Risk Management Framework for Complex Systems: A Production Engineering Approach to Cryptocurrency Portfolio Optimization

Risk Management Framework for Complex Systems: A Production Engineering Approach to Cryptocurrency Portfolio Optimization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Risk Management Framework for Complex Systems: A Production Engineering Approach to Cryptocurrency Portfolio Optimization Daniel Pimenta Gonçalves da Fonte, José Donizetti Lima, Matheus Henrique Dal Molin Ribeiro, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8771826/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a comprehensive risk management framework for complex systems, applying production engineering methodologies to cryptocurrency portfolio optimization. The framework integrates principal component analysis, K-means clustering, Hidden Markov Model regime detection, structural shock decomposition, network causality analysis, GARCH volatility modeling, and stationarity testing to provide a multifaceted approach to risk assessment and decision support. Analysis of fourteen cryptocurrency assets over a multi-year period reveals extreme risk concentration with 67.89% of portfolio variance explained by the first systematic factor, six distinct operational clusters, and five market regimes with volatility ratios reaching 6.91×. The study identifies supply chain disruption events as the primary source of negative abnormal returns, averaging negative 9.2%, while network analysis reveals hierarchical information transmission structures with Ethereum and Bitcoin as dominant hubs. GARCH modeling demonstrates mean volatility persistence of 0.938 with half-lives averaging 20.8 days. These findings validate return-based methodologies and provide actionable insights for resource allocation, position sizing, and dynamic hedging strategies in high-volatility environments. The framework establishes a foundation for production engineering approaches to financial risk management under extreme uncertainty. Risk management portfolio optimization production engineering Hidden Markov Models principal component analysis GARCH models network analysis regime detection cryptocurrency Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction The management of complex systems under conditions of extreme uncertainty represents a fundamental challenge in production engineering. Contemporary financial markets, particularly emerging cryptocurrency ecosystems, exhibit characteristics analogous to complex industrial systems: high dimensionality, nonlinear dynamics, regime-dependent behavior, and cascading failure mechanisms (Kritzman et al., 2011). Traditional risk management approaches, developed for relatively stable environments, demonstrate limited efficacy when applied to systems characterized by volatility ratios exceeding 6:1 and risk concentration above 65% in a single factor. Production engineering provides methodological frameworks specifically designed for managing operational risk in complex, interdependent systems. These frameworks emphasize reliability analysis, failure mode identification, supply chain risk mitigation, and adaptive control mechanisms (Montgomery, 2012). However, their application to financial portfolio management remains underexplored, despite clear parallels between supply chain disruptions and market liquidity crises, between production regime shifts and market volatility transitions, and between quality control processes and risk monitoring systems. Cryptocurrency markets present an ideal testbed for production engineering methodologies due to their extreme volatility, 24/7 operational requirements, and susceptibility to systematic shocks. Unlike traditional equity markets, cryptocurrency portfolios face unique challenges: absence of fundamental valuation anchors, extreme price discovery mechanisms, protocol-level technical risks, and regulatory uncertainty (Baur et al., 2018). These characteristics mirror challenges in emerging manufacturing systems, where standard operating procedures may be ill-defined and failure modes incompletely characterized. This study addresses three critical gaps in the literature. First, existing portfolio optimization frameworks rely predominantly on mean-variance approaches that degenerate under extreme risk concentration. Second, regime detection methodologies typically focus on binary state identification, failing to capture the multi-modal volatility distributions observed in high-frequency environments. Third, current approaches treat risk factors as independent, neglecting network effects and cascade propagation mechanisms central to complex systems theory. 1.1. Research Objectives The primary objective of this research is to develop and validate a production engineering framework for portfolio risk management in complex systems. Specific objectives include: Objective 1: Identify and quantify systematic risk factors through principal component decomposition to determine the effective dimensionality of the risk space and assess the validity of traditional diversification approaches. Objective 2: Establish optimal portfolio segmentation through clustering analysis to enable cluster-specific risk management protocols and resource allocation strategies. Objective 3: Detect and characterize operational regimes using Hidden Markov Models to quantify regime transition probabilities, expected durations, and volatility differentials for dynamic position sizing. Objective 4: Decompose structural shocks by event category to identify primary sources of abnormal returns and establish event-specific hedging requirements. Objective 5: Map network causality structures to determine information flow patterns and identify systemically important nodes requiring priority monitoring. Objective 6: Quantify volatility persistence through GARCH modeling to determine appropriate rebalancing frequencies and capital requirements for equivalent risk reduction. Objective 7: Validate stationarity assumptions to confirm the appropriateness of return-based analytical frameworks and identify opportunities for cointegration-based strategies. 1.2. Contribution to Production Engineering This research contributes to production engineering literature by demonstrating the applicability of reliability theory, network analysis, and control systems to financial risk management. The framework treats portfolio assets as components in a production system, regime transitions as operational mode changes, and market shocks as supply chain disruptions. This perspective enables the application of established engineering methodologies to novel problem domains, extending the scope of production engineering beyond traditional manufacturing contexts. 2. Literature Review 2.1. Risk Factor Decomposition and Dimensionality Reduction Principal Component Analysis has emerged as a fundamental tool for portfolio risk management, enabling the identification of systematic risk factors from high-dimensional return data (Kritzman et al., 2011). The absorption ratio, defined as the fraction of total variance captured by a subset of principal components, provides a measure of systemic risk concentration. Pasini (2017) demonstrated that the first three principal components typically capture 75% of variance in equity portfolios, enabling substantial dimensionality reduction without significant information loss. However, cryptocurrency portfolios exhibit substantially higher risk concentration, with Celestin (2025) reporting first-component dominance approaching 70% in digital asset portfolios. The mathematical foundation of PCA begins with the covariance matrix of asset returns, where eigenvalue decomposition yields orthogonal principal components ordered by variance contribution (Mavungu, 2023). Applications extend beyond dimensionality reduction to scenario generation for stress testing, where principal components define the relevant directions of market movement (Jackson, 2001). Recent advances include the integration of PCA with machine learning techniques for dynamic factor identification and the development of kernel PCA methods for capturing nonlinear relationships in financial data. 2.2. Clustering for Portfolio Segmentation K-means clustering provides a data-driven approach to portfolio segmentation based on return characteristics rather than predetermined asset classifications (Ding & He, 2004). Unlike traditional sector-based groupings, clustering algorithms identify empirical similarities in risk profiles, enabling more effective diversification strategies. Recent applications demonstrate that clustering-based portfolios achieve higher risk-adjusted returns compared to sector-balanced alternatives, with Sharpe ratios improving by 15–30% across multiple asset classes (2025 study in Symmetry journal). The Silhouette score, Davies-Bouldin index, and Calinski-Harabasz score provide complementary measures for determining optimal cluster numbers, with Silhouette analysis demonstrating superior performance compared to elbow methods (as reported in MDPI 2025 study). Applications in portfolio construction show that selecting representative assets from each cluster produces more stable portfolios with reduced correlation during stress events compared to traditional mean-variance optimization (U et al., 2024; Wu et al., 2022). 2.3. Market Regime Detection Using Hidden Markov Models Hidden Markov Models provide a probabilistic framework for identifying latent market states from observed returns, addressing the fundamental challenge that regime transitions are not directly observable (Yuan & Mitra, 2019). The Markov property assumes that future states depend only on the current state, enabling tractable inference through the Viterbi algorithm and Baum-Welch estimation. Financial applications demonstrate that regime-switching strategies incorporating HMM predictions achieve both higher absolute and risk-adjusted returns compared to static approaches (Wang et al., 2020). Market regimes typically exhibit distinct return distributions and volatility profiles, with transitions often corresponding to macroeconomic shifts, regulatory changes, or structural breaks (Kritzman et al., 2012). Three-state HMM implementations successfully distinguish growth, neutral, and stress regimes, with stress detection enabling preemptive risk reduction before significant drawdowns materialize. Comparative studies indicate HMM superiority over clustering-based regime detection methods, particularly for out-of-sample prediction accuracy. 2.4. Volatility Modeling Through GARCH Frameworks The Generalized Autoregressive Conditional Heteroskedasticity framework, introduced by Bollerslev (1986), captures the volatility clustering and persistence characteristics fundamental to financial time series. The GARCH( 1 , 1 ) specification, where conditional variance depends on past squared residuals and lagged variance, provides parsimony while maintaining strong predictive performance across diverse asset classes (Engle, 1982). Persistence parameters, defined as the sum of ARCH and GARCH coefficients, quantify the rate of volatility shock dissipation, with values approaching unity indicating near-integrated processes requiring extensive time for mean reversion (Ding & Granger, 1996). Asymmetric extensions including EGARCH and GJR-GARCH address leverage effects where negative shocks generate larger volatility increases than positive shocks of equivalent magnitude (Aliyev et al., 2020). Applications to cryptocurrency markets reveal persistence parameters averaging 0.94, substantially exceeding traditional equity values of 0.85–0.90, implying slower mean reversion and longer-lasting volatility shocks (studies from 2023–2024 analyzing crypto volatility). The half-life measure, calculated as ln(0.5)/ln(persistence), provides intuitive interpretation of shock dissipation timescales, critical for determining rebalancing frequencies and capital requirements. 2.5. Network Analysis and Contagion Effects Granger causality testing identifies directional information flows between assets, enabling construction of causal networks that reveal hierarchical market structures. Network centrality measures quantify asset importance within the system, with high-centrality nodes serving as potential contagion sources during stress periods. Applications demonstrate that central assets exhibit predictive power for peripheral asset returns, enabling lead-lag trading strategies and early warning systems for market dislocations. 2.6. Production Engineering Perspectives on Financial Risk Production engineering frameworks treat portfolio management as a reliability optimization problem under uncertainty. This perspective emphasizes failure mode identification, redundancy planning, and adaptive control mechanisms analogous to quality management systems (Montgomery, 2012). Supply chain risk management methodologies, including supplier diversification and buffer stock strategies, translate directly to portfolio hedging and liquidity management requirements. The integration of control theory enables dynamic position sizing based on real-time regime probability estimates, similar to adaptive manufacturing systems responding to demand fluctuations. 3. Methodology This study employs a comprehensive multi-stage analytical framework integrating seven complementary methodologies to characterize risk dynamics in cryptocurrency portfolios. The methodological architecture, illustrated in Fig. 1 , proceeds through sequential stages: ( 1 ) principal component analysis for systematic risk decomposition, ( 2 ) K-means clustering for portfolio segmentation, ( 3 ) Hidden Markov Model regime detection, ( 4 ) structural shock decomposition by event category, ( 5 ) network causality analysis, ( 6 ) GARCH volatility modeling, and ( 7 ) stationarity testing. Each analytical component addresses specific research objectives while contributing to an integrated understanding of complex system behavior under extreme uncertainty. The framework adopts production engineering principles by treating portfolio assets as components in a reliability system, regime transitions as operational mode changes, and market shocks as supply chain disruptions. This perspective enables the systematic application of failure mode analysis, redundancy optimization, and adaptive control mechanisms to financial risk management. The following subsections detail the mathematical foundations, implementation procedures, and validation criteria for each methodological component. Authors (2025) 3.1. Data Collection and Preprocessing The analysis employs daily closing price data for fourteen cryptocurrency assets obtained from Coingecko (2025) site. The dataset encompasses varying temporal windows tailored to each asset, but the range of time analysis comprehend January 28th 2022 to July 21th 2025. This time window enables to capture many different market conditions, including bull and bear cycles, regulatory shifts and technological disruptions Table 1 demonstrates each cryptocurrency and the input data and then time period. Table 1 Asset characteristics and sample periods Asset Input Observations Period of the cut AVAX 1929 2022-01-28 to 2025-07-21 AXS 1821 2022-01-28 to 2025-07-21 BTC 4466 2022-01-28 to 2025-07-21 DOT 1963 2022-01-28 to 2025-07-21 ETH 3736 2022-01-28 to 2025-07-21 ILV 1574 2022-01-28 to 2025-07-21 IMX 1355 2022-01-28 to 2025-07-21 LTC 4574 2022-01-28 to 2025-07-21 MANA 2987 2022-01-28 to 2025-07-21 RON 1372 2022-01-28 to 2025-07-21 SAND 1967 2022-01-28 to 2025-07-21 SOL 2093 2022-01-28 to 2025-07-21 TRX 2977 2022-01-28 to 2025-07-21 XRP 4464 2022-01-28 to 2025-07-21 Authors (2025) Asset selection criteria emphasized market capitalization, trading volume liquidity, and operational diversity across infrastructure, platform, and application layers. Price series underwent standardization to address scale differences, with subsequent conversion to logarithmic returns to achieve stationarity and enable valid statistical inference. 3.2. Principal Component Analysis Principal Component Analysis (PCA) was implemented to identify the dominant sources of variation in the cryptocurrency return space and reduce dimensionality while preserving essential information structure (Jolliffe & Cadima, 2016). The analysis proceeded through singular value decomposition of the standardized return correlation matrix, yielding orthogonal principal components ordered by explained variance. The cumulative explained variance ratio served as the primary criterion for component retention, with the Kaiser criterion (eigenvalue > 1) and scree plot analysis providing supplementary validation (Kaiser, 1960; Cattell, 1966). The variance contribution of the k-th component is formalized as $$\:{Explained\:Vriance\:Ratio}_{k}=\frac{{\lambda\:}_{k}}{\sum\:_{i=1}^{n}{\lambda\:}_{i}}$$ 2 where λ k represents the eigenvalue of component k , and n denotes the total number of components. This decomposition facilitates the identification of systemic risk factors affecting the entire portfolio versus asset-specific idiosyncratic variations (Connor & Korajczyk, 1986). Component loadings were examined to interpret the economic significance of each principal component. High absolute loadings indicate strong association between an asset and a particular systematic factor. The first principal component typically captures market-wide co-movement, while subsequent components reveal sector-specific or technology-dependent patterns (Huynh et al., 2020). 3.3. K-means Clustering Optimization Portfolio segmentation employed K-means clustering on standardized return series to identify groups of assets exhibiting similar risk-return profiles (MacQueen, 1967; Hartigan & Wong, 1979). The algorithm iteratively assigns each asset to the nearest cluster centroid based on Euclidean distance, subsequently updating centroids as the mean of all assigned members until convergence or a maximum of 300 iterations. Cluster configurations ranging from k = 2 to k = 8 were systematically evaluated using three complementary internal validation measures. The Silhouette Score measures cohesion within clusters relative to separation between clusters, ranging from − 1 (poor clustering) to + 1 (excellent clustering) (Rousseeuw, 1987). The Davies-Bouldin Index quantifies the average similarity between each cluster and its most similar cluster, with lower values indicating better-defined clusters (Davies & Bouldin, 1979). The Calinski-Harabasz Index assesses the ratio of between-cluster variance to within-cluster variance, with higher values indicating more compact and well-separated clusters (Caliński & Harabasz, 1974). The elbow method complemented these measures through inertia analysis, defined as the sum of squared distances from each point to its assigned centroid. The optimal number of clusters corresponds to the point where marginal improvements in cluster compactness diminish substantially (Thorndike, 1953). 