ABSTRACT Using a text‐based measure of peer opinions constructed from cryptocurrency‐related 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 risk‐neutral 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 investor’s 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.
Aashita Chhabra, Nabeela Hasan, Manzoor Ansari, Mansaf Alam
The usage of artificial intelligence (AI) has significantly transformed algorithmic trading in recent years, introducing advanced capabilities that enhance decision-making, automation, and risk management. AI algorithms can analyse huge amounts of data with unmatched speed and accuracy, identifying patterns, correlations, and anomalies in market data to enable more informed trading decisions. AI-powered predictive models forecast market trends and price movements based on historical data, news sentiment analysis, and other relevant factors, helping traders anticipate market shifts and optimize strategies. Automation of routine trading tasks, such as order execution, portfolio management, and risk assessment, allows human traders to focus on higher level strategy development and decision-making. AI enhances risk management by continuously monitoring market conditions and portfolio performance, dynamically adjusting trading strategies to minimize risks and maximize returns. It also enables complex quantitative analysis by processing data from multiple sources simultaneously, facilitating the development of sophisticated trading strategies. In high-frequency trading (HFT), AI-driven algorithms execute trades in microseconds, leveraging arbitrage opportunities and exploiting market inefficiencies. Machine learning (ML) algorithms adapt to evolving market conditions and learn from past trading experiences, continuously improving their performance. By reducing human emotions and biases in trading decisions, AI systems make objective, data-driven decisions based on quantitative criteria. The amalgamation of AI in algorithmic trading has revolutionized the industry, equipping traders with powerful tools to analyse data, manage risks, and execute trades with greater efficiency and precision. As AI technologies advance, their applications in trading will continue to become more sophisticated, driving further evolution in the field. As we review algorithmic trading and AI, it becomes evident that the fusion of technology and finance is transforming financial markets. This exploration will delve into the historical evolution, core strategies, market impact, ethical considerations, case studies, and future trends within the realm of algorithmic trading and AI. By examining these areas, we aim to uncover key insights into the transformative power of these technologies. From the past experience of algorithmic trading to the development of progressive strategies, such as analysing trends, statistical arbitrage, HFT, and ML-based approaches, the progression is embodied by major technological advancements and strategic innovations. Additionally, we will assess the market impact, including liquidity, price discovery, and regulatory considerations, highlighting both beneficiation and risks associated with algorithmic trading. As ethical and regulatory concerns gain prominence, it is crucial to closely examine algorithmic bias, fairness, and the broader impact of AI-driven trading practices [ 1 ]. Investigating AI-enhanced bitcoin trading algorithms for optimal investment strategies has led to several significant discoveries that provide insight into the present and potential future orientations of algorithmic trading in the cryptocurrency market. The use of AI techniques, including natural language processing (NLP), deep learning, and ML, has demonstrated substantial potential in refining bitcoin trading strategies. ML algorithms can analyse vast amounts of market data to identify trends and make informed trading decisions, leading to improved performance metrics like Rate of Interest (ROI) and Sharpe ratio. Additionally, deep learning systems enable the extraction of insights from sources containing text, such as current articles and media reviews, offering valuable inputs for trading strategies. The inclusion of AI-enhanced trading algorithms has increased automation and efficiency in bitcoin trading by executing transactions swiftly and accurately, eliminating human emotion and bias from decision-making. This results in more disciplined and consistent trading techniques while enhancing operational efficiency by reducing the time and cost associated with manual trade monitoring and management. Consequently, investors can focus on more strategic decisions. AI-powered trading algorithms have significantly altered investment strategies, enabling investors to diversify holdings, minimize risk, and make better informed decisions. By leveraging advanced analytical tools, adaptive strategies, and risk management procedures, investors can optimize their approaches to achieve desired returns while mitigating downside risk. Furthermore, the integration of AI methods with decentralized finance (DeFi) protocols has opened new opportunities for algorithmic trading strategies in emerging markets. The growing demand for transparency and ethical AI