ABSTRACT Using a textâbased measure of peer opinions constructed from cryptocurrencyârelated social media posts, we find that peer opinions contain valuable information about the prices of cryptocurrency options. Bitcoin options exhibit a volatility smile, which becomes steeper when peer opinions become bearish. The riskâneutral skewness of Bitcoin returns implied by options prices becomes more negative in times of bearish opinions. The predictability of peer opinions for Bitcoin option prices remains robust after controlling for momentum, volatility, demand pressures, news effects, and other sentiment measures, and exhibits no evidence of reversal over time. This effect is pronounced when Bitcoin attracts high investor attention, more diverse opinions about Bitcoin are expressed on social media, and Bitcoin options are more actively traded. We find similar results for Ethereum options.
Ferdous Ahmmed, Boakye Yam Boadi, Michael Guillemette
This study examined the relationship between margin trading and cryptocurrency investment using data from the 2018 and 2021 waves of the National Financial Capability Study (NFCS) Investor Survey. Guided by behavioral finance theory, which suggests that cognitive biases may influence risk-taking, the study explored whether margin loan use and margin calls are associated with higher cryptocurrency participation. Margin loans are inherently risky, as they must be repaid regardless of investment outcomes, and margin calls are triggered when an investorâs equity falls below a required threshold. The results showed a positive and statistically significant association between margin activity and cryptocurrency investment. Specifically, individuals with a margin loan were 17 percentage points more likely to invest in cryptocurrency, while those who have experienced a margin call were 23 percentage points more likely. Given the extreme volatility of cryptocurrencies, these results highlight the increased risks investors face when using leverage in speculative markets. The analysis is based on cross-sectional data from U.S. investors; therefore, the findings should be interpreted as correlational rather than causal.
Siang-Li Jheng, Alexandra Conda, Daniel Traian Pele, Wolfgang Karl Härdle
Abstract 2024 marks a significant milestone in integrating digital finance into the global financial landscape. The U.S. Securities and Exchange Commissionâs approval of Bitcoin and Ethereum ETFs signaled wider mainstream adoption. Shortly thereafter, Donald Trumpâs return to the presidency drove Bitcoin prices beyond $100,000. In light of these developments, we observe the rapid changes in cryptocurrency market prices, trends, and regulatory policies, which drive us to conduct a comprehensive review of cryptocurrencies assetâs literature and examine its robustness. Our study covers several themes: how cryptocurrencies fit into broader asset allocation strategies, techniques to create crypto-based indexes, current debates over speculative bubbles, and the evolution of valuation models to highlight the dual aspects of market opportunities and risks. Throughout our review, we compare previous studies with the latest data, seeking to determine which arguments continue to hold up and which require adjustment. Although digital assets have experienced multiple crashes, they often rebound more strongly than expected, making them a topic of intense debate among academics, regulators, and investors. We aim to assemble an organized summary of research findings, providing a comprehensive framework that unites historical evolution with recent shifts and future perspectives.
The adoption of cryptocurrency as a payment instrument by firms has sparked ongoing debates about how such strategic moves are perceived by key stakeholders. This study investigates how investors react when an e-commerce firm adds or withdraws from providing cryptocurrency as a payment option. To explore these aspects, we examine two cases: MercadoLibreâs decision to introduce Meli DĂłlar as a payment option, representing the inclusion of cryptocurrency, and eBayâs withdrawal from the Libra project, representing strategic exclusion. We assess the causal impact of these strategies by employing a Regression Discontinuity Design (RDD) and deriving the observation period by using an optimal bandwidth method. The results indicate that there was an immediate decline in share prices following the adoption of the Meli DĂłlar as a payment instrument and an immediate increase following the decision to withdraw from using Libra as a payment instrument. The findings suggest that including cryptocurrency as a payment method may run counter to investor expectations. This study contributes to the discourse on the viability of cryptocurrency adoption by e-commerce firms and emphasizes the importance of understanding how decisions around cryptocurrency convey market signals, which may have strategic implications for a firmâs overall strategy.
