Traditional finance evaluates active managers using static, linear averages. A fund is marketed as "Large Cap Value," so the industry measures its beta against a Value index over a five-year period.
The flaw is obvious: markets are not static, and neither are active managers. They deploy option overlays, hoard cash during volatility, and drift from their mandates. To understand a manager's true identity—their "DNA"—you cannot just look at where they stand on average. You have to map how they move when the underlying environment changes.
The goal is not to predict returns. It is to build a rigorous framework for testing structural equivalence: if two managers react to latent market shocks in the same way, they are running the same algorithm — human or systematic — regardless of what their prospectuses claim.
Before diving into the mathematics, the framework can be understood through two fundamental market analogies:
Imagine Chef A bakes a cake using cane sugar, and Chef B uses beet sugar. The ingredients are technically different, but the final nutritional profile is identical.
In finance, Manager A might hold Apple and Johnson & Johnson. Manager B might hold Microsoft and Procter & Gamble. If you only look at their 13F filings and stock tickers, they appear to be running different funds.
But this pipeline doesn't look at tickers. It measures their daily mathematical sensitivity to market volatility, their tilt toward large-cap companies, and their yield characteristics. If those mathematical footprints match exactly across different market regimes, the algorithm groups them together — they are taking the exact same structural risks.
Now imagine two funds marketed as "Dividend Growth."
To a retail investor reading the prospectus, these are identical funds. But the pipeline instantly spots the divergence. When the hidden market state shifts into a crash regime, Fund 1's trajectory stays steady, while Fund 2's trajectory sharply deviates.
Let's define the active management space mathematically, rather than conceptually. To test whether two managers are executing the same underlying strategy, I built a rigid, multi-stage pipeline.
Instead of holding individual stocks, I represent every manager as a continuous time-series of exposures across a k-dimensional Fama-French factor space (Mkt-RF, SMB, HML, RMW, CMA).
At any given time t, a manager is defined not by their holdings, but by a vector of their factor betas.
Standard ordinary least squares (OLS) regression fails when managers use non-linear instruments like covered calls (e.g., JEPQ). To counter this "non-linear illusion," I apply rolling, convex adjustments to the factor extraction based on John Hull's frameworks for derivatives. The goal is not raw returns — it is isolating the pure beta trajectory.
Beta trajectories cannot be evaluated in a vacuum. I use a Gaussian Mixture Model (GMM) to probabilistically cluster historical market data into distinct, unlabeled environments based on volatility and macroeconomic indicators.
Let S be the set of latent market regimes (e.g., S1 = Stable Bull, S2 = High-Volatility Crash, S3 = Rising Rate/Late-Cycle).
Comparing k-dimensional matrices across time is computationally heavy and introduces severe noise. To resolve this, I project the conditional, regime-specific betas into a lower-dimensional principal component space via Principal Component Analysis (PCA).
For every distinct regime in S, the manager's behavioral vector becomes a clean coordinate in a 2D or 3D space. PC1 typically represents the dominant axis (e.g., Aggressive Growth vs. Defensive Value), while PC2 captures secondary characteristics (e.g., Yield sensitivity).
This is where the framework becomes solvable in polynomial time. I construct a Bipartite Network Graph to map managers to their regime-specific behaviors.
The graph G = (U, V, E) is defined as:
The Edges (E): Edges are drawn between managers in U and behavioral coordinates in V based on an inverse Euclidean distance function. The closer a manager's behavior matches a specific risk profile in a specific regime, the heavier and thicker the edge weight.
Managers (Left) map to their factor behaviors across n distinct Market Regimes (Right).
The Result: If M1 and M2 share highly weighted edges to the exact same nodes in V across all regimes in S, the community detection algorithm automatically collapses them into a single functional cluster.
Given two funds marketed under different labels, the graph either collapses them into one cluster or it doesn't. No judgment call required — the topology is the answer.
To process this at institutional scale, I built the system like a manufacturing assembly line with swappable modules. If a firm wants to analyze commodities instead of equities, they swap the Fama-French lens for a macroeconomic factor model, leaving the GMM and Graph engines untouched.
However, executing this theoretical model on real-world data required navigating several structural gaps:
I deliberately restricted the initial universe to Equities Only (n=15 ETF sample size for the baseline test). The Fama-French model is a highly precise ruler designed exclusively to measure wood (Equities). It measures SMB (Small Minus Big market cap). If you try to run a Bond ETF through this pipeline, it breaks — you cannot use a wooden ruler to measure the temperature of an oven. Locking the scope guarantees a clean, reproducible result.
When matching fund inception dates across different market regimes, naive dataset merging resulted in dropping up to 80% of historical factor data due to missing-value overlaps. I implemented rigorous "Time Block" chronological segmentation:
This backward-filling and regime-preservation logic allowed me to maintain 100% of the overlapping factor data without diluting the covariance matrices.
I expanded the universe to ensure the Principal Components weren't being artificially warped by extreme outliers (e.g., hyper-growth funds like ARKK). By bootstrapping the variance, I confirmed that the core structural axis (PC1: Aggressive Growth vs. Defensive Value) remains mathematically stable regardless of the sample composition.
Summary: By feeding ambiguous historical returns through a rigid, modular pipeline of factor extraction, regime mapping, and bipartite graph theory, the system strips away the marketing noise of active management. What remains is the underlying algorithm of the portfolio manager.