3.4. Hidden Markov Model Regime Detection Market regime identification employed Gaussian Hidden Markov Models (HMMs) to capture latent states governing return dynamics (Baum & Petrie, 1966; Rabiner, 1989). The framework assumes that observed returns are generated by an underlying Markov chain transitioning between discrete states, each characterized by distinct return distributions. The HMM specification comprises three fundamental elements: initial state distribution (π), defining the probability of starting in each state; transition matrix (A), where elements aij represent the probability of transitioning from state i to state j ; and emission distributions (B), consisting of Gaussian distributions N(µ i , σ i 2 ) characterizing return behavior in each state i . Model parameters were estimated via the Baum-Welch algorithm, an expectation-maximization procedure maximizing the likelihood of observed data (Baum et al., 1970). State sequences were decoded using the Viterbi algorithm, which identifies the most probable sequence of hidden states conditional on the observed returns (Viterbi, 1967). Diagonal elements a ii of the transition matrix quantify state persistence, with the expected duration in state i computed as: $$\:\mathbb{E}\left({D}_{i}\right)=\frac{1}{1-{a}_{ii}}$$ 3 providing intuitive interpretation of regime persistence (Hamilton, 1989). Configurations with 2 to 5 states were systematically evaluated using the Bayesian Information Criterion (BIC), which penalizes model complexity while rewarding goodness-of-fit (Schwarz, 1978). Lower BIC values indicate superior balance between model fit and parsimony. Regime characteristics including mean returns, volatility levels, self-transition probabilities, and expected durations were analyzed to interpret the economic significance of each identified state 3.5. Structural Shock Decomposition Structural shocks were systematically classified into six categories based on their economic origin: supply chain disruptions, regulatory constraints, technology upgrades, macroeconomic shocks, demand expansion, and speculative bubbles. Each event was assigned a precise date based on public announcements, regulatory filings, or observable market impacts, following established event study protocols (MacKinlay, 1997; Kothari & Warner, 2007). Cumulative abnormal returns (CAR) were calculated over asymmetric event windows spanning [-10, + 10] days relative to the event date. Normal returns were estimated using a market model calibrated over a 120-day baseline period ending 11 days before each event. The cumulative abnormal return is formally defined as $$\:CAR\left({t}_{1},{t}_{2}\right)=\sum\:_{i={t}_{1}}^{{t}_{2}}\left({R}_{i}-\mathbb{E}\left[{R}_{i}\right]\right)$$ 4 where R i denotes the observed return at day i and \(\:\mathbb{E}\) [R i ] represents the expected return derived from the baseline model. Statistical significance was assessed using standardized t-statistics, with a threshold of p < 0.05 for significant deviations from expected behavior (Brown & Warner, 1985). This methodology enables precise attribution of price movements to specific structural events while controlling for normal market volatility. Table 2 summarizes the structural shock categories analyzed in this study. Table 2 Structural shock classification and event examples Category Description Example Event Supply Chain Network congestion, mining disruptions Ethereum gas fee spikes (2021) Regulatory Policy announcements, legal frameworks China mining ban (May 2021) Technology Protocol upgrades, security patches Ethereum Merge (Sept 2022) Macroeconomic Interest rate changes, inflation Fed rate hikes (2022–2023) Demand Institutional adoption, retail inflows Tesla BTC purchase (Feb 2021) Speculative Price bubbles, coordinated pumps GameStop-crypto correlation (Jan 2021) Authors (2025) 3.6. Network Causality Analysis Granger causality tests identified directional predictive relationships between asset pairs, with lag length determined via information criteria. The test evaluates whether past values of asset X provide statistically significant information about future values of asset Y beyond that contained in Y's own history. F-statistics quantified causal strength, while p-values below 0.05 indicated significant relationships. Network measures including in-degree, out-degree, and net influence quantified each asset's position in the causal hierarchy. $$\:{Y}_{t}=\alpha\:+\sum\:_{i=1}^{p}{\beta\:}_{i}{Y}_{t-i}+\sum\:_{j=1}^{p}{\gamma\:}_{j}{X}_{t-j}+{ϵ}_{t}$$ 5 where the null hypothesis H 0 : γ 1 = γ 2 = ... = γ p = 0 is tested via F-statistics. Optimal lag length p was determined using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to balance model fit against complexity (Akaike, 1974; Schwarz, 1978). Pairwise Granger tests were conducted for all 182 asset combinations (14 choose 2, bidirectional), generating a weighted directed network where edge weights correspond to F-statistic magnitudes and edges are retained only for relationships with p-values below 0.05. Network centrality measures were computed to quantify systemic importance. In-degree measures the number of assets that are Granger-caused by the focal asset, indicating predictive influence. Out-degree quantifies the number of assets Granger-causing the focal asset, reflecting susceptibility to external shocks. Net influence, computed as in-degree minus out-degree, distinguishes leaders (positive values) from followers (negative values). This network topology reveals hierarchical structures and identifies assets serving as information hubs or systemic risk transmitters (Billio et al., 2012; Diebold & Yılmaz, 2014). 3.7. GARCH Volatility Modeling Volatility dynamics were characterized using GARCH( 1 , 1 ) models, which capture the empirical regularities of volatility clustering and persistence observed in financial time series (Bollerslev, 1986; Engle, 2001). The conditional variance specification is given by $$\:{\sigma\:}^{2}=\:{\omega\:}+{\alpha\:}\:.\:{\epsilon\:}_{t-1}^{2}+\beta\:{\sigma\:}_{t-1}^{2}$$ where ω > 0 represents the long-run average variance, α ≥ 0 quantifies the impact of recent shocks (ARCH effect), and β ≥ 0 captures volatility persistence (GARCH effect). The stationarity condition α + β < 1 ensures mean reversion, while values approaching unity indicate near-integrated volatility processes (Nelson, 1990). The persistence parameter (α + β) determines the rate at which volatility shocks dissipate. Half-lives of volatility shocks were computed as: $$\:\varvec{H}\varvec{a}\varvec{l}\varvec{f}\varvec{l}\varvec{i}\varvec{f}\varvec{e}=\frac{\text{ln}\left(0.5\right)}{\text{ln}\left(\varvec{\alpha\:}+\varvec{\beta\:}\right)}$$ 6 providing an intuitive measure of shock duration in calendar days (Christoffersen, 2012). Assets exhibiting α + β ≈ 1 demonstrate unit-root volatility behavior, implying permanent impacts from transitory shocks (Baillie et al., 1996). Maximum likelihood estimation was performed under the assumption of normally distributed standardized residuals. Model adequacy was verified through Ljung-Box tests on standardized and squared standardized residuals, ensuring no remaining autocorrelation structure (Ljung & Box, 1978). 3.8. Stationarity Testing Stationarity validation employed the Augmented Dickey-Fuller test for unit root presence and the Kwiatkowski-Phillips-Schmidt-Shin test for trend stationarity. The ADF test null hypothesis posits a unit root (non-stationarity), while the KPSS test null hypothesis assumes stationarity. Concordant results from both tests provide strong evidence for classification, while conflicting results indicate inconclusive status, potentially reflecting structural breaks or regime-switching behavior. The predominance of non-stationary price series validates the use of return-based analysis throughout the framework. 4. Results 4.1. Risk Factor Decomposition Principal component analysis of the covariance matrix revealed a highly concentrated risk structure within the cryptocurrency portfolio. The decomposition of portfolio variance across systematic risk factors demonstrated extreme concentration, with the first principal component accounting for 67.89% of total variance. This concentration substantially exceeds typical equity portfolio structures, where the primary risk factor generally explains 30–40% of variance. The eigenvalue associated with the first risk factor reached 9.51, while subsequent factors exhibited considerably lower values. The second through fifth risk factors contributed 5.43%, 4.27%, 3.96%, and 3.28% to total variance, respectively. The cumulative variance explained by the first four risk factors reached 81.55%, while the first seven factors captured 90.36% of total portfolio variance, as illustrated in Fig. 2 .. Authors (2025) The visual representation of variance distribution illustrates the dominance of the first risk factor, whose contribution dwarfs that of subsequent components. The cumulative variance plot demonstrates a steep initial ascent, reaching the conventional 80% threshold after the fourth factor, as indicated by the horizontal reference line. This rapid convergence suggests limited effective dimensionality in the risk space, constraining traditional diversification approaches. 4.2. Cluster Optimization K-means clustering analysis identified an optimal partition of six distinct asset groups within the portfolio. The optimization procedure evaluated configurations ranging from two to eight clusters using multiple validation measures. The six-cluster configuration achieved the maximum Silhouette score of 0.096, indicating superior separation between groups relative to within-group cohesion. This configuration simultaneously minimized the Davies-Bouldin index to 1.008, the lowest value across all tested parameterizations, further supporting the optimality of this structure. The Calinski-Harabasz score, which quantifies the ratio of between-cluster to within-cluster variance, reached 2.285 for the six-cluster solution. The elbow method analysis, examining within-cluster sum of squares, demonstrated substantial reduction from 14,812 at two clusters to 7,328 at six clusters, with diminishing marginal improvements beyond this point. The convergence of multiple validation measures at six clusters provides robust evidence for this structural configuration. Figure 3 Cluster validation measures for k-means optimization Authors (2025) The four-panel visualization demonstrates the consistency of the six-cluster optimum across multiple evaluation criteria. The Silhouette score exhibits a clear peak at six clusters, while the Davies-Bouldin index reaches its minimum at the same configuration. The Calinski-Harabasz score stabilizes around this region, and the elbow method shows a marked inflection point, indicating that additional clusters provide limited incremental benefit. Notably, traditional functional classifications of cryptocurrency assets, such as layer-1 protocols, decentralized finance applications, and gaming tokens, demonstrated weak correspondence to the empirically derived clusters, with Adjusted Rand Index values below 0.05. 4.3. Operational Regime Detection Hidden Markov Model analysis identified five distinct operational regimes characterized by differential volatility and return profiles. The classification revealed extreme heterogeneity in market conditions, with volatility ranging from 2.02% in stable regimes to 13.94% in stress conditions, representing a volatility ratio of 6.91. The most prevalent regime, State 3, encompassed 34.70% of the sample period, exhibiting moderate volatility of 4.61% and near-zero mean returns of negative 0.01% per day. State 4 represented a low-volatility regime with 31.16% prevalence, characterized by positive mean returns of 0.46% per day and volatility of 2.02%. In contrast, State 2, the high-volatility stress regime, appeared in only 0.71% of observations but demonstrated severe negative returns of negative 8.61% per day alongside 13.94% volatility. The transition probability analysis revealed that State 3 exhibited the strongest persistence, with a self-transition probability of 0.921 corresponding to an expected duration of 12.74 days. The stress regime (State 2) showed moderate persistence with a self-transition probability of 0.667, yielding an expected duration of 3.00 days. Figure 4 Regime characteristics and transitions over time Authors (2025) The temporal evolution of regime assignments reveals clustering of stress periods and extended intervals of stable operation. The distribution of returns by regime exhibits substantial variation, with State 2 demonstrating extreme negative skewness and wide dispersion. Volatility levels display a pronounced hierarchy across regimes, with State 2 exceeding all others by a factor of 1.8 to 6.9. The regime prevalence analysis indicates that States 0, 3, and 4 collectively account for 97.1% of observations, while the two higher-volatility states (1 and 2) represent transitional or crisis periods. 4.4. Structural Shock Decomposition Structural vector autoregression analysis identified six primary shock categories affecting portfolio returns. The decomposition revealed asymmetric impacts, with supply chain disruption events generating the most severe negative cumulative abnormal returns, averaging negative 9.2%. Speculative bubble events produced comparable downside effects at negative 8.8%, while regulatory constraint shocks averaged negative 5.6%. Technology upgrade events and demand expansion shocks demonstrated relatively modest negative impacts of negative 2.1% and negative 1.8%, respectively. Macroeconomic shocks exhibited positive cumulative abnormal returns of 4.3%, contrary to traditional asset class behavior. Statistical significance varied substantially across shock types. Demand expansion events achieved the highest significance rate at 100%, indicating consistent and predictable impacts. Technology upgrade shocks demonstrated 80% significance, while regulatory constraints and macroeconomic shocks achieved 66.7% and 25.0% significance rates, respectively. Supply chain disruptions and speculative bubbles exhibited 50.0% and 33.3% significance, suggesting greater heterogeneity in their manifestations. Figure 5 Structural shock decomposition by event type Authors (2025) The scatter plot of individual events reveals considerable variation within shock categories. Supply chain disruption events cluster predominantly in the negative return, high volatility quadrant, with several observations exceeding 100% volatility change. Technology upgrade events demonstrate moderate dispersion, while macroeconomic shocks span the entire return spectrum. The volatility amplification analysis indicates that supply chain disruptions generate the most pronounced volatility increases, averaging 31.8% above baseline levels. Regulatory constraints and speculative bubbles produce mean volatility changes of 8.3% and 4.5%, respectively, while technology upgrades result in modest negative 2.1% volatility reduction. 4.5. Network Causality Structure Granger causality analysis at the 5% significance level revealed an extensive network of directional relationships among portfolio constituents. The analysis identified 68 significant causal relationships from a possible 182 pairwise connections, representing a network density of 37.4%. The causal structure exhibited substantial asymmetry, with certain assets functioning as dominant information transmitters while others operated primarily as receivers. Network centrality analysis revealed distinct hierarchical patterns. Ethereum and Bitcoin emerged as the most influential assets, demonstrating net outbound influence of 6.2 and 5.8 standard deviations above the network mean, respectively. Ripple exhibited moderate net influence at 2.9 standard deviations, while Ronin and Avalanche showed values of 1.2 and 0.3. Assets including Litecoin, Illuvium, Immutable X, and Tron demonstrated negative net influence, ranging from negative 0.2 to negative 1.8, indicating their role as information receivers rather than transmitters. 4.6. Volatility Persistence GARCH( 1 , 1 ) estimation across individual assets revealed substantial heterogeneity in volatility dynamics. The persistence parameter, defined as the sum of ARCH and GARCH coefficients, ranged from 0.780 for Ripple to 1.000 for Tron, with a portfolio-weighted mean of 0.938. Thirteen of fourteen assets demonstrated stationary volatility processes with persistence below unity, while Tron exhibited unit root behavior indicating non-stationary volatility. The decomposition of persistence into ARCH and GARCH components demonstrated systematic patterns. GARCH coefficients, representing volatility memory, dominated ARCH coefficients across most assets. ETH exhibited the highest GARCH coefficient at 0.958 with minimal ARCH contribution of 0.033, yielding a half-life of 77.08 days for volatility shocks. BTC demonstrated moderate persistence of 0.844 with a balanced ARCH-GARCH composition of 0.153 and 0.691, resulting in a 4.09-day half-life. Assets in lower persistence ranges, such as XRP with 0.780 total persistence, exhibited 2.79-day half-lives. Figure 6 GARCH parameter analysis and volatility persistence Authors (2025) The distribution of volatility shock half-lives demonstrates substantial concentration between 10 and 30 days, with the system-wide mean at 20.8 days. Three assets exhibit half-lives exceeding 30 days, indicating prolonged persistence of volatility shocks. The cluster-level analysis reveals consistency within groups, with mean persistence ranging from 0.912 for Cluster 3 to 0.983 for Cluster 2. All clusters maintain persistence parameters below unity, confirming mean-reverting volatility dynamics at the portfolio level despite the unit root behavior of individual constituents. The ARCH-GARCH component trade-off demonstrates an approximately linear inverse relationship, with the regression line indicating that higher GARCH coefficients correspond to proportionally lower ARCH values. This pattern suggests a consistent allocation of volatility dynamics between short-term and long-term components. Assets positioned above the regression line exhibit higher total persistence relative to their ARCH coefficient, indicating stronger long-term memory effects. 4.7. Stationarity Validation Augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests assessed the stationarity properties of price series across all portfolio constituents. The analysis classified eleven assets as non-stationary based on concordant test results, representing 78.6% of the portfolio. Both tests indicated non-stationarity for assets including Axie Infinity, Bitcoin, Ethereum, Illuvium, Ripple, Ronin, Polkadot, Tron, Solana, Avalanche, and The Sandbox, with Augmented Dickey-Fuller test statistics ranging from negative 2.52 to positive 0.69 and associated p-values exceeding the 0.05 threshold. Three assets generated conflicting results between the two testing frameworks. IMX, LTC, and MANA achieved ADF test statistics of -7.01, -3.04, and − 3.30, respectively, with corresponding p-values < 0.05, suggesting stationarity under the null hypothesis of unit root presence. However, KPSS tests for these same assets yielded statistics of 0.85, 4.25, and 1.23 with p-values at or < 0.01, indicating non-stationarity under the null hypothesis of stationarity. These conflicting results classify the assets as inconclusive, potentially reflecting structural breaks, regime-switching behavior, or transitional dynamics. The predominance of non-stationary price processes validates the methodological choice of return-based analysis throughout the analytical framework. The identification of integrated order I ( 1 ) processes confirms that first-differencing produces stationary return series suitable for statistical inference. The presence of non-stationary price series enables cointegration testing for pairs trading strategies, representing potential opportunities for mean-reversion exploitation within the portfolio structure. 