Post 1 - A Brief History of Financial Theory

Why This Matters

Despite what people may tell you, money is everything.

It’s your ticket to eat, to drink, to live, to play, to get married, to take care of a child, to take care of your parents, to make it to the birth of your grandchild, to take a vacation, to eventually leaving those you love a little bit of breathing room once you’re gone.

How to earn, grow, and hold onto money is very under-taught here in the US. If you don’t step foot in the financial realm on a day-to-day basis, it can be a bit confusing. From the thousands of influencers online to money managers at banks to all other types of investors, all of these guys and gals are likely telling you many different things. That is what makes finance so interesting: No one really has it figured out. We can model the precise movement of heavenly bodies millions of light years away, but we cannot accurately describe how the market will behave next week.

Part of the reason you hear different things online is due to the fact that everyone has different goals. I have much different investing goals relative to someone who is 85 years old. Or a day trader. Or a meme-coin investor.

Another reason is people grow up and learn differently. People who grew up through the era of high inflation of the 70s and 80s probably think about risk and return a little differently than the younger generations who, until recently, hadn’t seen the CPI top 5% in their lifetime. Someone who grows up with rich parents thinks about money and lifestyle much differently than someone who has been fighting paycheck to paycheck their entire lives. Sometimes people are just luckier; those who made millions during the cryptocurrency bubble had a much different mindset and value system than, say, Warren Buffet. The author Morgan Housel, probably my personal favorite finance writer out there, puts it perfectly: Your personal experiences with money make up maybe 0.00000001% of what’s happened in the world, but maybe 80% of how you think the world works. There are a lot of lessons to be gleaned from that, even outside of finance.

At the core of everyone’s differing opinions are differences in values. Valuation, in a broad sense, is the art of coming to a conclusion of worth. These valuations are the fundamental opinions that differ in the financial realm, and all those people with differing experiences throughout their lives value things differently. It is the interaction of all these people with differing opinions that makes financial forecasting harder than forecasting objects millions of light-years away.

Even with these differing opinions, there has been an accepted consensus on which financial tools and heuristics, developed by some of the brightest mathematicians and economists the world has known, are to be used to come to these conclusions of worth and make a decision. These mainstream tools and heuristics are taught to everyone in business school, from your “lowly” state school to your prestigious private school (speaking from experience here). Once released into the real world, every person or company, as they are practicing, likely comes up with a different spin on these tools/heuristics/rules for valuation; their own way of coming up with assumptions, using potentially unique insights to come to what they believe is the best singular conclusion of value. However, even with these variations, I still see a problem with the mainstream.

I have been alive for almost 27 years and have lived through three once-in-a-lifetime failures of the financial system: The dot-com bubble in the 2000s, the Great Financial Crisis of 2007/2008, and the COVID crash. Each of these eras is marred by greed and hubris only for the everyday American to be left holding the bag. As participants and stewards of the financial markets, our mistakes launch us into recessions, banks into failure, and everyday people out of work. Innocent people who are just trying to get by and feed their kids have their lives thrown completely upside down when markets go awry. I believe this is suffering that can be minimized if we can just work and think a little harder.

And here is where, I believe, the problem lies: No one seems to question the very nature of what exactly it is that we are doing; the very nature of coming to this idea of a “valuation”. How were these current norms, which seem to be getting us into extreme amounts of financial trouble every decade or so, solidified into standard practice? Are they actually leading us to correct answers, and it is just this ethereal idea of the market that misbehaves? Most importantly, is the plumbing, or the underlying theory, regarding the way we value today even, correct?

It is time to question. The posts that follow will be a meditation not on how to make better underwriting/modeling, valuation, and risk management decisions using the same standard tools used today, but ultimately, these posts are a meditation on the very tools themselves. It is time to bring you down the rabbit hole that has consumed a couple of years of my life, and will likely consume many, many more. But before I take you on a journey forward, it is crucial to understand where we came from.

Two Tests

March, 1900 - University of Paris

At the turn of the 19th century, Louis Jean-Baptiste Alphonse Bachelier, a young Ph.D. candidate at the University of Paris, sat in front of a jury to determine the fate of his future career. Academic careers for Ph.D.’s at prestigious institutions were few and far between, but after years of hard work, he was almost there. Two final tests lay in his path, both to be judged by a panel of three renowned academics. The jury consisted of Joseph Boussinesq, Paul Appell, and Henri Poincaré, the latter being one of the most prominent mathematicians in history (and was regarded as such at the time). The first test, an important one to do well on if one has a desire to become a professor, was to demonstrate Bachelier’s knowledge on a “standard” topic via an oral exam. Bachelier was tested on fluid mechanics (a specialty of Boussinesq). He passed with flying colors.

