Greening crypto portfolios: the diversification and safe haven potential of clean cryptocurrencies

Abstract

The environmental concerns associated with energy-intensive cryptocurrencies have led to the rise of clean cryptocurrencies, which aim to balance financial innovation and sustainability. This study investigates whether clean cryptocurrencies improve portfolio resilience while promoting environmental goals in the cryptocurrency market. Using dynamic correlation-based hedge and safe-haven regression models, relative risk ratio analysis with higher-order moments risks, and multiple portfolio optimization strategies, we assess the impact of integrating clean cryptocurrencies into portfolios composed mainly of traditional cryptocurrencies. The results show that clean cryptocurrencies consistently reduce tail risk during periods of market stress; however, this risk reduction does not always result in higher returns or better risk-adjusted performance. These findings have important implications for both investors and policymakers. Clean cryptocurrencies can help investors manage tail risk and align with ESG goals, but their implementation requires a careful assessment of return expectations and investment constraints. Policymakers are encouraged to create a regulatory framework that fosters sustainable digital asset development while protecting investors and ensuring market stability. This study contributes to a deeper understanding of clean cryptocurrencies’ role in sustainable investment strategies within the evolving digital asset landscape.

Introduction

Since its inception in 2008, Bitcoin, the first decentralized cryptocurrency, has driven the rapid expansion of the digital asset market. This growth has introduced several benefits, including decentralized governance, enhanced security, lower transaction costs, and improved financial accessibility (Naeem et al. 2023). As of 2024, more than 20,200 cryptocurrencies are actively traded worldwide (Chen and Nguyen, 2024), with total market capitalization exceeding $2 trillion¹. However, the increasing adoption of cryptocurrencies has also raised concerns regarding their environmental impact, primarily due to the substantial energy consumption required for mining and transaction validation (Mora et al. 2018). Notably, Bitcoin alone consumes approximately 204.5 TWh annually, while Ethereum’s energy usage reaches nearly 92.69 TWh per year². These substantial energy demands have intensified regulatory scrutiny and discussions on mitigating the environmental footprint of cryptocurrency networks, particularly in the context of the ongoing climate crisis and global energy challenges (VriesJ, 2023).

The emergence of clean cryptocurrencies, which use energy-efficient consensus mechanisms and integrate renewable energy sources, has been proposed as a sustainable alternative to dirty (energy-intensive) cryptocurrencies (Ren and Lucey, 2022a). Existing studies have examined various aspects of clean cryptocurrencies, including their market behavior (Ren and Lucey, 2022b; Chen and Nguyen, 2024), role as hedging instruments for clean energy stocks (Ren and Lucey, 2022a), and risk spillover effects with dirty cryptocurrencies (Pham et al. 2022; Marco et al. 2023). In addition, some research has explored their contribution to equity portfolio diversification (Ali et al. 2024; Esparcia et al. 2024). However, whether clean cryptocurrencies provide effective diversification benefits and serve as a hedge or safe haven against the risks associated with their energy-intensive counterparts remains an open question. Given the growing market demand for sustainable and ESG-aligned assets, understanding their risk-mitigation properties within cryptocurrency portfolios is crucial for both investors and policymakers.

To address this gap, this paper examines whether the inclusion of clean cryptocurrencies in cryptocurrency portfolios enhances diversification, mitigates downside risk, and improves risk-adjusted returns, particularly in relation to energy-intensive cryptocurrencies. We adopt a comprehensive empirical framework based on Ali et al. (2024), integrating dynamic correlation-based hedge and safe-haven regression models, relative risk ratio analysis using a four-moment modified Conditional Value at Risk (CVaR) framework, and portfolio optimization strategies that account for returns, volatility, and risk-adjusted performance measures. This approach extends beyond pairwise connectedness analyses by assessing portfolio-level diversification effects, offering a more holistic evaluation of the role of clean cryptocurrencies in cryptocurrency portfolio management. Specifically, this study makes three key contributions to the literature on cryptocurrency portfolio management and sustainable investing.

First, it provides a comprehensive risk-return analysis of clean cryptocurrencies, particularly in their role as diversification instruments for energy-intensive cryptocurrencies. While previous studies have examined the behavioral and sentiment differences between clean and dirty cryptocurrencies (Ren and Lucey, 2022b; Chen and Nguyen, 2024), their practical implications for portfolio management, especially in mitigating downside risk and enhancing risk-adjusted performance, remain under-explored. By quantitatively assessing the resilience of clean cryptocurrencies under extreme market conditions, this study offers valuable insights for investors seeking to optimize portfolio allocations with a sustainability-oriented approach.

Second, unlike prior research that have primarily focused on inter-class diversification between cryptocurrencies and traditional assets, such as clean energy stocks (Ren and Lucey, 2022a) or broader equity portfolios (Esparcia et al. 2024; Ali et al. 2024), this study shifts attention to intra-class diversification within the cryptocurrency market. This perspective is particularly relevant given that cryptocurrency investors may face barriers to accessing traditional financial markets, have concentrated exposure to protocol-layer risks, and are more inclined to optimize their asset allocation within the crypto ecosystem (BIS, 2023). By exploring the role of clean cryptocurrencies in mitigating the risks specific to the cryptocurrency market, this study presents a novel sustainability-driven asset allocation strategy that aligns with the needs of crypto-native investors.

Finally, this study advances the methodological framework by integrating multiple empirical techniques to provide a comprehensive investment analysis. While previous research has predominantly relied on econometric models such as quantile-on-quantile regressions (Duan et al. 2024), time-varying parameter vector autoregressive (TVP-VAR) models (Duan et al. 2023), and quantile spillover indices (Pham and Nguyen, 2022; Sharif et al. 2023), this study combines regression-based safe-haven tests, relative risk ratio analysis using higher-moment risk measures, and portfolio optimization strategies incorporating performance evaluation models. This approach not only enhances the understanding of bilateral risk dynamics between clean and energy-intensive cryptocurrencies but also provides a holistic assessment of their portfolio-level diversification benefits.

Our findings offer novel insights into the practical implications of integrating clean cryptocurrencies into portfolio management. While allocating clean cryptocurrencies to portfolios of energy-intensive cryptocurrencies consistently reduces tail risk, the broader impact on portfolio returns, volatility, and risk-adjusted performance remains nuanced. These results have significant implications for investors, portfolio managers, and regulators, particularly as the cryptocurrency market matures and demand for environmentally sustainable investment strategies grows.

The remainder of this paper is organized as follows: section “Literature review” provides a literature review. Section “Methodology” introduces the safe-haven framework, relative risk ratio analysis, portfolio optimization strategies, and evaluation approaches. Section “Data and results” discusses the data and empirical results. Finally, section “Conclusion” concludes.

Literature review

Cryptocurrency market dynamics

The rapid expansion of the cryptocurrency market has prompted extensive research on its characteristics³. Studies on market efficiency yield mixed evidence regarding whether cryptocurrencies conform to the efficient market hypothesis. Some findings suggest that Bitcoin’s efficiency is unstable but improves over time (e.g., Tiwari et al. 2018; Vidal-Tomás and Ibañez, 2018; Noda, 2021; Fernandes et al. 2022). Additionally, cryptocurrencies exhibit higher volatility than gold, foreign currencies, and equities, often attributed to speculative trading (e.g., Dwyer, 2015; Dyhrberg, 2016; Blau, 2018; Aliu et al. 2021). Indeed, bubble behavior has been identified in Bitcoin prices (e.g., Corbet et al. 2018; Geuder et al. 2019; Huber and Sornette, 2022).

Another strand of research explores the relationship between cryptocurrencies and traditional financial assets, with conflicting findings (e.g., Khalfaoui et al. 2022; Mo et al. 2022; Karimi et al. 2023; Bhanja et al. 2023; Hanif et al. 2023). Baur et al. (2018) report that Bitcoin maintains low correlation with stocks, bonds, and commodities, even during financial crises. However, Nedved and Kristoufek (2023) find that Bitcoin moves in tandem with stock markets, while oil and gold can serve as safe havens. Other studies highlight significant risk spillovers between cryptocurrencies and financial markets, particularly under volatile conditions (e.g., Ji et al. 2019; Zeng et al. 2020; Umar et al. 2021; Hsu et al. 2021; Naeem et al. 2022). These conflicting findings raise the question of whether cryptocurrencies serve as effective diversification tools or hedging instruments (Stensås et al. 2019; Kliber et al. 2019; Nkrumah-Boadu et al. 2022). Some studies argue that cryptocurrencies fail to provide safe-haven benefits during market downturns (e.g., Bouri et al. 2017; Shahzad et al. 2019, 2020; Charfeddine et al. 2020; Conlon and McGee, 2020; Kyriazis, 2020; Huang et al. 2021; Ustaoğlu, 2023)⁴.

