Search Results (53)

This paper introduces a new framework for high-dimensional covariance matrix estimation, the Blockwise Exponential Covariance Model (BECM), which extends the traditional block-partitioned representation to the log-covariance domain. By exploiting the block-preserving properties of the matrix logarithm and exponential transformations, the proposed model guarantees strict positive definiteness while substantially reducing the number of parameters to be estimated through a blockwise log-covariance parameterization, without imposing any rank constraint. Within each block, intra- and inter-group dependencies are parameterized through interpretable coefficients and kernel-based similarity measures of factor loadings, enabling a data-driven representation of nonlinear groupwise associations. Using monthly stock return data from the U.S. stock market, we conduct extensive rolling-window tests to evaluate the empirical performance of the BECM in minimum-variance portfolio construction. The results reveal three main findings. First, the BECM consistently outperforms the Canonical Block Representation Model (CBRM) and the native 1/N benchmark in terms of out-of-sample Sharpe ratios and risk-adjusted returns. Second, adaptive determination of the number of clusters through cross-validation effectively balances structural flexibility and estimation stability. Third, the model maintains numerical robustness under fine-grained partitions, avoiding the loss of positive definiteness common in high-dimensional covariance estimators. Overall, the BECM offers a theoretically grounded and empirically effective approach to modeling complex covariance structures in high-dimensional financial applications. Full article

Accurately forecasting the dynamic linkages among carbon, energy, and stock markets is essential for effective risk management and the design of energy transition strategies. This study proposes a BOHB-optimized Multivariable Graph Neural Network (BOHB-MSGNN) framework to forecast dynamic correlations derived from a DCC-GARCH model. Using data from the EU ETS market and related energy and stock markets, we document strong and persistent interconnectedness across markets, with the carbon market exhibiting the closest linkage to natural gas, followed by coal, stocks, and oil. Moreover, the proposed BOHB-MSGNN model significantly outperforms benchmark models in predicting dynamic risk correlations across multiple error metrics, owing to its ability to capture both intra-series and inter-series dependencies. Minimum-variance portfolios based on predicted correlations achieve returns similar to those using realized correlations. Forecasts also suggest a moderate decline in future correlations, highlighting diversification opportunities. These results offer practical implications for portfolio allocation, risk management, and carbon market policy. Full article

The optimal allocation of funds within a portfolio is a central research focus in finance. Conventional mean-variance models often concentrate a significant portion of funds in a limited number of high-risk assets. To promote diversification, Shannon Entropy is widely applied. This paper develops a portfolio optimization model that incorporates Shannon Entropy alongside a risk diversification principle aimed at minimizing the maximum individual asset risk. The study combines empirical analysis with numerical simulations. First, empirical data are used to assess the theoretical model’s effectiveness and practicality. Second, numerical simulations are conducted to analyze portfolio performance under extreme market scenarios. Specifically, the numerical results indicate that for fixed values of the risk balance coefficient and minimum expected return, the optimal portfolios and their return distributions are similar when the risk is measured by standard deviation, absolute deviation, or standard lower semi-deviation. This suggests that the model exhibits robustness to variations in the risk function, providing a relatively stable investment strategy. Full article

This paper evaluates the performance and portfolio role of Artificial Intelligence (AI) and Blockchain exchange-traded funds (ETFs) based on monthly returns from 2010 to 2025. The findings show that both AI and Blockchain ETFs generate positive alpha and high standalone returns but also display considerable drawdown risk. Their weak correlations with each other and with broad indices highlight diversification benefits, particularly when combined with U.S. benchmarks. Portfolio optimization reveals that Global Minimum Variance (GMV) and Tangency portfolios ascribe lower weights to these ETFs, while Risk Parity portfolios have a more balanced exposure, helping to diversify risks. Efficient frontier analysis highlights that the inclusion of AI and Blockchain ETFs improves the attainable risk–return profiles, even if they are not a dominant allocation. The findings stress that AI and Blockchain ETFs are suitable as satellite holdings. When applied judiciously, they offer the potential to improve diversification and risk-adjusted performance; however, concentrated bets subject investors to undue downside risks. Positioning portfolios around broad-based indices and overlaying modest thematic tilts emerges as a prudent approach to capturing innovation-driven upsides without compromising long-term portfolio resilience. Full article