practices underscores the importance of understanding algorithmic decision-making and adhering to ethical standards, with future AI developments expected to enhance algorithm transparency and incorporate ethical principles and regulatory frameworks. The future trajectory of AI-boosted cryptocurrency trading algorithms will be shaped by advancements in AI methods, multidisciplinary research, and the application of responsible AI practices. Cutting-edge techniques like generative adversarial networks (GANs) and deep reinforcement learning (DRL) promise to improve the predictability and adaptability of algorithmic trading strategies. Additionally, integrating AI algorithms with DeFi protocols presents significant opportunities for innovation and efficiency in decentralized trade and finance. These findings underscore the transformative potential of AI technology in revolutionizing risk management and investment approaches in the cryptocurrency space. By embracing emerging trends, fostering transparency and responsible AI practices, and utilizing advanced AI techniques, investors can optimize their strategies and navigate the complexities of the bitcoin market more effectively [ 2 ]. Algorithmic stock trading has become a cornerstone of modern financial markets, with the majority of trades now fully automated. DRL agents have demonstrated their prowess in mastering complex games like Chess and Go. Similarly, the stock market&s;s historical price series and movements can be seen as a complex environment with imperfect information, where the objective is to maximize returns and minimize risks. This chapter reviews the advancements in DRL for automated low-frequency quantitative stock trading. Many of the studies examined are proof-of-concept and are conducted in unrealistic settings without real-time trading applications. Although these studies demonstrate statistically significant performance improvements over established baseline strategies, they fall short of achieving a satisfactory level of profitability. Furthermore, there is a significant lack of experimental testing on real-time, online trading platforms and a scarcity of meaningful comparisons between DRL-based agents and human traders or different DRL models. We conclude that while DRL in stock trading shows immense potential to rival professional traders under ideal conditions, the research is still in its early developmental stages [ 3 ]. The adoption of AI in algorithmic trading has enhanced market efficiency and liquidity by enabling faster and more accurate trade executions. AI algorithms facilitate real-time assessment and adaptive trading, helping to maintain market stability and reduce volatility. However, the rise of AI in trading has introduced significant regulatory and ethical challenges, such as concerns over market manipulation, insider trading, and the need for robust regulatory frameworks to ensure market integrity [ 4 , 5 ]. Continuous monitoring and regulatory vigilance are essential to address the potential risks associated with AI-driven trading systems. AI, particularly through ML and genetic algorithms, has enabled the creation of more sophisticated and adaptive trading strategies, optimizing parameters and portfolio allocations to enhance performance in HFT [ 5 , 6 ]. AI-driven pattern recognition techniques have improved market anomaly detection, leading to more accurate market predictions and better risk management [ 5 ]. AI-based trading systems have outperformed traditional trading methods by efficiently analysing large datasets and generating profitable trading strategies. Despite high initial costs, AI trading systems have proven to be more lucrative for large financial firms due to their ability to quickly adapt and optimize trading strategies [ 6 ]. Emerging AI techniques, such as deep learning and adversarial learning, are expected to further revolutionize algorithmic trading by providing more advanced models for market analysis and decision-making. The continuous exploration and integration of new AI technologies will shape the future of algorithmic trading, highlighting the need for ongoing research and development (R&D) [ 2 , 7 ]. The integration of AI has significantly transformed algorithmic trading in recent years by introducing advanced capabilities that enhance decision-making, automation, and risk management [ 8 ]. Here are some key ways AI has made an impact:
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 Commission’s approval of Bitcoin and Ethereum ETFs signaled wider mainstream adoption. Shortly thereafter, Donald Trump’s 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 asset’s 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: MercadoLibre’s decision to introduce Meli Dólar as a payment option, representing the inclusion of cryptocurrency, and eBay’s 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 Dólar 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 firm’s 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 investors’ irrationality may be more pronounced during certain periods. Furthermore, investors’ 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 market’s 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.