Clean cryptocurrencies financial characteristics

The environmental impact of energy-intensive cryptocurrencies has raised concerns among ESG-focused investors, as traditional cryptocurrencies like Bitcoin rely on the Proof-of-Work (PoW) consensus mechanism, which is associated with high energy consumption and significant carbon emissions (Corbet and Yarovaya, 2020; Wendl et al. 2023). Studies suggest downside risk spillovers between Bitcoin and carbon markets, highlighting the climate-related financial risks posed by PoW-based cryptocurrencies (Di Febo et al. 2021). These concerns have led to increasing calls for regulatory interventions and the adoption of sustainable alternatives (Schinckus, 2021). In response, the cryptocurrency market has witnessed the emergence of clean cryptocurrencies, which utilize energy-efficient consensus mechanisms such as Proof- of-Stake (PoS), the Ripple Protocol, and the Stellar Protocol. These alternatives aim to facilitate a low-carbon transition while maintaining the core benefits of decentralization, security, and financial accessibility (Ren and Lucey, 2022a).

An important question arises as to whether clean cryptocurrencies exhibit fundamentally different financial characteristics from their energy-intensive counterparts. Existing studies present contradictory views on this issue. On one hand, some researchers argue that clean and dirty cryptocurrencies exhibit similar market dynamics and investor behavior. For example, Haq and Bouri (2022) find that both types of cryptocurrencies exhibit identical co-movements with cryptocurrency uncertainty indices, particularly in the short term. Husain et al. (2023) explore the dynamic linkages between green cryptocurrencies, green investments, conventional commodities, and equities, showing that green cryptocurrencies function as diversifiers but lack hedging or safe-haven properties, behaving similarly to conventional cryptocurrencies. Ren and Lucey (2022b) suggest that cryptocurrency assets do not universally serve as safe havens for clean energy stocks. Similarly, Esparcia et al. (2024) show that both traditional and green cryptocurrencies provide diversification opportunities for equity portfolios.

Conversely, other studies suggest that clean cryptocurrencies exhibit weaker financial linkages with traditional markets than their energy-intensive counterparts, implying potential diversification benefits. For instance, Duan et al. (2023) report that clean cryptocurrencies are less integrated into the broader financial system than dirty cryptocurrencies. Marco et al. (2023) find heterogeneous return connectedness between clean and dirty cryptocurrencies and U.S. environmental stock market indexes. Moreover, Sharif et al. (2023) observe that clean cryptocurrencies are more closely linked to green economy indices than to conventional assets, reinforcing their distinct investment profile. Differences in market behavior have also been noted. Ren and Lucey (2022b) show that herding behavior is more pronounced for dirty cryptocurrencies in bearish markets. Ndubuisi and Urom (2023) highlight that investor attention to sustainability significantly influences clean cryptocurrency prices, suggesting that market sentiment, rather than fundamental differences, primarily drives their valuation.

The relationship between clean and dirty cryptocurrencies remains complex. Pham et al. (2022) find that clean cryptocurrencies exhibit a low correlation with Bitcoin and Ethereum, except during high volatility periods when dependencies increase. The uncertain financial relationship between clean and dirty cryptocurrencies raises important questions about their role in portfolio construction. Specifically, whether clean cryptocurrencies enhance diversification, hedge against market downturns, or serve as safe-haven assets remains an open debate. These considerations are particularly relevant in the broader context of cryptocurrency portfolio optimization.

Cryptocurrency portfolio optimization

Research on cryptocurrency portfolio optimization highlights the potential benefits of diversification within cryptocurrency portfolios. Liu (2019) demonstrates that diversification across different cryptocurrencies can significantly enhance the Sharpe ratio and utility of a portfolio, though sophisticated optimization models do not consistently outperform the simple 1/N portfolio in terms of the Sharpe ratio. Similarly, Borri (2019) finds that cryptocurrency portfolios outperform individual cryptocurrencies in terms of risk-adjusted and conditional returns. More recent studies have explored the implications of including centralized cryptocurrencies (altcoins) in decentralized cryptocurrency portfolios (e.g., Nguyen et al. 2019; Aysan et al. 2021; Khaki et al. 2023). Although earlier studies acknowledge the diversification potential among cryptocurrencies, they fail to distinguish between dirty and clean cryptocurrencies, particularly regarding the potential of clean cryptocurrencies to mitigate downside risk. This distinction is relevant for investors seeking diversification within cryptocurrency portfolios and policymakers aiming to decarbonize the cryptocurrency market by directing the use of crypto technology toward climate change mitigation efforts.

Summary and research implications

While prior studies have examined the market behavior, risk spillovers, and financial integration of clean cryptocurrencies, their role in cryptocurrency portfolio optimization remains largely unexplored. Existing research presents conflicting findings on whether clean cryptocurrencies behave similarly to energy-intensive counterparts (Haq and Bouri, 2022; Husain et al. 2023; Esparcia et al. 2024) or exhibit weaker financial linkages (Duan et al. 2023). Although extensive research has analyzed the diversification potential of cryptocurrency (Liu, 2019; Borri, 2019; Nguyen et al. 2019; Aysan et al. 2021; Khaki et al. 2023), little attention has been given to how clean cryptocurrencies influence risk-adjusted returns within cryptocurrency portfolios. Recent studies suggest that green assets exhibit safe haven properties (Rizvi et al. 2022) and can enhance portfolio efficiency (Akhtaruzzaman et al. 2023), but whether similar benefits extend to clean cryptocurrencies remains unclear.

Moreover, prior research has primarily focused on inter-class diversification between cryptocurrencies and other assets (Ren and Lucey, 2022a; Esparcia et al. 2024; Ali et al. 2024), rather than intra-class diversification within the cryptocurrency market, an aspect particularly relevant given crypto-native investment constraints. Additionally, evidence that news sentiment significantly influences cryptocurrency returns (Banerjee et al. 2022) underscores the need to examine whether clean cryptocurrencies exhibit distinct risk dynamics under extreme market conditions. Addressing these gaps, this study expands the existing literature by providing an in-depth analysis of the financial characteristics of clean cryptocurrencies and their implications for portfolio construction. By isolating their risk-mitigation properties and diversification potential within cryptocurrency portfolios, independent of cross-market movements, this research offers valuable insights into sustainable investment strategies tailored to the evolving digital asset landscape.

Methodology

In this section, we present a comprehensive empirical framework to evaluate the safe-haven properties and portfolio implications of clean cryptocurrencies through three complementary approaches. First, we employ hedge and safe-haven regression tests to establish base relationships. Second, we extend the analysis to assess tail risk using modified CVaR-based risk measures. Third, we examine portfolio optimization strategies by comparing dirty-only and mixed cryptocurrency portfolios. Finally, we outline a detailed estimation procedure and performance evaluation criteria to ensure robust empirical results. Together, these methods provide a multi-faceted assessment of the potential role of clean cryptocurrencies in risk management and portfolio diversification.

Safe-haven tests

Our methodology for investigating the role of clean cryptocurrencies as hedges or safe-haven assets against dirty cryptocurrencies is based on the estimation framework proposed by Baur and Lucey (2010) and Baur and McDermott (2010). Following Ren and Lucey (2022a), Akhtaruzzaman et al. (2021), Peng (2020) and Stensås et al. (2019), we first estimate the correlation between dirty and clean cryptocurrency asset pairs using the DCC-GARCH model proposed by Engle (2002).

