Statistical arbitrage portfolio construction based on preference relations

ArXiv ID: 2310.08284 “View on arXiv”

Authors: Unknown

Abstract

Statistical arbitrage methods identify mispricings in securities with the goal of building portfolios which are weakly correlated with the market. In pairs trading, an arbitrage opportunity is identified by observing relative price movements between a pair of two securities. By simultaneously observing multiple pairs, one can exploit different arbitrage opportunities and increase the performance of such methods. However, the use of a large number of pairs is difficult due to the increased probability of contradictory trade signals among different pairs. In this paper, we propose a novel portfolio construction method based on preference relation graphs, which can reconcile contradictory pairs trading signals across multiple security pairs. The proposed approach enables joint exploitation of arbitrage opportunities among a large number of securities. Experimental results using three decades of historical returns of roughly 500 stocks from the S&P 500 index show that the portfolios based on preference relations exhibit robust returns even with high transaction costs, and that their performance improves with the number of securities considered.

Keywords: Statistical Arbitrage, Pairs Trading, Preference Relation Graphs, Portfolio Construction, Signal Reconciliation, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper introduces complex graph theory and preference relation frameworks (e.g., potential method) requiring advanced mathematics for signal reconciliation, while providing extensive empirical validation with 30 years of S&P 500 data and robustness testing against transaction costs.

  flowchart TD
    A["Research Goal:<br>Reconcile Contradictory<br>Pairs Trading Signals"] --> B["Methodology:<br>Preference Relation Graphs"]
    B --> C["Data Input:<br>Historical Returns<br>~500 S&P 500 Stocks<br>30 Years"]
    C --> D["Process:<br>Construct Preference Graph<br>and Reconcile Signals"]
    D --> E["Output:<br>Robust Portfolio<br>Construction"]
    E --> F["Key Outcome 1:<br>Sustained Returns<br>Even w/ High Transaction Costs"]
    E --> G["Key Outcome 2:<br>Performance Improves<br>with More Securities"]