Stylized facts, volatility dynamics and risk measures of cryptocurrencies

Bruzgė, Rasa et al. Article Stylized facts, volatility dynamics and risk measures of cryptocurrencies Journal of Business Economics and Management (JBEM) Provided in Cooperation with: Vilnius Gediminas Technical University (VILNIUS TECH) Suggested Citation: Bruzgė, Rasa et al. (2023) : Stylized facts, volatility dynamics and risk measures of cryptocurrencies, Journal of Business Economics and Management (JBEM), ISSN 2029-4433, Vilnius Gediminas Technical University, Vilnius, Vol. 24, Iss. 3, pp. 527-550, https://doi.org/10.3846/jbem.2023.19118 This Version is available at: https://hdl.handle.net/10419/317637 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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E-mail: [email protected] This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Journal of Business Economics and Management ISSN 1611-1699 / eISSN 2029-4433 2023 Volume 24 Issue 3: 527–550 https://doi.org/10.3846/jbem.2023.19118 STYLIZED FACTS, VOLATILITY DYNAMICS AND RISK MEASURES OF CRYPTOCURRENCIES Rasa BRUZGĖ 1, Jurgita ČERNEVIČIENĖ 2, Alfreda ŠAPKAUSKIENĖ 3*, Aida MAČERINSKIENĖ 4, Saulius MASTEIKA 5, Kęstutis DRIAUNYS 6 1,3,4Faculty of Economics and Business Administration, Vilnius University, Vilnius, Lithuania 2Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, Kaunas, Lithuania 5,6Kaunas Faculty, Vilnius University, Vilnius, Lithuania Received 9 March 2023; accepted 26 April 2023 Abstract. This study explores the stylized facts, volatility clustering, other highly irregular behaviour, and risk measures of cryptocurrencies’ returns. By analysing bitcoin, ripple, and ethereum daily data we establish evidence of strong dependencies among analysed cryptocurrencies. This paper provides new insights about cryptocurrency behaviour and the main measures of risk and detailed comparative analysis with tech-stocks. Comprehensive research on stylized facts confirmed high risk for both cryptocurrencies and tech-stocks with cryptocurrencies being even riskier. Empirical research findings are useful in developing dependence and risk strategies for investment and hedging purposes, especially during more volatile periods in the markets as there was confirmed existence of volatility clusters when high volatility periods are followed by low volatility periods. Sensitivity analysis and measures of Value-at-Risk (VaR) and Expected Shortfall (ES) show the amount of losses investors can expect in the worst case scenario. Our results confirm the existence of predictability, volatility clustering, and possibilities for arbitrage opportunities. Findings could be beneficial for investors and policymakers as well as for scientific purposes as findings give us a better understanding of the behaviour of cryptocurrencies. Keywords: cryptocurrency, risk measures, volatility clustering, stylized facts, value-at-risk, expected shortfall. JEL Classification: G1, G12, G17. Introduction Cryptocurrencies have attracted enormous attention from investors, regulators, and the media since bitcoin was introduced in 2008. The cryptocurrency market is expanding extremely fast however still there are many topics underexplored academically. Novel empirical research concludes that the best-known bitcoin cryptocurrency acts more like a financial asset than a currency but has attractive features as a medium of exchange, as well (Katsiampa etal., 2022). There is no doubt that bitcoin represents a unique financial instrument having its advantages 528 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies and disadvantages (Polasik etal., 2016). Cryptocurrencies differ in their functionality and mainly they can be used as a medium of exchange which allows investors and speculators to include cryptocurrencies in their investment portfolios. There are extensive studies on how bitcoin and other cryptocurrencies can be used in a diversified portfolio as a hedge against losses (Salisu etal., 2019; Fakhfekh & Jeribi, 2019). However, what remains a sore point of analysis is the question of how risky are cryptocurrencies and whether could we predict the volatility of cryptocurrency returns to be prepared to take action before big volatility periods. Wang etal. (2022) studies asymmetric contagion effects between stock and cryptocurrency markets. Le etal. (2021) uncover that the connectedness among green bonds, fintech, and cryptocurrencies is very high. Symitsi and Chalvatzis (2019) employ an asymmetric multivariate VARGARCH model to study spillover effects between Bitcoin and energy and technology companies. Empirical researches make clear that financial markets are extensively analyzed and compared with