Let ${r}_{t}$ represent an n × 1 vector of return series pairs ${r}_{1,t}$ and ${r}_{2,t}$ conditional on the information set ${I}_{t-1}$

$${{\rm{r}}}_{{\rm{t}}}={{{\mu }}}_{{\rm{t}}}+{{{\varepsilon }}}_{{\rm{t}}}$$

(1)

$${\varepsilon }_{t}={H}_{t}^{1/2}{z}_{t}$$

(2)

where ${\varepsilon }_{t}$ denotes the vector of residuals; ${z}_{t}$ is an 2 × 1 i.i.d random vector of errors with E(${z}_{i,t}$) = 0 and E(${{\rm{z}}}_{{\rm{i}},{\rm{t}}}^{2}$) = 1; ${H}_{t}$ is an 2 × 2 conditional covariance matrix, decomposed as

$${H}_{t}={D}_{t}{R}_{t}{D}_{t}$$

(3)

$${D}_{t}={{ {diag}}}({h}_{1,t}^{1/2},{h}_{2,t}^{1/2})$$

(4)

$${R}_{t}={{ {diag}}}({q}_{1,t}^{-1/2},{q}_{2,t}^{-1/2}){Q}_{t}{{ {diag}}}({q}_{1,t}^{-1/2},{q}_{2,t}^{-1/2})$$

(5)

where ${D}_{t}$ is an 2 × 2 diagonal matrix with conditional standard deviations $\sqrt{{{h}}_{{i},{t}}}$ on the diagonal, and ${R}_{t}$ is the conditional correlation matrix.

The dynamic conditional correlation (DCC) model, as introduced by Engle (2002), is estimated in a two-step process. Initially, the univariate conditional variance in ${D}_{t}$ is modeled using a GARCH(1,1) process:

$${h}_{i,t}={\omega }_{i}+{\alpha }_{i}{\varepsilon }_{i,t-1}^{2}+{\beta }_{i}{h}_{i,t-1}$$

(6)

where ω, α, β > 0 and $\alpha +\beta < 1$ to ensure that the conditional variance ${h}_{i,t}$ is positive and stationary. Subsequently, the standardized residuals ${z}_{i,t}={\varepsilon }_{i,t}/\sqrt{{{h}}_{{i},{t}}}$ are utilized to estimate the conditional correlations R_t. In Eq. (5), ${Q}_{t}$ is an asymmetric positive definite matrix, specified as

$${Q}_{t}=(1-{\theta }_{1}-{\theta }_{2})\bar{Q}+{\theta }_{1}{z}_{t-1}\acute{{z}_{t-1}}+{\theta }_{2}{Q}_{t-1}$$

(7)

where $\bar{Q}$ is the unconditional correlation matrix of standardized residuals. The parameters ${\theta }_{1}$ and ${\theta }_{2}$ are non-negative scalar satisfying ${\theta }_{1}+{\theta }_{2} < 1.$ The correlation estimator is defined by

$${\rho }_{{ij},t}=\frac{{q}_{{ij},t}}{\sqrt{{q}_{{ii},t}{q}_{{ij},t}}},i,j=1,2,\,{{\rm {and}}}\,i\,\ne\, j$$

(8)

Given the dynamic conditional correlations established between clean and dirty cryptocurrencies, we next evaluate the hedging and safe-haven properties of clean cryptocurrencies against dirty cryptocurrencies. Following Baur and McDermott (2010), the dynamic conditional correlation ${{{\rm {DCC}}}}_{t}$ is regressed on dummy variables that capture extreme movements in dirty cryptocurrency assets:

$${{ {DC}{C}}}_{{ij},t}={c}_{0}+{c}_{1}D({r}_{{{ {dirt}{y}}}_{i}}{q}_{10})+{c}_{2}D({r}_{{{ {dirt}{y}}}_{i}}{q}_{5})+{c}_{3}D({r}_{{{ {dirt}{y}}}_{i}}{q}_{1})$$

(9)

where ${D}(...)$ are dummy variables capturing extreme negative returns of a dirty cryptocurrency at the 10%, 5%, and 1% quantiles of the distribution. Following Baur and Lucey (2010) and Baur and McDermott (2010), we adopt the definition of clean cryptocurrency from Ren and Lucey (2022a) to characterize the roles of clean cryptocurrency as follows: A clean cryptocurrency is a diversifier for a dirty cryptocurrency if ${c}_{0}$ is significantly positive (but not one); it is as a weak hedge if ${c}_{0}$ is insignificantly different from zero; and it is a strong hedge if ${c}_{0}$ is negative. A clean cryptocurrency functions as a weak (strong) safe haven for a dirty cryptocurrency under some market conditions if any of ${c}_{1}$, ${c}_{2}$ or ${c}_{3}$ are non-positive (significantly negative). The key characteristic of a diversifier or hedge is its effectiveness on average, whereas a safe haven is characterized by its ability to provide protection during specific periods.

Relative risk ratios

To further investigate the safe-haven properties of clean cryptocurrencies, we employ a tail risk measure based on the modified Conditional Value-at-Risk (CVaR) proposed by Favre and Galeano (2002). The modified CVaR extends the traditional CVaR by integrating additional higher moments of the return distribution. This advanced approach offers a more refined and accurate depiction of potential losses in the distribution’s tail, which is particularly crucial in cryptocurrency contexts where extreme events occur more frequently. The modified CVaR is defined as the expected value of losses that exceed the VaR_p threshold, mathematically expressed as

$${{{ {CVaR}}}}_{ {{p}}}(\alpha )=E({R}_{\rm {{p}}}| > {{{ {VaR}}}}_{{ {p}}}(\alpha ))$$

(10)

Here ${R}_{{\rm {p}}}$ represents the negative of portfolio returns, and E denotes the expected value. The modified ${{\rm {{VaR}}}}_{{\rm {p}}}$ is derived using the four-moment Cornish–Fisher expansion (Cornish and Fisher, 1937), defined as

$$\begin{array}{c}\hat{Z}(\alpha ,{S}_{{\rm {P}}},{K}_{{\rm {p}}})=z(\alpha )+\frac{1}{6}(z{(\alpha )}^{2}-1){S}_{{\rm {p}}}+\frac{1}{24}(z{(\alpha )}^{3}-3z(\alpha )){K}_{{\rm {p}}}\\ -\frac{1}{36}(2z{(\alpha )}^{3}-5z(\alpha )){S}_{{\rm {p}}}^{2}\end{array}$$

(11)

$${{{ {VaR}}}}_{{ {p}}}(\alpha )=-{\mu }_{\rm {{p}}}-{\sigma }_{\rm {{p}}}\hat{Z}(\alpha ,{S}_{\rm {{p}}},{K}_{{\rm {p}}})$$

(12)

where $z(\alpha )$ is the $\alpha$ quantile of the standard normal distribution, and ${\mu }_{{\rm {p}}}$, ${\sigma }_{{\rm {p}}}$, ${S}_{{\rm {p}}}$, and ${K}_{\rm {{p}}}$ denote the mean, standard deviation, skewness, and excess kurtosis of the portfolio’s return distribution, respectively.

To evaluate the impact of clean cryptocurrencies on the tail risk of portfolios dominated by dirty cryptocurrencies, we apply the relative risk ratio approach based on the modified CVaR (Bredin et al. 2017). This approach compares the CVaR of a portfolio before and after the inclusion of clean cryptocurrencies. Specifically, we calculate the relative risk ratio as

$${{\rm{RR}}}_{{\rm{CVaR}}}=\frac{{{\rm{CVaR}}}_{{\rm{mix}}}}{{{\rm{CVaR}}}_{{\rm{dirty}}}}$$

(13)

Here, ${{\rm{CVaR}}}_{{\rm{dirty}}}$ is the CVaR of a portfolio consisting solely of dirty cryptocurrencies, ${{\rm{CVaR}}}_{{\rm{mix}}}$ is the CVaR of a portfolio that includes both dirty and clean cryptocurrencies.

The relative risk ratio approach has been used in previous studies to investigate the safe-haven property of cryptocurrencies relative to equities (e.g., Conlon and McGee, 2020; Conlon et al. 2020; Ali et al. 2022, 2024). It is used here as a metric to quantify the extent to which clean cryptocurrencies mitigate the tail risk of portfolios dominated by dirty cryptocurrencies. A ratio greater than one indicates that the inclusion of clean cryptocurrencies reduces tail risk, suggesting a potential safe-haven effect. Conversely, a ratio close to one implies limited risk reduction benefits.

Portfolio construction

Having quantified the tail risk mitigation provided by clean cryptocurrencies using the relative risk ratio approach, we now turn to portfolio optimization techniques to further examine the diversification benefits they offer. By incorporating clean cryptocurrencies into portfolios dominated by dirty cryptocurrencies, we can assess how they affect the overall risk and return profile, shedding light on their role in portfolio construction and management.