Most reinforcement learning (RL) methods for portfolio optimization remain limited to single markets and a single algorithmic paradigm, which restricts their adaptability to regime shifts and heterogeneous conditions. This paper introduces a generalized version of the Modular Portfolio Learning System (MPLS), extending beyond its initial PPO backbone to integrate four RL algorithms: Proximal Policy Optimization (PPO), Deep Q-Network (DQN), Deep Deterministic Policy Gradient (DDPG), and Soft Actor-Critic (SAC). Building on its modular design, MPLS leverages specialized components for sentiment analysis, volatility forecasting, and structural dependency modeling, whose signals are fused within an attention-based decision framework. Unlike prior approaches, MPLS is evaluated independently on three major equity indices (S&P 500, DAX 30, and FTSE 100) across diverse regimes including stable, crisis, recovery, and sideways phases. Experimental results show that MPLS consistently achieved higher Sharpe ratios—typically +40–70% over Minimum Variance Portfolio (MVP) and Risk Parity (RP)—while limiting drawdowns and Conditional Value-at-Risk (CVaR) during stress periods such as the COVID-19 crash. Turnover levels remained moderate, confirming cost-awareness. Ablation and variance analyses highlight the distinct contribution of each module and the robustness of the framework. Overall, MPLS represents a modular, resilient, and practically relevant framework for risk-aware portfolio optimization. Full article

The present research proposes a methodology for portfolio construction that integrates the Black–Litterman model with expected returns generated through simulations under dynamic Capital Asset Pricing Model (CAPM) with conditional betas, estimated via Approximate Bayesian Computation Markov Chain Monte Carlo (ABC-MCMC). Bayesian estimation enables the incorporation of volatility regimes and the adjustment of each asset’s sensitivity to the market, thereby delivering expected returns that more accurately reflect the structural state of the assets compared to historical methods. This strategy is applied to the United States stock market, and the results suggest that the Black–Litterman portfolio performs competitively against portfolios optimised using the classic Markowitz model, even maintaining the same fixed weights throughout the month. Specifically, it has been demonstrated to outperform the minimum variance portfolio with regard to cumulative return and attains a Sharpe ratio that approaches the Markowitz maximum Sharpe portfolio, although it does so with a distinct and more concentrated asset allocation. It has been observed that, while the maximum return portfolio attains the highest absolute profit, it does so at the expense of significantly higher volatility. Full article

This study is designed to investigate the dynamic risk transmission processes between clean energy ETFs and ESG indices in the BRICS countries—Brazil, India, China, and South Africa—while excluding Russia due to the lack of consistent data availability during the study period, which coincides with the Russia–Ukraine conflict. The analysis is conducted on daily data obtained from DataStream, spanning from 27 October 2021 to 5 January 2024. By applying a time-varying parameter vector autoregression (TVP-VAR) modeling framework, we considered examining the global market conditions and economic shocks’ effects on these indices’ interconnectedness, including COVID-19 and geopolitical tensions. In this context, clean energy ETFs turned out to stand as net shock transmitters throughout volatile market spans, while ESG indices proved to act as net receivers. Moreover, we undertook to estimate both of the minimum variance and minimum connectedness portfolios’ hedging efficiency and performance. The findings highlight that introducing clean energy indices into investment strategies helps boost financial outcomes while maintaining sustainability goals. Indeed, the minimum connectedness portfolio consistently delivers superior risk-adjusted returns across varying market circumstances. In this respect, the present study provides investors, regulators, and policymakers with practical insights. Investors may optimize their portfolios by integrating clean energy and ESG indexes, useful for achieving financial and sustainability aims. Similarly, regulators might apply the findings to establish reliable green investment norms and strategies. Thus, this work underscores the crucial role of dynamic portfolio management in optimizing risk and return in the globally evolving green economy. Full article

