006, all investors in the Medallion Fund were current or former employees of Renaissance Technologies and their family members. This was intended to keep the Medallion Fund's total value at around $5 billion, a figure reached by employee capital alone.

Renaissance Technologies did not close its doors entirely to outside investors. It launched two new funds with a minimum investment of $20 million, aimed primarily at institutions such as pension managers. The funds were capped at $100 billion and limited to U.S.-listed stocks, unlike the Medallion Fund’s foreign-exchange and commodity-futures trading. Their longer horizons and long-equity focus also made them more similar to public investment funds.

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