Consider a risk-averse investor who seeks to minimize portfolio risk, subject to a non-short-selling constraint and a minimum return target, by distributing their wealth among n risky assets. We will denote the portfolio return as ${{R}}_{{\rm{p}}}$ and represent the vector of portfolio weights as ${\bf{X}}=({{\rm{x}}}_{1},{{\rm{x}}}_{2}\ldots ,{{\rm{x}}}_{{n}})$. The expected portfolio return is denoted by ${\rm{E}}({{R}}_{{\rm{p}}})$, with the lower bound being the in-sample average return of an equally weighted portfolio. To account for the trade-off between risk and reward, volatility and tail risks, we employed four portfolio optimization models. These models were implemented in the statistical software R using the fPortfolio library package.

Mean-variance framework

The classical mean-variance model, developed by Markowitz (1952), offers a framework for determining the optimal weights of assets in an investment portfolio to achieve the lowest possible risk (measured by variance) at a given expected portfolio return level.

$$\begin{array}{c}{{\min}}_{{x}}{\rm{Var}}({{R}}_{{\rm{p}}})\\ {\rm{s}}.{\rm{t}}.E\left({R}_{p}\right)\ge {\bar{r}},\sum\limits_{i=1}^{n}{x}_{i}=1,\,{x}_{i}\ge 0,i=1,\ldots ,n\end{array}$$

(14)

where $E\left({R}_{p}\right)$ and ${\rm{Var}}\left({R}_{p}\right)$ denote the expected returns and variance of n asset portfolio, respectively. The in-sample covariance matrix can be employed to estimate ${\rm{Var}}\left({R}_{p}\right)$.

Tangency portfolio

The tangency portfolio is the portfolio of risky assets with the highest volatility-adjusted returns

$$\begin{array}{c}\begin{array}{c}{\max }_{{x}}\frac{{\rm{E}}\left({\rm{R}}_{{\rm{p}}}\right)-{{r}}_{{\rm{f}}}}{{\rm{Var}}\left({\rm{R}}_{{\rm{p}}}\right)}\\ {\rm{s}}.{\rm{t}}.{\sum }_{{i}=1}^{{n}}{{x}}_{{i}}=1,\,{{x}}_{{i}}\ge 0,{i}=1,\ldots ,{n}\end{array}\\ \end{array}$$

(15)

where $E\left({R}_{{\rm {p}}}\right)$ and ${\rm{Var}}\left({R}_{{\rm {p}}}\right)$ are the expected returns and variance of n asset portfolio, respectively; ${r}_{f}$ denotes the risk-free rate which is set at zero.

Global minimum variance optimization

Building on the mean-variance framework and the tangency portfolio concept, we consider global minimum variance portfolio optimization. This approach aims to minimize portfolio variance without requiring explicit estimates of expected return, making it a suitable choice when return forecasts are uncertain or risk minimization is the primary goal. When short selling is permitted, the problem can be formulated as

$${{\rm{m}}{\rm{in}}}_{{x}}{\rm{Var}}({{R}}_{{{p}}})$$

(16)

$${{s}}.{{t}}.{\sum }_{i=1}^{n}{x}_{i}=1$$

(17)

Here, ${x}_{i}$ can be any real number, which means that the portfolio can hold long and short positions in the assets. This flexibility enables the portfolio to fully utilize the risk reduction potential of diversification and hedging. In practice, short-selling may be restricted for regulatory, practical or strategic reasons. Thus, we also consider the optimization problem under a no short selling constraint:

$${{\rm{m}}{\rm{in}}}_{{x}}{\rm{Var}}({{R}}_{{\rm{p}}})$$

(18)

$${\rm{s}}.{\rm{t}}.{\sum }_{i=1}^{n}{x}_{i}=1,{x}_{i}\ge 0,i=1,\ldots ,n$$

(19)

In adherence to this constraint, the portfolio weights are mandated to be non-negative, thereby signifying along-only investment approach.

Estimation

The aim of this research is to examine the diversification effects of clean cryptocurrencies. To achieve this, two types of portfolios are evaluated: dirty cryptocurrency portfolios and portfolios that consist of a mixture of dirty and clean cryptocurrencies. Both portfolios utilize the same optimization models mentioned in section “Portfolio construction” for comparison. The unconditional analysis is employed for both portfolios using the full sample data to provide an initial indication of the optimal portfolio weights among the cryptocurrencies and the resulting portfolio efficiency. Subsequently, a rolling window approach is applied for conditional portfolio construction. This approach involves using a fixed window size of t and constructing the one-day ahead out-of-sample forecast portfolio weights at time t + 1 using data from the previous t days. The estimation sample is then shifted by one day, the models are re-estimated, and the forecast portfolio weights for day t + 2 are generated, and so on, until the sample is complete. Expected returns are calculated using the corresponding sample mean over the estimation sample.

Evaluation

Each portfolio undergoes daily re-balancing, and the realized portfolio return is calculation the re-balancing date. For instance, the realized return ${R}_{{\rm {p}}}$ of the portfolio at time t + 1 is computed based on the portfolio weights ${{\bf{X}}}_{t}=({x}_{1},{x}_{2},\ldots ,{x}_{n}{)}_{t}^{{\prime} }$ at time t and the realized returns ${{\bf{R}}}_{t+1}=({R}_{1},{R}_{2},\ldots ,{R}_{n}{)}_{t+1}^{{\prime} }$ of the individual n assets at time t + 1. This calculation is represented as

$${R}_{{ {p}},t+1}={{\bf{X}}}_{t}^{{\prime} }{{\bf{R}}}_{t+1}$$

(20)

To assess performance during the out-of-sample period [t + 1, T] where T denotes the total sample size, we follow Kuang (2021) and evaluate risk-adjusted return ratios and portfolio turnover. Several risk-adjusted measures are considered in this evaluation, including the Sharpe ratio $({{\rm {SR}}}_{{\rm {p}}})$, Calmar ratio ${({\rm{CR}}}_{{\rm{p}}})$, Sortino ratio ${({\rm{S}}{\rm{T}}}_{{\rm{p}}})$, Omega ratio ${(\Omega }_{{\rm{p}}})$, and modified Sharpe ratio ${({\rm{M}}{\rm{SR}}}_{{\rm{p}}})$. The Sharpe ratio uses the standard deviation of returns as the risk measure but does not differentiate between upside and downside variance. On the other hand, the Calmar and Sortino ratios focus on downside risk, while the modified Sharpe ratio incorporates extreme risk. The Omega ratio is a probability-weighted measure of gains and losses, based on a target return threshold. For further details about each ratio’s specifications, refer to the information provided below:

$${{{ {SR}}}}_{{ {p}}}=\frac{{\bar{R}}_{{\rm {P}}}}{{\hat{{{\sigma }}}}_{{\rm{p}}}}$$

(21)

where ${\bar{R}}_{{\rm {P}}}$ represents the annualized geometric mean return and ${\hat{{{\sigma }}}}_{{\rm{p}}}$ denotes the annualized standard deviation of portfolio return.

$${{\rm{CR}}}_{{\rm{p}}}=\frac{{\bar{R}}_{P}}{\left|{\rm{MDD}}\right|}$$

(22)

where $\left|{\rm{MDD}}\right|$ is the absolute value of the maximum drawdown of a portfolio.

$${{{ {ST}}}}_{{\rm {p}}}=\frac{{\bar{R}}_{{ {P}}}-{R}_{{ {T}}}}{{\left({\int }_{-{{\infty }}}^{T}{({R}_{T}-x)}^{2}f(x){{\rm {d}}x}\right)}^{1/2}}$$

(23)

where R_T is the target or required rate of return (assumed to be zero).

$${\Omega }_{{\rm {p}}}=\frac{{\int }_{\tau }^{{{\infty }}}\left(1-F(x)\right){\rm{d}}x}{{\int }_{-{{\infty }}}^{\tau }F\left(x\right){\rm{d}}x}$$

(24)

where F represents the cumulative distribution function of returns, and τ denotes the threshold that distinguishes gains from loss, assumed to be zero.

$${{{\rm {MSR}}}}_{{\rm {P}}}=\frac{{{\bar{R}}}_{{\rm {p}}}}{{{\rm{CVaR}}}_{\alpha }}$$

(25)

where ${{\rm{CVaR}}}_{{\rm{\alpha }}}$ represents the modified conditional value at risk of portfolio return at a given confidence level α.