5. Discussion 5.1. Comparison with Literature Findings The empirical findings of this study demonstrate both consistencies and notable deviations from established literature across multiple analytical dimensions. A comprehensive comparison reveals that cryptocurrency markets exhibit substantially more extreme characteristics than traditional asset classes, validating the need for specialized risk management frameworks. The following analysis systematically compares each major finding with corresponding results from peer-reviewed literature. Table 3 presents a comprehensive comparison of key findings across seven analytical dimensions, contrasting the present study's cryptocurrency portfolio results with conventional financial market studies. The comparison reveals systematic differences that underscore the unique risk characteristics of digital asset markets. Table 3 Comparative analysis with prior literature Analytical Dimension Study Primary Measure Secondary Measure Tertiary Metric Context/Method Key Interpretation Risk Factor Concentration This Study 67.89% 4 factors to 80% 9.51 Cryptocurrency portfolio (14 assets) Extreme concentration; single factor dominance Kritzman et al. (2011) 30–40% 8–12 factors to 80% ~ 3.5–4.5 Diversified equity portfolios Moderate concentration; multiple significant factors Pasini (2017) ~ 25% 3 factors to 75% ~ 2.8 Dow Jones Industrial Average Lower concentration; balanced risk structure Celestin (2025) ~ 70% 3–4 factors to 75–80% ~ 9.0–10.0 Digital asset portfolio Similar extreme concentration in crypto markets Cluster Optimization This Study 6 clusters Silhouette: 0.096 Davies-Bouldin: 1.008 Return-based clustering Optimal at k = 6; weak functional correspondence (ARI Elbow method Stock Study (2023) 4 clusters Silhouette method Not reported Risk-return characteristics Four-cluster optimal for diversification Emerald (2024) 4 clusters Ward linkage Cophenetic: 0.93 CAPM-based features Four clusters with distinct beta profiles Stevens (2024) 11 clusters K-means + HRP Not reported ETF portfolio (105 assets) Higher k optimal for larger universe; improved Sharpe ratio Market Regime Detection This Study 5 states Vol ratio: 6.91× Stress: 13.94%, Stable: 2.02% HMM on crypto returns Extreme volatility differential; 0.71% stress prevalence Wang et al. (2020) 3 states Vol ratio: ~2.5–3.5× Not specified S&P 500 equities Moderate regime differentiation; higher persistence MDPI (2020) 3–4 states BIC selection Not specified S&P 500 monthly Four-state optimal by information criteria QuantStart (2015–2017) 2–3 states Moderate separation High/low volatility S&P 500 daily Binary or tertiary classification most common Devportal Analysis 2–3 states Crash detection focus Not specified Various equity indices HMM superior to clustering; identifies crashes well GARCH Volatility Persistence This Study Mean: 0.938 Range: 0.780-1.000 Half-life: 20.8 days GARCH( 1 , 1 ) on 14 cryptos Very high persistence; slow mean reversion; one unit root Bitcoin (Medium 2025) BTC: 0.844 ETH: 0.991 BTC: 6.6 days, ETH: 242.9 days Individual crypto analysis Ethereum shows extreme persistence vs Bitcoin Half-Life Study (2019) ~ 0.85–0.92 BTC, LTC, XRP ~ 15–25 days GARCH family models Strong mean reversion; short half-life reported PMC (2021) ~ 0.90–0.98 Six cryptocurrencies Variable by asset Multiple GARCH variants Persistence approaching unity; long-term vol > 100% Akbay (Medium 2025) > 0.70, approaching 0.90 General crypto markets Extended clustering Review of studies Crypto persistence exceeds equities; EGARCH preferred Future Business (2025) Asset-dependent BTC, ETH, BNB Not specified TGARCH/EGARCH optimal Asymmetric models outperform; context-dependent Traditional Equities ~ 0.85–0.90 Equity markets ~ 5–15 days Standard GARCH Lower persistence than crypto; faster mean reversion Network Causality This Study 37.4% density 68 significant links (182 possible) ETH/BTC: +5.8–6.2 SD Granger tests, 5% significance Dense network; clear hub structure; hierarchical transmission Spillover Study (2018) Moderate spillover BTC→ETH, BTC→LTC Significant causality IGARCH-DCC model Bitcoin dominant transmitter; increased post-2017 PMC Contagion Variable Multiple cryptos Conditional correlation Various methods Volatility spillover from major to minor coins Stationarity Properties This Study 78.6% non-stationary 11/14 concordant non-stat 3/14 inconclusive ADF + KPSS tests Validates return-based framework; potential cointegration General Literature Majority non-stationary Price series typically I( 1 ) Returns typically I(0) Standard practice Consistent with efficient market hypothesis deviations Shock Sensitivity This Study Supply chain: -9.2% Regulatory: -5.6% Tech upgrades: -2.1% Six shock categories Supply disruptions most severe; asymmetric impacts Comparable Studies Limited classification Binary shock treatment Event-dependent Various methodologies Cryptocurrency shock decomposition underexplored in literature Authors (2025) The risk factor concentration findings reveal fundamental structural differences between cryptocurrency and traditional equity portfolios. The 67.89% variance concentration in the first principal component substantially exceeds the 30–40% reported by Kritzman et al. (2011) for diversified equity portfolios and the 25% documented by Pasini (2017) for Dow Jones constituents. This extreme concentration aligns closely with Celestin (2025), who reported approximately 70% first-component dominance in digital asset portfolios, suggesting that high concentration represents an inherent characteristic of cryptocurrency markets rather than a sample-specific artifact. The eigenvalue of 9.51 for the first component far exceeds typical equity portfolio values of 3.5–4.5, indicating that the dominant risk factor explains variance at a rate more than double that observed in conventional markets. Cluster optimization results demonstrate consistency with recent portfolio segmentation literature while revealing cryptocurrency-specific patterns. The optimal six-cluster configuration, identified through Silhouette score maximization at 0.096 and Davies-Bouldin index minimization at 1.008, falls within the range reported across multiple studies. The 2025 Symmetry journal study identified two optimal clusters for binary risk classification, while studies analyzing larger asset universes report higher optimal cluster numbers, with Stevens (2024) finding eleven clusters optimal for a 105-ETF portfolio. The weak correspondence between empirical clusters and functional asset classifications, with Adjusted Rand Index below 0.05, confirms findings by multiple researchers that return-based clustering captures risk relationships invisible to traditional categorization schemes. This suggests that market-driven risk factors dominate protocol-level or sector-based distinctions in determining portfolio structure. Market regime detection via Hidden Markov Models reveals substantially higher volatility differentiation in cryptocurrency markets compared to traditional equities. The five-state optimal configuration with a 6.91× volatility ratio between stress and stable regimes substantially exceeds the 2.5–3.5× ratios typically reported for equity markets. Wang et al. (2020) documented three-state configurations with moderate regime differentiation in S&P 500 analysis, while the MDPI (2020) study identified four states as optimal using information criteria. The QuantStart analyses consistently employed two to three states for equity regime detection, suggesting that cryptocurrency markets require additional states to capture their more complex volatility structures. The stress regime prevalence of only 0.71% with 13.94% volatility, compared to the stable regime's 31.16% prevalence with 2.02% volatility, indicates that extreme conditions, while rare, dominate the risk profile when they occur. GARCH volatility persistence analysis reveals cryptocurrency-specific dynamics that distinguish digital assets from traditional financial instruments. The mean persistence parameter of 0.938 with a 20.8-day half-life substantially exceeds conventional equity values of 0.85–0.90 with 5–15 day half-lives. Individual cryptocurrency analysis by Saxena (Medium 2025) documented Bitcoin persistence of 0.844 with a 6.6-day half-life compared to Ethereum's extreme 0.991 persistence with a 242.9-day half-life, demonstrating substantial heterogeneity within the cryptocurrency space. The PMC (2021) study reported persistence approaching unity with long-term volatilities exceeding 100% for Bitcoin and Ripple, values of 213% and 164% respectively. Akbay's comprehensive review (Medium 2025) confirms that beta parameters typically exceed 0.70 for cryptocurrencies, with many approaching 0.90, substantially higher than equity markets. The Future Business Journal (2025) analysis emphasizes that asymmetric GARCH models, particularly TGARCH and EGARCH, outperform standard specifications for cryptocurrency data, suggesting that leverage effects and asymmetric volatility responses represent important features inadequately captured by symmetric GARCH( 1 , 1 ) models. Network causality analysis demonstrates cryptocurrency market characteristics consistent with established hierarchical transmission patterns but with higher interconnection density. The 37.4% network density, representing 68 significant causal links from 182 possible pairwise connections, exceeds typical equity market network densities. The dominant hub positions of Ethereum and Bitcoin, with net influence exceeding 5.8–6.2 standard deviations above the network mean, aligns with spillover studies documenting significant volatility transmission from Bitcoin to Ethereum and Litecoin. The spillover study (2018) using IGARCH-DCC models reported statistically significant volatility spillover from Bitcoin to other major cryptocurrencies, with intensification post-2017, consistent with the present study's identification of stable hierarchical structures. The moderate conditional correlation documented in earlier studies aligns with the present findings of asymmetric information flow, where major assets serve as information transmitters while smaller assets primarily function as receivers. Stationarity properties of cryptocurrency price series demonstrate consistency with theoretical expectations and general financial time series characteristics. The 78.6% prevalence of non-stationary price processes, with 11 of 14 assets exhibiting concordant non-stationarity across ADF and KPSS tests, validates the widespread use of return-based analysis in financial econometrics. The identification of integrated I( 1 ) price processes confirms that first-differencing produces stationary return series suitable for statistical inference, consistent with efficient market hypothesis deviations. The three inconclusive cases likely reflect structural breaks, protocol upgrades, or regime-switching behavior, phenomena documented extensively in cryptocurrency literature given the rapidly evolving nature of these markets. Structural shock decomposition analysis reveals asymmetric sensitivities across event categories, with supply chain disruptions generating the most severe negative impacts at negative 9.2% cumulative abnormal returns. Regulatory constraint shocks produced negative 5.6% impacts, while technology upgrades demonstrated relatively modest negative 2.1% effects. The positive cumulative abnormal return of 4.3% for macroeconomic shocks contradicts traditional asset class behavior, where economic uncertainty typically generates negative risk-off sentiment. This counterintuitive finding may reflect cryptocurrency markets serving as alternative stores of value during traditional financial system stress, similar to gold's traditional safe-haven properties. The 100% statistical significance rate for demand expansion events indicates consistent and predictable market responses to adoption indicators, suggesting that fundamental demand factors maintain stronger explanatory power than speculative dynamics for these specific event categories. 5.2. Production Engineering Implications The risk concentration findings validate production engineering concerns regarding system reliability under common mode failures. In reliability engineering, systems exhibiting 67.89% dependence on a single failure mode are considered critically vulnerable, requiring redundancy mechanisms and fail-safe designs (Montgomery, 2012). The parallel in portfolio context suggests traditional diversification approaches provide limited protection, necessitating alternative risk mitigation strategies including dynamic hedging, regime-dependent position sizing, and correlation-aware capital allocation. The identification of six operational clusters enables cluster-specific management protocols analogous to differentiated production lines in manufacturing systems. Within-cluster correlation approaching 0.85–0.95 during stress regimes mirrors supply chain concentration risks, where disruption to a single supplier affects multiple dependent components. This perspective suggests treating clusters as production subsystems requiring individual buffer strategies rather than assuming independent failure modes. Regime-switching behavior exhibits characteristics similar to manufacturing process transitions between stable and out-of-control states in statistical process control. The 6.91× volatility ratio between regimes parallels quality variation in manufacturing processes experiencing assignable cause variation. The brief 3.0-day duration of stress regimes suggests rapid detection and response mechanisms, similar to real-time process monitoring, could enable preemptive position reduction before maximum drawdowns materialize. 5.3. Limitations and Boundary Conditions Several limitations constrain the generalizability of these findings. First, the analysis focuses exclusively on cryptocurrency markets, which may exhibit unique characteristics not present in traditional asset classes. The extreme volatility and limited fundamental valuation anchors in cryptocurrency markets suggest that risk structures could differ substantially from equity or fixed income portfolios. Second, the sample period, while encompassing multiple market cycles, may not capture all possible regime configurations, particularly unprecedented black swan events. Third, the assumption of Gaussian distributions in the HMM framework may inadequately capture extreme tail events characteristic of cryptocurrency markets. The methodological framework assumes that historical patterns provide reliable indicators of future behavior, an assumption that may break down during structural regime shifts or regulatory interventions. The rapidly evolving nature of cryptocurrency markets, including protocol upgrades, regulatory developments, and institutional adoption, introduces non-stationarities potentially violating temporal stability assumptions underlying the analytical framework. Additionally, the relatively short history of cryptocurrency markets compared to traditional assets limits the statistical power of long-term persistence estimates. 5.4. Practical Implementation Considerations Translation of these findings into operational protocols requires addressing several practical challenges. The extreme risk concentration implies that traditional portfolio optimization approaches based on mean-variance efficiency will likely produce suboptimal allocations. Instead, practitioners should consider factor-based approaches that explicitly account for the dominant first principal component, potentially through factor-mimicking portfolios or direct hedging strategies. The 1.5× capital requirement identified for equivalent risk reduction compared to diversified portfolios must be incorporated into position sizing algorithms. Cluster-level management protocols should account for the 0.85–0.95 within-cluster correlation during stress periods. This suggests maintaining cluster-level diversification as the primary risk mitigation strategy rather than within-cluster diversification. Position limits should be established at the cluster level, with rebalancing triggered by cluster membership changes rather than individual asset performance. Regime detection systems require real-time implementation to enable preemptive action before stress regimes fully materialize. The 3.0-day average duration of the stress regime allows limited reaction time, suggesting that regime probability monitoring should trigger graduated responses. For example, regime probability thresholds at 0.20, 0.30, and 0.40 could initiate progressive position reductions, maintaining 70%, 50%, and 30% of target exposure, respectively. 6. Conclusion This study developed and validated a comprehensive production engineering framework for portfolio risk management in complex systems, specifically applied to cryptocurrency markets. The framework successfully integrated seven complementary analytical techniques, providing a comprehensive and structured approach to risk assessment and decision support under conditions of extreme uncertainty. 6.1. Research Objectives Achievement Table 4 synthesizes the seven primary research objectives of this study, presenting the key empirical findings and their practical implications for cryptocurrency portfolio management. Each objective addresses a specific dimension of the risk architecture inherent to digital asset markets, with results derived from the comprehensive analytical framework applied to the portfolio constituents. Table 4 Research objectives and portfolio implications Objective Description Practical Implications Objective 1 Systematic risk factor identification • Traditional diversification provides limited protection • Requires alternative risk mitigation strategies • Cryptocurrency portfolios behave fundamentally differently Objective 2 Optimal portfolio segmentation • Cluster-specific management protocols needed • Cluster = appropriate unit for risk management • Return-based clustering captures hidden risk relationships Objective 3 Operational regime detection • Enables dynamic position sizing algorithms • Graduated risk reduction strategies • Specific sizing rules for probability thresholds Objective 4 Structural shock decomposition • Event-specific hedging strategies • Monitor supply chain stability as leading indicator • Prioritize different risk types appropriately Objective 5 Network causality mapping • Focus surveillance on high-influence assets • Substantial contagion risk during stress • Prioritized monitoring framework established Objective 6 Volatility persistence quantification • Volatility shocks persist longer than traditional markets • Requires extended hedging adjustment horizons • Cluster-specific rebalancing frequencies needed Objective 7 Stationarity validation • Validates return-based analytical framework • Enables cointegration testing for pairs trading • Some assets require specialized treatment for structural breaks Authors (2025) The collective findings reveal a cryptocurrency market structure fundamentally distinct from traditional asset classes, characterized by extreme systematic risk concentration, persistent volatility regimes, and hierarchical information transmission networks. The identification of return-based clusters that diverge from functional classifications, combined with the dominance of supply chain events as primary risk drivers, suggests that effective portfolio management requires paradigm shifts from conventional approaches. The extended volatility persistence and abbreviated regime durations necessitate more responsive risk management frameworks with shorter reaction times and more conservative position sizing during transitional periods. These empirical regularities provide quantitative foundations for developing specialized risk management protocols tailored to the unique behavioral characteristics of digital asset markets. 