Portfolio Construction: A Network Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data
2.2. Portfolio Construction
2.2.1. Rolling Window
2.2.2. Networks of Stocks and Their Centralities
- weighted degree centrality (“strength”)
- weighted eigenvector centrality (“eigen”)
- weighted efficiency—Latora closeness (“closeness”)
- in and out degree centrality (“in-degree” and “out-degree”) calculated on the corresponding unweighted-directed network. This network results from the Adjacency Matrix, which has binary values 0 and 1, indicating the absence or existence of causal relationships, correspondingly.
- in and out weighted degree centrality (“in-strength” and “out-strength”)
- in and out weighted eigenvector centrality (“in-eigen” and “out-eigen”)
2.2.3. Selection of Stocks
- Selection 1: Only 4 out of 26 stocks under consideration (Table 1) are selected, based on some centrality criterion, as follows:
- ○
- The four top stocks (central) with highest centrality are selected (“top”)
- ○
- The four middle stocks with intermediate centrality are selected (“mid”)
- ○
- The four bottom stocks (peripheral) with lowest centrality are selected (“bot”)
- Selection 2: All 26 stocks under consideration (Table 1) are selected.
2.2.4. Investing Weights
- Weighting 1: Markowitz investing weights (MPT), which minimize the portfolio risk for a given return, namely: the return resulting from 1/N allocation [14].
- Weighting 2: Centrality-based investing weights, which allocate higher investing weights at peripheral nodes-stocks with lower centrality value. We model this relationship of “centrality-investment” with two ways:
- ○
- “Lin”: Investing weights , which follow a linear relationship with the centrality of nodes-stocks included in the portfolio.
- ○
- “Quad”: Investing weights , which follow a quadratic relationship with the centrality of nodes-stocks included in the portfolio.
2.3. Portfolio Performance
2.3.1. Time Horizon for Portfolio Performance
- Long-term investing (24 Years): Evaluation of portfolio performance for all 24-years, cumulatively
- Short-term investing (1 Year): Evaluation of portfolio performance for each year, separately
- Intraday trading (1 Day): Evaluation of portfolio performance for each day, separately
2.3.2. Indicators for Portfolio Performance
- Return [2]
- Risk
- Risk-adjusted return
2.4. Network Structure Indices
3. Results
3.1. Results on Portfolio Performance
3.1.1. Results on Long-Term Investing
3.1.2. Results on Short-Term Investing
3.1.3. Results on Intraday Trading
3.2. Results on Network Structure
4. Discussion
4.1. Discussion on Portfolio Performance
4.1.1. Discussion on Long-Term Investing
4.1.2. Discussion on Short-Term Investing
4.1.3. Discussion on Intraday Trading
4.2. Discussion on Network Structure
4.3. Significance of the Study—Comparison of the Key Findings with Respect to the Relevant Literature
4.4. Limitations of the Study—Areas for Future Work
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Portfolio Abbreviation | Portfolio Construction | ||||
---|---|---|---|---|---|
Network Weights (2.2.2) | Number of Stocks (2.2.3) | Centrality (2.2.2) | Centrality Value (2.2.3) | Investing Weights (2.2.4) | |
“bot_strength” | Pearson correlation | 4/26 | strength | lowest | Markowitz |
“mid_strength” | Pearson correlation | 4/26 | strength | intermediate | Markowitz |
“top_strength” | Pearson correlation | 4/26 | strength | highest | Markowitz |
“Lin_strength” | Pearson correlation | 26/26 | strength | all | |
“Quad_strength” | Pearson correlation | 26/26 | strength | all | |
“bot_eigen” | Pearson correlation | 4/26 | eigenvector | lowest | Markowitz |
“mid_eigen” | Pearson correlation | 4/26 | eigenvector | intermediate | Markowitz |
“top_eigen” | Pearson correlation | 4/26 | eigenvector | highest | Markowitz |
“Lin_eigen” | Pearson correlation | 26/26 | eigenvector | all | |
“Quad_eigen” | Pearson correlation | 26/26 | eigenvector | all | |