Turnover is a metric that measures the frequency at which fund managers buy or sell assets in a portfolio within a time frame. It indicates the costs associated with regular portfolio re-balancing. Specifically, turnover during the period $({{t}}_{1},{{t}}_{2})$ can be calculated using the following equation:

$${\rm{TO}}={\sum }_{t={t}_{1}}^{{t}_{2}-1}{\sum }_{i=1}^{n}\left(\left|{x}_{i,t+1}-{x}_{i,t}\right|\right)$$

(26)

where ${{x}}_{{i},{t}}$ represents the weight of an individual asset ${i}$ at time t.

Data and results

We first follow the criteria established by Ren and Lucey (2022a) to identify the five most prominent dirty and clean cryptocurrencies based on market capitalization. The dirty cryptocurrencies include Bitcoin (BTC), Ethereum (ETH), Bitcoin Cash (BCH), Ethereum Classic (ETC), and Litecoin (LTC), which utilize Proof-of-Work (PoW) algorithms and consume significant energy during mining and transactions. In contrast, the green cryptocurrencies in focus are Cardano (ADA), Ripple (XRP), IOTA (MIOTA), Stellar (XLM), and Nano (NANO), which use energy-saving consensus mechanisms such as Proof-of-Stake (PoS), Ripple Protocol, Stellar Protocol, and others. The dataset used for the analysis includes daily indices from 2 January 2018, to 8 May 2023, sourced from Coincodex⁵. All indices are denominated in US dollars, and daily log returns are calculated for analysis.

Table 1 presents a statistical summary of the daily return series for all indices over the sample period. It is worth noting that all cryptocurrencies except BTC and ETH have negative returns. BTC has the lowest standard deviation and tail risk but is more negatively skewed compared to other counterparts. Conversely, XLM and NANO show the highest maximum one-day profits with positive skewness. Meanwhile, MIOTA and NANO have the highest tail risks. Augmented Dickey–Fuller, ARCH, and Jarque-Bera tests confirm the stationary nature of all return series, with evidence of volatility clustering and departure from a normal distribution. Table 2 shows the Pearson pairwise correlations between all indices. Notably, dirty and clean cryptocurrencies show a positive correlation of approximately 70%, indicating a significant co-movement effect despite the use of different consensus algorithms.

Table 1 Summary statistics.

Table 2 Correlation.

Figure 1 shows the dynamic conditional correlations between each pair of dirty and clean cryptocurrencies over time. Across all pairs, the correlations show significant fluctuations over time, with the highest recorded correlation exceeding 0.9. Interestingly, some pairs experienced negative correlations at certain points in time, such as the ETH & ADA pair, which has a minimum correlation of −0.22 in early 2018, and the BTC & NANO pair, which has a correlation as low as −0.17 during the first half of 2021. The degree of fluctuation varies between the different pairs. In particular, the ETH & XRP, LTC & XRP, and BTC & XRP pairs show the highest volatility in their correlations. In contrast, the BCH & XLM pair shows the most stable correlation pattern over time. These findings highlight the dynamic and heterogeneous nature of the relationships between dirty and clean cryptocurrencies. The observed fluctuations in correlations, especially the instances of negative correlations, suggest that there may be periods when clean cryptocurrencies can act as weak safe havens for dirty cryptocurrencies. The differential volatility between pairs also highlights the importance of taking into account the specific characteristics of individual cryptocurrencies when building diversified portfolios.

Fig. 1: Dynamic conditional correlation.

The graphs show the dynamic conditional correlation between dirty cryptocurrencies (Bitcoin-BTC, Ethereum-ETH, Bitcoin Cash-BCH, Ethereum Classic-ETC, Litecoin-LTC) and their equally weighted portfolio (EW) with clean cryptocurrencies (Cardano-ADA, Ripple-XRP, IOTA-MIOTA, Stellar-XLM, Nano-NANO) over a sample period from 3 January 2018 to 8 May 2023.

The top panel of the Fig. 2 shows the annualized return and risk, represented by volatility, for the 10 cryptocurrencies. BTC demonstrates the most favorable risk-return trade-off, with the highest returns and lowest risks, followed by ETH. In contrast, MIOTA and NANO offer the lowest returns and highest risks, suggesting that dirty cryptocurrencies may have more favorable characteristics than clean ones. The lower panel of Fig. 2 displays the cumulative returns of individual cryptocurrencies over the sample period. It reveals that BTC and ETH generate higher returns than other cryptocurrencies, albeit with higher volatility. These qualitative findings indicate that other cryptocurrencies may serve as useful diversifiers to mitigate the risks associated with BTC and ETH. However, it remains uncertain whether the inclusion of clean cryptocurrencies as a diversification strategy offers any additional benefits, which warrants further investigation.

Fig. 2: Returns and risk.

The top graph illustrates the annualized return and volatility of 10 cryptocurrencies, specifically, Bitcoin (BTC), Ethereum (ETH), Bitcoin Cash (BCH), Ethereum Classic (ETC), Lite- coin (LTC), Cardano (ADA), Ripple (XRP), IOTA (MIOTA), Stellar (XLM), and Nano (NANO). The bottom graph shows the cumulative returns of the aforementioned cryptocurrencies over a sample period beginning on 3 January 2018 and ending on 8 May 2023.

Safe-haven analysis

Table 3 summarizes the empirical results on the hedge and safe-haven properties of clean cryptocurrencies against dirty cryptocurrencies. All hedge coefficients c₀ are significantly positive for all pairs, suggesting that clean cryptocurrencies do not act as a direct hedge against dirty cryptocurrencies during the sample period. The coefficients c₂ and c₃ corresponding to extremely negative returns of dirty cryptocurrencies at 5% and 1% quantiles, respectively, are mostly negative for most asset pairs. Some of these coefficients are statistically significant, suggesting that clean cryptocurrencies can be weak or strong safe havens in times of market stress. This is particularly evident for the pairs involving ETC at the 5% quantile and BCH at the 1% quantile, where clean cryptocurrencies consistently emerge as strong safe havens. In contrast, the coefficients c₁, corresponding to extremely negative returns of dirty cryptocurrencies at the 10% quantile are more mixed. Most pairs with BTC show positive values c₁, but they are not statistically significant. The mixed nature of the c₁ coefficients suggests that the safe-haven properties of clean cryptocurrencies depend on the specific assets.

Table 3 Hedge and safe-haven analysis.

In summary, the results suggest that clean cryptocurrencies can be used as diversifiers and safe havens for dirty cryptocurrencies under extreme market conditions (5% and 1% quantiles). However, the effectiveness of clean cryptocurrencies as a safe haven is contingent on the choice of underlying assets. These findings imply that investors with substantial exposure to dirty cryptocurrencies may wish to include clean cryptocurrencies in their portfolios to potentially benefit from safe-haven characteristics while also promoting environmental responsibility. Further investigation through portfolio construction is required to more fully assess the risk diversification and safe-haven properties.

Relative risk ratio analysis

Based on the safe-haven analysis, we have shown that clean cryptocurrencies have the potential to act as a safe haven for dirty cryptocurrencies in times of market stress. To assess the tail risk mitigation provided by clean cryptocurrencies, we applied the relative risk ratio approach using a modified CVaR measure. We constructed portfolios by mixing each dirty cryptocurrency with clean cryptocurrencies, gradually increasing the weight of clean cryptocurrencies from 0 to 1 in increments of 0.025. Figures 3 and 4 report the changes in the relative risk ratio (RRR) for CVaR95 and CVaR99, for portfolios consisting of BTC, ETH, BCH, ETC, LTC, and an equally weighted portfolio of dirty cryptocurrencies (EW) combined with a clean cryptocurrency, such as ADA, XRP, MIOTA, XLM, and NANO.

Fig. 3: Relative risk ratio: BTC & ETH & BCH.

The graphs present the relative modified Conditional Value-at-Risk (CVaR) ratios at the 95% and 99% confidence levels for BTC, ETH, and BCH portfolios. The ratios compare portfolios with varying allocations to clean cryptocurrencies (ADA, XRP, MIOTA, XLM, NANO) against portfolios with no clean cryptocurrency allocation. Ratios below 1 indicate improved tail risk protection from clean cryptocurrency inclusion. The analysis covers the period from 3 January 2018 to 8 May 2023.