the cryptocurrency market. However, scientific literature has not yet covered the comparison between one of the most popular cryptocurrencies and tech-stocks by performing stylized facts analysis covering the evaluation of risk measures, and volatility dynamics of returns. Even though research about Bitcoin is evolving, the existing literature lacks any test about volatility clustering and periods of large, recurrent arbitrage opportunities occurring in highintensity periods. This paper provides a systematic review of the empirical literature based on the major topics that have been associated with the market for cryptocurrencies. Evaluation of stylized facts, volatility, and risk remains the key point for a better understanding of cryptocurrencies and their behavior. Our results indicate the existence of similar behavior between cryptocurrency and tech-stock markets. Both markets are sensitive to shocks and are considered to be risky with cryptocurrencies being even riskier. However, it does not appear that those markets are correlated. These results suggest bitcoin may offer diversification benefits for investors against technology sector risk. Research gives relevant insights for investors as it explores measures of risk which have to be considered before investing. For scientists, our results give a better understanding of cryptocurrency behavior in the cryptocurrency adoption phase as it’s still a very new and growing asset class. This paper explores stylized facts of different functionality cryptocurrencies, naming bitcoin, ethereum and ripple, compares them with tech-stocks, and gives significant contributions. First, we started our analysis with a systematic analysis of scientific literature. We gave a detailed comparative analysis of information and evaluated descriptive statistics. We explored stylized facts such as autocorrelation, volatility clustering, normality, and outliers, measured extreme values and tails dependency, calculated correlation coefficients over time, cross-correlations with different lags, and rolling correlations through all the periods between different cryptocurrency pairs. We evaluated the similarity between tech-stocks and cryptocurrencies using rolling correlations. Finally, we estimated Value-at-Risk (Var) and Expected Shortfall (ES) with historical, modified, and gaussian methods for both cryptocurrencies and tech-stocks. We checked the accuracy of modeling using a back-testing technique. Logical analysis is used to summarize the results. The paper is organized as follows. Section 1 is devoted to the scientific literature review. Section 2 sets out the methodology and describes the data. Section 3 interprets the results of cryptocurrency stylized facts analysis, extensive correlation analysis, and sensitivity analysis of VaR and ES risk measures. Backtesting is used to evaluate the accuracy of modeling. Section 3 provides a comparison with tech-stocks and tech-stocks sensitivity analysis. The last section gives conclusions and points out the main findings. Journal of Business Economics and Management, 2023, 24(3): 527–550 529 1. Literature review Risk and volatility are usually associated with the efficiency of the market. As cryptocurrencies are considered to be the riskiest financial instrument, scientists usually explore the efficiency of the cryptocurrency market (Makarov & Schoar, 2020; Tran & Leirvik, 2020; Urquhart, 2017). Efficiency topic leads to arbitrage which was particularly precisely analysed by Chaim and Laurini (2019), Elendner etal. (2016), Ji etal. (2019), and Sifat etal. (2019). All these papers demonstrate that the cryptocurrency market is a developing market with arbitrage potential as prices are inefficient. More specific actual and not potential arbitrage analysis was done by Bruzgė and Šapkauskienė (2022) who gave valuable insights into arbitrage topic. Scientists explored high frequency unique arbitrage data in thirteen cryptocurrency exchanges and found that investors can mitigate their trading risks by knowing which exchanges are attractive for arbitrage trading. However, high frequency trading comes with additional risks which have to be taken into account before investing. There are different high frequency trading (HFT) strategies which were analyzed and tested by Vaitonis and Masteika (2021) who created the testing method for the automated HFT strategies and confirmed that daily closing price statistical arbitrage strategies can be effectively applied in HFT. Moreover, cryptocurrency market is unique as cryptocurrencies are connected to Bitcoin and there exists long-term memory dependency on Bitcoin. Jiang etal. (2018) offered a new efficiency index with a rolling window