Paper: arXiv 2604.16773

Authors: Revant Nayar, Dnyanesh Kulkarni, El Mehdi Ainasse

Abstract

We develop \emph{Topological Risk Parity} (TRP), a tree-based portfolio construction approach intended for long/short, market neutral, factor-aware portfolios. The method is motivated by the dominance of passive/factor flows that naturally create a tree-like structure in markets. We introduce two implementation variants: (i) a rooted minimum-spanning-tree allocator, and (ii) a market/sector-anchored variant referred to here as \emph{Semi-Supervised TRP}, which imposes SPY as the root node and the 11 sector ETFs as the second layer. In both cases, the key object is a sparse rooted topology extracted from a correlation-distance graph, together with a propagation law that maps signed signals into portfolio weights. Relative to classical Hierarchical Risk Parity (HRP), TRP is non-binary and designed for signed cross-sectional signals and hedged long-short portfolios: it preserves signal direction while using return-dependence geometry to shape exposures. It accounts for the fact that there is imperfect correlation between parent and child nodes, and thus does not propagate weights entirely to the children. We can also impose economically motivated hierarchy that involves industries, sub-industries or factors, etc. This makes it much more robust to macroeconomic shocks and crises, where within-cluster correlations might spike. These features make TRP well suited for market-neutral, equity stat-arb or L/S trend-type strategies, where enforcing neutrality or limiting exposures at the market, sector or factor level is extremely important.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous graph-theoretic framework utilizing MSTs, ultrametric properties, and recursive signal propagation in signed space, bridging theoretical topology with practical, implementable portfolio construction guidelines.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Market-Neutral L/S Portfolio Construction] --> B[<b>Data Inputs:</b> Market Returns & Signed Signals]
    B --> C[<b>Computational Process:</b> Extract Sparse Rooted Topology from Correlation-Distance Graph]
    C --> D{<b>TRP Variants</b>}
    D --> E[Rooted MST Allocator]
    D --> F[Semi-Supervised: Sector/Factor Anchored]
    E & F --> G[<b>Outcomes:</b> Robust Exposure Control & Preserved Signal Direction]