Portfolio Selection via Topological Data Analysis

ArXiv ID: 2308.07944 “View on arXiv”

Authors: Unknown

Abstract

Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique characteristics of multivariate time series data from stock markets. We present a two-stage method for constructing an investment portfolio of common stocks. The method involves the generation of time series representations followed by their subsequent clustering. Our approach utilizes features based on Topological Data Analysis (TDA) for the generation of representations, allowing us to elucidate the topological structure within the data. Experimental results show that our proposed system outperforms other methods. This superior performance is consistent over different time frames, suggesting the viability of TDA as a powerful tool for portfolio selection.

Keywords: Topological Data Analysis (TDA), Time Series Clustering, Portfolio Management, Multivariate Time Series, Representation Learning, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics from Topological Data Analysis (persistence diagrams, landscapes) which significantly increases complexity, while also providing a detailed experimental pipeline with backtesting on multiple time frames and financial metrics.

  flowchart TD
    A["Research Goal: Enhance Portfolio Management<br/>using Topological Data Analysis"] --> B["Input: Multivariate Time Series Data<br/>from Stock Markets"]
    B --> C["Stage 1: Feature Extraction<br/>Topological Data Analysis TDA"]
    C --> D["Stage 2: Representation Learning<br/>Time Series Clustering"]
    D --> E["Key Outcome: Constructed Investment Portfolio"]
    E --> F["Key Finding: Consistent Outperformance<br/>vs. Traditional Methods"]