Fig. 4: Relative risk ratio: ETC, LTC, and EW.

The graphs present the relative modified Conditional Value-at-Risk (CVaR) ratios at the 95% and 99% confidence levels for ETC, LTC and equally weighted dirty cryptocurrency (EW) portfolios. The ratios compare portfolios with varying allocations to clean cryptocurrencies (ADA, XRP, MIOTA, XLM, NANO) against portfolios with no clean cryptocurrency allocation. Ratios below 1 indicate improved tail risk protection from clean cryptocurrency inclusion. The analysis covers the period from 3 January 2018 to 8 May 2023.

All figures show a U-shaped pattern, indicating that, as the weight of clean cryptocurrencies increases, the relative risk ratio (measured as the CVaR of the dirty cryptocurrency divided by the CVaR of the mixed portfolio) initially decreases. This suggests that the addition of clean cryptocurrencies initially reduces tail risk. However, as the weight of clean cryptocurrencies continues to increase beyond a certain point, the relative risk ratio starts to increase, implying that the tail risk of the mixed portfolio starts to increase again.

The tail risk mitigation of different clean cryptocurrencies varies, as do the optimal weights for maximizing risk mitigation. The smallest optimal weight is about 25% in NANO. When the weight exceeds this value, the portfolio risk increases more significantly, especially for CVaR99, indicating that NANO has a weaker ability to mitigate extreme tail risk. In contrast, the highest optimal weights are over 35% for ADA and MIOTA. The risk reduction effect of these two cryptocurrencies is the best among all clean cryptocurrencies. Even when the weights exceed the optimal values, the increase in portfolio risk is relatively slow and still lower than the CVaR of pure dirty cryptocurrency portfolios. The reason why ADA and MIOTA have a better ability to reduce risk is that their return series have relatively low kurtosis. XRP and NANO have higher kurtosis, so they inherently have higher CVaR95 and CVaR99 than other cryptocurrencies, which limits their ability to mitigate tail risk.

Overall, these results show that different clean cryptocurrencies play different roles in tail risk management. The U-shaped curves indicate that there exists an optimal proportion of clean cryptocurrencies to reduce the tail risk of the portfolio, and that the tail risk of the portfolio may increase when the proportion exceeds this value. The differences in the optimal proportions and the effectiveness of risk reduction among clean cryptocurrencies imply that it is necessary to take into account the characteristics of individual assets when constructing diversified portfolios.

Unconditional optimization

Having examined tail risk mitigation through the relative risk ratio analysis, we now turn to unconditional portfolio optimization using the full sample data. This analysis aims to determine the optimal allocation to different cryptocurrencies, with a particular focus on the impact of including clean cryptocurrencies.

As illustrated in Fig. 5, the inclusion of clean cryptocurrencies has a minimal impact on the weight allocation for the global minimal variance (GMV) and the tangency portfolio (TP). The majority of the allocation is still concentrated on BTC due to its relatively lower volatility and higher risk-adjusted returns. For the mean-variance (MV) portfolio, when considering only dirty cryptocurrencies, BTC receives a weighting of over 60%, and BCH receives a weighting of approximately 30%. However, when clean cryptocurrencies are included, they receive a combined weight of almost 50%. The weightings are spread across XRP, MIOTA, XLM, and NANO, indicating a diversification benefit.

Fig. 5: Portfolio weights.

This figure compares optimal portfolio allocations under three different optimization strategies from 3 January, 2018 to 8 May, 2023. The graphs (left) show portfolios composed only of dirty cryptocurrencies, while the graphs (right) include both dirty and clean cryptocurrencies. The optimization strategies are: (1) global minimum variance portfolio without short selling (top), minimizing overall portfolio volatility; (2) mean-variance portfolio (middle), balancing return and risk; and (3) tangency portfolio (bottom), maximizing the Sharpe ratio. The weights sum to 100% and indicate the optimal allocation to each cryptocurrency.

Figure 6 shows the cryptocurrency allocation weights for different return and volatility risk targets with and without clean cryptocurrencies. As the target returns increase, the allocation to BTC also increases, which is intuitive as BTC is a core component of the portfolio. The inclusion of clean cryptocurrencies adds more choices to the portfolio such as MIOTA, XRP, XLM, and NANO, which leads to a richer set of alternatives that can provide additional diversification benefits.

Fig. 6: MV frontier.

The graphs show the optimal cryptocurrency allocation weights across different return–volatility combinations. The graph (top) displays the allocation weights for dirty cryptocurrencies only, while the graph (bottom) shows the results for expanded investment universe including both dirty and clean cryptocurrencies.

Conditional optimization

Building on the insights from unconditional optimization, we now proceed to the conditional portfolio optimization based on out-of-sample evaluation. This approach allows us to assess the robustness of portfolio allocations and the diversification benefits of clean cryptocurrencies under changing market conditions. By evaluating the portfolio performance out-of-sample, we can gain a better understanding of how these portfolios perform in real-world scenarios, providing practical guidance for investors looking to construct diversified cryptocurrency portfolios.

Table 4 shows the average portfolio weights during the out-of-sample period for different optimization models. BTC is allocated more than 40% in all strategies and portfolios. The weights of other cryptocurrencies differ across optimization strategies. For portfolios with only dirty cryptocurrencies, the TP strategy gives ETH a higher weight than LTC due to its better volatility risk-adjusted returns. GMV strategy allocates over 94% to BTC because it has the lowest volatility. For portfolios with both clean and dirty cryptocurrencies, the MV optimization strategy assigns high weights to XRP and XLM. These are consistent with the unconditional optimization results.

Table 4 Portfolio weights.

Figures 7 and 8 show the cumulative returns and drawdown risk for portfolios containing only dirty cryptocurrencies (D) and those containing both clean and dirty cryptocurrencies (DC) under the mean-variance (MV), the tangency portfolio (TP), the global minimum variance (GMV), and the GMV with short selling (GMV(Short)) strategies. Across all optimization strategies, portfolios composed solely of dirty cryptocurrencies exhibit higher cumulative returns compared to those that also include clean cryptocurrencies. This suggests that the inclusion of clean cryptocurrencies does not necessarily enhance the overall return profile of the portfolios. In particular, the GMV(Short) strategy, which allows short selling, achieves higher cumulative returns than the standard GMV strategy, indicating that short selling can be beneficial in enhancing the portfolio performance. The drawdown risk of the portfolios combining clean and dirty cryptocurrencies is generally higher than that of portfolios containing only dirty cryptocurrencies. Notably, during the COVID-19 pandemic in 2020, the addition of clean cryptocurrencies did not serve to reduce the drawdown risk within the dirty cryptocurrency portfolios. This finding suggests that the diversification benefits of clean cryptocurrencies were limited during this period of extreme market volatility.

Fig. 7: Out-of-sample performance: MV and TP portfolio.

The figures show the cumulative return and drawdown of the portfolio consisting solely of dirty cryptocurrencies (D) and the portfolio that is a combination of dirty and clean cryptocurrencies (DC) following the mean-variance (MV) and tangency portfolio (TP). The out-of-sample evaluation period is from 2 January 2019 to 8 May 2023. The daily return of dirty cryptocurrencies portfolio based on the MV strategy is illustrated in the middle panel. The comparison demonstrates the impact of including clean cryptocurrencies on portfolio performance and risk metrics over time.

Fig. 8: Out-of-sample performance: GMV and GMV(Short) portfolio.

The figures show the cumulative return and drawdown of the portfolio consisting solely of dirty cryptocurrencies (D) and the portfolio that is a combination of dirty and clean cryptocurrencies (DC) following the global minimum variance (GMV) and the global minimum variance with short selling (GMVshort) strategy. The out-of-sample evaluation period is from 2 January 2019 to 8 May 2023. The daily return of dirty cryptocurrencies portfolio based on GMV strategy is illustrated in the middle panel. This analysis demonstrates how short-selling constraints and clean cryptocurrency inclusion affect portfolio performance.