In this study, we investigate the return propagation mechanism, hedging effectiveness, and portfolio performance across several common agricultural commodities, crude oil, and S&P 500 index, ranging from July 2000 to June 2024 by using a time-varying parameter vector autoregression (TVP-VAR) connectedness approach and three common multiple assets portfolio optimization strategies. The empirical results show that, the total connectedness peaked during the 2008 global financial crisis, followed by the European debt crisis and the COVID-19 pandemic, while it remained relatively lower at the onset of the Russia-Ukraine conflict. In the transmission mechanism, commodities and S&P 500 index exhibit distinct and dynamic characteristics as transmitters or receivers. Portfolio analysis reveals that, with exception of the COVID-19 pandemic, all three dynamic portfolios outperform the S&P 500 benchmark across major global crises. Additionally, the minimum correlation and minimum connectedness strategies are superior than transitional minimum variance method in most scenarios. Our findings have implications for policymakers in preventing systemic risk, for investors in managing portfolio risk, and for farmers and agribusiness enterprises in enhancing economic benefits. Full article

This study examined the dynamic interconnectedness and portfolio implications within the cryptocurrency ecosystem, focusing on five representative digital assets across the core functional categories: Layer 1 cryptocurrencies (Bitcoin (BTC) and Ethereum (ETH)), decentralized finance (Uniswap (UNI)), stablecoins (Dai), and crypto infrastructure tokens (Maker (MKR)). Using the Extended Joint Connectedness Approach within a Time-Varying Parameter VAR framework, the analysis captured time-varying spillovers of return shocks and revealed a heterogeneous structure of systemic roles. Stablecoins consistently acted as net absorbers of shocks, reinforcing their defensive profile, while governance tokens, such as MKR, emerged as persistent net transmitters of systemic risk. Foundational assets like BTC and ETH predominantly absorbed shocks, contrary to their perceived dominance. These systemic roles were further translated into portfolio design, where connectedness-aware strategies, particularly the Minimum Connectedness Portfolio, demonstrated superior performance relative to traditional variance-based allocations, delivering enhanced risk-adjusted returns and resilience during stress periods. By linking return-based systemic interdependencies with practical asset allocation, the study offers a unified framework for understanding and managing crypto network risk. The findings carry practical relevance for portfolio managers, algorithmic strategy developers, and policymakers concerned with financial stability in digital asset markets. Full article

This study investigates portfolio optimization for SET50 stocks using Deep Reinforcement Learning (DRL) algorithms to address market volatility. Five DRL algorithms—Advantage Actor–Critic (A2C), Proximal Policy Optimization (PPO), Deep Deterministic Policy Gradient (DDPG), Soft Actor–Critic (SAC), and Twin Delayed DDPG (TD3)—were evaluated for their effectiveness in managing risk and optimizing returns. We propose an Iterative Model Combining Algorithm (IMCA) that dynamically adjusts model weights based on market conditions to enhance performance. Our results demonstrate that IMCA consistently outperformed traditional strategies, including the Minimum Variance model. IMCA achieved a cumulative return of 14.20% and a Sharpe Ratio of 0.220, compared to the Minimum Variance model’s return of −4.35% and Sharpe Ratio of 0.018. This research highlights the adaptability and robustness of DRL algorithms for portfolio management, particularly in emerging markets like Thailand. It underscores the advantages of dynamic, data-driven strategies over static approaches. Full article

The portfolio selection problem has been a central focus in financial research. A complete portfolio selection process includes two stages: stock pre-selection and portfolio optimization. However, most existing studies focus on portfolio optimization, often overlooking stock pre-selection. To address this problem, this paper presents a novel two-stage approach that integrates deep learning with portfolio optimization. In the first stage, we develop a stock trend prediction model for stock pre-selection called the AGC-CNN model, which leverages a convolutional neural network (CNN), self-attention mechanism, Graph Convolutional Network (GCN), and k-reciprocal nearest neighbors (k-reciprocal NN). Specifically, we utilize a CNN to capture individual stock information and a GCN to capture relationships among stocks. Moreover, we incorporate the self-attention mechanism into the GCN to extract deeper data features and employ k-reciprocal NN to enhance the accuracy and robustness of the graph structure in the GCN. In the second stage, we employ the Global Minimum Variance (GMV) model for portfolio optimization, culminating in the AGC-CNN+GMV two-stage approach. We empirically validate the proposed two-stage approach using real-world data through numerical studies, achieving a roughly 35% increase in Cumulative Returns compared to portfolio optimization models without stock pre-selection, demonstrating its robust performance in the Average Return, Sharp Ratio, Turnover-adjusted Sharp Ratio, and Sortino Ratio. Full article