The second test was much tougher; it was a defense of his original research. The defense of his thesis Théorie de la Spéculation was going to be an uphill battle from the beginning. His thesis wasn’t on any topic within the mathematical style of the day - it was about the lowly-regarded speculation of French bonds on the Bourse, the French exchange. In 1900, the study of financial markets was not yet a field considered by academics. In fact, the study of what was essentially considered “gambling” at the time was quite an inappropriate topic for a Ph.D. candidate seeking a prestigious mathematics career. Nonetheless, Bachelier thought he had something great.

In 1900, there were around 70 billion francs of international and domestic bonds outstanding on the Bourse. An exchange this large allowed for the creation of these “side bets,” or derivatives as we call them today. Bachelier’s goal was to be able to price these derivatives. First, he had to figure out how bond prices moved in the first place.

Bachelier’s approach was unique. Establishing probabilities of price movements, rather than relying on the typical “something happens and prices react” conclusion ex-post was a new and interesting way to think at the time.

Through his research, he made a particularly peculiar discovery: he found that price movements “may, by analogy with certain physical theories, be called the Law of Radiation (or Diffusion) of Probability.” Said another way, price movements are analogous to the diffusion of molecules in a chamber or heat through a substance. In both scenarios, the interactions between “actors”, whether it be participants in a market or molecules in a chamber, are too complicated to model and predict perfectly. But, he found that when you took a step back and viewed the system through a probabilistic lens, things became more clear.

He concluded that security prices “randomly walk.” This means that with no new information added in the system, the price of a security is deemed fair and any future price movement up or down is equally likely. Think of a drunk man wandering down a street, two steps forward, three steps back, two to the side, one forward, etc. On average, the drunk man gets nowhere – each direction he stumbles is equally likely (this is actually how the name “random walk” came about).

Bachelier was actually the first person to come up with such a theory – A famous physicist discovered the same phenomenon completely independent of Bachelier (and it is said that Bachelier’s paper is even more rigorous) five years later in 1905 by studying the motion of pollen particles in water. This physicist was the first to mathematically model the physical phenomenon now called Brownian Motion. It was a big discovery and was mathematical evidence that atoms and molecules exist. It was one of the first major scientific contributions made by Albert Einstein.

Price movements randomly walking is an extraordinary claim – it means that the movement of prices within financial markets, the “random walk,” can be described using Gauss’ normal distribution, or bell curve. All the convenient statistical tools associated with Gauss’ bell curve can be applied. How convenient!

How did his theory stack up to reality? Bachelier calculated that there was a 40% chance to make a profit from a certain derivative, and when he looked back at real trading data, he found that 39% of those derivatives yielded a profit. His theory worked - the magic of the market was now caught on paper, ready to be used by the world.

So, Bachelier laid out this revolutionary theory to the jury. Poincaré observed that Bachelier had stumbled upon some original conclusions, but suggested “the most unusual one should have been more fully developed.” The other judges must have agreed - Bachelier received an “honorable mention,” which was not the mark that would guarantee a future prestigious academic career. Bachelier spent the next almost 30 years of his life battling for recognition as a high school teacher and adjunct professor, hopping from institution to institution. This experience would leave him jaded.

In 1926, Bachelier finally got a major opportunity. He applied for the university chair in mathematics vacancy in Dijon (vacancies like these were quite rare). His only competition was Georges Cerf, a man 18 years younger than he was. There was a problem: a mathematics professor sitting on the committee to fill this vacancy, Maurice Gevrey, adamantly disliked Bachelier (Bachelier did himself no favors. He notoriously thought he was one of the most intelligent mathematicians on the planet and would claim as much on his resumé; humbleness was a virtue he lacked). Gevrey ended up “finding an unforgivable mistake” in Bachelier’s work. Paul Lévy, another incredibly influential probabilist and mathematician, would confirm the error. Bachelier was not given the job.

In response to Lévy, Bachelier wrote a scathing letter claiming to be blackballed, that his career had been sabotaged, that Cerf was too young and never served in WWI as he had, that Gevrey’s conduct “would not astonish anyone who knew the weakness of his character,” that another committee member “is well known for his ingenuity: he was able to make a vacuum of his physics course,” (by boring the students to death) and claimed that Lévy had not even bothered to read his work. Bachelier would conclude his criticism by accusing Lévy of favoring Cerf because they were both Jews. Yikes.

Bachelier would end up retiring about a decade later in 1937 after serving a lesser professorial chair role at Besançon. He would die in 1946, at the age of 76, relatively unknown and unrecognized.

Lévy would later admit, in correspondence with Benoit Mandelbrot, that Bachelier was indeed blackballed and that he had only read the passage within which the mistake existed (and Gevrey highlighted). Lévy, after reading Bachelier’s full work, realized that the mistake was quite minor in the context of the full paper. Bachelier would finally get the recognition he deserved, and his thesis would ultimately launch the modern portfolio theory revolution. His ideas would become the backbone of decades of revolutionary financial theory, all still practiced today. There was one problem for Bachelier though - This recognition came just four years after his death.

Sometimes, life isn’t fair.

Thank you for reading