Better risk signals produce better portfolios. Here is where the standard models fall short — and what replaces them.
Every price tick, trade, and order in financial markets is transmitted by photons and electrons. The bid-ask spread on a stock is a pattern of electrical signals in fiber optic cables and server memory. The price on a screen exists because photons make contact with a retina. Financial data is only ever represented by physical objects, or particles.
The equations that govern how asset prices move through time — stochastic differential equations — are mathematically identical to the equations that govern how particles move through space. Nelson (1966) proved the formal equivalence: the stochastic differential equations governing diffusion processes are isomorphic to the Schrödinger equation. Solutions developed in physics over decades — for noise separation, transition probabilities, multi-body interactions — apply to financial data without significant modification.
Black-Scholes and Markowitz are the standard models of modern finance. Both are built on stochastic differential equations that mathematical physicists solved decades ago, but both make simplifying assumptions — constant volatility, normal distributions, static correlations — which discards mathematical structures that the physical equations retain, structures that turned out to describe real phenomena.
Solving the same equations without those simplifications yields different tools. Instanton tunneling computes the probability of transitioning between market regimes without assuming stability. Nelson decomposition separates asset return drift from noise without averaging over historical prices. A non-local potential term captures how all assets in a portfolio influence each other simultaneously, not just in pairwise correlations.
Additionally, the indicators and metrics used by technical analysts — moving averages, VIX, RSI — are derived solely from the price history of individual assets. They measure what already happened to one variable at a time. The governing equations used in canonical quantitative portfolio optimization, and in extension, how we redefine the assumptions made by classical portfolio analysts through isomorphic mapping onto physical equations, describe something different: how all assets move together, how their joint distribution evolves, and what the current state of that distribution implies about what comes next.
Black-Scholes assumes constant volatility. Markowitz assumes normally distributed returns. Both are known to be wrong — volatility clusters, returns have fat tails, correlations collapse during stress. These models dropped terms from the governing equations to make the math tractable in use with existing financial technology. However, the dropped terms describe the phenomena these models miss — including the very dynamics that drive both crashes and outsized returns. Retaining those terms changes what you can compute.
The visualization shows the gap: what Black-Scholes assumes (red) versus what markets actually do (green). The tails and the clustering are not noise. They are structure that the original equations describe and the simplified models discard.
Factor models, mean-variance optimization, and machine learning all work the same way: fit parameters to historical data, then project forward. When the market changes structure, the projection breaks. Classical financial models compensate by computing their uncertainty, and selling an insurance product that pays out when they’re wrong.
The equations described in our models work differently. They take the current configuration of prices, correlations, and volatility as input and compute drift, risk structure, and transition probabilities directly from that configuration. Our assumption is not that the future will be like the past — it is that only what exists now can be treated as what is real, and known.
Physicists have debated these ontological questions — what counts as real, what can be known — for a century. We apply their conclusions.
Traditional wealth management extracts 1–2% annually in fees. That sounds small. It is not. Over 30 years, this compounds into a massive transfer of wealth from clients to managers.
A million dollars at 7% gross return becomes $7.6 million in 30 years. At 6% net — after a 1% fee — it becomes $5.7 million. The fee consumed $1.9 million. Nearly a quarter of the wealth that should have been yours.
The fee structure has not changed since the 1990s. The underlying technology has become a million times cheaper.
Why the time between generating an investment insight and acting on it is the single most important variable in portfolio management.
Read more →Bohmian and quantum-field models borrowed from mathematical physics offer structural advantages over traditional factor-based approaches when applied to portfolio construction.
Read more →Institutional-grade allocation technology has been concentrated in a few zip codes for decades. Software changes that equation permanently.
Read more →The gap between what wealth management costs to deliver and what clients are charged has never been wider. Automation closes it.
Read more →Explore live model portfolios, real-time performance data, and the research behind the allocation methodology.
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