“bot_closeness” | Pearson correlation | 4/26 | Latora closeness | lowest | Markowitz |
“mid_closeness” | Pearson correlation | 4/26 | Latora closeness | intermediate | Markowitz |
“top_closeness” | Pearson correlation | 4/26 | Latora closeness | highest | Markowitz |
“Lin_closeness” | Pearson correlation | 26/26 | Latora closeness | all | |
“Quad_closeness” | Pearson correlation | 26/26 | Latora closeness | all | |
“bot_in_strength” | Transfer Entropy | 4/26 | in-strength | lowest | Markowitz |
“mid_in_strength” | Transfer Entropy | 4/26 | in-strength | intermediate | Markowitz |
“top_in_strength” | Transfer Entropy | 4/26 | in-strength | highest | Markowitz |
“Lin_in_strength” | Transfer Entropy | 26/26 | in-strength | all | |
“Quad_in_strength” | Transfer Entropy | 26/26 | in-strength | all | |
“bot_out_strength” | Transfer Entropy | 4/26 | out-strength | lowest | Markowitz |
“mid_out_strength” | Transfer Entropy | 4/26 | out-strength | intermediate | Markowitz |
“top_out_strength” | Transfer Entropy | 4/26 | out-strength | highest | Markowitz |
“Lin_out_strength” | Transfer Entropy | 26/26 | out-strength | all | |
“Quad_out_strength” | Transfer Entropy | 26/26 | out-strength | all | |
“bot_in_degree” | Transfer Entropy | 4/26 | in-degree | lowest | Markowitz |
“mid_in_degree” | Transfer Entropy | 4/26 | in-degree | intermediate | Markowitz |
“top_in_degree” | Transfer Entropy | 4/26 | in-degree | highest | Markowitz |
“Lin_in_degree” | Transfer Entropy | 26/26 | in-degree | all | |
“Quad_in_degree” | Transfer Entropy | 26/26 | in-degree | all | |
“bot_out_degree” | Transfer Entropy | 4/26 | out-degree | lowest | Markowitz |
“mid_out_degree” | Transfer Entropy | 4/26 | out-degree | intermediate | Markowitz |
“top_out_degree” | Transfer Entropy | 4/26 | out-degree | highest | Markowitz |
“Lin_out_degree” | Transfer Entropy | 26/26 | out-degree | all | |
“Quad_out_degree” | Transfer Entropy | 26/26 | out-degree | all | |
“bot_in_eigen” | Transfer Entropy | 4/26 | in-eigenvector | lowest | Markowitz |
“mid_in_eigen” | Transfer Entropy | 4/26 | in-eigenvector | intermediate | Markowitz |
“top_in_eigen” | Transfer Entropy | 4/26 | in-eigenvector | highest | Markowitz |
“Lin_in_eigen” | Transfer Entropy | 26/26 | in-eigenvector | all | |
“Quad_in_eigen” | Transfer Entropy | 26/26 | in-eigenvector | all | |
“bot_out_eigen” | Transfer Entropy | 4/26 | out-eigenvector | lowest | Markowitz |
“mid_out_eigen” | Transfer Entropy | 4/26 | out-eigenvector | intermediate | Markowitz |
“top_out_eigen” | Transfer Entropy | 4/26 | out-eigenvector | highest | Markowitz |
“Lin_out_eigen” | Transfer Entropy | 26/26 | out-eigenvector | all | |
“Quad_out_eigen” | Transfer Entropy | 26/26 | out-eigenvector | all | |
“DJIA” | The index Dow Jones Industrial Average (DJIA) | ||||
“MPT” | The Markowitz portfolio composed of 26/26 stocks based on Modern Portfolio Theory (MPT) |
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AAPL | Apple | JPM | JPMorgan Chase |
AMGN | Amgen | KO | Coca-Cola |
AXP | American Express | MCD | McDonald’s |
BA | Boeing | MMM | 3M |
CAT | Caterpillar | MRK | Merck |
CSCO | Cisco | MSFT | Microsoft |
CVX | Chevron | NKE | Nike |
DIS | Disney | PG | Procter & Gamble |
HD | Home Depot | TRV | Travelers Companies Inc |
HON | Honeywell | UNH | UnitedHealth |
IBM | IBM | VZ | Verizon |
INTC | INTC Intel | WBA | Walgreen |
JNJ | Johnson & Johnson | WMT | Wal-Mart |
1998 | 1999 | 2000 | … | 2021 | 2022 |
---|---|---|---|---|---|
Data | Evaluation | ||||
Data | Evaluation | ||||
… | … | ||||
Data | Evaluation |
Pearson Correlation Network | Transfer Entropy Network |
---|---|
Statistical Correlation | Causal Relationship |
Undirected | Directed |
Linear | Non-Linear |
Threshold is set to 10% | No Threshold is applied, due to the use of “Effective Transfer Entropy” |
Pearson Correlation Network | Transfer Entropy Network | ||
---|---|---|---|
Undirected Network | Directed Network | ||