The popularity of cryptocurrencies as alternative investments has grown in recent years. However, it remains unclear whether cryptocurrency investors behave irrationally in a similar way to emerging market investors. Using a systematic literature review, this study aims to compare the factors related to the presence of behavioural biases in the cryptocurrency and emerging stock markets. This study highlights similarities and differences between cryptocurrency and emerging stock market investor behaviour. Thus, the study's novelty arises from comparing the role of behavioural inclinations in cryptocurrency and emerging stock markets. The findings indicate that the small amount or lack of available information about small-cap emerging stocks or cryptocurrencies may reinforce investor sentiment and herding behaviour. The herding behaviour among investors in both markets may stem from following the most popular investment trends. Investors in cryptocurrency and emerging stock markets also tend to overreact to market sentiment and changes in market conditions. Extreme market conditions may affect the strength of herding behaviour, disposition effect, price clustering, anomalous behaviour, investor sentiment and uncertainty. Thus, cryptocurrency and emerging stock markets are informationally inefficient most of the time, whilst investorsâ irrationality may be more pronounced during certain periods. Furthermore, investorsâ behaviour in the cryptocurrency and emerging stock markets is more consistent with the adaptive market hypothesis than the efficient market hypothesis. This research suggests that cryptocurrency and emerging stock market investors should actively manage investment portfolios. Policymakers should be more concerned about information accessibility and quality, especially in the case of small-cap investment assets. JEL codes: G14;G15;G41
This systematic meta-review analyzes over 75 papers (2020-2025) applying deep learning (DL) techniques to cryptocurrency trading, adhering to PRISMA guidelines. It evaluates various DL architectures, including LSTM, GRU, CNN, and Transformers, and finds that DL methods outperform traditional approaches in managing the high volatility and non-linear patterns of crypto markets. Key findings highlight the promise of hybrid and ensemble models, the benefits of integrating blockchain data, sentiment analysis, and macroeconomic factors for improved predictions, and the potential of deep reinforcement learning for developing autonomous trading strategies with risk-adjusted returns. However, challenges such as model interpretability, nonstationary data, and real-world deployment persist. The review emphasizes emerging directions like explainable AI (XAI) for transparent decision-making and high-frequency trading applications, providing a critical synthesis of methodologies, empirical results, and research gaps to inform both academic research and practical trading system development.
Susanna Levantesi, Gabriella Piscopo, Alba Roviello
Accurate estimation of cryptocurrency market volatility is crucial for investors. The Crypto Volatility Index (CVI) was developed to measure the marketâs expectations for the 30-day implied volatility of Bitcoin and Ethereum to address the growing demand for reliable predictions. This study explores the relationship between the CVI and the volatility of traditional financial markets, including the Gold Volatility Index (GVZ), the Crude Oil Volatility Index (OVX), and the S&P500 Volatility Index (VIX). Three other variables are also analyzed: the USD to EUR exchange rate (USDEUR), the Federal Reserve interest rate (FED), and the NASDAQ index. The aim of the research is explanatory: the input variables and the CVI are observed contemporaneously to catch the complex relation between them. Using Pearson correlation, distance correlation, and mutual information, we demonstrate the presence of non-linear relationships between some variables in the dataset. Explanatory analysis is conducted using machine learning techniques, specifically the Random Forest (RF) algorithm and Gradient Boosting Machines (GBM) to account for these potential non-linear interactions. These methods are better suited than standard linear models for identifying complex relationships. In particular, the RF algorithm reaches a better level of accuracy than GBM and avoids overfitting.