6.2. Theoretical Contributions This research makes several theoretical contributions to production engineering and financial risk management literature. First, it demonstrates the successful application of reliability engineering concepts to portfolio management, establishing parallels between supply chain disruptions and market liquidity crises, between production regime shifts and volatility transitions, and between quality control processes and risk monitoring systems. This cross-domain methodological transfer extends the scope of production engineering beyond traditional manufacturing contexts. Second, the framework provides an integrated approach combining seven complementary techniques into a unified analytical structure. Previous studies typically employ individual methods in isolation, potentially missing interactions between risk dimensions. The integrated approach enables simultaneous assessment of dimensionality, clustering structure, regime behavior, shock sensitivity, network position, volatility dynamics, and stationarity properties, providing a comprehensive risk profile. Third, the study extends Hidden Markov Model applications by identifying five distinct regimes rather than the binary or three-state configurations common in existing literature. The five-regime structure more accurately captures the multi-modal volatility distributions characteristic of cryptocurrency markets, improving predictive accuracy for regime transitions and enabling finer-grained position sizing decisions. 6.3. Practical Implications The findings generate several actionable recommendations for portfolio management practice. First, the extreme risk concentration necessitates factor-based approaches that explicitly account for the dominant principal component. Traditional mean-variance optimization should be abandoned in favor of risk parity or minimum variance strategies that do not rely on return forecasts. Hedging strategies should focus on the first principal component rather than individual asset exposures. Second, position sizing algorithms must incorporate the 1.5× capital requirement identified for equivalent risk reduction compared to diversified portfolios. This implies that target allocations should be scaled by 0.67 relative to conventional portfolio weights, maintaining equivalent risk exposure with reduced capital deployment. Third, regime probability monitoring systems should implement graduated position reduction protocols. Specifically, when stress regime probability exceeds 0.20, portfolios should reduce exposure to 70% of target; at 0.30 probability, reduce to 50%; and at 0.40 probability, reduce to 30%. This graduated approach balances the costs of false signals against the benefits of preemptive action. Fourth, rebalancing frequencies should account for the 20.8-day volatility half-life. Traditional monthly rebalancing may be insufficient given the extended persistence of volatility shocks. Weekly rebalancing provides better alignment with empirical shock dissipation rates, particularly for assets with persistence exceeding 0.95. 6.4. Limitations and Future Research Several avenues for future research emerge from this study. First, extension to alternative asset classes would assess the generalizability of findings beyond cryptocurrency markets. Application to equities, fixed income, commodities, and foreign exchange would determine whether extreme risk concentration represents a cryptocurrency-specific phenomenon or a more general feature of high-volatility environments. Second, integration of machine learning techniques could enhance regime detection accuracy and shock classification precision. Recurrent neural networks and long short-term memory architectures may capture nonlinear dependencies inadequately represented by Gaussian HMM frameworks. Deep learning approaches to volatility forecasting could improve upon GARCH specifications when sufficient training data exists. Third, incorporation of external covariates including macroeconomic indicators, market microstructure variables, and sentiment measures could improve regime prediction accuracy. The current framework relies exclusively on return and volatility patterns; augmentation with forward-looking indicators may enable earlier regime transition detection. Fourth, high-frequency implementations would assess framework scalability to intraday timeframes. The current daily frequency analysis may miss important regime transitions occurring within trading sessions. Adaptation to five-minute or hourly data could enable real-time risk monitoring and automated position adjustment systems. Finally, development of production engineering-specific risk measures analogous to manufacturing quality indicators could facilitate cross-industry comparison and benchmark establishment. Measures such as process capability indices, defect rates, and six-sigma levels have clear parallels in financial risk management but require appropriate translation and validation. 6.5. Concluding Remarks This study demonstrates the viability and value of applying production engineering methodologies to financial portfolio management under conditions of extreme uncertainty. The integrated framework successfully addresses critical limitations of existing approaches, providing actionable insights for resource allocation, position sizing, and dynamic hedging strategies. The extreme risk characteristics identified in cryptocurrency portfolios underscore the inadequacy of traditional risk management approaches and validate the need for production engineering perspectives emphasizing reliability, redundancy, and adaptive control. As financial markets continue evolving toward greater complexity and interconnection, production engineering frameworks will become increasingly essential for effective risk management in complex systems. Declarations Ethical Approval and Consent to Participate This study did not involve human participants, human data, human tissue, or animals. Therefore, ethical approval and consent to participate are not applicable to this work. Consent for Publication Not applicable. This manuscript does not contain any individual person's data in any form, including individual details, images, or videos. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The work was conducted independently without external financial support. Data Availability Statement The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request. 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University of Technology – Pato Branco","correspondingAuthor":true,"prefix":"","firstName":"Érick","middleName":"Oliveira","lastName":"Rodrigues","suffix":""}],"badges":[],"createdAt":"2026-02-03 06:38:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8771826/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8771826/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102406180,"identity":"a97e748b-43f7-4eed-a244-3c1760173ac8","added_by":"auto","created_at":"2026-02-11 11:18:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":240605,"visible":true,"origin":"","legend":"\u003cp\u003eFramework scheme\u003c/p\u003e\n\u003cp\u003eAuthors 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validation measures for k-means optimization\u003c/p\u003e\n\u003cp\u003eAuthors (2025)\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8771826/v1/ddeac5578a1896322dc1d2d9.png"},{"id":102406303,"identity":"116a467f-3d8c-45ed-b399-5a9124e6e580","added_by":"auto","created_at":"2026-02-11 11:18:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1100696,"visible":true,"origin":"","legend":"\u003cp\u003eRegime characteristics and transitions over time\u003c/p\u003e\n\u003cp\u003eAuthors (2025)\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8771826/v1/aa47d94a0284474db46ca8dc.png"},{"id":102406302,"identity":"391dc877-aa01-4150-a1db-47d7864e4506","added_by":"auto","created_at":"2026-02-11 11:18:26","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":824975,"visible":true,"origin":"","legend":"\u003cp\u003eStructural shock decomposition by event type\u003c/p\u003e\n\u003cp\u003eAuthors (2025)\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8771826/v1/272f1ad48b22d194c4bbe708.png"},{"id":102406318,"identity":"ebbd0b73-9f0b-4bc1-9df6-ea2c3875a32b","added_by":"auto","created_at":"2026-02-11 11:18:32","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":988553,"visible":true,"origin":"","legend":"\u003cp\u003eGARCH parameter analysis and volatility persistence\u003c/p\u003e\n\u003cp\u003eAuthors (2025)\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8771826/v1/9849b157f4f41f5b0ef3e14f.png"},{"id":102745552,"identity":"a3c7f63a-4673-4f03-bcf7-657a0bf9ce78","added_by":"auto","created_at":"2026-02-16 08:51:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6022931,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8771826/v1/afbb4d86-5675-4b7e-9dac-ef8ab0ce6159.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Risk Management Framework for Complex Systems: A Production Engineering Approach to Cryptocurrency Portfolio Optimization","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe management of complex systems under conditions of extreme uncertainty represents a fundamental challenge in production engineering. Contemporary financial markets, particularly emerging cryptocurrency ecosystems, exhibit characteristics analogous to complex industrial systems: high dimensionality, nonlinear dynamics, regime-dependent behavior, and cascading failure mechanisms (Kritzman et al., 2011). Traditional risk management approaches, developed for relatively stable environments, demonstrate limited efficacy when applied to systems characterized by volatility ratios exceeding 6:1 and risk concentration above 65% in a single factor.\u003c/p\u003e \u003cp\u003eProduction engineering provides methodological frameworks specifically designed for managing operational risk in complex, interdependent systems. These frameworks emphasize reliability analysis, failure mode identification, supply chain risk mitigation, and adaptive control mechanisms (Montgomery, 2012). However, their application to financial portfolio management remains underexplored, despite clear parallels between supply chain disruptions and market liquidity crises, between production regime shifts and market volatility transitions, and between quality control processes and risk monitoring systems.\u003c/p\u003e \u003cp\u003eCryptocurrency markets present an ideal testbed for production engineering methodologies due to their extreme volatility, 24/7 operational requirements, and susceptibility to systematic shocks. Unlike traditional equity markets, cryptocurrency portfolios face unique challenges: absence of fundamental valuation anchors, extreme price discovery mechanisms, protocol-level technical risks, and regulatory uncertainty (Baur et al., 2018). These characteristics mirror challenges in emerging manufacturing systems, where standard operating procedures may be ill-defined and failure modes incompletely characterized.\u003c/p\u003e \u003cp\u003eThis study addresses three critical gaps in the literature. First, existing portfolio optimization frameworks rely predominantly on mean-variance approaches that degenerate under extreme risk concentration. Second, regime detection methodologies typically focus on binary state identification, failing to capture the multi-modal volatility distributions observed in high-frequency environments. Third, current approaches treat risk factors as independent, neglecting network effects and cascade propagation mechanisms central to complex systems theory.\u003c/p\u003e \u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003e1.1. Research Objectives\u003c/h2\u003e \u003cp\u003eThe primary objective of this research is to develop and validate a production engineering framework for portfolio risk management in complex systems. Specific objectives include:\u003c/p\u003e \u003cp\u003eObjective 1: Identify and quantify systematic risk factors through principal component decomposition to determine the effective dimensionality of the risk space and assess the validity of traditional diversification approaches.\u003c/p\u003e \u003cp\u003eObjective 2: Establish optimal portfolio segmentation through clustering analysis to enable cluster-specific risk management protocols and resource allocation strategies.\u003c/p\u003e \u003cp\u003eObjective 3: Detect and characterize operational regimes using Hidden Markov Models to quantify regime transition probabilities, expected durations, and volatility differentials for dynamic position sizing.\u003c/p\u003e \u003cp\u003eObjective 4: Decompose structural shocks by event category to identify primary sources of abnormal returns and establish event-specific hedging requirements.\u003c/p\u003e \u003cp\u003eObjective 5: Map network causality structures to determine information flow patterns and identify systemically important nodes requiring priority monitoring.\u003c/p\u003e \u003cp\u003eObjective 6: Quantify volatility persistence through GARCH modeling to determine appropriate rebalancing frequencies and capital requirements for equivalent risk reduction.\u003c/p\u003e \u003cp\u003eObjective 7: Validate stationarity assumptions to confirm the appropriateness of return-based analytical frameworks and identify opportunities for cointegration-based strategies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e1.2. Contribution to Production Engineering\u003c/h2\u003e \u003cp\u003eThis research contributes to production engineering literature by demonstrating the applicability of reliability theory, network analysis, and control systems to financial risk management. The framework treats portfolio assets as components in a production system, regime transitions as operational mode changes, and market shocks as supply chain disruptions. This perspective enables the application of established engineering methodologies to novel problem domains, extending the scope of production engineering beyond traditional manufacturing contexts.\u003c/p\u003e \u003c/div\u003e"},{"header":"2. Literature Review","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Risk Factor Decomposition and Dimensionality Reduction\u003c/h2\u003e \u003cp\u003ePrincipal Component Analysis has emerged as a fundamental tool for portfolio risk management, enabling the identification of systematic risk factors from high-dimensional return data (Kritzman et al., 2011). The absorption ratio, defined as the fraction of total variance captured by a subset of principal components, provides a measure of systemic risk concentration. Pasini (2017) demonstrated that the first three principal components typically capture 75% of variance in equity portfolios, enabling substantial dimensionality reduction without significant information loss. However, cryptocurrency portfolios exhibit substantially higher risk concentration, with Celestin (2025) reporting first-component dominance approaching 70% in digital asset portfolios.\u003c/p\u003e \u003cp\u003eThe mathematical foundation of PCA begins with the covariance matrix of asset returns, where eigenvalue decomposition yields orthogonal principal components ordered by variance contribution (Mavungu, 2023). Applications extend beyond dimensionality reduction to scenario generation for stress testing, where principal components define the relevant directions of market movement (Jackson, 2001). Recent advances include the integration of PCA with machine learning techniques for dynamic factor identification and the development of kernel PCA methods for capturing nonlinear relationships in financial data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Clustering for Portfolio Segmentation\u003c/h2\u003e \u003cp\u003eK-means clustering provides a data-driven approach to portfolio segmentation based on return characteristics rather than predetermined asset classifications (Ding \u0026amp; He, 2004). Unlike traditional sector-based groupings, clustering algorithms identify empirical similarities in risk profiles, enabling more effective diversification strategies. Recent applications demonstrate that clustering-based portfolios achieve higher risk-adjusted returns compared to sector-balanced alternatives, with Sharpe ratios improving by 15\u0026ndash;30% across multiple asset classes (2025 study in Symmetry journal).\u003c/p\u003e \u003cp\u003eThe Silhouette score, Davies-Bouldin index, and Calinski-Harabasz score provide complementary measures for determining optimal cluster numbers, with Silhouette analysis demonstrating superior performance compared to elbow methods (as reported in MDPI 2025 study). Applications in portfolio construction show that selecting representative assets from each cluster produces more stable portfolios with reduced correlation during stress events compared to traditional mean-variance optimization (U et al., 2024; Wu et al., 2022).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Market Regime Detection Using Hidden Markov Models\u003c/h2\u003e \u003cp\u003eHidden Markov Models provide a probabilistic framework for identifying latent market states from observed returns, addressing the fundamental challenge that regime transitions are not directly observable (Yuan \u0026amp; Mitra, 2019). The Markov property assumes that future states depend only on the current state, enabling tractable inference through the Viterbi algorithm and Baum-Welch estimation. Financial applications demonstrate that regime-switching strategies incorporating HMM predictions achieve both higher absolute and risk-adjusted returns compared to static approaches (Wang et al., 2020).\u003c/p\u003e \u003cp\u003eMarket regimes typically exhibit distinct return distributions and volatility profiles, with transitions often corresponding to macroeconomic shifts, regulatory changes, or structural breaks (Kritzman et al., 2012). Three-state HMM implementations successfully distinguish growth, neutral, and stress regimes, with stress detection enabling preemptive risk reduction before significant drawdowns materialize. Comparative studies indicate HMM superiority over clustering-based regime detection methods, particularly for out-of-sample prediction accuracy.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Volatility Modeling Through GARCH Frameworks\u003c/h2\u003e \u003cp\u003eThe Generalized Autoregressive Conditional Heteroskedasticity framework, introduced by Bollerslev (1986), captures the volatility clustering and persistence characteristics fundamental to financial time series. The GARCH(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) specification, where conditional variance depends on past squared residuals and lagged variance, provides parsimony while maintaining strong predictive performance across diverse asset classes (Engle, 1982). Persistence parameters, defined as the sum of ARCH and GARCH coefficients, quantify the rate of volatility shock dissipation, with values approaching unity indicating near-integrated processes requiring extensive time for mean reversion (Ding \u0026amp; Granger, 1996).\u003c/p\u003e \u003cp\u003eAsymmetric extensions including EGARCH and GJR-GARCH address leverage effects where negative shocks generate larger volatility increases than positive shocks of equivalent magnitude (Aliyev et al., 2020). Applications to cryptocurrency markets reveal persistence parameters averaging 0.94, substantially exceeding traditional equity values of 0.85\u0026ndash;0.90, implying slower mean reversion and longer-lasting volatility shocks (studies from 2023\u0026ndash;2024 analyzing crypto volatility). The half-life measure, calculated as ln(0.5)/ln(persistence), provides intuitive interpretation of shock dissipation timescales, critical for determining rebalancing frequencies and capital requirements.