used for testing the existence of long-term memory in the Bitcoin market. The results support other scientists’ findings that the bitcoin market is inefficient (Bariviera, 2017; Chuen etal., 2018; Corbet etal., 2018). Also, a time-varying approach used by Jiang etal. (2022) makes an advantage when used for tracking the dynamic efficiency. One of the main reasons why efficiency is not maintained is the lack of reasonable pricing mechanisms and irrational behavior of investors. An effective market cannot have any mispricing. If there exists any possibility for mispricing it leads to arbitrage that increases investors’ interest and leads to stronger deviations, uncertainty, and volatility. Makarov and Schoar (2020) performed extensive research on bitcoin arbitrage topics and found that bitcoin experiences big recurring deviations in prices across different exchanges. Another finding is that price deviations usually exist among countries or regions but not within the same country. Price differences between geographical regions were confirmed by other scientists, as well (Omane-Adjepong etal., 2019; Thaqeb & Algharabali, 2019). Cryptocurrency markets exhibit periods of large, recurrent arbitrage opportunities across exchanges due to the high volatility associated with risk. Bitcoin becomes not just attractive for arbitrage but also could work well as a diversifier for hedging speculators’ investments. Comprehensive research on extreme values was made by Borri (2019) who explored conditional tail-risk and found that idiosyncratic risk can be reduced, and portfolios of cryptocurrencies could offer attractive returns and hedging properties when included in investors’ portfolios. Also, Gkillas and Katsiampa (2018) by investigating the extreme value theory analyzed the behavior of the returns of the five largest cryptocurrencies and found that bitcoin cash has the highest potential for gain and loss. Canh etal. (2019) as well as Beneki etal. (2019) dived deeper into the volatility topic and explored systematic risk and found that volatility spillovers exist with strong positive correlations among cryptocurrencies which offers diversification benefits and hedging abilities within the cryptocurrency market itself. As research by Makrichoriti and Moratis’s (2016) show Bitcoin is fully independent of external factors coming from the capital, bond, and 530 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies commodity market. Those results lead to the conclusion that cryptocurrencies can be used as hedging. Evidence by Corbet etal. (2018) further justifies bitcoin as a potential risk factor in the maximization of returns of conventional financial assets. It means that by including bitcoin investors not only can hedge their investment portfolio but also maximize the returns. Salisu etal. (2019) claim that bitcoin price exhibits such predictive powers that investors and policymakers can exploit such information when making future decisions which may minimize risks and uncertainties associated with financial assets. Risks were precisely analyzed in the scientific literature by evaluating such risk measures as Value-at-Risk (VaR) and Expected Shortfall (Hrytsiuk etal., 2019; Likitratcharoen etal., 2018; Pele & Mazurencu-Marinescu-Pele, 2019; Trucíos etal., 2019). Besides the function of risk evaluation these measures of risk increase the accuracy of forecasting (Jiang etal., 2022; Görgen etal., 2022; Müller etal., 2022). Jiang etal. (2022) used a method capturing the stylized facts and found that including analysis of stylized facts in the analysis is useful for capturing sudden changes in the density of cryptocurrency returns. Müller etal. (2022) suggested that the main driver for the returns of cryptocurrencies is the conditional standard deviation and not the distribution of the error term. Görgen etal. (2022) compared VaR with random forest and showed that the random forest method significantly improves the forecasting performance and helps more clearly to access risks of cryptocurrencies that are prone to speculation and hypes and have the most active users. Furthemore, empirical findings by Qian etal. (2022) showed that bitcoin’s price is affected by different volatility regimes. In our paper, by taking into the account the main risk measures and stylized facts we will broaden the existing research by exploring the volatility clusters. Due to technological nature bitcoin and other cryptocurrencies are usually compared with tech-stocks. Chu etal. (2021) explored bitcoin comparing it which tech-stocks and found that individuals see bitcoin more as an investment than a technology. Abakah etal. (2023) explored bitcoin and artificial intelligence stocks and