Paper: arXiv 2407.04500

Abstract

In this paper, we introduce the Dynamic Modularity-Spectral Algorithm (DynMSA), a novel approach to identify clusters of stocks with high intra-cluster correlations and low inter-cluster correlations by combining Random Matrix Theory with modularity optimisation and spectral clustering. The primary objective is to uncover hidden market structures and find diversifiers based on return correlations, thereby achieving a more effective risk-reducing portfolio allocation. We applied DynMSA to constituents of the S&P 500 and compared the results to sector- and market-based benchmarks. Besides the conception of this algorithm, our contributions further include implementing a sector-based calibration for modularity optimisation and a correlation-based distance function for spectral clustering. Testing revealed that DynMSA outperforms baseline models in intra- and inter-cluster correlation differences, particularly over medium-term correlation look-backs. It also identifies stable clusters and detects regime changes due to exogenous shocks, such as the COVID-19 pandemic. Portfolios constructed using our clusters showed higher Sortino and Sharpe ratios, lower downside volatility, reduced maximum drawdown and higher annualised returns compared to an equally weighted market benchmark.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.0/10 (capped from 8.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical techniques including Random Matrix Theory, modularity optimization, and spectral clustering, with detailed derivations in the methodology section. It demonstrates high empirical rigor through extensive backtesting on S&P 500 constituents, showing outperformance against benchmarks with specific metrics (Sharpe/Sortino ratios, drawdowns) and sensitivity to regime changes like COVID-19.

Research Flowchart

  flowchart TD
  A["Research Goal: Identify Stable Stock Clusters<br>for Risk-Reduced Portfolio Allocation"] --> B["Methodology: DynMSA Algorithm"]
  B --> C["Random Matrix Theory Filtering<br>Remove Market Noise"]
  C --> D["Modularity Optimisation<br>Sector-based Calibration"]
  D --> E["Spectral Clustering<br>Correlation-based Distance"]
  E --> F["Apply to S&P 500 Data"]
  F --> G{"Key Outcomes"}
  G --> H["Outperformed Benchmarks<br>Higher Sharpe/Sortino Ratios"]
  G --> I["Detected Regime Shifts<br>e.g., COVID-19 Pandemic"]

Cited References (51)

  1. Hierarchical structure in financial markets (1999)
  2. Fast unfolding of communities in large networks (2008)
  3. Community Detection for Correlation Matrices (2015)
  4. Community detection in graphs (2010)
  5. Building diversified portfolios that outperform out of sample (2016)
  6. Finding and evaluating community structure in networks (2004)
  7. Consensus clustering in complex networks (2012)
  8. Portofolio selection (1952)
and 43 more
  1. Spread of risk across financial markets: better to invest in the peripheries (2013)
  2. A random matrix theory approach to financial cross-correlations (2000)
  3. Safety first and the holding of assets (1952)
  4. A tutorial on spectral clustering (2007)
  5. From Louvain to Leiden: guaranteeing well-connected communities (2019)
  6. Resolution limit in community detection (2007)
  7. Multiscale correlation networks analysis of the US stock market: a wavelet analysis (2017)
  8. Sentiment correlation in financial news networks and associated market movements (2021)
  9. Stock network stability in times of crisis (2014)
  10. A statistical method for evaluating systematic relationships (1958)
  11. Normalized cuts and image segmentation (2000) — link
  12. Asymmetric correlations of equity portfolios (2002)
  13. Extreme correlation of international equity markets (2001)
  14. Noise dressing of financial correlation matrices (1999)
  15. Noisy covariance matrices and portfolio optimization II (2003)
  16. Random matrix approach to cross correlations in financial data (2002)
  17. Cleaning large correlation matrices: tools from random matrix theory (2017)
  18. Distribution of eigenvalues for some sets of random matrices (1967)
  19. Clustering and information in correlation based financial networks (2004)
  20. Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks (2009)
  21. Comparing partitions (1985)
  22. Objective criteria for the evaluation of clustering methods (1971)
  23. Clustering financial time series: How long is enough? (2016) — link
  24. The myth of diversification (2009)
  25. The Myth of Diversification Reconsidered (2021)
  26. Equity market connectedness across regimes of geopolitical risks: Historical evidence and theory (2023)
  27. Contagious investor sentiment and international markets (2017)
  28. Stability and similarity in financial networks—How do they change in times of turbulence? (2021)
  29. A tool for filtering information in complex systems (2005)
  30. Understanding changes in the topology and geometry of financial market correlations during a market crash (2021)
  31. Dynamics of cluster structures in a financial market network (2014)
  32. What can cluster analysis offer in investing?-Measuring structural changes in the investment universe (2021)
  33. Interconnectedness in the global financial market (2021)
  34. Measuring financial asset return and volatility spillovers, with application to global equity markets (2009)
  35. International stock return comovements (2009)
  36. Financial contagion during COVID–19 crisis (2021)
  37. Equity portfolio diversification (2008)
  38. Risk parity and diversification (2011)
  39. Honey, I Shrunk the Sample Covariance Matrix (2004)
  40. Common risk factors in the returns on stocks and bonds (1993)
  41. A five-factor asset pricing model (2015)
  42. Industry classification schemes: An analysis and review (2016)
  43. Industry classifications and return comovement (2007)

0 of 51 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.