Clustering Digital Assets Using Path Signatures: Application to Portfolio Construction

ArXiv ID: 2410.23297 “View on arXiv”

Authors: Unknown

Abstract

We propose a new way of building portfolios of cryptocurrencies that provide good diversification properties to investors. First, we seek to filter these digital assets by creating some clusters based on their path signature. The goal is to identify similar patterns in the behavior of these highly volatile assets. Once such clusters have been built, we propose “optimal” portfolios by comparing the performances of such portfolios to a universe of unfiltered digital assets. Our intuition is that clustering based on path signatures will make it easier to capture the main trends and features of a group of cryptocurrencies, and allow parsimonious portfolios that reduce excessive transaction fees. Empirically, our assumptions seem to be satisfied.

Keywords: Path Signature, Clustering, Portfolio Construction, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper introduces mathematically advanced path signature theory (rough paths, iterated integrals) to finance, scoring high on math complexity. It includes a clear empirical setup with portfolio construction and comparative backtests on cryptocurrencies, though it lacks public code/datasets or heavy statistical validation, placing it above moderate empirical rigor.

  flowchart TD
    RQ["Research Goal:<br>Develop crypto portfolio construction<br>via clustering for diversification"] --> Input["Data Input:<br>Historical price data<br>of digital assets"]
    Input --> PathSig["Methodology:<br>Compute Path Signatures<br>for each asset time series"]
    PathSig --> Cluster["Methodology:<br>Apply Clustering algorithm<br>on Path Signatures"]
    Cluster --> Portfolios["Computation:<br>Construct portfolios<br>from clusters"]
    Portfolios --> Eval["Computation:<br>Compare performance to<br>unfiltered universe"]
    Eval --> Outcomes["Key Findings:<br>Clustering enables parsimonious,<br>trend-capturing portfolios with<br>good diversification and lower fees"]