In this note, we make a comparison between a novel machine learning method, Long Short-Term Memory (LSTM), and two trading strategies using technical analysis: Exponential Moving Average (EMA) crossing and Moving Average Convergence/Divergence with Average Directional Index (MACD+ADX). The purpose is to use trading signals to maximize profits in the Bitcoin digital commodity. The comparison was motivated by the approval of the first spot Bitcoin exchange-traded funds (ETFs) by the U.S. Securities and Exchange Commission (SEC) on January 9, 2024. The results show that the LSTM algorithm delivers a cumulative return of approximately 65.23% over a testing period of less than nine months, significantly outperforming both the EMA and MACD+ADX strategies, as well as the baseline buy-and-hold approach typically followed by fundamental investors. Our work highlights the potential for further integration between machine learning and technical analysis in the evolving landscape of cryptocurrency markets.
Bitcoin's return volatility from 2014 to 2022 reveals significant changes in response to political and macroeconomic developments, particularly during the 2016 and 2020 U.S. presidential elections. In 2016, Bitcoin exhibited modest price movement and low volatility, while in 2020, the asset experienced dramatic price increases and heightened volatility, reflecting increased market maturity and institutional interest. Political uncertainty, regulatory shifts, and market sentiment played crucial roles in shaping volatility dynamics during these periods. Using GARCH(1,1) and EGARCH(1,1) models, time-varying volatility patterns and asymmetric effects of market shocks are analyzed. GARCH results confirm volatility clustering and high persistence, whereas EGARCH captures leverage effects, showing that negative shocks influence volatility more than positive ones. Visualizations of conditional variance support these findings, indicating that Bitcoin reacts more intensely to adverse news, especially during politically turbulent periods. Residual diagnostics suggest model adequacy and enhance the reliability of insights. These results underscore Bitcoin's evolving role as a financial asset increasingly affected by global events and investor sentiment, offering valuable implications for market participants and policymakers monitoring risk in cryptocurrency markets.
Hamdan Bukenya Ntare, John Weirstrass Muteba Mwamba, Franck AdĂŠkambi
There has been growing interest among investors to include cryptocurrencies in their portfolios because of their diversification potential. However, the diversification role of cryptocurrencies when added to South African bank equities is yet to be determined. This study rigorously evaluates asset co-movement and diversification benefits of integrating cryptocurrencies into South African bank equity portfolios. Using advanced financial engineering techniques, including multi-asset particle swarm optimizer (MA-PSO), random optimizer, and a static equal-weighted portfolio (EWP) model, this study analyzed the dynamic portfolio performance and diversification of cryptocurrencies in the 2017â2024 period. The portfolio performance of the three methods is also compared with the results from the traditional one-period meanâvariance optimization (MVO) method. The findings underscore the superiority of dynamic models over static EWP in assessing the impact of cryptocurrency inclusion in bank equity portfolios. While pre-COVID-19 studies identified cryptocurrencies as effective hedges against market downturns, this protective role appears attenuated in the post-COVID-19 era. The dynamic MA-PSO model emerges as the optimal approach, delivering better-diversified portfolios. Consequently, South African portfolio managers must carefully evaluate investor risk tolerance before incorporating cryptocurrencies, with regulators imposing stringent guidelines to mitigate potential losses.
This study examines the temporary impact of major global news on bitcoin absolute price changes from 2018 to 2023, focusing on information related to the COVID-19 pandemic, inflation, and the Russia-Ukraine conflict. Using Bloomberg news and high-frequency data, the analysis is conducted in two stages. First, hourly price data and only highly significant news are analysed over the entire period. Second, second-by-second data from the CME Bitcoin Real Time Index (BRTI) is employed for key dates, incorporating broader news categories. The results show that bitcoin investors need approximately 45 minutes to process each news item on COVID-19 and war as information continuously flows into the market. This constant information processing enables investors to anticipate highly significant news on these topics up to two hours before its publication. Conversely, inflation-related news exhibits concentrated effects around scheduled release times. The findings highlight the necessity of selecting appropriate time frequencies for the analysis to avoid misinterpretation. Overall, the study highlights the significant impact that relevant global news has on bitcoin price volatility, suggesting that bitcoin markets are becoming increasingly integrated with traditional financial markets.
