Paper: arXiv 2404.00187

Abstract

We investigate an application of network centrality measures to portfolio optimization, by generalizing the method in [“Pozzi, Di Matteo and Aste, \emph{“Spread of risks across financial markets: better to invest in the peripheries”}, Scientific Reports 3:1665, 2013”], that however had significant limitations with respect to the state of the art in network theory. In this paper, we systematically compare many possible variants of the originally proposed method on S&P 500 stocks. We use daily data from twenty-seven years as training set and their following year as test set. We thus select the best network-based methods according to different viewpoints including for instance the highest Sharpe Ratio and the highest expected return. We give emphasis in new centrality measures and we also conduct a thorough analysis, which reveals significantly stronger results compared to those with more traditional methods. According to our analysis, this graph-theoretical approach to investment can be used successfully by investors with different investment profiles leading to high risk-adjusted returns.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced network theory concepts and mathematical derivations for various centrality measures, indicating high mathematical complexity. It is empirically rigorous with a large-scale backtest on S&P 500 data over 28 years, using Sharpe ratio and expected returns for model selection, though it lacks explicit code or live implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimize portfolio using graph centralities"] --> B["Data Input<br>S&P 500 stocks (27 years daily data)"]
  B --> C["Methodology<br>Compute centrality variants & compare"]
  C --> D["Computational Process<br>Backtest on training set & validate on test set"]
  D --> E{"Evaluation Metrics"}
  E --> F["Max Sharpe Ratio<br>Best Risk-Adjusted Returns"]
  E --> G["Max Expected Return<br>Highest Profitability"]
  E --> H["New Centrality Measures<br>Superior to traditional methods"]
  F --> I["Outcome<br>Successful strategy for diverse investor profiles"]

Cited References (21)

  1. Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs (2022) — link
  2. On the exponential generating function for non-backtracking walks (2018) — link
  3. The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis (2018) — link
  4. Non-backtracking walk centrality for directed networks (2018) — link
  5. Matching exponential-based and resolvent-based centrality measures (2016) — link
  6. Spread of risk across financial markets: better to invest in the peripheries (2013) — link
  7. Network Properties Revealed through Matrix Functions (2010) — link
  8. Networks: An Introduction (2010) — link
and 13 more
  1. Comparison of Prim and Kruskal on Shanghai and Shenzhen 300 Index Hierarchical Structure Tree (2009) — link
  2. Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? (2009) — link
  3. Correlation based networks of equity returns sampled at different time horizons (2006) — link
  4. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003) — link
  5. Geometry of minimum spanning trees on scale-free networks (2003) — link
  6. Modern Portfolio Theory, 1950 to Date (1997) — link
  7. Portfolio Selection (1971) — link
  8. Structure of complex networks (2005)
  9. Risk and asset allocation (2005) — link
  10. Finland. Supported by an Academy of Finland grant (Suomen Akatemian p¨a¨at¨os 331240)
  11. The methods proposed outperform other previously proposed methods such as the MST
  12. Using the weights calculated in step 3, we invest in these portfolios in year t + 1, and calculate the portfolios realised returns
  13. We calculate the weights of equally-weighted and optimal portfolios for these m stocks based on their returns in year t

0 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.