Marcos Florencio · July 10, 2026
The Black-Litterman model is one of the most elegant ideas in portfolio construction. It has one well-known weakness: the views it depends on are, in practice, whatever the investor says they are. Our new paper proposes a way to ground those views in data.
The problem: subjective views, subjective confidence
Black-Litterman starts from the equilibrium returns π implied by the market and blends them with a set of investor views. Those views are expressed through three objects:
- P, the pick matrix, which says which assets each view is about;
- q, the view vector, which says what return each view expects;
- Ω, the view uncertainty matrix, which says how much each view should be trusted.
The posterior expected returns then follow in closed form:
The math is clean. The inputs are not. In most applications, q and especially Ω are elicited by hand: an analyst states a view and then guesses how confident they are in it. That process is subjective, hard to audit, and impossible to scale across a large universe of assets updated every week.
Neural predicates as view generators
The paper replaces hand-written views with neural predicates: learnable functions that evaluate a logical statement about an asset and return a probability distribution over market stances, such as bearish, neutral and bullish, rather than a single hard answer.
Predicates are organized in a compositional hierarchy. Low-level predicates read structured financial analysis data (profitability, balance sheet strength, earnings consistency, valuation) and higher-level predicates combine their outputs, much like an investment philosophy combines individual criteria into a final verdict. This is the same structure our agents follow when they evaluate a company.
Every view becomes a distribution, and every distribution carries its own confidence.
From distributions to P, q and Ω
The key step is a direct mapping from predicate outputs to the Black-Litterman inputs:
- P is built from the assets the predicates evaluate, one view per asset.
- q is derived from the stance distribution: the more probability mass on bullish, the higher the expected return of the view.
- Ω is derived from the shape of that same distribution. A sharp, decisive output yields a small uncertainty and a view that pulls the posterior strongly; a flat, ambivalent one yields a large uncertainty and a view the model largely ignores.
View confidence is therefore no longer something an investor declares. It is measured from the model's own output, providing a data-driven alternative to subjective uncertainty elicitation.
Two properties that matter
Interpretability. Because every view comes from an explicit chain of predicates, any portfolio weight can be traced back through that logical chain to the underlying data. A position is never just "what the model said": it is the result of specific, inspectable criteria.
Differentiability. Every step, from the predicates to the Black-Litterman posterior and the resulting weights, is differentiable. That means the whole pipeline can be trained end to end against portfolio-level objectives, instead of tuning each component in isolation.
A different kind of rigor
Classical quantitative finance often treats qualitative judgment and statistical modeling as separate worlds: analysts form opinions, and models consume numbers. Neural predicates bridge that gap. They keep the structure of human reasoning, with criteria that can be named, read and challenged, while giving the model a precise, probabilistic language to express how strongly each conclusion holds.
The practical consequence is consistency. The same evidence always produces the same view with the same confidence, whether it is the first asset evaluated on a Friday night or the hundredth. As the universe grows, the quality of the views does not depend on how many analysts are available to write them.
Why this matters for Finxer.ai
This paper is the formal foundation of the engine behind our portfolio: agent evaluations become views, their confidence becomes Ω, and Black-Litterman turns both into weights. For a deeper dive, read the full paper.