Purpose: This study aims to examines advanced portfolio management techniques using Long Short-Term Memory (LSTM) networks, the study was applied to investing in cryptocurrencies whose markets are characterized by high-frequency trading, and using behavioral finance models based on the concept of return-risk and deep learning based on the work of artificial neural networks (ANN) and long-term memory (LSTM) algorithms Design/Methodology/Approach: This study adopts quantitative approach. Moreover, A random portfolio consisting of 25 cryptocurrencies was selected based on the database of the website: https://finance.yahoo.com/crypto/ during the period 2021-2024 AD and programming the Python language. And an attempt to evaluate the performance of the models used in accurately predicting the optimal relative weights of the investment portfolio, which proved the relative effectiveness of deep learning models by estimating the values of the mean square error (MSE) at a level of 0.0218% to predict the optimal portfolio weights for 5 days based on training 80% and testing 20% of the study data. Findings: The second hypothesis of this study was accepted, which states the effectiveness of deep learning algorithms to predict the weights of optimal portfolios with a return estimated at 1.7239% and a risk of 1.1219% and a Sharpe index value estimated at 1.5365%, while the Markowitz return-risk model portfolio came with a return rate estimated at 31.15% and a risk of 39.05%. With no diversification of investment on all portfolio assets and a Sharpe index value of 0.7978%. Practical Implications: This study provides important insights that machine learning offers significant advantages in portfolio optimization, from improved forecasting of asset returns to dynamic rebalancing, better risk management, and automation. The ability to handle high-dimensional, non-linear, and non-stationary data makes ML an ideal tool for optimizing portfolios in complex and fast-moving markets; especially in cryptocurrency markets. However, challenges like data quality, overfitting, and interpretability must be addressed to ensure effective deployment of ML in real-world portfolio. Originality/Value: This study provides an original and timely contribution to understanding the use of deep learning for portfolio optimization represents a significant advancement over traditional financial models by offering several original and valuable benefits. These include the ability to capture complex non-linear relationships, dynamic rebalancing in response to real-time data, processing of unstructured data (like sentiment analysis), advanced risk management, and the integration of high-dimensional data. The combination of these capabilities enables more accurate, adaptive, and robust portfolio optimization, ultimately enhancing portfolio performance and reducing risk.
A common assumption in cryptocurrency markets is a positive relationship between total-value-locked (TVL) and cryptocurrency returns. To test this hypothesis we examine whether the returns of TVL-sorted portfolios can be explained by common cryptocurrency factors. We find evidence that portfolios formed on TVL exhibit returns that are linear functions of aggregate crypto market returns, that is they can be replicated with appropriate weights on the crypto market portfolio. Thus, strategies based on TVL can be priced with standard asset pricing tools. This result holds true both for total TVL and a simple TVL measure that removes a number of ways TVL may be overstated.
Traditional portfolio optimization techniques predominantly rely on the classical meanâvariance framework introduced by Markowitz, which focuses on balancing expected returns against risk, typically measured by variance. However, in volatile and structur-ally unstable markets such as cryptocurrencies, this approach often fails to capture the full spectrum of uncertainty and diversification potential. This paper introduces an al-ternative methodology grounded in entropy, a fundamental concept in information theory that quantifies uncertainty and disorder. By incorporating entropy into the portfolio optimization process, we offer a more generalizable, distribution-free approach that enhances diversification and resilience.We develop and analyze three distinct en-tropy-based models: the maximum Shannon entropy model, the second-order entropy (Tsallis) model, and the maximum weighted Shannon entropy model. These formula-tions extend the traditional meanâvariance approach by integrating nonlinear uncer-tainty measures, enabling a richer representation of investor preferences and asset in-terdependencies. Analytical solutions to the proposed models are derived using the method of Lagrange multipliers, ensuring mathematical rigor and interpretability.The proposed models are empirically validated using a portfolio composed of four leading cryptocurrenciesâBitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)âwith market data from January to March 2025. The case studies demonstrate how entropy-based optimization leads to well-diversified portfolios, robust under market turbulence and heavy-tailed return distributions. Notably, the models facilitate dynamic adjustments in asset allocation in response to shifts in returnârisk characteristics and entropy levels. This study contributes to the ongoing generalization of portfolio theory by positioning entropy as both a diversification enhancer and a structural risk measure. It provides theoretical insight, practical tools for asset allocation in high-volatility environments, and paves the way for future research in entropy-driven financial optimization frameworks.