found that portfolio investors can benefit by including these assets in their diversified portfolios. Wang etal. (2022) found dependences between stock and cryptocurrency markets and their results help to predict the development trend of the high-tech industry. In this paper, we compare bitcoin with tech-stocks by extending existing research from an individual perspective to the research on volatility topic. Literature analysis showed that cryptocurrency market is inefficient compared with gold and stock markets. Stronger deviations, uncertainty, and volatility are the results of the irrational behavior of investors. This confirms the need for scientists to fill the research gap and give a better understanding of cryptocurrencies. Literature analysis shows that cryptocurrencies offer diversification benefits and can work as a hedge in the investment portfolio. Scientific research explores volatility clustering and seasonal patterns in the cryptocurrency market, however, still there is a lack of empirical research which performs sensitivity analysis of both cryptocurrencies and tech-stocks and gives valuable insights into the volatility clustering and the risk in these markets. 2. Methodology 2.1. Data In this study, we analyze daily closing data for the 3 cryptocurrencies bitcoin, ripple and ethereum. Cryptocurrencies have different functionality which is why it is interesting to compare how they react to each other and to external factors. Bitcoin is a purely peer-to-peer version of Journal of Business Economics and Management, 2023, 24(3): 527–550 531 decentralized digital currency, while ethereum is used for smart contracts functionality and ripple is the first global real-time gross settlement network (RTGS) which enables banks to send realtime international payments across networks. Data for each cryptocurrency is taken from the earliest date publicly available online at https://coinmarketcap.com. Data used for bitcoin starts from 2013-04-29, for ethereum starts from 2013-08-04 and for ripple starts from 2015-08-08. All cryptocurrencies have data until 2021-12-31. All figures and tables in our empirical research are created by authors using the data we have, R programming language and Microsoft Excel. 2.2. Methods The empirical analysis is based on daily returns, calculated as the difference in the log of prices. For each cryptocurrency, daily returns were computed by 1 log 100, t t t P rP−  = ×    (1) with t P being the closing on day t. We explored stylized facts such as outliers, autocorrelation, volatility clustering and normality. In first step, we excluded the biggest outlier for each cryptocurrency to give more reasonable results. We tested the normality of cryptocurrency returns using the Jarque-Bera and ShapiroWilk tests. The Jarque-Bera test is based on skewness and kurtosis and is defined as: ( ) 2 2 3 , 64 K N JB S  −  = +   (2) where S, K, and N represent the skewness, the kurtosis, and the sample size. The Shapiro– Wilk test is defined as: ( ) ( ) ( ) 2 1 2 1 , n ii i n i i aX SW XX = = = − ∑ ∑ (3) where ( ) i X are the ordered random sample values, X is sample mean, i a is constants that derived generated from the means, variances and covariances of the order statistics of a sample of size n from a normal distribution. When the p-value is less than or equal to 0.05, the test rejects the normality hypothesis. Autocorrelation analysis provides information about the presence of a significant periodic component in the data set. The correlation between returns separated by τ periods is evaluated by the autocorrelation of a set of n observations with lag τ:  ( )( ) ( ) 2 , 11 / , 0, nn r tt t tt rrr r rr −τ τ +τ = = ρ = − − − τ> ∑∑ (4) where r the sample mean of all n observations, ˆ ρ indicates that the sample statistic estimates a correlation parameter ρ of a stochastic process when the data come from a stationary process. The two subscripts τ and r respectively state the lag and the series that provide the estimates. 532 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies The Ljung-Box statistic shows the existence of significant first-order autocorrelation in the residuals. In general, the Ljung-Box test is defined as: ( ) 2 1 , ˆ 2 mk k r Q nn nk = = + − ∑ (5) where ˆ k r is the estimated autocorrelation of the series at lag k, and m is the number of lags being tested. If p-value of the test is less than 0.05 with 95 percent confidence level we can reject the null hypothesis of the test, that the model does not exhibit lack of fit, and conclude that the data values are dependent which means that returns data is suitable for ARCH modelling. The ARCH-LM test is a Lagrange multiplier test to evaluate the importance of