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Network Analysis and Contagion Effects\u003c/h2\u003e \u003cp\u003eGranger causality testing identifies directional information flows between assets, enabling construction of causal networks that reveal hierarchical market structures. Network centrality measures quantify asset importance within the system, with high-centrality nodes serving as potential contagion sources during stress periods. Applications demonstrate that central assets exhibit predictive power for peripheral asset returns, enabling lead-lag trading strategies and early warning systems for market dislocations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.6. Production Engineering Perspectives on Financial Risk\u003c/h2\u003e \u003cp\u003eProduction engineering frameworks treat portfolio management as a reliability optimization problem under uncertainty. This perspective emphasizes failure mode identification, redundancy planning, and adaptive control mechanisms analogous to quality management systems (Montgomery, 2012). Supply chain risk management methodologies, including supplier diversification and buffer stock strategies, translate directly to portfolio hedging and liquidity management requirements. The integration of control theory enables dynamic position sizing based on real-time regime probability estimates, similar to adaptive manufacturing systems responding to demand fluctuations.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eThis study employs a comprehensive multi-stage analytical framework integrating seven complementary methodologies to characterize risk dynamics in cryptocurrency portfolios. The methodological architecture, illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, proceeds through sequential stages: (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) principal component analysis for systematic risk decomposition, (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) K-means clustering for portfolio segmentation, (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) Hidden Markov Model regime detection, (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) structural shock decomposition by event category, (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e) network causality analysis, (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) GARCH volatility modeling, and (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e) stationarity testing. Each analytical component addresses specific research objectives while contributing to an integrated understanding of complex system behavior under extreme uncertainty. The framework adopts production engineering principles by treating portfolio assets as components in a reliability system, regime transitions as operational mode changes, and market shocks as supply chain disruptions. This perspective enables the systematic application of failure mode analysis, redundancy optimization, and adaptive control mechanisms to financial risk management. The following subsections detail the mathematical foundations, implementation procedures, and validation criteria for each methodological component.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAuthors (2025)\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Data Collection and Preprocessing\u003c/h2\u003e \u003cp\u003eThe analysis employs daily closing price data for fourteen cryptocurrency assets obtained from Coingecko (2025) site. The dataset encompasses varying temporal windows tailored to each asset, but the range of time analysis comprehend January 28th 2022 to July 21th 2025. This time window enables to capture many different market conditions, including bull and bear cycles, regulatory shifts and technological disruptions Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e demonstrates each cryptocurrency and the input data and then time period.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAsset characteristics and sample periods\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAsset\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInput Observations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePeriod of the cut\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAVAX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAXS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBTC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4466\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDOT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eETH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3736\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eILV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1574\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIMX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLTC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4574\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMANA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2987\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRON\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSAND\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSOL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2093\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTRX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2977\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXRP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2022-01-28 to 2025-07-21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003eAuthors (2025)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAsset selection criteria emphasized market capitalization, trading volume liquidity, and operational diversity across infrastructure, platform, and application layers. Price series underwent standardization to address scale differences, with subsequent conversion to logarithmic returns to achieve stationarity and enable valid statistical inference.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Principal Component Analysis\u003c/h2\u003e \u003cp\u003ePrincipal Component Analysis (PCA) was implemented to identify the dominant sources of variation in the cryptocurrency return space and reduce dimensionality while preserving essential information structure (Jolliffe \u0026amp; Cadima, 2016). The analysis proceeded through singular value decomposition of the standardized return correlation matrix, yielding orthogonal principal components ordered by explained variance. The cumulative explained variance ratio served as the primary criterion for component retention, with the Kaiser criterion (eigenvalue\u0026thinsp;\u0026gt;\u0026thinsp;1) and scree plot analysis providing supplementary validation (Kaiser, 1960; Cattell, 1966).\u003c/p\u003e \u003cp\u003eThe variance contribution of the k-th component is formalized as\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{Explained\\:Vriance\\:Ratio}_{k}=\\frac{{\\lambda\\:}_{k}}{\\sum\\:_{i=1}^{n}{\\lambda\\:}_{i}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eλ\u003c/em\u003e\u003csub\u003e\u003cem\u003ek\u003c/em\u003e\u003c/sub\u003e represents the eigenvalue of component \u003cem\u003ek\u003c/em\u003e, and n denotes the total number of components. This decomposition facilitates the identification of systemic risk factors affecting the entire portfolio versus asset-specific idiosyncratic variations (Connor \u0026amp; Korajczyk, 1986). Component loadings were examined to interpret the economic significance of each principal component. High absolute loadings indicate strong association between an asset and a particular systematic factor. The first principal component typically captures market-wide co-movement, while subsequent components reveal sector-specific or technology-dependent patterns (Huynh et al., 2020).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.3. K-means Clustering Optimization\u003c/h2\u003e \u003cp\u003ePortfolio segmentation employed K-means clustering on standardized return series to identify groups of assets exhibiting similar risk-return profiles (MacQueen, 1967; Hartigan \u0026amp; Wong, 1979). The algorithm iteratively assigns each asset to the nearest cluster centroid based on Euclidean distance, subsequently updating centroids as the mean of all assigned members until convergence or a maximum of 300 iterations. Cluster configurations ranging from k\u0026thinsp;=\u0026thinsp;2 to k\u0026thinsp;=\u0026thinsp;8 were systematically evaluated using three complementary internal validation measures.\u003c/p\u003e \u003cp\u003eThe Silhouette Score measures cohesion within clusters relative to separation between clusters, ranging from \u0026minus;\u0026thinsp;1 (poor clustering) to +\u0026thinsp;1 (excellent clustering) (Rousseeuw, 1987). The Davies-Bouldin Index quantifies the average similarity between each cluster and its most similar cluster, with lower values indicating better-defined clusters (Davies \u0026amp; Bouldin, 1979). The Calinski-Harabasz Index assesses the ratio of between-cluster variance to within-cluster variance, with higher values indicating more compact and well-separated clusters (Caliński \u0026amp; Harabasz, 1974). The elbow method complemented these measures through inertia analysis, defined as the sum of squared distances from each point to its assigned centroid. The optimal number of clusters corresponds to the point where marginal improvements in cluster compactness diminish substantially (Thorndike, 1953).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Hidden Markov Model Regime Detection\u003c/h2\u003e \u003cp\u003eMarket regime identification employed Gaussian Hidden Markov Models (HMMs) to capture latent states governing return dynamics (Baum \u0026amp; Petrie, 1966; Rabiner, 1989). The framework assumes that observed returns are generated by an underlying Markov chain transitioning between discrete states, each characterized by distinct return distributions. The HMM specification comprises three fundamental elements: initial state distribution (π), defining the probability of starting in each state; transition matrix (A), where elements aij represent the probability of transitioning from state \u003cem\u003ei\u003c/em\u003e to state \u003cem\u003ej\u003c/em\u003e; and emission distributions (B), consisting of Gaussian distributions N(\u0026micro;\u003csub\u003ei\u003c/sub\u003e, σ\u003csub\u003ei\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e) characterizing return behavior in each state \u003cem\u003ei\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eModel parameters were estimated via the Baum-Welch algorithm, an expectation-maximization procedure maximizing the likelihood of observed data (Baum et al., 1970). State sequences were decoded using the Viterbi algorithm, which identifies the most probable sequence of hidden states conditional on the observed returns (Viterbi, 1967). Diagonal elements \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003eii\u003c/em\u003e\u003c/sub\u003e of the transition matrix quantify state persistence, with the expected duration in state \u003cem\u003ei\u003c/em\u003e computed as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\mathbb{E}\\left({D}_{i}\\right)=\\frac{1}{1-{a}_{ii}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eproviding intuitive interpretation of regime persistence (Hamilton, 1989). Configurations with 2 to 5 states were systematically evaluated using the Bayesian Information Criterion (BIC), which penalizes model complexity while rewarding goodness-of-fit (Schwarz, 1978). Lower BIC values indicate superior balance between model fit and parsimony. Regime characteristics including mean returns, volatility levels, self-transition probabilities, and expected durations were analyzed to interpret the economic significance of each identified state\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.5. Structural Shock Decomposition\u003c/h2\u003e \u003cp\u003eStructural shocks were systematically classified into six categories based on their economic origin: supply chain disruptions, regulatory constraints, technology upgrades, macroeconomic shocks, demand expansion, and speculative bubbles. Each event was assigned a precise date based on public announcements, regulatory filings, or observable market impacts, following established event study protocols (MacKinlay, 1997; Kothari \u0026amp; Warner, 2007). Cumulative abnormal returns (CAR) were calculated over asymmetric event windows spanning [-10, +\u0026thinsp;10] days relative to the event date. Normal returns were estimated using a market model calibrated over a 120-day baseline period ending 11 days before each event.\u003c/p\u003e \u003cp\u003eThe cumulative abnormal return is formally defined as\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:CAR\\left({t}_{1},{t}_{2}\\right)=\\sum\\:_{i={t}_{1}}^{{t}_{2}}\\left({R}_{i}-\\mathbb{E}\\left[{R}_{i}\\right]\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e denotes the observed return at day \u003cem\u003ei\u003c/em\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mathbb{E}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e[R\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e]\u003c/em\u003e represents the expected return derived from the baseline model. Statistical significance was assessed using standardized t-statistics, with a threshold of p\u0026thinsp;\u0026lt;\u0026thinsp;0.05 for significant deviations from expected behavior (Brown \u0026amp; Warner, 1985). This methodology enables precise attribution of price movements to specific structural events while controlling for normal market volatility. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes the structural shock categories analyzed in this study.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStructural shock classification and event examples\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e Category\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExample Event\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSupply Chain\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNetwork congestion, mining disruptions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eEthereum gas fee spikes (2021)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRegulatory\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePolicy announcements, legal frameworks\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eChina mining ban (May 2021)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eTechnology\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProtocol upgrades, security patches\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eEthereum Merge (Sept 2022)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMacroeconomic\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInterest rate changes, inflation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eFed rate hikes (2022\u0026ndash;2023)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDemand\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInstitutional adoption, retail inflows\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eTesla BTC purchase (Feb 2021)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSpeculative\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePrice bubbles, coordinated pumps\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eGameStop-crypto correlation (Jan 2021)\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003eAuthors (2025)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.6. Network Causality Analysis\u003c/h2\u003e \u003cp\u003eGranger causality tests identified directional predictive relationships between asset pairs, with lag length determined via information criteria. The test evaluates whether past values of asset X provide statistically significant information about future values of asset Y beyond that contained in Y's own history. F-statistics quantified causal strength, while p-values below 0.05 indicated significant relationships. Network measures including in-degree, out-degree, and net influence quantified each asset's position in the causal hierarchy.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{Y}_{t}=\\alpha\\:+\\sum\\:_{i=1}^{p}{\\beta\\:}_{i}{Y}_{t-i}+\\sum\\:_{j=1}^{p}{\\gamma\\:}_{j}{X}_{t-j}+{ϵ}_{t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere the null hypothesis H\u003csub\u003e0\u003c/sub\u003e: γ\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;γ\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;...\u0026thinsp;=\u0026thinsp;γ\u003csub\u003ep\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0 is tested via F-statistics. Optimal lag length p was determined using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to balance model fit against complexity (Akaike, 1974; Schwarz, 1978). Pairwise Granger tests were conducted for all 182 asset combinations (14 choose 2, bidirectional), generating a weighted directed network where edge weights correspond to F-statistic magnitudes and edges are retained only for relationships with p-values below 0.05.\u003c/p\u003e \u003cp\u003eNetwork centrality measures were computed to quantify systemic importance. In-degree measures the number of assets that are Granger-caused by the focal asset, indicating predictive influence. Out-degree quantifies the number of assets Granger-causing the focal asset, reflecting susceptibility to external shocks. Net influence, computed as in-degree minus out-degree, distinguishes leaders (positive values) from followers (negative values). This network topology reveals hierarchical structures and identifies assets serving as information hubs or systemic risk transmitters (Billio et al., 2012; Diebold \u0026amp; Yılmaz, 2014).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.7. GARCH Volatility Modeling\u003c/h2\u003e \u003cp\u003eVolatility dynamics were characterized using GARCH(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) models, which capture the empirical regularities of volatility clustering and persistence observed in financial time series (Bollerslev, 1986; Engle, 2001). The conditional variance specification is given by\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}^{2}=\\:{\\omega\\:}+{\\alpha\\:}\\:.\\:{\\epsilon\\:}_{t-1}^{2}+\\beta\\:{\\sigma\\:}_{t-1}^{2}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere ω\u0026thinsp;\u0026gt;\u0026thinsp;0 represents the long-run average variance, α\u0026thinsp;\u0026ge;\u0026thinsp;0 quantifies the impact of recent shocks (ARCH effect), and β\u0026thinsp;\u0026ge;\u0026thinsp;0 captures volatility persistence (GARCH effect). The stationarity condition α\u0026thinsp;+\u0026thinsp;β\u0026thinsp;\u0026lt;\u0026thinsp;1 ensures mean reversion, while values approaching unity indicate near-integrated volatility processes (Nelson, 1990). The persistence parameter (α\u0026thinsp;+\u0026thinsp;β) determines the rate at which volatility shocks dissipate. Half-lives of volatility shocks were computed as:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\varvec{H}\\varvec{a}\\varvec{l}\\varvec{f}\\varvec{l}\\varvec{i}\\varvec{f}\\varvec{e}=\\frac{\\text{ln}\\left(0.5\\right)}{\\text{ln}\\left(\\varvec{\\alpha\\:}+\\varvec{\\beta\\:}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eproviding an intuitive measure of shock duration in calendar days (Christoffersen, 2012). Assets exhibiting \u003cem\u003eα\u0026thinsp;+\u0026thinsp;β\u0026thinsp;\u0026asymp;\u0026thinsp;1\u003c/em\u003e demonstrate unit-root volatility behavior, implying permanent impacts from transitory shocks (Baillie et al., 1996). Maximum likelihood estimation was performed under the assumption of normally distributed standardized residuals. Model adequacy was verified through Ljung-Box tests on standardized and squared standardized residuals, ensuring no remaining autocorrelation structure (Ljung \u0026amp; Box, 1978).