In this paper, we design and implement a web crawler system based on the Solana blockchain for the automated collection and analysis of market data for popular non-fungible tokens (NFTs) on the chain. Firstly, the basic information and transaction data of popular NFTs on the Solana chain are collected using the Selenium tool. Secondly, the transaction records of the Magic Eden trading market are thoroughly analyzed by combining them with the Scrapy framework to examine the price fluctuations and market trends of NFTs. In terms of data analysis, this paper employs time series analysis to examine the dynamics of the NFT market and seeks to identify potential price patterns. In addition, the risk and return of different NFTs are evaluated using the mean-variance optimization model, taking into account their characteristics, such as illiquidity and market volatility, to provide investors with data-driven portfolio recommendations. The experimental results show that the combination of crawler technology and financial analytics can effectively analyze NFT data on the Solana blockchain and provide timely market insights and investment strategies. This study provides a reference for further exploration in the field of digital currencies.
Hong Qu, Krzysztof Gogol, Florian GrĂśtschla, Claudio J. Tessone
Decentralized Finance (DeFi) lending enables permissionless borrowing via smart contracts. However, it faces challenges in optimizing interest rates, mitigating bad debt, and improving capital efficiency. Rule-based interest-rate models struggle to adapt to dynamic market conditions, leading to inefficiencies. This work applies Offline Reinforcement Learning (RL) to optimize interest rate adjustments in DeFi lending protocols. Using historical data from Aave protocol, we evaluate three RL approaches: Conservative Q-Learning (CQL), Behavior Cloning (BC), and TD3 with Behavior Cloning (TD3-BC). TD3-BC demonstrates superior performance in balancing utilization, capital stability, and risk, outperforming existing models. It adapts effectively to historical stress events like the May 2021 crash and the March 2023 USDC depeg, showcasing potential for automated, real-time governance.
Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as MeanâVariance optimization, are effective, but often fail to account for diversification adequately. This study introduces the MeanâVarianceâEntropy (MVE) model, which integrates Tsallis entropy into the classic MeanâVariance framework to enhance portfolio diversification and risk management. Entropy, specifically second-order entropy, penalizes excessive concentration in the portfolio, encouraging a more balanced and diversified allocation of assets. The model is applied to a portfolio of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Cardano (ADA), and Binance Coin (BNB). The performance of the MVE model is compared with that of the traditional MeanâVariance model, and results demonstrate that the entropy-enhanced model provides better diversification, although with a slightly lower Sharpe ratio. The findings suggest that while the entropy-adjusted model results in a slightly lower Sharpe ratio, it offers better diversification and a more resilient portfolio, especially in volatile markets. This study demonstrates the potential of incorporating entropy into portfolio optimization as a means to mitigate concentration risk and improve portfolio performance. The approach is particularly beneficial for markets such as cryptocurrency, where volatility and asset correlations fluctuate rapidly. This paper contributes to the growing body of literature on portfolio optimization by offering a more diversified, robust, and risk-adjusted approach to asset allocation
Samet GĂźnay, Emrah Ä°smail Ăevik, Mehmet Fatih BuÄan, Sel DibooÄlu ¡ 5 authors
Abstract Utilizing blockchain technology is transforming traditional business practices into a new paradigm, giving rise to what we refer to as blockchained models. This paper uses wavelet coherence analysis to identify the connectedness of blockchained sectoral indices with Bitcoin and the Fear and Greed Index that represents investor sentiment in the cryptocurrency market. Results show persistent and positive correlations between sector returns and investor sentiment and sectoral return series lead investor sentiment. The relationship between Bitcoin and sectoral indices is consistent for return series and suggests an in-phase (positive) relationship between these variables at all frequencies. We usually have found negative correlations for the co-movements of investor sentiment and sectoral volatility, where investor sentiment leads to sector return volatilities. The application of blockchain technology across various sectors, coupled with the proliferation of altcoins, appears to drive distinct price developments in these cryptocurrency sectors. These developments are predominantly influenced by sentimental factors, often diverging from the trends of Bitcoin.
