uncertainty
Iman Ebrahimi; Hadi Mokhtari; Mohammad Taghi Rezvan
Abstract
In today’s world, investment in the cryptocurrency market is regarded as one of the most attractive yet high-risk opportunities. Given the rapid growth of this market and its impact on the global economy, examining the importance and challenges associated with cryptocurrency investments is essential. ...
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In today’s world, investment in the cryptocurrency market is regarded as one of the most attractive yet high-risk opportunities. Given the rapid growth of this market and its impact on the global economy, examining the importance and challenges associated with cryptocurrency investments is essential. This paper, as a novel contribution, simultaneously explores the design of a cryptocurrency portfolio and the subsequent optimal allocation of investments in this market, considering both risk and return. In the first stage, the focus is on constructing a portfolio in the cryptocurrency market using relevant indices. After forming this initial portfolio, capital allocation is optimized. This approach allows for the creation of a portfolio that aligns with the investor’s risk preferences while also considering passive portfolio management. In the second stage, equally weighted portfolios are created relative to the market portfolio, as well as other portfolios selected based on criteria such as the highest market capitalization and the best risk-return ratios, using the Markowitz, Sharpe, and Sortino models. For the optimal allocation of these portfolios, metaheuristic algorithms based on particle swarm optimization are employed. The results show that portfolios including cryptocurrencies with the highest market capitalization exhibit lower risk, and the strategy based on the Sharpe model outperforms the other models.IntroductionThe rapid evolution of cryptocurrency markets has created both opportunities and challenges for investors. Unlike traditional assets, cryptocurrencies are highly volatile, decentralized, and driven by technological innovations such as blockchain. These unique features demand new approaches to portfolio design and optimization. Traditional models, such as Markowitz’s mean-variance theory, provide valuable foundations but are insufficient for capturing the complexity of crypto markets. Recent advances in heuristic and metaheuristic optimization have introduced promising tools to address these challenges. This study contributes by integrating portfolio formation with optimal allocation strategies while considering both risk and return. By employing passive management approaches alongside advanced optimization models, it seeks to create robust portfolios that reflect investors’ preferences. The research particularly emphasizes evaluating the performance of different models, including Markowitz, Sharpe, and Sortino, in combination with metaheuristic methods, offering practical insights for effective decision-making in cryptocurrency investments.Research BackgroundPortfolio optimization has long been a central topic in financial management, evolving from classical mean-variance models to more advanced risk-adjusted approaches. With the emergence of cryptocurrencies, scholars have increasingly focused on adapting these models to highly volatile, fast-growing markets. Prior studies have explored strategies such as equal-weight portfolios, maximum Sharpe ratio, and risk-parity allocations, often with mixed results. Additionally, machine learning and heuristic methods, including genetic algorithms and deep learning, have been applied to enhance prediction and asset allocation. However, most research addresses either portfolio formation or allocation optimization in isolation. A gap remains in simultaneously considering both aspects under realistic conditions. Furthermore, studies on passive portfolio management in cryptocurrency markets are limited. This research addresses these gaps by combining index-based portfolio construction with optimal allocation through particle swarm optimization (PSO), benchmarking results against classical genetic algorithms and well-established financial models.MethodThe study employs a two-stage methodology. First, cryptocurrency portfolios are constructed using different strategies: market index portfolios, equally weighted portfolios, and portfolios based on criteria such as the highest market capitalization and superior return-to-risk ratios. These portfolios are then evaluated using three established financial models: Markowitz’s mean-variance, Sharpe ratio, and Sortino ratio. In the second stage, the allocation of assets within each portfolio is optimized using the particle swarm optimization (PSO) algorithm, chosen for its ability to handle non-linear, NP-hard optimization problems. The PSO implementation is fine-tuned to balance exploration and exploitation, ensuring reliable convergence. To validate robustness, results are compared against those obtained from classical genetic algorithms. Data on the top 50 cryptocurrencies were collected from CRIX and Yahoo Finance over multiple horizons (30, 90, 180, and 365 days). Key performance metrics include return, variance, standard deviation, and risk-adjusted ratios, providing a comprehensive view of portfolio efficiency.Discussion and ResultsThe findings indicate that portfolios composed of cryptocurrencies with the highest market capitalization consistently exhibit lower risk levels compared to alternatives. Among the evaluation models, the Sharpe-based strategy outperformed others, delivering superior risk-adjusted returns. The Sortino model also proved effective in emphasizing downside risk, aligning with investor concerns in volatile markets. Conversely, some Markowitz-based portfolios produced higher variance, highlighting the limitations of variance as a sole risk measure in cryptocurrency investments. Across different time horizons, return-to-standard deviation ratios provided robust selection criteria, particularly when optimized through PSO. Comparisons with the genetic algorithm demonstrated PSO’s efficiency in convergence and accuracy, especially in capturing optimal weight distributions. The results suggest that integrating metaheuristic optimization with traditional financial models significantly improves portfolio performance. Overall, evidence supports the importance of market capitalization and model choice in shaping effective investment strategies, with PSO-based Sharpe optimization yielding the most promising outcomes.ConclusionThis research demonstrates that simultaneous portfolio formation and optimal allocation, when supported by advanced optimization techniques, can effectively balance risk and return in cryptocurrency investments. Portfolios weighted toward large-cap cryptocurrencies proved less risky, while the Sharpe model consistently delivered superior outcomes compared to Markowitz and Sortino. The application of particle swarm optimization enabled efficient identification of optimal weights, outperforming classical genetic algorithms in accuracy and stability. Importantly, the study highlights the relevance of passive portfolio management strategies in volatile digital markets, providing investors with practical tools to mitigate risks while maximizing returns. The findings emphasize the necessity of adopting scientific, data-driven methods rather than speculative approaches in crypto trading. Future research may extend this work by incorporating multi-objective optimization, hybrid algorithms, or alternative risk measures, offering deeper insights into dynamic portfolio strategies in evolving digital financial ecosystems.