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e3.8. Stationarity Testing\u003c/h2\u003e \u003cp\u003eStationarity validation employed the Augmented Dickey-Fuller test for unit root presence and the Kwiatkowski-Phillips-Schmidt-Shin test for trend stationarity. The ADF test null hypothesis posits a unit root (non-stationarity), while the KPSS test null hypothesis assumes stationarity. Concordant results from both tests provide strong evidence for classification, while conflicting results indicate inconclusive status, potentially reflecting structural breaks or regime-switching behavior. The predominance of non-stationary price series validates the use of return-based analysis throughout the framework.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Risk Factor Decomposition\u003c/h2\u003e \u003cp\u003ePrincipal component analysis of the covariance matrix revealed a highly concentrated risk structure within the cryptocurrency portfolio. The decomposition of portfolio variance across systematic risk factors demonstrated extreme concentration, with the first principal component accounting for 67.89% of total variance. This concentration substantially exceeds typical equity portfolio structures, where the primary risk factor generally explains 30\u0026ndash;40% of variance.\u003c/p\u003e \u003cp\u003eThe eigenvalue associated with the first risk factor reached 9.51, while subsequent factors exhibited considerably lower values. The second through fifth risk factors contributed 5.43%, 4.27%, 3.96%, and 3.28% to total variance, respectively. The cumulative variance explained by the first four risk factors reached 81.55%, while the first seven factors captured 90.36% of total portfolio variance, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e..\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAuthors (2025)\u003c/p\u003e \u003cp\u003eThe visual representation of variance distribution illustrates the dominance of the first risk factor, whose contribution dwarfs that of subsequent components. The cumulative variance plot demonstrates a steep initial ascent, reaching the conventional 80% threshold after the fourth factor, as indicated by the horizontal reference line. This rapid convergence suggests limited effective dimensionality in the risk space, constraining traditional diversification approaches.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Cluster Optimization\u003c/h2\u003e \u003cp\u003eK-means clustering analysis identified an optimal partition of six distinct asset groups within the portfolio. The optimization procedure evaluated configurations ranging from two to eight clusters using multiple validation measures. The six-cluster configuration achieved the maximum Silhouette score of 0.096, indicating superior separation between groups relative to within-group cohesion. This configuration simultaneously minimized the Davies-Bouldin index to 1.008, the lowest value across all tested parameterizations, further supporting the optimality of this structure.\u003c/p\u003e \u003cp\u003eThe Calinski-Harabasz score, which quantifies the ratio of between-cluster to within-cluster variance, reached 2.285 for the six-cluster solution. The elbow method analysis, examining within-cluster sum of squares, demonstrated substantial reduction from 14,812 at two clusters to 7,328 at six clusters, with diminishing marginal improvements beyond this point. The convergence of multiple validation measures at six clusters provides robust evidence for this structural configuration.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFigure 3 Cluster validation measures for k-means optimization\u003c/em\u003e \u003c/p\u003e \u003cp\u003e Authors (2025)\u003c/p\u003e \u003cp\u003eThe four-panel visualization demonstrates the consistency of the six-cluster optimum across multiple evaluation criteria. The Silhouette score exhibits a clear peak at six clusters, while the Davies-Bouldin index reaches its minimum at the same configuration. The Calinski-Harabasz score stabilizes around this region, and the elbow method shows a marked inflection point, indicating that additional clusters provide limited incremental benefit. Notably, traditional functional classifications of cryptocurrency assets, such as layer-1 protocols, decentralized finance applications, and gaming tokens, demonstrated weak correspondence to the empirically derived clusters, with Adjusted Rand Index values below 0.05.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Operational Regime Detection\u003c/h2\u003e \u003cp\u003eHidden Markov Model analysis identified five distinct operational regimes characterized by differential volatility and return profiles. The classification revealed extreme heterogeneity in market conditions, with volatility ranging from 2.02% in stable regimes to 13.94% in stress conditions, representing a volatility ratio of 6.91. The most prevalent regime, State 3, encompassed 34.70% of the sample period, exhibiting moderate volatility of 4.61% and near-zero mean returns of negative 0.01% per day.\u003c/p\u003e \u003cp\u003eState 4 represented a low-volatility regime with 31.16% prevalence, characterized by positive mean returns of 0.46% per day and volatility of 2.02%. In contrast, State 2, the high-volatility stress regime, appeared in only 0.71% of observations but demonstrated severe negative returns of negative 8.61% per day alongside 13.94% volatility. The transition probability analysis revealed that State 3 exhibited the strongest persistence, with a self-transition probability of 0.921 corresponding to an expected duration of 12.74 days. The stress regime (State 2) showed moderate persistence with a self-transition probability of 0.667, yielding an expected duration of 3.00 days.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFigure 4 Regime characteristics and transitions over time\u003c/em\u003e \u003c/p\u003e \u003cp\u003e Authors (2025)\u003c/p\u003e \u003cp\u003eThe temporal evolution of regime assignments reveals clustering of stress periods and extended intervals of stable operation. The distribution of returns by regime exhibits substantial variation, with State 2 demonstrating extreme negative skewness and wide dispersion. Volatility levels display a pronounced hierarchy across regimes, with State 2 exceeding all others by a factor of 1.8 to 6.9. The regime prevalence analysis indicates that States 0, 3, and 4 collectively account for 97.1% of observations, while the two higher-volatility states (1 and 2) represent transitional or crisis periods.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Structural Shock Decomposition\u003c/h2\u003e \u003cp\u003eStructural vector autoregression analysis identified six primary shock categories affecting portfolio returns. The decomposition revealed asymmetric impacts, with supply chain disruption events generating the most severe negative cumulative abnormal returns, averaging negative 9.2%. Speculative bubble events produced comparable downside effects at negative 8.8%, while regulatory constraint shocks averaged negative 5.6%. Technology upgrade events and demand expansion shocks demonstrated relatively modest negative impacts of negative 2.1% and negative 1.8%, respectively. Macroeconomic shocks exhibited positive cumulative abnormal returns of 4.3%, contrary to traditional asset class behavior.\u003c/p\u003e \u003cp\u003eStatistical significance varied substantially across shock types. Demand expansion events achieved the highest significance rate at 100%, indicating consistent and predictable impacts. Technology upgrade shocks demonstrated 80% significance, while regulatory constraints and macroeconomic shocks achieved 66.7% and 25.0% significance rates, respectively. Supply chain disruptions and speculative bubbles exhibited 50.0% and 33.3% significance, suggesting greater heterogeneity in their manifestations.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFigure 5 Structural shock decomposition by event type\u003c/em\u003e \u003c/p\u003e \u003cp\u003e Authors (2025)\u003c/p\u003e \u003cp\u003eThe scatter plot of individual events reveals considerable variation within shock categories. Supply chain disruption events cluster predominantly in the negative return, high volatility quadrant, with several observations exceeding 100% volatility change. Technology upgrade events demonstrate moderate dispersion, while macroeconomic shocks span the entire return spectrum. The volatility amplification analysis indicates that supply chain disruptions generate the most pronounced volatility increases, averaging 31.8% above baseline levels. Regulatory constraints and speculative bubbles produce mean volatility changes of 8.3% and 4.5%, respectively, while technology upgrades result in modest negative 2.1% volatility reduction.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Network Causality Structure\u003c/h2\u003e \u003cp\u003eGranger causality analysis at the 5% significance level revealed an extensive network of directional relationships among portfolio constituents. The analysis identified 68 significant causal relationships from a possible 182 pairwise connections, representing a network density of 37.4%. The causal structure exhibited substantial asymmetry, with certain assets functioning as dominant information transmitters while others operated primarily as receivers.\u003c/p\u003e \u003cp\u003eNetwork centrality analysis revealed distinct hierarchical patterns. Ethereum and Bitcoin emerged as the most influential assets, demonstrating net outbound influence of 6.2 and 5.8 standard deviations above the network mean, respectively. Ripple exhibited moderate net influence at 2.9 standard deviations, while Ronin and Avalanche showed values of 1.2 and 0.3. Assets including Litecoin, Illuvium, Immutable X, and Tron demonstrated negative net influence, ranging from negative 0.2 to negative 1.8, indicating their role as information receivers rather than transmitters.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e4.6. Volatility Persistence\u003c/h2\u003e \u003cp\u003eGARCH(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) estimation across individual assets revealed substantial heterogeneity in volatility dynamics. The persistence parameter, defined as the sum of ARCH and GARCH coefficients, ranged from 0.780 for Ripple to 1.000 for Tron, with a portfolio-weighted mean of 0.938. Thirteen of fourteen assets demonstrated stationary volatility processes with persistence below unity, while Tron exhibited unit root behavior indicating non-stationary volatility.\u003c/p\u003e \u003cp\u003eThe decomposition of persistence into ARCH and GARCH components demonstrated systematic patterns. GARCH coefficients, representing volatility memory, dominated ARCH coefficients across most assets. ETH exhibited the highest GARCH coefficient at 0.958 with minimal ARCH contribution of 0.033, yielding a half-life of 77.08 days for volatility shocks. BTC demonstrated moderate persistence of 0.844 with a balanced ARCH-GARCH composition of 0.153 and 0.691, resulting in a 4.09-day half-life. Assets in lower persistence ranges, such as XRP with 0.780 total persistence, exhibited 2.79-day half-lives.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFigure 6 GARCH parameter analysis and volatility persistence\u003c/em\u003e \u003c/p\u003e \u003cp\u003e Authors (2025)\u003c/p\u003e \u003cp\u003eThe distribution of volatility shock half-lives demonstrates substantial concentration between 10 and 30 days, with the system-wide mean at 20.8 days. Three assets exhibit half-lives exceeding 30 days, indicating prolonged persistence of volatility shocks. The cluster-level analysis reveals consistency within groups, with mean persistence ranging from 0.912 for Cluster 3 to 0.983 for Cluster 2. All clusters maintain persistence parameters below unity, confirming mean-reverting volatility dynamics at the portfolio level despite the unit root behavior of individual constituents.\u003c/p\u003e \u003cp\u003eThe ARCH-GARCH component trade-off demonstrates an approximately linear inverse relationship, with the regression line indicating that higher GARCH coefficients correspond to proportionally lower ARCH values. This pattern suggests a consistent allocation of volatility dynamics between short-term and long-term components. Assets positioned above the regression line exhibit higher total persistence relative to their ARCH coefficient, indicating stronger long-term memory effects.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e4.7. Stationarity Validation\u003c/h2\u003e \u003cp\u003eAugmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests assessed the stationarity properties of price series across all portfolio constituents. The analysis classified eleven assets as non-stationary based on concordant test results, representing 78.6% of the portfolio. Both tests indicated non-stationarity for assets including Axie Infinity, Bitcoin, Ethereum, Illuvium, Ripple, Ronin, Polkadot, Tron, Solana, Avalanche, and The Sandbox, with Augmented Dickey-Fuller test statistics ranging from negative 2.52 to positive 0.69 and associated p-values exceeding the 0.05 threshold.\u003c/p\u003e \u003cp\u003eThree assets generated conflicting results between the two testing frameworks. IMX, LTC, and MANA achieved ADF test statistics of -7.01, -3.04, and \u0026minus;\u0026thinsp;3.30, respectively, with corresponding p-values\u0026thinsp;\u0026lt;\u0026thinsp;0.05, suggesting stationarity under the null hypothesis of unit root presence. However, KPSS tests for these same assets yielded statistics of 0.85, 4.25, and 1.23 with p-values at or \u0026lt;\u0026thinsp;0.01, indicating non-stationarity under the null hypothesis of stationarity. These conflicting results classify the assets as inconclusive, potentially reflecting structural breaks, regime-switching behavior, or transitional dynamics.\u003c/p\u003e \u003cp\u003eThe predominance of non-stationary price processes validates the methodological choice of return-based analysis throughout the analytical framework. The identification of integrated order I (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) processes confirms that first-differencing produces stationary return series suitable for statistical inference. The presence of non-stationary price series enables cointegration testing for pairs trading strategies, representing potential opportunities for mean-reversion exploitation within the portfolio structure.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Comparison with Literature Findings\u003c/h2\u003e \u003cp\u003eThe empirical findings of this study demonstrate both consistencies and notable deviations from established literature across multiple analytical dimensions. A comprehensive comparison reveals that cryptocurrency markets exhibit substantially more extreme characteristics than traditional asset classes, validating the need for specialized risk management frameworks. The following analysis systematically compares each major finding with corresponding results from peer-reviewed literature.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents a comprehensive comparison of key findings across seven analytical dimensions, contrasting the present study's cryptocurrency portfolio results with conventional financial market studies. The comparison reveals systematic differences that underscore the unique risk characteristics of digital asset markets.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative analysis with prior literature\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalytical Dimension\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePrimary Measure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSecondary Measure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTertiary Metric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eContext/Method\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eKey Interpretation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRisk Factor Concentration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e67.89%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4 factors to 80%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCryptocurrency portfolio (14 assets)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExtreme concentration; single factor dominance\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKritzman et al. (2011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e30\u0026ndash;40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8\u0026ndash;12 factors to 80%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;3.5\u0026ndash;4.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDiversified equity portfolios\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eModerate concentration; multiple significant factors\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePasini (2017)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;25%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3 factors to 75%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;2.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDow Jones Industrial Average\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eLower concentration; balanced risk structure\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCelestin (2025)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u0026ndash;4 factors to 75\u0026ndash;80%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;9.0\u0026ndash;10.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDigital asset portfolio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSimilar extreme concentration in crypto markets\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCluster Optimization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6 clusters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSilhouette: 0.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDavies-Bouldin: 1.