Maninder Singh, William Bjorndahl, Gagangeet Singh Aujla, Joseph Camp
In the era of continuously increasing demand for bandwidth and revolutionary wireless technologies, efficient spectrum management is essential. This paper proposes a novel multi-tier tokenization approach for dynamic spectrum management. Leveraging the concept of heterogeneous tokenization of spectrum bands, we develop a decentralized framework based on blockchain technology that enables the sharing of spectrum among users. The spectrum space is represented by multi-planes, the first plane consists of unique spectrum bands converted into NFTs for long-term allocations, while the second plane involves subdividing these NFT spectrum bands for short-term usage by retail users through fungible tokens. The fungible tokens are dynamically traded and mapped using particle swarm optimization (PSO) to manage demand and supply. The paper presents formal models of the involved entities and algorithms for creating multi-tier tokens, dynamic token trading and demand-supply mapping using PSO. To enhance privacy, a zero-knowledge proof (ZKP) based approach is employed for user authentication. The proposed framework offers a secure, transparent, and scalable solution for spectrum management, addressing the limitations of traditional centralized approaches. Simulation results demonstrate the effectiveness of the framework in dynamic spectrum access, while providing privacy-aware and scalable solutions suitable for future wireless networks, including 6G.
Abstract We use transaction-level data from the Bitcoin exchange Mt.Gox, including over 1.4 million transactions from more than 45,000 traders, to investigate the role of technical chart patterns in the early Bitcoin market from April 2011 to September 2013. Employing a pattern recognition algorithm, we identify hourly trading signals for five major chart patterns. Buy signals of these patterns are associated with an average increase in abnormal trading volume of more than 53%. Trades executed during buy signal periods yield significantly higher average returns than those made during non-signal periods. Traders who use chart patterns more frequently are more likely to generate right-skewed return distributions, engage in more active trading, and achieve higher average roundtrip returns. Our research suggests that chart pattern trading was a crucial tool for Mt.Gox clients, highlighting the importance of technical heuristics in shaping the dynamics in a less efficient and unregulated market environment. By leveraging a comprehensive transaction dataset from a major cryptocurrency exchange, we provide unique insights into the actual trading behavior of the first Bitcoin adopters. This sets our work apart from previous studies that mainly rely on backtesting technical strategies using publicly available price data.
Suwan Long, Ying Xie, Zhengyuan Zhou, Brian M. Lucey ¡ 5 authors
This paper examines the relationship between cryptocurrency market dynamics and investor sentiment, employing advanced techniques like time-variant Granger causality and asymmetric time-varying parameter vector autoregression (TVP-VAR) frequency connectivity. We create unique sentiment analysis tools, including a custom cryptocurrency sentiment lexicon, to deeply analyze content in the cryptocurrency domain, particularly focusing on investor discussions and viewpoints. Our findings demonstrate a significant, evolving link between market sentiment and cryptocurrency movements. A key observation is that the volatility of shock transmission is tightly connected to major market events, often influenced by large-scale investors, or âwhalesâ. Our study indicates that market sentiment consistently affects both short- and long-term cryptocurrency volatility, underlining the crucial influence of investor sentiment in driving the dynamics of the cryptocurrency market. This underscores the importance of understanding investor sentiment for predicting and navigating the cryptocurrency market.