Researchers usually specify risk aversion coefficients from 1 (lowest) to M (highest) for a portfolio to indicate active or passive approaches. How effective is this practice? Recent studies suggest that the global minimum variance portfolio (GMVP) is statistically equivalent to portfolios with extensive risk aversion coefficients (the GMVP-equivalent). Expressing the risk aversion coefficient as a Taylor series of the target return and efficient set constants, we generalize the previous result to the non-GMVP-equivalents and segment mean-variance portfolios according to a hierarchy of risk aversion coefficients. In this paper, we show that hierarchical risk aversion coefficients are superior to isometric attributes. Full article

FinTech stocks are an important new asset class that reflects the rapidly growing FinTech sector. This paper studies the practical implications of using gold, silver, and basket-of-precious-metals (gold, silver, platinum, palladium) ETFs to diversify risk in FinTech stocks. Downside risk reduction is estimated using relative risk ratios based on CVaR. The analysis shows that gold provides the most downside risk protection. For a 5% CVaR, a 30% portfolio weight for gold reduces the downside risk by about 25%. The minimum variance and minimum correlation three-asset (FinTech, gold, and silver) portfolios (with portfolio weights estimated using a TVP-VAR model) have the highest risk-adjusted returns (Sharpe ratio, Omega ratio) followed by the fixed-weight FinTech and gold portfolio. These results show the benefits of diversifying an investment in FinTech stocks with precious metals. These results are robust to weekly or monthly portfolio rebalancing and reasonable transaction costs. Full article

In this study, we apply a novel approach of portfolio diversification—the robust maximum diversified (RMD)—to a small and developing economy’s stock market. Using monthly returns data from August 2019 to May 2024 of 18/19 stocks listed on Fiji’s South Pacific Stock Exchange (SPX), we construct the RMD portfolio and simulate with additional constraints. To implement the RMD portfolio, we replace the covariance matrix with a matrix comprising unexplained variations. The RMD procedure diversifies weights, and not risks, hence we need to run a pairwise regression between two assets (stocks) and extract the R-square to create a P-matrix. We compute each asset’s beta using the market-weighted price index, and the CAPM to calculate market-adjusted returns. Next, together with other benchmark portfolios (1/N, minimum variance, market portfolio, semi-variance, maximum skewness, and the most diversified portfolio), we examine the expected returns against the risk-free (RF) rate. From the simulations, in terms of expected return, we note that eight portfolios perform up to the RF rate. Specifically, for returns between 4 and 5%, we find that max. RMD with positive Sharpe and Sortino (as constraints) and the most diversified portfolio offer comparable returns, although the latter has slightly lower standard deviation and downside volatility and contains 94% of all the stocks. Portfolios with returns between 5% and the RF rate are the minimum-variance, the semi-variance, and the max. RMD with positive Sharpe; the latter coincides with the RF rate and contains the most (94%) stocks compared to the other two. An investor with a diversification objective, some risk tolerance and return preference up to the RF rate can consider the max. RMD with positive Sharpe. However, depending on the level of risk-averseness, the minimum-variance or the semi-variance portfolio can be considered, with the latter having lower downside volatility. Two portfolios offer returns above the RF rate—the market portfolio (max. Sharpe) and the maximum Sortino. Although the latter has the highest return, this portfolio is the least diversified and has the largest standard deviation and downside volatility. To achieve diversification and returns above the RF rate, the market portfolio should be considered. Full article

An efficient and effective portfolio provides maximum return potential with minimum risk by choosing an optimal balance among assets. Therefore, the objective of this study is to analyze the performance of optimized portfolios in minimizing risk and achieving maximum returns in the dynamics of Timor-Leste’s equity portfolio in the international capital market for the period from January 2006 to December 2019. The empirical findings of this study indicate that the correlation matrix showed that JPM has a very strong positive correlation with one of the twenty assets, namely BAC (0.80). Moreover, the optimal portfolio of the twenty stocks exceeding 10% consists of four consecutive stocks, namely DGE.L (10.69%), NSRGY (10.37%), JPM (10.04%), and T (10.03%). In addition, the minimum portfolio consists of two stocks with a minimum variance of more than 10%, namely SAP.DE (11.20%) and DGE.L (10.39%). The evaluation of the optimal portfolio using Markowitz parameters also showed that the highest expected return and the lowest risk were 1.22% and 3.12%, respectively. Full article