Concept note for a deep dive on why much of modern finance is a statistical scam, using large language models, information theory, and chaos to show that most “alpha” and expert prediction is indistinguishable from noise.
The Scientific Proof of the Scam
For decades, finance has sustained the myth that markets can be meaningfully predicted. Behind sophisticated charts, statistical models, and expert narratives, a more uncomfortable reality emerges: much of what is presented as “science” is, at best, probabilistic engineering applied to systems that are fundamentally chaotic.
Modern AI models, especially Large Language Models (LLMs), offer a fascinating mirror for understanding this illusion. They show how far modeling can go… and exactly where it hits its limits.
1. LLMs: deterministic functions dressed up as randomness
At first glance, an LLM seems mysterious, almost magical. Yet mathematically, there is nothing mystical about it: it is a deterministic function. Give it the same input, with the same parameters and the same internal state, and it will always produce the same logits – the raw scores before they are turned into probabilities.
Randomness does not appear inside the network itself, but at the generation step:
- The network computes logits in a perfectly deterministic way.
- A softmax function turns these logits into a probability distribution over all possible next tokens.
- A sampling step draws one token from this distribution.
If we fix a random seed or always take the most probable token (temperature = 0, greedy decoding), the behavior becomes strictly deterministic. In other words: the “randomness” is a design choice, not an intrinsic property of the model.
This distinction is crucial for finance: just like in portfolio management, the same model can be exploited in a very conservative or very exploratory way depending on how much randomness we allow into the system.
2. Softmax: an old concept for a new world
It is tempting to think of softmax as a modern invention born with deep learning. In reality, it is a modern wrapper around a 19th‑century idea: the Boltzmann distribution.
- Historically:
- 1868: Ludwig Boltzmann formalizes a law that describes the probability that a physical system occupies a given energy state.
- Early 20th century: Gibbs and others generalize these ideas.
- 1940s–1950s: Monte Carlo methods are developed.
- 1989: John Bridle popularizes the term softmax in machine learning.
- Softmax takes a list of real scores (logits), applies the exponential function, then normalizes everything to obtain a probability distribution. This is not a trick:
- it guarantees positive, normalized probabilities;
- it amplifies small differences in scores;
- it fits into a deep framework of entropy maximization under constraints, shared by statistical physics and information theory.
- The temperature parameter comes directly from thermodynamics:
- low temperature → very concentrated distribution (one outcome dominates);
- high temperature → more uniform distribution (more uncertainty).
LLMs therefore do not invent a new law of the world; they exploit an old one that describes how energy (or information) distributes in complex systems. What changed is not the formula, but the scale: the internet, GPUs, and billions of parameters.
3. When “science” meets markets: the limits of causality
Once we accept that models are deterministic but used in probabilistic ways, another question arises: how far can we really do science on a system like a financial market?
This is where econometrics and tools such as instrumental variables reveal their limits.
- In theory, a good instrument should correct endogeneity by isolating a genuinely “exogenous” source of variation. In practice:
- the key assumption (the instrument affects the outcome only through the variable of interest) is not testable on data;
- in a world where “everything is connected to everything,” believing that a variable touches the outcome only through a single clean channel is often wishful thinking;
- weak instruments produce unstable estimates, sometimes worse than no correction at all.
Even when the conditions seem to be met, we typically identify a Local Average Treatment Effect (LATE) on a specific subpopulation, not a universal law. On paper, this looks like “science”; in reality, it often rests on a scaffold of fragile assumptions.
4. Quant vs traditional management: same game, same illusions
One might hope that modern quantitative models, supercharged with AI, will finally pull finance out of this gray zone.
- The facts are less flattering:
- Most traditional active funds underperform their benchmarks over long horizons.
- Quantitative funds, despite their sophistication, do not systematically and persistently outperform either.
- Those that shine for a few years often end up reverting toward the mean, or underperforming.
Two explanations coexist:
- Some managers and quant teams truly are better… but their edge is temporary, because markets learn, copy, and adapt.
- In a universe with thousands of funds, a few exceptional trajectories are statistically inevitable, even if everyone is effectively playing heads or tails.
At the aggregate level, whether we replace humans with models or the other way around, the same law seems to hold: > It is extraordinarily hard to beat, over time, a market you are part of.
5. The three‑body problem: why prediction is structurally impossible
To see why this difficulty is more than just a “talent gap,” we can look to physics: the three‑body problem.
- With two bodies in interaction (for example a planet and its star), we can write exact equations to describe their motion. With three bodies, the system becomes chaotic:
- small changes in initial conditions → radically different trajectories in the long run;
- no general closed‑form solution;
- the only option is numerical simulation, useful in the short term but quickly losing predictive power.
- Financial markets look much more like a system with millions of bodies than a two‑body system:
- countless human and algorithmic actors,
- rules of the game that keep changing (regulation, technology, products),
- permanent feedback loops (prices influence decisions, which influence prices).
In such a universe, searching for a simple, stable law to “predict” future prices is a bit like demanding a closed‑form equation for every possible gravitational system: the very request is ill‑posed.
6. So why do we still pay so much for this?
If perfect prediction is impossible, why do we keep paying large sums to armies of managers, quants, and strategists to attempt it?
- Several human and institutional reasons:
- We hate the idea that no one is truly in control of the system.
- We prefer a competence story (“this fund knows what it’s doing”) to a randomness story (“we are all in the same chaos”).
- The industry’s economic incentives are aligned with selling the illusion of mastery, not with acknowledging structural limits.
This is not a conspiracy but an economy of reassurance: we pay as much to reduce our anxiety about uncertainty as to chase extra performance.
7. What LLMs really reveal
- LLMs are not infallible oracles; they are machines for exploiting regularities in past data, with a layer of controlled randomness to avoid monotony. In this sense, they look a lot like quantitative finance:
- same mathematical building blocks (probabilities, entropy, optimization);
- same power to describe and simulate;
- same limits when it comes to pure causality or foolproof prediction in a chaotic system.
The “scientific proof of the scam” is not that everything is deliberately fraudulent. It is subtler, and more unsettling:
> We have coated with a scientific gloss practices that ultimately rest on systems too complex to be reliably predicted.
Models — statistical, econometric, or neural — are powerful tools for local understanding. But when we sell them as machines that transform chaos into certainty, that is where the scam begins, even if everyone involved starts out in good faith.
- Real decency, in finance as in AI, may begin here:
- acknowledging the structural limits of our models;
- using compute power to illuminate uncertainty, not to deny it;
- accepting that in an “N‑body” universe, a large share of what truly matters will remain, no matter what we do, fundamentally unpredictable.