To assess the performance of cryptocurrency portfolios, we compute the annualized return, standard deviation, and Sharpe ratio of portfolios formed using MV, TP, GMV, and GMV(Short) strategies with a 250-day rolling window. The results are shown in Figs. 9 and 10. First, we compare the performance of the different optimization strategies. The MV strategy produces higher mean returns and lower standard deviations than the TP strategy, resulting in higher risk-adjusted returns (Sharpe ratio). The GMV(Short) strategy exhibits higher returns and superior risk-adjusted returns (Sharpe ratio) than the GMV strategy, though its volatility performance is not consistently better. Next, we compare the performance of portfolios containing only dirty cryptocurrencies (D) with those containing both clean and dirty cryptocurrencies (DC). For the MV and TP strategies, the dirty cryptocurrency-only portfolio had higher volatility than the combined dirty and clean cryptocurrency portfolio until the end of 2020. However, from the beginning of 2021, the volatility performance of the pure dirty cryptocurrency portfolio improved. Throughout the entire period, the pure dirty cryptocurrency portfolio generally averages higher mean returns and Sharpe ratios under the MV and TP strategies compared to the combined portfolio. Similar trends are observed for the GMV and GMV(Short) strategies. Before 2021, the combined portfolio demonstrated lower volatility, but after 2021, the pure dirty cryptocurrency portfolio showed lower volatility. Despite this shift in volatility, the combined portfolio consistently delivered higher returns, leading to a higher Sharpe ratio.

Fig. 9: Rolling performance: MV and TP portfolios.

The figure presents rolling performance metrics including annualized return, standard deviation, and Sharpe ratio for mean-variance (MV) and tangency portfolio (TP) strategies using a 252-day rolling window. The graphs compare portfolios containing only dirty cryptocurrencies (D) versus those combining dirty and clean cryptocurrencies (DC).

Fig. 10: Rolling performance: GMV and GMV(Short) portfolios.

The figure presents rolling performance metrics including annualized return, standard deviation, and Sharpe ratio for Global Minimum Variance without short selling (GMV) and with short selling strategies (GMVShort) using a 252-day rolling window. The graphs compare portfolios containing only dirty cryptocurrencies (D) versus those combining dirty and clean cryptocurrencies (DC).

These results, reflecting the average performance over a 250-day rolling window, suggest that the COVID-19 outbreak in 2020 marked a significant turning point in the volatility performance of cryptocurrency portfolios. The inclusion of clean cryptocurrencies may have contributed to increased portfolio volatility during periods of extreme market stress, such as the COVID-19 pandemic. The COVID-19 pandemic, characterized by extreme market stress and a global liquidity crunch, represents a unique scenario that may have obscured the safe-haven characteristics of clean cryptocurrencies. During such periods of heightened uncertainty, even assets with potential safe-haven status can be subject to general risk-off sentiment, leading to a uniform decline in asset prices. This phenomenon is consistent with the observation that the addition of clean cryptocurrencies did not reduce the drawdown risk within dirty cryptocurrency portfolios during the pandemic. It implies that during periods of severe market turmoil, the diversification benefits of clean cryptocurrencies may be limited due to the overriding influence of a broad risk aversion among investors.

Table 5 presents the average performance of portfolios containing only dirty cryptocurrencies and those with both dirty and clean cryptocurrencies over the out-of-sample period. The results show that adding clean cryptocurrencies to dirty cryptocurrency portfolios has several effects. For all optimization strategies, the mean returns decreased when clean cryptocurrencies were added. For the risk minimization strategies (GMV and GMV(Short)), volatility decreased. However, due to the decrease in mean returns, the Sharpe ratio also decreased. For the risk-return balanced strategies (EW, MV, and TP), volatility increased. For all strategies, CVaR95 and CVaR99 decreased significantly, with CVaR99 decreasing more than CVaR95. In particular, the decrease in CVaR99 was more significant, with reductions of more than 15% and 23% for the GMV and GMV(Short) strategies, respectively. Moreover, the modified Sharpe ratio of the GMV(Short) strategy improved. Finally, turnover rates increased for the combined portfolios. This increased turnover may be due to the more complex management requirements and the wider range of assets that need to be monitored and adjusted in combined portfolios.

Table 5 Portfolio performance.

Overall, these findings suggest that the inclusion of clean cryptocurrencies in dirty cryptocurrencies portfolios leads to a decrease in mean returns and mixed effects on volatility and risk-adjusted returns, depending on the strategy employed. However, the addition of clean cryptocurrencies significantly reduced the CVaR, particularly at the 99th percentile, suggesting enhanced tail risk mitigation. The decrease in CVaR is consistent with the notion that clean cryptocurrencies serve as a weak safe haven. They do not necessarily act as a direct hedge against the losses of dirty cryptocurrencies but provide diversification benefits that help mitigate extreme losses, even if other measures of risk such as volatility and drawdown do not decrease. This is a valuable insight for investors looking to manage tail risk in their portfolios, especially in volatile and uncertain markets.

Robustness tests

Alternative conditional models

To further enhance the robustness of our safe-haven analysis, we employ an alternative modeling approach. Specifically, we implement the asymmetric DCC model proposed by Cappiello et al. (2006) with a multivariate t-distribution and GARCH(1,1) based on t-innovations to capture potential fat tails and asymmetric effects in cryptocurrency correlations. Furthermore, we estimate the asymmetric DCC model alongside GJR-GARCH(1,1) to account for leverage effects in both volatility dynamics and correlation structures. The findings remain qualitatively consistent across these specifications, reinforcing the robustness of our results.

Sub-period analysis

To assess the robustness of the results, we split the out-of-sample observations into four sub-periods: 2019, 2010, 2011 and 2022 to May 2023. This allows us to compare the performance of portfolios with only dirty cryptocurrencies to those with a mix of clean and dirty cryptocurrencies under all optimization strategies in varying market conditions. The findings indicate that across all sub-periods, the inclusion of clean cryptocurrencies results in a reduction in CVaR under all optimization strategies. However, the impact on average returns, volatility, and maximum drawdown is mixed. These results align with those observed over the full period.

Rolling window

For conditional portfolio strategies, a rolling estimation window of 250 observations and an evaluation period spanning 1096 out-of-sample data points were employed. To assess the impact of the size of the rolling window and the duration of the evaluation period on performance, a sensitivity analysis was undertaken using 500 observations for estimation and the remaining 846 data points for evaluation. The results show that the use of 500 observations for estimation is consistent with the results obtained using the 250-rolling estimation window.

Sub-portfolio analysis

As shown in Table 4, the exclusion of BTC and ADA, which constitute the most dominant assets in the portfolio composition, led to a more balanced weighting allocation between dirty and clean cryptocurrencies. The out-of-sample performance reported in Tables 6 and 7 show that the CVaRs (at both 95% and 99% confidence) of the combined dirty and clean cryptocurrency portfolio are lower than those of the dirty cryptocurrency portfolio. This finding is consistent with the results of the entire portfolio.

Table 6 Portfolio weights (excl. BTC and ADA).

Table 7 Portfolio performance (excl. BTC and ADA).

Discussion and implications

This study examines the role of clean cryptocurrencies as a potential diversifier or safe havens within the volatile cryptocurrency market, particularly in relation to their energy-intensive counterparts. Our findings indicate that clean cryptocurrencies can serve as safe havens for dirty cryptocurrencies during periods of market stress. However, their effectiveness varies across asset pairs. While integrating clean cryptocurrencies into a portfolio can mitigate tail risk, this diversification does not consistently improve portfolio performance in terms of returns, volatility, or risk-adjusted measures.

Our study extends previous research on the diversification, hedging, and safe-haven properties of clean cryptocurrencies. Ren and Lucey (2022a) find that clean energy serves as a safe haven for both clean and dirty cryptocurrencies, particularly during periods of heightened volatility. Our findings support the notion that while clean cryptocurrencies do not function as direct hedges, they provide significant tail risk reduction benefits for dirty cryptocurrencies. This contrasts with Husain et al. (2023), who identify that financial uncertainty weakens the hedging or safe-haven properties of green cryptocurrencies for other assets. Our results are consistent with Esparcia et al. (2024) and Ali et al. (2024), who highlight the diversification benefits of green cryptocurrencies in equity portfolios. These findings suggest that investors seeking risk mitigation rather than return enhancement may benefit from incorporating clean cryptocurrencies into portfolios, particularly during periods of heightened market stress. Moreover, regulators should recognize their emerging role in sustainable finance and consider whether their integration into ESG-focused policies could contribute to broader financial stability.

