Pairs Trading Using a Novel Graphical Matching Approach

Paper: arXiv 2403.07998

Abstract

Pairs trading, a strategy that capitalizes on price movements of asset pairs driven by similar factors, has gained significant popularity among traders. Common practice involves selecting highly cointegrated pairs to form a portfolio, which often leads to the inclusion of multiple pairs sharing common assets. This approach, while intuitive, inadvertently elevates portfolio variance and diminishes risk-adjusted returns by concentrating on a small number of highly cointegrated assets. Our study introduces an innovative pair selection method employing graphical matchings designed to tackle this challenge. We model all assets and their cointegration levels with a weighted graph, where edges signify pairs and their weights indicate the extent of cointegration. A portfolio of pairs is a subgraph of this graph. We construct a portfolio which is a maximum weighted matching of this graph to select pairs which have strong cointegration while simultaneously ensuring that there are no shared assets within any pair of pairs. This approach ensures each asset is included in just one pair, leading to a significantly lower variance in the matching-based portfolio compared to a baseline approach that selects pairs purely based on cointegration. Theoretical analysis and empirical testing using data from the S&P 500 between 2017 and 2023, affirm the efficacy of our method. Notably, our matching-based strategy showcases a marked improvement in risk-adjusted performance, evidenced by a gross Sharpe ratio of 1.23, a significant enhancement over the baseline value of 0.48 and market value of 0.59. Additionally, our approach demonstrates reduced trading costs attributable to lower turnover, alongside minimized single asset risk due to a more diversified asset base.

Complexity vs Empirical Score

• Math Complexity: 6.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced graph theory (maximum weighted matching) and cointegration analysis, placing it in the higher math complexity range; it also provides concrete empirical results on S&P 500 data (2017-2023) with reported Sharpe ratios and turnover metrics, indicating strong backtest readiness.

Research Flowchart

  flowchart TD
  A["Research Goal: Optimize Pairs Trading Portfolio<br>by minimizing shared assets and variance"] --> B
  subgraph B ["Methodology: Graph Theory Approach"]
      direction LR
      B1["Data: S&P 500 Stocks 2017-2023"] --> B2["Compute Cointegration Weights"] --> B3["Construct Weighted Graph<br>Nodes=Assets, Edges=Cointegration"] --> B4["Compute Maximum Weighted Matching<br>to Select Non-Overlapping Pairs"]
  end
  B --> C["Outcomes: Matching Portfolio"]
  C --> D{"Performance Metrics"}
  D --> E["Gross Sharpe Ratio: 1.23<br>vs 0.48 (Baseline) & 0.59 (Market)"]
  D --> F["Lower Variance & Turnover<br>Minimized Single Asset Risk"]

Cited References (40)

1. Random Graphs (2001)
2. Direct Estimation of Equity Market Impact (2005) — link
3. Statistical Arbitrage in the US Equities Market (2010)
4. Optimal Portfolio Diversification Using the Maximum Entropy Principle (2008) — link
5. Trading strategies with copulas (2013)
6. High Frequency Equity Pairs Trading: Transaction Costs, Speed of Execution and Patterns in Returns (2010)
7. Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy (2013)
8. Maximum drawdown, recovery, and momentum (2021)

0 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.