From: veritasium
The modern financial landscape, characterized by multi-trillion dollar industries and sophisticated approaches to risk, has its roots deeply embedded in the principles of mathematics and physics [00:00:00]. Many of the most successful individuals in finance, particularly those who have consistently outperformed the market, were not traditional traders but instead physicists, scientists, and mathematicians [00:00:30].
Mathematicians in Finance: Jim Simons vs. Isaac Newton
In 1988, mathematics professor Jim Simons established the Medallion Investment Fund [00:00:34]. Over the next three decades, the Medallion fund delivered an astounding 66% annual return, far surpassing the market average [00:00:40]. This unparalleled success made Jim Simons the wealthiest mathematician of all time [01:00:00].
However, mathematical prowess does not inherently guarantee success in financial markets. A notable example is Isaac Newton, who, despite his immense intellect, lost approximately a third of his wealth in the South Sea Company bubble of 1720 [02:09:00]. When questioned about his losses, Newton famously remarked, “I can calculate the motions of the heavenly bodies, but not the madness of people” [02:16:00]. The contrasting fortunes of Simons and Newton highlight the evolution of applying scientific methods to financial markets.
Louis Bachelier and the Random Walk Theory
A foundational figure in modeling financial markets mathematically was Louis Bachelier, born in 1870 [02:33:00]. While working at the Paris Stock Exchange (the Bourse), Bachelier became particularly interested in contracts known as options [02:51:00].
The Origins and Mechanics of Options
The earliest known options were bought around 600 BC by the Greek philosopher Thales of Miletus [03:10:00]. Thales, anticipating a large olive harvest, paid a small fee to secure the right to rent olive presses at a specified price later in the summer [03:29:00]. When his prediction proved correct, he profited by renting the presses at a higher market rate [03:46:00]. This was effectively the first “call option” [03:54:00].
- Call Option: Gives the holder the right, but not the obligation, to buy an asset at a set “strike price” by a future date [03:58:00].
- Put Option: Gives the holder the right, but not the obligation, to sell an asset at a set “strike price” by a future date [04:06:00].
Options offer several advantages:
- Limited Downside: Losses are limited to the premium paid for the option [05:32:00].
- Leverage: A small investment in options can yield a much larger percentage return compared to buying the underlying stock directly [05:43:00].
- Hedging: Options can be used to mitigate risk by offsetting potential losses in other investments [06:16:00].
Bachelier’s Innovation: The Random Walk
Despite their long history, options lacked a systematic pricing method; traders typically relied on bargaining [06:47:00]. Bachelier, intrigued by probability, sought a mathematical solution for pricing options and proposed this as his PhD topic to Henri Poincaré [07:15:00].
Bachelier realized that while numerous factors influence stock prices, making accurate predictions impossible, the best assumption is that at any given moment, the stock price is equally likely to move up or down [08:00:00]. This led him to theorize that, over the long term, stock prices follow a “random walk,” akin to a coin flip determining each next move [08:14:00]. This concept aligns with the Efficient Market Hypothesis, which suggests that if market prices were predictable, traders would exploit those predictions, causing the prices to adjust instantly and eliminating the predictability [08:27:00].
To visualize the random walk, a Galton Board demonstrates that while the path of any single ball is unpredictable, the collective distribution of many random paths forms a predictable pattern: a normal distribution [09:24:00]. Bachelier applied this to stock prices, asserting that the expected future price of a stock is described by a normal distribution centered on the current price and spreading out over time [10:20:00]. He termed this the “radiation of probabilities” [11:02:00].
Bachelier’s model remarkably rediscovered the exact equation used to describe how heat radiates, first found by Joseph Fourier in 1822 [10:48:00]. However, because his work was in finance, the physics community largely overlooked it [11:07:00].
Connecting to Brownian Motion and Atomic Theory
The mathematics of the random walk would later independently solve a long-standing mystery in physics: Brownian motion [11:12:00]. In 1827, Scottish botanist Robert Brown observed that microscopic particles suspended in water moved randomly [11:21:00]. The cause of this “Brownian motion” remained unknown for 80 years [11:54:00].
In 1905, Albert Einstein provided the explanation: Brownian motion is caused by trillions of invisible molecules colliding with the particle from all directions [11:58:00]. He hypothesized that occasionally, more molecules hit from one side, causing the particle to jump [12:28:00]. Einstein’s derivation assumed that the particle was equally likely to move in any direction at any time, just like stock prices [12:33:00]. Thus, the expected location of a Brownian particle is also described by a normal distribution that broadens with time, a phenomenon known as diffusion [12:52:00]. By solving this mystery, Einstein provided definitive evidence for the existence of atoms and molecules [13:07:00], unaware that Bachelier had already uncovered the random walk concept five years prior [13:13:00].
Bachelier’s work culminated in a mathematical method to price options by calculating the expected return for both buyers and sellers, arguing that the fair price is when these expected returns are equal [14:01:00]. However, his work went largely unnoticed by both physicists and traders [14:42:00].