Since Trump took office, cryptocurrencies have received widespread attention. The Bitcoin market has witnessed a brief bull market, fluctuating within the range of $95,000 to $110,000, with investors' enthusiasm for investment remaining high. On February 22, 2025, the Bitcoin market witnessed a sharp decline, triggering a large number of margin calls. It was later revealed that this plunge was initially triggered by panic selling due to a wave of Bitcoin thefts. However, the theft of Bitcoin cannot be regarded as the main reason for this sharp drop. Traders are also a factor, especially their psychological fluctuations and irrational behaviors before and after margin calls. By studying the original articles in psychological finance, behavioral finance and neuroscience, combined with the specific manifestations of the anchoring effect and loss aversion psychology of Bitcoin market traders, this paper explores how traders' excessive reliance on anchor points and loss aversion lead to irrational behaviors and adverse trading outcomes, with the aim of reducing cognitive biases and improving decision-making for market traders under uncertainty. This study reveals that anchoring effect and loss aversion significantly affect the decision-making process of Bitcoin traders. Understanding these psychological factors can help traders manage risks more effectively and make more rational investment choices.
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 Adékambi
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 2017–2024 period. The portfolio performance of the three methods is also compared with the results from the traditional one-period mean–variance 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.
Purpose The aim of this research is to analyze the relationship between the MAX effect and the sentiment associated with the news in the cryptocurrency market. Design/methodology/approach The study uses natural language processing to build the sentiment indicator derived from news headlines about cryptocurrencies. Further, a survey-based sentiment indicator is also utilized. The study undertakes analysis at both the portfolio level (Decile analysis) and at the cross-sectional level (using the Fama-Macbeth Regression). Findings The results demonstrate a positive MAX effect in the cryptocurrency market. When the investor sentiment interacts with the MAX effect, the positive MAX effect continues to exist. However, the strength of the MAX coefficient decreases, suggesting that the sentiment factor drove the standalone MAX effect to a large extent. Further, small-sized and low-priced cryptocurrencies tend to showcase lottery anomaly higher than their counterparts. The availability heuristic is higher in small-cap cryptocurrencies. Due to loss aversion bias, the negative sentiment does not lead to a negative MAX effect. Practical implications It will be useful for the growing investor base in the cryptocurrency market in devising investment strategies. Originality/value The study presents empirical evidence on the impact of behavioral variables on the MAX effect. The study examines the interplay of cryptocurrency investor sentiment and the MAX effect using three novel sentiment proxies.
Purpose This study examines the performance of pair trading strategy in the cryptocurrency market under three statistical approaches including distance, cointegration and a hybrid method combining both distance and cointegration approaches. Design/methodology/approach The research uses daily, 4-h, 1-h, 15-min and 5-min data from the top 50 cryptocurrencies (by market capitalization) listed on Binance during three distinct periods: the bullish period of 2020, the stable period of 2021 and the bearish period of 2022. To perform a sensitivity analysis of the model, four approaches were implemented. First, both fixed and dynamic thresholds were applied across all three methods to assess their impact on trading results. Second, three standard deviations of 1.44, 1.65 and 2 were used, representing the coverage of normal data points in 85%, 90% and 95% of the time, respectively, to evaluate their influence on model profitability. Third, three different exit thresholds were employed to determine the extent to which changes in trade closure thresholds affect profitability. Fourth, the effect of the number of pairs in the portfolio on the model’s profitability was examined. Findings The findings from these approaches highlight the inefficiency of the cryptocurrency market and demonstrate the profitability of pair trading across various time frames, particularly in high-frequency time frames such as 15-min and 5-min intervals. Moreover, the results show that using a fixed threshold significantly outperforms a dynamic threshold in terms of both returns and Sharpe ratio. Additionally, the findings indicate a positive impact of altering the entry thresholds, exit thresholds and the number of pairs in the portfolio on the profitability of the models. Practical implications Due to the increasing attention to cryptocurrencies in investment management, the proposed model and the results of this study can be significantly used by cryptocurrency market traders, portfolio managers and fintech to achieve significant returns along with the increase in market liquidity. Originality/value This article has used pair trading strategies in the cryptocurrency market as a form of high-frequency trading for the first time. In addition, this article has proposed a hybrid approach based on the combination of distance and cointegration criteria to increase the efficiency of pair detection in the cryptocurrency market. It has evaluated the pair trading strategy in the form of different entry and exit criteria for a cryptocurrency.
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.