Our study also contributes to the understanding of the relationship between clean and dirty cryptocurrencies. Sharif et al. (2023) and Duan et al. (2023) highlight the stronger link of clean cryptocurrencies to green economy indices and their weaker connection to the broader financial system compared to dirty cryptocurrencies. We extend these findings by showing that the safe-haven potential of clean cryptocurrencies is partly due to these different linkage dynamics. Pham and Nguyen (2022) find that green cryptocurrencies have weak links to dirty cryptocurrencies, except during periods of extreme volatility such as the COVID-19 pandemic. Similarly, Duan et al. (2024) and Będowska-Sójka and Kliber (2024) observe that the relationship between clean and dirty cryptocurrencies fluctuates under extreme market conditions, influenced by factors such as cross-border arbitrage. Given these distinct linkage dynamics, policymakers should assess whether regulatory frameworks should differentiate between clean and dirty cryptocurrencies, particularly in the context of systemic risk mitigation and liquidity constraints. Incorporating clean cryptocurrencies into broader climate-aware financial regulations could enhance their integration into mainstream financial markets while addressing their inherent volatility concerns.

The economic rationale behind these findings lies in the distinct characteristics of clean and dirty cryptocurrencies. Ren and Lucey (2022a) note that herding behavior is more prevalent in dirty cryptocurrencies, particularly during down- turns, whereas clean cryptocurrencies tend to herd with dirty ones only during bull markets. This implies that clean cryptocurrencies may exhibit greater market independence, offering diversification benefits during periods of market stress. Chen and Nguyen (2024) further show that positive economic news amplifies herding among clean cryptocurrencies, while dirty cryptocurrencies exhibit pronounced anti-herding behavior under similar conditions. In declining markets, clean cryptocurrencies exhibit stronger herding if investor sentiment remains optimistic, whereas in rising markets, anti-herding is more pronounced. This distinct behavior and sensitivity to news sentiment allows clean cryptocurrencies to mitigate tail risk in portfolios dominated by dirty assets. However, their higher volatility and nascent market structure contribute to their inconsistent impact on portfolio performance metrics, including returns, volatility, drawdown risk, and risk-adjusted measures. Policymakers should assess whether regulatory frameworks need to account for the heightened volatility and sentiment-driven behavior of clean cryptocurrencies, particularly in the context of investor protection and systemic risk mitigation.

While our study employs a comprehensive framework to assess the risk dynamics of clean cryptocurrencies and provides valuable insights into their role as weak safe-haven assets, further research is warranted. Future studies could enhance this understanding by employing non-linear dependence structures and alternative risk modeling approaches. For example, copula-based methods (Banerjee and Pradhan, 2024) could provide deeper insights into the tail dependencies between clean and dirty cryptocurrencies, especially under extreme market conditions. In addition, high-frequency-based CVaR models (Banerjee, 2023) could improve event-driven risk analysis, allowing for a more granular assessment of market reactions to geopolitical shocks and regulatory changes. Beyond risk modeling, incorporating multi-criteria optimization techniques, such as fuzzy TODIM combined with genetic algorithms (Banerjee et al. 2024b), could better account for investor preferences, transaction costs, and environmental constraints in portfolio construction. These advanced optimization frameworks could help develop more robust portfolio strategies, balancing financial performance with sustainability objectives while considering real-world trading constraints.

From a systemic risk perspective, future studies could explore dynamic spillover networks that integrate climate risk and uncertainty in climate policy (Banerjee et al. 2024a) to identify how environmental factors influence risk propagation within the cryptocurrency ecosystem. Furthermore, the adoption of double-layer network models and CoVaR-based systemic risk analysis (Banerjee et al. 2025) could provide a broader framework to examine contagion effects between clean cryptocurrencies and traditional financial markets. Understanding these contagion dynamics is crucial for assessing the stability of clean cryptocurrencies within multi-asset portfolios, particularly as climate-related regulations shape market structures and risk transmission channels.

Conclusion

This study examines the diversification and safe-haven properties of clean cryptocurrencies in the context of sustainable investing, with a particular focus on their interactions with dirty cryptocurrencies. The findings provide three key insights. First, while clean cryptocurrencies do not serve as direct hedges, they exhibit weak safe-haven features for dirty cryptocurrencies during periods of market stress, though their efficacy varies by asset pair. Second, incorporating clean cryptocurrencies into dirty cryptocurrency portfolios effectively reduces tail risk, regardless of the portfolio optimization strategy employed. However, risk reduction may not always result in higher portfolio returns, volatility, drawdown risk, or risk-adjusted performance indicators. Third, the tail risk diversification benefits of clean cryptocurrencies remain robust across different market conditions, estimation windows, and portfolio compositions.

The results of this study have important implications for investors and portfolio managers considering clean cryptocurrencies in their investment strategies. Given their ability to mitigate tail risk, clean cryptocurrencies can serve as valuable components of tail risk management strategies, particularly during periods of heightened market stress. However, as their safe-haven effectiveness varies across asset pairs, portfolio managers should conduct rigorous risk assessments when selecting specific clean cryptocurrencies for inclusion. Moreover, as clean cryptocurrencies do not consistently enhance portfolio returns or other risk-adjusted measures, they should be viewed primarily as defensive assets rather than as return-enhancing components. Portfolio construction should balance the benefits of risk reduction against potential performance trade-offs, potentially integrating dynamic allocation models that adjust exposure to clean cryptocurrency based on evolving market conditions. Institutional investors must also consider liquidity and market depth constraints when incorporating clean cryptocurrencies into large portfolios. Compared to dominant cryptocurrencies such as Bitcoin and Ethereum, clean cryptocurrencies have lower market capitalization and liquidity, requiring careful position sizing to minimize execution risk and price volatility while ensuring alignment with overall portfolio objectives.

Beyond investment considerations, this study offers insights for policymakers and regulators seeking to promote sustainable investment practices in the cryptocurrency market. Regulators could introduce incentives, such as tax benefits or ESG certifications, to encourage the adoption of clean cryptocurrencies and support the transition to sustainability-oriented digital assets. In addition, the establishment of standardized environmental metrics to assess cryptocurrency sustainability would enhance market transparency and enable investors to make more informed decisions. Given the demonstrated benefits of clean cryptocurrencies in tail risk mitigation, regulators should also explore their potential role in enhancing financial stability, possibly including them in sustainable finance frameworks or developing guidelines for their inclusion in institutional portfolios.

Despite these findings, there are several limitations to this study. Data limitations pose a significant challenge, particularly with respect to the market capitalization, liquidity, and historical depth of clean cryptocurrencies. As the clean cryptocurrency sector is still in its infancy, many assets lack long-term price histories and deep liquidity, which may limit the statistical power of inferences. In addition, the relatively small market capitalization of clean cryptocurrencies compared to Bitcoin and Ethereum may affect their risk-return characteristics and diversification potential. Moreover, this study focuses on a specific subset of clean and dirty cryptocurrencies, which may limit the generalizability of the findings to the broader cryptocurrency market. Furthermore, this study does not explicitly examine the fundamental drivers of clean and dirty cryptocurrency performance, such as regulatory developments, technological advances, and changes in investor sentiment, all of which could provide deeper insight into the evolving market dynamics of clean cryptocurrencies.

Future research could address these limitations and extend this study in several directions. First, as clean cryptocurrency markets mature and more comprehensive datasets become available, future studies could validate these findings with broader samples and longer historical data, improving the robustness of statistical inferences and providing a clearer picture of the long-term viability of clean cryptocurrencies. Second, further research could also explore the determinants of clean cryptocurrency performance, examining how regulatory frameworks, technological innovation, and investor sentiment shape their risk-return characteristics. Third, while this study focuses on intra-class diversification within the cryptocurrency market, future research could explore inter-class diversification, assessing how clean cryptocurrencies interact with traditional sustainable assets such as ESG stocks and green bonds. Moreover, future research could employ advanced multi-criteria optimization techniques to better account for investor preferences, transaction costs, and environmental constraints in portfolio construction. In addition, methodological advances could refine analytical frameworks by incorporating copula-based models for tail-dependency analysis, high-frequency-based CVaR models for granular risk assessment, dynamic network models that account for climate risk and policy uncertainty interventions, and double-layer network models with CoVaR-based for systemic risk analysis. These approaches would provide deeper insights into the role of clean cryptocurrencies in ESG-focused portfolios and their systemic implications within an evolving climate policy landscape.