The increasing interaction between the equity market and cryptocurrencies has raised concerns about volatility spillovers; however, empirical evidence about sectoral-specific spillover effects in emerging markets is scarce and hard to find. Existing research mainly concentrates on developed markets and aggregate equity indices, leaving a research gap in comprehending how sectoral indices variations impact market interactions in developing financial markets like Thailand. This article investigates the mean and volatility spillover effects between the Thai stock market and leading cryptocurrencies from April 2019 to April 2024. Applying bivariate VAR (1)-BEKK-GARCH (1,1) with an asymmetry model, this study examines the aggregate and sectoral-specific mean and volatility spillovers across major Thai stock market sectors. The findings reveal the significant mean spillover effect from cryptocurrencies to the Thai stock market with sectoral variation, while sectors such as industrials and financials exerted significant linkages, and the agricultural and food sector remains unaffected. Additionally, volatility spillovers were predominantly transmitted from the Thai equity market to cryptocurrency. Moreover, asymmetry effects were observed, with the asymmetry effects mainly transmitted from the Thai equity market to cryptocurrency. These findings provide critical insights for both individual and institutional investors on risk management and portfolio diversification while also helping policymakers with guidance on regulatory measures to mitigate systemic risks in emerging financial markets.
This paper provides the first empirical evidence of whether the introduction of US spot Bitcoin ETFs affected the returns and volatility of major cryptocurrencies. Using data from December 18, 2017 to March 15, 2024, we apply an event-study methodology within a GARCH-based framework. Our results reveal a significant effect of the introduction of spot Bitcoin ETFs on cryptocurrency returns and volatility. The analysis shows a positive impact for Bitcoin, Ethereum, and Litecoin spot price returns around the event date. The volatility of Bitcoin and Ripple spot markets decreased following the introduction of spot Bitcoin ETFs, which supports the stabilization hypothesis for these two cases. We also examine the volatility spillovers using a wavelet coherence approach, and reveal significant volatility spillovers from Grayscale Bitcoin ETF to Bitcoin futures and to a lesser extend to the Bitcoin spot market. Our findings enhance the limited understanding of the price discovery and functioning of the cryptocurrency markets, which could be useful for investors, regulators, and policymakers. ⢠Study the impact of introduction of Spot Bitcoin ETFs on the cryptocurrency market. ⢠Apply event study methodology within a GARCH framework. ⢠Find a positive impact for Bitcoin, Ethereum, and Litecoin spot price returns. ⢠Volatility of Bitcoin and Ripple decreased, supporting the stabilization hypothesis. ⢠Wavelet coherence analysis reveals volatility spillovers from Bitcoin ETF to Bitcoin futures.
Traditional portfolio optimization techniques predominantly rely on the classical meanâvariance framework introduced by Markowitz, which focuses on balancing expected returns against risk, typically measured by variance. However, in volatile and structur-ally unstable markets such as cryptocurrencies, this approach often fails to capture the full spectrum of uncertainty and diversification potential. This paper introduces an al-ternative methodology grounded in entropy, a fundamental concept in information theory that quantifies uncertainty and disorder. By incorporating entropy into the portfolio optimization process, we offer a more generalizable, distribution-free approach that enhances diversification and resilience.We develop and analyze three distinct en-tropy-based models: the maximum Shannon entropy model, the second-order entropy (Tsallis) model, and the maximum weighted Shannon entropy model. These formula-tions extend the traditional meanâvariance approach by integrating nonlinear uncer-tainty measures, enabling a richer representation of investor preferences and asset in-terdependencies. Analytical solutions to the proposed models are derived using the method of Lagrange multipliers, ensuring mathematical rigor and interpretability.The proposed models are empirically validated using a portfolio composed of four leading cryptocurrenciesâBitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)âwith market data from January to March 2025. The case studies demonstrate how entropy-based optimization leads to well-diversified portfolios, robust under market turbulence and heavy-tailed return distributions. Notably, the models facilitate dynamic adjustments in asset allocation in response to shifts in returnârisk characteristics and entropy levels. This study contributes to the ongoing generalization of portfolio theory by positioning entropy as both a diversification enhancer and a structural risk measure. It provides theoretical insight, practical tools for asset allocation in high-volatility environments, and paves the way for future research in entropy-driven financial optimization frameworks.