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eReturn-based clustering\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eOptimal at k\u0026thinsp;=\u0026thinsp;6; weak functional correspondence (ARI\u0026thinsp;\u0026lt;\u0026thinsp;0.05)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSymmetry (2025)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2 clusters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSilhouette preferred\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot reported\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eProfitability measures\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBinary risk classification; Silhouette\u0026thinsp;\u0026gt;\u0026thinsp;Elbow method\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStock Study (2023)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4 clusters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSilhouette method\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot reported\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRisk-return characteristics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFour-cluster optimal for diversification\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEmerald (2024)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4 clusters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWard linkage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCophenetic: 0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCAPM-based features\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFour clusters with distinct beta profiles\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStevens (2024)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e11 clusters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eK-means\u0026thinsp;+\u0026thinsp;HRP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot reported\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eETF portfolio (105 assets)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHigher k optimal for larger universe; improved Sharpe ratio\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMarket Regime Detection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5 states\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVol ratio: 6.91\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStress: 13.94%, Stable: 2.02%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHMM on crypto returns\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExtreme volatility differential; 0.71% stress prevalence\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWang et al. (2020)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3 states\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVol ratio: ~2.5\u0026ndash;3.5\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot specified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u0026amp;P 500 equities\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eModerate regime differentiation; higher persistence\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMDPI (2020)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u0026ndash;4 states\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBIC selection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot specified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u0026amp;P 500 monthly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eFour-state optimal by information criteria\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQuantStart (2015\u0026ndash;2017)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u0026ndash;3 states\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eModerate separation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHigh/low volatility\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eS\u0026amp;P 500 daily\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBinary or tertiary classification most common\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDevportal Analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u0026ndash;3 states\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCrash detection focus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot specified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eVarious equity indices\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eHMM superior to clustering; identifies crashes well\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGARCH Volatility Persistence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean: 0.938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRange: 0.780-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHalf-life: 20.8 days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGARCH(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) on 14 cryptos\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVery high persistence; slow mean reversion; one unit root\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBitcoin (Medium 2025)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBTC: 0.844\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eETH: 0.991\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBTC: 6.6 days, ETH: 242.9 days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eIndividual crypto analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEthereum shows extreme persistence vs Bitcoin\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHalf-Life Study (2019)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0.85\u0026ndash;0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBTC, LTC, XRP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;15\u0026ndash;25 days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGARCH family models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eStrong mean reversion; short half-life reported\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePMC (2021)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0.90\u0026ndash;0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSix cryptocurrencies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVariable by asset\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMultiple GARCH variants\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePersistence approaching unity; long-term vol\u0026thinsp;\u0026gt;\u0026thinsp;100%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAkbay (Medium 2025)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026gt;\u0026thinsp;0.70, approaching 0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGeneral crypto markets\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExtended clustering\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eReview of studies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCrypto persistence exceeds equities; EGARCH preferred\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFuture Business (2025)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAsset-dependent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBTC, ETH, BNB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot specified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTGARCH/EGARCH optimal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAsymmetric models outperform; context-dependent\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTraditional Equities\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e~\u0026thinsp;0.85\u0026ndash;0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEquity markets\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;5\u0026ndash;15 days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStandard GARCH\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eLower persistence than crypto; faster mean reversion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNetwork Causality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37.4% density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e68 significant links (182 possible)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eETH/BTC: +5.8\u0026ndash;6.2 SD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGranger tests, 5% significance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eDense network; clear hub structure; hierarchical transmission\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpillover Study (2018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eModerate spillover\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBTC\u0026rarr;ETH, BTC\u0026rarr;LTC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSignificant causality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eIGARCH-DCC model\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eBitcoin dominant transmitter; increased post-2017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePMC Contagion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMultiple cryptos\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eConditional correlation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eVarious methods\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eVolatility spillover from major to minor coins\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStationarity Properties\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e78.6% non-stationary\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11/14 concordant non-stat\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3/14 inconclusive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eADF\u0026thinsp;+\u0026thinsp;KPSS tests\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eValidates return-based framework; potential cointegration\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGeneral Literature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMajority non-stationary\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePrice series typically I(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReturns typically I(0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStandard practice\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eConsistent with efficient market hypothesis deviations\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eShock Sensitivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eThis Study\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSupply chain: -9.2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRegulatory: -5.6%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTech upgrades: -2.1%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSix shock categories\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSupply disruptions most severe; asymmetric impacts\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComparable Studies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLimited classification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBinary shock treatment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEvent-dependent\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eVarious methodologies\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCryptocurrency shock decomposition underexplored in literature\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eAuthors (2025)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe risk factor concentration findings reveal fundamental structural differences between cryptocurrency and traditional equity portfolios. The 67.89% variance concentration in the first principal component substantially exceeds the 30\u0026ndash;40% reported by Kritzman et al. (2011) for diversified equity portfolios and the 25% documented by Pasini (2017) for Dow Jones constituents. This extreme concentration aligns closely with Celestin (2025), who reported approximately 70% first-component dominance in digital asset portfolios, suggesting that high concentration represents an inherent characteristic of cryptocurrency markets rather than a sample-specific artifact. The eigenvalue of 9.51 for the first component far exceeds typical equity portfolio values of 3.5\u0026ndash;4.5, indicating that the dominant risk factor explains variance at a rate more than double that observed in conventional markets.\u003c/p\u003e \u003cp\u003eCluster optimization results demonstrate consistency with recent portfolio segmentation literature while revealing cryptocurrency-specific patterns. The optimal six-cluster configuration, identified through Silhouette score maximization at 0.096 and Davies-Bouldin index minimization at 1.008, falls within the range reported across multiple studies. The 2025 Symmetry journal study identified two optimal clusters for binary risk classification, while studies analyzing larger asset universes report higher optimal cluster numbers, with Stevens (2024) finding eleven clusters optimal for a 105-ETF portfolio. The weak correspondence between empirical clusters and functional asset classifications, with Adjusted Rand Index below 0.05, confirms findings by multiple researchers that return-based clustering captures risk relationships invisible to traditional categorization schemes. This suggests that market-driven risk factors dominate protocol-level or sector-based distinctions in determining portfolio structure.\u003c/p\u003e \u003cp\u003eMarket regime detection via Hidden Markov Models reveals substantially higher volatility differentiation in cryptocurrency markets compared to traditional equities. The five-state optimal configuration with a 6.91\u0026times; volatility ratio between stress and stable regimes substantially exceeds the 2.5\u0026ndash;3.5\u0026times; ratios typically reported for equity markets. Wang et al. (2020) documented three-state configurations with moderate regime differentiation in S\u0026amp;P 500 analysis, while the MDPI (2020) study identified four states as optimal using information criteria. The QuantStart analyses consistently employed two to three states for equity regime detection, suggesting that cryptocurrency markets require additional states to capture their more complex volatility structures. The stress regime prevalence of only 0.71% with 13.94% volatility, compared to the stable regime's 31.16% prevalence with 2.02% volatility, indicates that extreme conditions, while rare, dominate the risk profile when they occur.\u003c/p\u003e \u003cp\u003eGARCH volatility persistence analysis reveals cryptocurrency-specific dynamics that distinguish digital assets from traditional financial instruments. The mean persistence parameter of 0.938 with a 20.8-day half-life substantially exceeds conventional equity values of 0.85\u0026ndash;0.90 with 5\u0026ndash;15 day half-lives. Individual cryptocurrency analysis by Saxena (Medium 2025) documented Bitcoin persistence of 0.844 with a 6.6-day half-life compared to Ethereum's extreme 0.991 persistence with a 242.9-day half-life, demonstrating substantial heterogeneity within the cryptocurrency space. The PMC (2021) study reported persistence approaching unity with long-term volatilities exceeding 100% for Bitcoin and Ripple, values of 213% and 164% respectively. Akbay's comprehensive review (Medium 2025) confirms that beta parameters typically exceed 0.70 for cryptocurrencies, with many approaching 0.90, substantially higher than equity markets. The Future Business Journal (2025) analysis emphasizes that asymmetric GARCH models, particularly TGARCH and EGARCH, outperform standard specifications for cryptocurrency data, suggesting that leverage effects and asymmetric volatility responses represent important features inadequately captured by symmetric GARCH(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) models.\u003c/p\u003e \u003cp\u003eNetwork causality analysis demonstrates cryptocurrency market characteristics consistent with established hierarchical transmission patterns but with higher interconnection density. The 37.4% network density, representing 68 significant causal links from 182 possible pairwise connections, exceeds typical equity market network densities. The dominant hub positions of Ethereum and Bitcoin, with net influence exceeding 5.8\u0026ndash;6.2 standard deviations above the network mean, aligns with spillover studies documenting significant volatility transmission from Bitcoin to Ethereum and Litecoin. The spillover study (2018) using IGARCH-DCC models reported statistically significant volatility spillover from Bitcoin to other major cryptocurrencies, with intensification post-2017, consistent with the present study's identification of stable hierarchical structures. The moderate conditional correlation documented in earlier studies aligns with the present findings of asymmetric information flow, where major assets serve as information transmitters while smaller assets primarily function as receivers.\u003c/p\u003e \u003cp\u003eStationarity properties of cryptocurrency price series demonstrate consistency with theoretical expectations and general financial time series characteristics. The 78.6% prevalence of non-stationary price processes, with 11 of 14 assets exhibiting concordant non-stationarity across ADF and KPSS tests, validates the widespread use of return-based analysis in financial econometrics. The identification of integrated I(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) price processes confirms that first-differencing produces stationary return series suitable for statistical inference, consistent with efficient market hypothesis deviations. The three inconclusive cases likely reflect structural breaks, protocol upgrades, or regime-switching behavior, phenomena documented extensively in cryptocurrency literature given the rapidly evolving nature of these markets.\u003c/p\u003e \u003cp\u003eStructural shock decomposition analysis reveals asymmetric sensitivities across event categories, with supply chain disruptions generating the most severe negative impacts at negative 9.2% cumulative abnormal returns. Regulatory constraint shocks produced negative 5.6% impacts, while technology upgrades demonstrated relatively modest negative 2.1% effects. The positive cumulative abnormal return of 4.3% for macroeconomic shocks contradicts traditional asset class behavior, where economic uncertainty typically generates negative risk-off sentiment. This counterintuitive finding may reflect cryptocurrency markets serving as alternative stores of value during traditional financial system stress, similar to gold's traditional safe-haven properties. The 100% statistical significance rate for demand expansion events indicates consistent and predictable market responses to adoption indicators, suggesting that fundamental demand factors maintain stronger explanatory power than speculative dynamics for these specific event categories.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Production Engineering Implications\u003c/h2\u003e \u003cp\u003eThe risk concentration findings validate production engineering concerns regarding system reliability under common mode failures. In reliability engineering, systems exhibiting 67.89% dependence on a single failure mode are considered critically vulnerable, requiring redundancy mechanisms and fail-safe designs (Montgomery, 2012). The parallel in portfolio context suggests traditional diversification approaches provide limited protection, necessitating alternative risk mitigation strategies including dynamic hedging, regime-dependent position sizing, and correlation-aware capital allocation.\u003c/p\u003e \u003cp\u003eThe identification of six operational clusters enables cluster-specific management protocols analogous to differentiated production lines in manufacturing systems. Within-cluster correlation approaching 0.85\u0026ndash;0.95 during stress regimes mirrors supply chain concentration risks, where disruption to a single supplier affects multiple dependent components. This perspective suggests treating clusters as production subsystems requiring individual buffer strategies rather than assuming independent failure modes.\u003c/p\u003e \u003cp\u003eRegime-switching behavior exhibits characteristics similar to manufacturing process transitions between stable and out-of-control states in statistical process control. The 6.91\u0026times; volatility ratio between regimes parallels quality variation in manufacturing processes experiencing assignable cause variation. The brief 3.0-day duration of stress regimes suggests rapid detection and response mechanisms, similar to real-time process monitoring, could enable preemptive position reduction before maximum drawdowns materialize.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Limitations and Boundary Conditions\u003c/h2\u003e \u003cp\u003eSeveral limitations constrain the generalizability of these findings. First, the analysis focuses exclusively on cryptocurrency markets, which may exhibit unique characteristics not present in traditional asset classes. The extreme volatility and limited fundamental valuation anchors in cryptocurrency markets suggest that risk structures could differ substantially from equity or fixed income portfolios. Second, the sample period, while encompassing multiple market cycles, may not capture all possible regime configurations, particularly unprecedented black swan events. Third, the assumption of Gaussian distributions in the HMM framework may inadequately capture extreme tail events characteristic of cryptocurrency markets.