Network-based diversification of stock and cryptocurrency portfolios

TL;DR

This study develops a network-based portfolio diversification framework that integrates linear and non-linear asset relationships via Pearson correlation and mutual information, transforming these into distance graphs and applying community detection (Louvain on MST and Affinity Propagation) to identify asset communities. Using data from the S&P 500 and the Top 203 cryptocurrencies across 2019–2022, including the COVID-19 and Ukraine war periods, the authors evaluate asset selection strategies based on PCA and centrality measures within both full graphs and co-occurrence networks. Results indicate that stock portfolios frequently outperform baselines under network-based frameworks, with Louvain-based co-occurrence strategies yielding high returns and lower volatility, whereas crypto portfolios exhibit greater volatility and less consistent gains, with crisis periods disrupting established patterns. The work highlights the potential and limitations of network-based diversification for traditional and digital assets, suggesting future enhancements through data preprocessing, robustness to extreme events, and hybrid portfolios combining multiple network representations $($e.g., using $D^C_{ij}$ and $D^M_{ij}$)$ to improve practical applicability.

Abstract

Maintaining a balance between returns and volatility is a common strategy for portfolio diversification, whether investing in traditional equities or digital assets like cryptocurrencies. One approach for diversification is the application of community detection or clustering, using a network representing the relationships between assets. We examine two network representations, one based on a standard distance matrix based on correlation, and another based on mutual information. The Louvain and Affinity propagation algorithms were employed for finding the network communities (clusters) based on annual data. Furthermore, we examine building assets' co-occurrence networks, where communities are detected for each month throughout a whole year and then the links represent how often assets belong to the same community. Portfolios are then constructed by selecting several assets from each community based on local properties (degree centrality), global properties (closeness centrality), or explained variance (Principal component analysis), with three value ranges (max, med, min), calculated on a maximal spanning tree or a fully connected community sub-graph. We explored these various strategies on data from the S\&P 500 and the Top 203 cryptocurrencies with a market cap above 2M USD in the period from Jan 2019 to Sep 2022. Moreover, we study into more details the periods of the beginning of the COVID-19 outbreak and the start of the war in Ukraine. The results confirm some of the previous findings already known for traditional stock markets and provide some further insights, while they reveal an opposing trend in the crypto-assets market.

Figures (12)

• Figure 1: Methodological framework for constructing investment portfolios: a comprehensive overview of strategies employed. The symbols represent: Cor – Correlation, MI – Mutual information, ($\sim$) – co-occurrence, $C_C$ – Closeness centrality, $C_D$ – Degree centrality, PCA – Principal component analysis, FG – Full graph, MST – Minimum spanning tree, LV – Louvain, and AP – Affinity propagation.
• Figure 2: Distribution of the Pearson correlation coefficient and mutual information in the cryptocurrency and stock market data from January 2019 to September 2022.
• Figure 3: Network communities of cryptocurrencies and stocks derived from historical prices from January 2019 to September 2022, using the Louvain algorithm. The networks are minimal spanning trees derived from the Pearson correlation coefficient and mutual information calculated from the normalized log-returns of asset prices.
• Figure 4: Matrix visualizations of cryptocurrencies and stock markets derived from historical prices from January 2019 to September 2022, clustered by Affinity propagation. The matrices are derived from the Pearson correlation coefficient and mutual information calculated from the normalized log-returns of asset prices.
• Figure 5: Return vs. volatility of the examined investment portfolios composed of stocks during the entire observed period, from January 2019 to August 2022. The symbols represent: Cor – Correlation, MI – Mutual information, ($\sim$) – co-occurrence, $C_C$ – Closeness centrality, $C_D$ – Degree centrality, PCA – Principal component analysis, FG – Full graph, MST – Minimum spanning tree, LV – Louvain, and AP – Affinity propagation. A detailed description of all symbols is provided in Figure \ref{['fig:port_meth']}.