Weight Matrix with elements | Weight Matrix with elements | ||
Absolute Weight Matrix with positive elements | Weight Matrix of Distances defined as: with | Adjacency Matrix with elements 0 or 1 defined as: | Weight Matrix with elements |
Weighted Degree Centrality (“strength”) | In Degree Centrality (“in-degree”) & Out Degree Centrality (“out-degree”) | In Weighted Degree Centrality (“in-strength”) & Out Weighted Degree Centrality (“out-strength”) | |
Weighted Eigenvector Centrality (“eigen”) | In Weighted Eigenvector Centrality (“in-eigen”) & Out Weighted Eigenvector Centrality (“out-eigen”) | ||
Weighted Efficiency Latora Closeness (“closeness”) |
Investing Weights | |||
---|---|---|---|
Weighting 1 | Weighting 2 | ||
Selection of Stocks | Selection 1 | Combination A | |
Selection 2 | Combination B | Combination C |
Year | Event |
---|---|
1998 | Russian Financial Crisis |
2001 | 9/11 Terrorist Attacks |
2002 | Stock Market Downturn of 2002 |
2008 | Global Financial Crisis |
2011 | Downgrade of US Federal Government Credit Rating |
2015 | Chinese Stock Market Turbulence (Stock Market sell-off) |
2020 | COVID-19 Pandemic |
2022 | Russian-Ukrainian War |
Data (2.1) | Daily Returns (adjusted for splits) from January 1998 to December 2022 | ||||||||
Rolling Window (2.2.1) | Window of 2 years, rolling by one year at a time Estimation of correlation network and portfolio construction Evaluation of Portfolio Performance | ||||||||
Nodes (2.2.2) | 26 stocks from index Dow Jones Industrial Average (DJIA) | ||||||||
Network Construction (2.2.2) | Pearson Correlation | Transfer Entropy | |||||||
Network Weights (2.2.2) | |||||||||
Selection of Stocks in the portfolio (2.2.3) | Index DJIA (Benchmark A) | Markowitz Portfolio based on MPT (Benchmark B) | Network Approach to Portfolio Construction | ||||||
26/26 | 26/26 | 4/26 | |||||||
Selection of All Stocks with different centrality-based investing weights | Top 4 Highest Centrality | Middle 4 Middle Centrality | Bottom 4 Lowest Centrality | ||||||
Investing Weights of the portfolio (2.2.4) | Markowitz Weights for all 26 stocks: Minimize Risk (SD)for a given Return, which results from 1/N allocation | Markowitz Weights for the 4 selected stocks | Markowitz Weights for the 4 selected stocks | Markowitz Weights for the 4 selected stocks | |||||
Investing Horizon for portfolio performance (2.3.1) | Long-term (24 Years) | Short-term (1 Year) | Intraday Trading (1 Day) | ||||||
Indicators for portfolio performance (2.3.2) | Return | Risk | Risk-adjusted return | ||||||
Total Risk (SD) | Systematic Risk (Beta coefficient) | Sharpe Ratio (Adjusted Return to Total Risk) | Treynor Ratio (Adjusted Return to Systematic Risk) |
Pearson Correlation Network | Transfer Entropy Network | ||
---|---|---|---|
Undirected Network | Directed Network | ||
Weight Matrix with elements | Weight Matrix with elements | ||
Adjacency Matrix with elements 0 or 1 defined as: | Absolute Weight Matrix with positive elements | Adjacency Matrix with elements 0 or 1 defined as: | Weight Matrix with elements |
Density | Weighted Density | Density | Weighted Density |
Degree Centralization | Weighted Degree Centralization | Degree Centralization | Weighted Degree Centralization |
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Ioannidis, E.; Sarikeisoglou, I.; Angelidis, G. Portfolio Construction: A Network Approach. Mathematics 2023, 11, 4670. https://doi.org/10.3390/math11224670
Ioannidis E, Sarikeisoglou I, Angelidis G. Portfolio Construction: A Network Approach. Mathematics. 2023; 11(22):4670. https://doi.org/10.3390/math11224670
Chicago/Turabian StyleIoannidis, Evangelos, Iordanis Sarikeisoglou, and Georgios Angelidis. 2023. "Portfolio Construction: A Network Approach" Mathematics 11, no. 22: 4670. https://doi.org/10.3390/math11224670
APA StyleIoannidis, E., Sarikeisoglou, I., & Angelidis, G. (2023). Portfolio Construction: A Network Approach. Mathematics, 11(22), 4670. https://doi.org/10.3390/math11224670