\u003c/p\u003e \u003cp\u003eThe methodological framework assumes that historical patterns provide reliable indicators of future behavior, an assumption that may break down during structural regime shifts or regulatory interventions. The rapidly evolving nature of cryptocurrency markets, including protocol upgrades, regulatory developments, and institutional adoption, introduces non-stationarities potentially violating temporal stability assumptions underlying the analytical framework. Additionally, the relatively short history of cryptocurrency markets compared to traditional assets limits the statistical power of long-term persistence estimates.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e5.4. Practical Implementation Considerations\u003c/h2\u003e \u003cp\u003eTranslation of these findings into operational protocols requires addressing several practical challenges. The extreme risk concentration implies that traditional portfolio optimization approaches based on mean-variance efficiency will likely produce suboptimal allocations. Instead, practitioners should consider factor-based approaches that explicitly account for the dominant first principal component, potentially through factor-mimicking portfolios or direct hedging strategies. The 1.5\u0026times; capital requirement identified for equivalent risk reduction compared to diversified portfolios must be incorporated into position sizing algorithms.\u003c/p\u003e \u003cp\u003eCluster-level management protocols should account for the 0.85\u0026ndash;0.95 within-cluster correlation during stress periods. This suggests maintaining cluster-level diversification as the primary risk mitigation strategy rather than within-cluster diversification. Position limits should be established at the cluster level, with rebalancing triggered by cluster membership changes rather than individual asset performance.\u003c/p\u003e \u003cp\u003eRegime detection systems require real-time implementation to enable preemptive action before stress regimes fully materialize. The 3.0-day average duration of the stress regime allows limited reaction time, suggesting that regime probability monitoring should trigger graduated responses. For example, regime probability thresholds at 0.20, 0.30, and 0.40 could initiate progressive position reductions, maintaining 70%, 50%, and 30% of target exposure, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis study developed and validated a comprehensive production engineering framework for portfolio risk management in complex systems, specifically applied to cryptocurrency markets. The framework successfully integrated seven complementary analytical techniques, providing a comprehensive and structured approach to risk assessment and decision support under conditions of extreme uncertainty.\u003c/p\u003e \u003cdiv id=\"Sec34\" class=\"Section2\"\u003e \u003ch2\u003e6.1. Research Objectives Achievement\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e synthesizes the seven primary research objectives of this study, presenting the key empirical findings and their practical implications for cryptocurrency portfolio management. Each objective addresses a specific dimension of the risk architecture inherent to digital asset markets, with results derived from the comprehensive analytical framework applied to the portfolio constituents.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResearch objectives and portfolio implications\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePractical Implications\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSystematic risk factor identification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Traditional diversification provides limited protection\u003c/p\u003e \u003cp\u003e\u0026bull; Requires alternative risk mitigation strategies\u003c/p\u003e \u003cp\u003e\u0026bull; Cryptocurrency portfolios behave fundamentally differently\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOptimal portfolio segmentation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Cluster-specific management protocols needed\u003c/p\u003e \u003cp\u003e\u0026bull; Cluster\u0026thinsp;=\u0026thinsp;appropriate unit for risk management\u003c/p\u003e \u003cp\u003e\u0026bull; Return-based clustering captures hidden risk relationships\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOperational regime detection\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Enables dynamic position sizing algorithms\u003c/p\u003e \u003cp\u003e\u0026bull; Graduated risk reduction strategies\u003c/p\u003e \u003cp\u003e\u0026bull; Specific sizing rules for probability thresholds\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStructural shock decomposition\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Event-specific hedging strategies\u003c/p\u003e \u003cp\u003e\u0026bull; Monitor supply chain stability as leading indicator\u003c/p\u003e \u003cp\u003e\u0026bull; Prioritize different risk types appropriately\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNetwork causality mapping\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Focus surveillance on high-influence assets\u003c/p\u003e \u003cp\u003e\u0026bull; Substantial contagion risk during stress\u003c/p\u003e \u003cp\u003e\u0026bull; Prioritized monitoring framework established\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVolatility persistence quantification\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Volatility shocks persist longer than traditional markets\u003c/p\u003e \u003cp\u003e\u0026bull; Requires extended hedging adjustment horizons\u003c/p\u003e \u003cp\u003e\u0026bull; Cluster-specific rebalancing frequencies needed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eObjective 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStationarity validation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026bull; Validates return-based analytical framework\u003c/p\u003e \u003cp\u003e\u0026bull; Enables cointegration testing for pairs trading\u003c/p\u003e \u003cp\u003e\u0026bull; Some assets require specialized treatment for structural breaks\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003eAuthors (2025)\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe collective findings reveal a cryptocurrency market structure fundamentally distinct from traditional asset classes, characterized by extreme systematic risk concentration, persistent volatility regimes, and hierarchical information transmission networks. The identification of return-based clusters that diverge from functional classifications, combined with the dominance of supply chain events as primary risk drivers, suggests that effective portfolio management requires paradigm shifts from conventional approaches.\u003c/p\u003e \u003cp\u003eThe extended volatility persistence and abbreviated regime durations necessitate more responsive risk management frameworks with shorter reaction times and more conservative position sizing during transitional periods. These empirical regularities provide quantitative foundations for developing specialized risk management protocols tailored to the unique behavioral characteristics of digital asset markets.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec35\" class=\"Section2\"\u003e \u003ch2\u003e6.2. Theoretical Contributions\u003c/h2\u003e \u003cp\u003eThis research makes several theoretical contributions to production engineering and financial risk management literature. First, it demonstrates the successful application of reliability engineering concepts to portfolio management, establishing parallels between supply chain disruptions and market liquidity crises, between production regime shifts and volatility transitions, and between quality control processes and risk monitoring systems. This cross-domain methodological transfer extends the scope of production engineering beyond traditional manufacturing contexts.\u003c/p\u003e \u003cp\u003eSecond, the framework provides an integrated approach combining seven complementary techniques into a unified analytical structure. Previous studies typically employ individual methods in isolation, potentially missing interactions between risk dimensions. The integrated approach enables simultaneous assessment of dimensionality, clustering structure, regime behavior, shock sensitivity, network position, volatility dynamics, and stationarity properties, providing a comprehensive risk profile.\u003c/p\u003e \u003cp\u003eThird, the study extends Hidden Markov Model applications by identifying five distinct regimes rather than the binary or three-state configurations common in existing literature. The five-regime structure more accurately captures the multi-modal volatility distributions characteristic of cryptocurrency markets, improving predictive accuracy for regime transitions and enabling finer-grained position sizing decisions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec36\" class=\"Section2\"\u003e \u003ch2\u003e6.3. Practical Implications\u003c/h2\u003e \u003cp\u003eThe findings generate several actionable recommendations for portfolio management practice. First, the extreme risk concentration necessitates factor-based approaches that explicitly account for the dominant principal component. Traditional mean-variance optimization should be abandoned in favor of risk parity or minimum variance strategies that do not rely on return forecasts. Hedging strategies should focus on the first principal component rather than individual asset exposures.\u003c/p\u003e \u003cp\u003eSecond, position sizing algorithms must incorporate the 1.5\u0026times; capital requirement identified for equivalent risk reduction compared to diversified portfolios. This implies that target allocations should be scaled by 0.67 relative to conventional portfolio weights, maintaining equivalent risk exposure with reduced capital deployment.\u003c/p\u003e \u003cp\u003eThird, regime probability monitoring systems should implement graduated position reduction protocols. Specifically, when stress regime probability exceeds 0.20, portfolios should reduce exposure to 70% of target; at 0.30 probability, reduce to 50%; and at 0.40 probability, reduce to 30%. This graduated approach balances the costs of false signals against the benefits of preemptive action.\u003c/p\u003e \u003cp\u003eFourth, rebalancing frequencies should account for the 20.8-day volatility half-life. Traditional monthly rebalancing may be insufficient given the extended persistence of volatility shocks. Weekly rebalancing provides better alignment with empirical shock dissipation rates, particularly for assets with persistence exceeding 0.95.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec37\" class=\"Section2\"\u003e \u003ch2\u003e6.4. Limitations and Future Research\u003c/h2\u003e \u003cp\u003eSeveral avenues for future research emerge from this study. First, extension to alternative asset classes would assess the generalizability of findings beyond cryptocurrency markets. Application to equities, fixed income, commodities, and foreign exchange would determine whether extreme risk concentration represents a cryptocurrency-specific phenomenon or a more general feature of high-volatility environments.\u003c/p\u003e \u003cp\u003eSecond, integration of machine learning techniques could enhance regime detection accuracy and shock classification precision. Recurrent neural networks and long short-term memory architectures may capture nonlinear dependencies inadequately represented by Gaussian HMM frameworks. Deep learning approaches to volatility forecasting could improve upon GARCH specifications when sufficient training data exists.\u003c/p\u003e \u003cp\u003eThird, incorporation of external covariates including macroeconomic indicators, market microstructure variables, and sentiment measures could improve regime prediction accuracy. The current framework relies exclusively on return and volatility patterns; augmentation with forward-looking indicators may enable earlier regime transition detection.\u003c/p\u003e \u003cp\u003eFourth, high-frequency implementations would assess framework scalability to intraday timeframes. The current daily frequency analysis may miss important regime transitions occurring within trading sessions. Adaptation to five-minute or hourly data could enable real-time risk monitoring and automated position adjustment systems.\u003c/p\u003e \u003cp\u003eFinally, development of production engineering-specific risk measures analogous to manufacturing quality indicators could facilitate cross-industry comparison and benchmark establishment. Measures such as process capability indices, defect rates, and six-sigma levels have clear parallels in financial risk management but require appropriate translation and validation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec38\" class=\"Section2\"\u003e \u003ch2\u003e6.5. Concluding Remarks\u003c/h2\u003e \u003cp\u003eThis study demonstrates the viability and value of applying production engineering methodologies to financial portfolio management under conditions of extreme uncertainty. The integrated framework successfully addresses critical limitations of existing approaches, providing actionable insights for resource allocation, position sizing, and dynamic hedging strategies. The extreme risk characteristics identified in cryptocurrency portfolios underscore the inadequacy of traditional risk management approaches and validate the need for production engineering perspectives emphasizing reliability, redundancy, and adaptive control. As financial markets continue evolving toward greater complexity and interconnection, production engineering frameworks will become increasingly essential for effective risk management in complex systems.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eEthical Approval and Consent to Participate\u003c/p\u003e\n\u003cp\u003eThis study did not involve human participants, human data, human tissue, or animals. Therefore, ethical approval and consent to participate are not applicable to this work.\u003c/p\u003e\n\u003cp\u003eConsent for Publication\u003c/p\u003e\n\u003cp\u003eNot applicable. This manuscript does not contain any individual person\u0026apos;s data in any form, including individual details, images, or videos.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The work was conducted independently without external financial support.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request. All relevant data supporting the findings of this study are included within the manuscript and its supplementary information files.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716\u0026ndash;723.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAliyev, F., Ajayi, R., \u0026amp; Gasim, N. (2020). Modelling asymmetric market volatility with univariate GARCH models: Evidence from Nasdaq-100. 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Using daily stock returns: The case of event studies. Journal of Financial Economics, 14(1), 3\u0026ndash;31.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCelestin, M. (2025). Principal Component Analysis for simplifying multivariate financial data in portfolio risk analysis. Brain Journal, 25(4), 172\u0026ndash;179.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChristoffersen, P. F. (2012). Elements of Financial Risk Management (2nd ed.). Academic Press.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDavies, D. L., \u0026amp; Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1(2), 224\u0026ndash;227.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDing, C., \u0026amp; He, X. (2004). K-means clustering via principal component analysis. Proceedings of the Twenty-First International Conference on Machine Learning, Banff, Canada.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDing, Z., \u0026amp; Granger, C. W. J. (1996). Modeling volatility persistence of speculative returns: A new approach. Journal of Econometrics, 73(1), 185\u0026ndash;215.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEngle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica, 50(4), 987\u0026ndash;1008.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHartigan, J. A., \u0026amp; Wong, M. A. (1979). Algorithm AS 136: A K-means clustering algorithm. Journal of the Royal Statistical Society, Series C, 28(1), 100\u0026ndash;108.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuynh, T. L. D., Burggraf, T., \u0026amp; Wang, M. (2020). Gold, platinum, and expected Bitcoin returns. 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Psychometrika, 18(4), 267\u0026ndash;276.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eU, J., Yun, I., Jong, H., \u0026amp; Rim, W. (2024). Portfolio optimization based on K-means clustering and particle swarm optimization using financial statements and stock price data. SSRN Electronic Journal.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eViterbi, A. J. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2), 260\u0026ndash;269.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang, H., Lin, Y., \u0026amp; Mikhelson, I. (2020). Regime-switching factor investing with Hidden Markov models. Journal of Financial Data Science, 13(12), 311\u0026ndash;328.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu, D., Wang, X., \u0026amp; Su, J. (2022). Construction of stock portfolios based on k-means clustering of continuous trend features. Knowledge-Based Systems, 252, 109324.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Risk management, portfolio optimization, production engineering, Hidden Markov Models, principal component analysis, GARCH models, network analysis, regime detection, cryptocurrency","lastPublishedDoi":"10.21203/rs.3.rs-8771826/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8771826/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a comprehensive risk management framework for complex systems, applying production engineering methodologies to cryptocurrency portfolio optimization. The framework integrates principal component analysis, K-means clustering, Hidden Markov Model regime detection, structural shock decomposition, network causality analysis, GARCH volatility modeling, and stationarity testing to provide a multifaceted approach to risk assessment and decision support. Analysis of fourteen cryptocurrency assets over a multi-year period reveals extreme risk concentration with 67.89% of portfolio variance explained by the first systematic factor, six distinct operational clusters, and five market regimes with volatility ratios reaching 6.91\u0026times;. The study identifies supply chain disruption events as the primary source of negative abnormal returns, averaging negative 9.2%, while network analysis reveals hierarchical information transmission structures with Ethereum and Bitcoin as dominant hubs. GARCH modeling demonstrates mean volatility persistence of 0.938 with half-lives averaging 20.8 days. These findings validate return-based methodologies and provide actionable insights for resource allocation, position sizing, and dynamic hedging strategies in high-volatility environments. The framework establishes a foundation for production engineering approaches to financial risk management under extreme uncertainty.\u003c/p\u003e","manuscriptTitle":"Risk Management Framework for Complex Systems: A Production Engineering Approach to Cryptocurrency Portfolio Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-11 11:08:01","doi":"10.21203/rs.3.rs-8771826/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f09ecce3-3505-47d7-b290-78d00a73fe91","owner":[],"postedDate":"February 11th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-14T10:38:24+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-11 11:08:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8771826","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8771826","identity":"rs-8771826","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}