Ed Thorpe: From Blackjack to Dynamic Hedging
In the 1950s, physics graduate Ed Thorpe, while pursuing his PhD, discovered a way to beat the casino at blackjack by inventing card counting [16:04:00]. He would bet more when the odds favored him and less when they didn’t [16:30:00]. When casinos countered his strategy by adding more card decks, Thorpe transferred his skills to “the biggest casino on Earth”: the stock market [16:50:00].
Thorpe pioneered a type of hedging called “dynamic hedging” [17:16:00]. This involves continuously adjusting a portfolio of options and underlying stocks to maintain a neutral risk position [17:50:00]. For example, if a call option seller faces increased risk as the stock price rises, they can buy units of the underlying stock to offset potential losses [17:54:00]. This allows profits with minimal risk from price fluctuations [18:11:00].
Thorpe also developed a more accurate option pricing model than Bachelier’s, one that accounted for a general “drift” (trend) in stock prices over time, not just randomness [19:00:00]. He used this model to identify undervalued options to buy and overvalued ones to short-sell [19:35:00].
The Black-Scholes-Merton Equation
Thorpe’s proprietary model was eventually superseded in 1973 by a landmark equation developed by Fischer Black and Myron Scholes, with Robert Merton independently publishing his version based on stochastic calculus [19:50:00].
The core idea behind the Black-Scholes-Merton equation was that if a risk-free portfolio of options and stocks (like Thorpe’s delta hedging) could be constructed in an efficient market, it should only yield the risk-free rate (e.g., US treasury bonds) [20:26:00]. They combined this concept with an improved version of Bachelier’s model, which incorporated both random movement and a general drift [20:53:00].
Impact and Legacy
The Black-Scholes-Merton equation provided an explicit formula for pricing options based on input parameters [21:32:00]. Its publication coincided with the founding of the Chicago Board Options Exchange in 1973 [21:21:00]. This led to one of the fastest adoptions of an academic idea by industry in the social sciences [21:53:00].
The formula quickly became the benchmark for options trading on Wall Street [22:01:00]. It spurred the growth of multi-trillion dollar markets, including options, credit default swaps, OTC derivatives, and securitized debt [22:21:00].
Derivatives, financial securities whose value is derived from another, have grown to several hundred trillion dollars globally, far exceeding the value of their underlying securities [24:45:00]. This is because derivatives allow for the creation of many versions of an underlying asset, offering tailored risk-reward profiles [25:30:00].
Derivatives offer crucial benefits, such as hedging against specific risks (e.g., an airline hedging against rising oil prices) [22:56:00]. They also provide significant leverage, as demonstrated in the GameStop phenomenon where a small investment in options could control a much larger value of stock, rapidly driving up prices [24:03:00].
While these markets contribute to liquidity and stability during normal times, they can exacerbate market dislocations during periods of stress, potentially leading to large market crashes [26:05:00].
In 1997, Merton and Scholes were awarded the Nobel Prize in economics for their work, with Black acknowledged posthumously [26:43:00].
Jim Simons and Renaissance Technologies: Quant Finance at its Peak
With the Black-Scholes-Merton equation widely available, hedge funds needed new ways to find market inefficiencies. This led to the rise of quantitative finance, epitomized by Jim Simons and Renaissance Technologies [27:01:00].
Before entering finance, Simons was a distinguished mathematician, known for his work on Riemann geometry, which impacted knot theory, quantum field theory, and quantum computing [27:14:00]. His Chern-Simons theory laid foundational mathematical groundwork for string theory [27:23:00].
Simons founded Renaissance Technologies in 1978 with the strategy of using machine learning to uncover patterns in stock market data [27:39:00]. Drawing on his Cold War experience breaking Russian codes by extracting patterns from data, he believed a similar approach could succeed in finance [28:10:00]. He hired top scientists, often those with PhDs in physics, astronomy, and mathematics, specifically seeking those with no prior finance background [28:21:00].
One notable hire was Leonard Baum, a pioneer of Hidden Markov Models [29:07:00]. These models, inspired by Einstein’s inference of atoms from Brownian motion, aim to identify unobservable factors that influence observable market phenomena [29:11:00]. Leveraging these and other data-driven strategies, the Medallion fund became the highest-returning investment fund ever [29:26:00].
The success of the Medallion Fund has even led some economists to question the validity of the Efficient Market Hypothesis, suggesting that market predictabilities exist for those with the right models, training, and computational power [29:38:00].
Ultimately, the impact of mathematicians and physicists on financial markets extends beyond wealth creation. By modeling market dynamics, they have offered new insights into risk, created entirely new markets, and helped eliminate market inefficiencies by accurately pricing derivatives [30:34:00]. Ironically, the very act of discovering and exploiting patterns in the market might eventually lead to a perfectly efficient market where all price movements are truly random [30:49:00].