autoregressive conditional heteroskedastic (ARCH) effects. We evaluated correlation, cross-correlation and rolling correlation coefficients. Correlation measures the degree to which two variables move in relation to each other. Cross-correlation show the similarities in the movement of two factors over time and rolling correlations are simply applying a correlation between two time series over time. After comprehensive data analysis, we performed sensitivity analysis, measured Value-at-risk (VaR) and Expected Shortfall (ES) on year by year basis in 2016–2021 and back-tested results. Sensitivity analysis of the cryptocurrency returns started from an interpretation of summary statistics and evaluation of its historical changes. Estimation of two major tail risk measures Value-at-Risk (VaR) and Expected Shortfall (ES) give a good understanding of the risk of cryptocurrency returns. VaR is a function of two parameters: the time horizon (n days) and the confidence level (α%). It is the loss level over N days that has a probability of only (100-α) % of being exceeded. The most simple way to define VaR, according to McNeil etal. (2015) is to imagine, that the VaR of our portfolio at the confidence level α ∈ (0, 1) is given by the smallest number l such that the probability that the loss L exceeds l is no larger than (1– α). It is defined as given in (6) formula: ( ) { } ( ) { } inf : 1 inf : L VaR l RPL l l RF l α= ∈ > ≤ −α = ∈ ≥α . (6) The historical method of VaR is a non-parametric VaR estimation method using the historical distribution and the probability quantile of the distribution. The return at the correct quantile (usually 95% or 99%), is the non-parametric VaR estimate. This method assumes that all possible future variations have been experienced in the past and that the historically simulated distribution is identical to the return’s distribution over the forward-looking risk horizon. Modified VaR measure incorporates skewness and kurtosis via an analytical estimation using a Cornish Fisher (a special case of a Taylor) expansion. The resulting measure is referred to variously as “Cornish Fisher VaR”. According to Artzner etal. (1999), the expected shortfall is the conditional expectation of loss given that the loss is beyond the VaR level. Yamai and Yoshiba (2005) define the expected shortfall as given in (7) formula: ( ) ( ) ,ES X E X X VaR X αα = ≥ (7) where X is a random variable denoting the loss of a given portfolio. The expected shortfall indicates the average loss when the loss exceeds the VaR level. Journal of Business Economics and Management, 2023, 24(3): 527–550 533 Back-testing is the practice of evaluating risk measurement procedures by comparing ex-ante estimates/forecasts of risk measures with ex-post realized losses and gains. It tests how well risk estimates would have performed in the past. It allows us to evaluate whether a model and estimation procedure produce credible risk measure estimates. Methodologies fall into three categories: coverage tests, distribution tests and independence tests. Coverage tests assess whether the frequency of exceedances is consistent with the quantile of loss a VaR measure is intended to reflect. Distribution tests are goodness-of-fit tests applied to the overall loss distributions forecast by complete VaR measures. Independence tests assess whether results appear to be independent of one period to next. Our empirical research use coverage tests as a back-testing technique. Also, by using rolling correlations we compared how bitcoin is correlated with tech-stocks and performed the same sensitivity analysis for tech-stocks. 3. Results 3.1. Data analysis– descriptive statistics and quantiles We started our analysis with descriptive statistics as it summarizes the characteristics of a data set. We evaluated measures of central tendency for bitcoin, ethereum and ripple and analysed measures of variability to provide basic information about variables in a dataset. From descriptive statistics, we can see that our data are following big variations. Table 1. Descriptive statistics of bitcoin daily returns per all analysed period and different years from 2013 to 2021 Variance SD Min Max Mean Skew Kurt Median BTC_Price 14388863 3793.27 68.43 19497.4 3126.08 1.26 0.82 736.52 BTC_Ret_all 0.0018 0.0427 –0.2337 0.4297 0.0026 0.5049 9.7027 0.0018 BTC_Ret_2013 0.0047 0.0685 –0.2337 0.4297 0.009 0.8921 8.1305 0.0073 BTC_Ret_2014 0.0015 0.0391 –0.1887 0.1929 –0.0016 –0.0239 5.6712 –0.0017 BTC_Ret_2015 0.0013 0.036 –0.2115 0.1782 0.0015 –0.868 7.8131 0.0012 BTC_Ret_2016 0.0006 0.0252 –0.1533 0.1195 0.0025 –0.279 8.8065 0.0018 BTC_Ret_2017 0.0025 0.05 –0.1874 0.2525 0.0085 0.4385 3.8035 0.0088 BTC_Ret_2018 0.0018 0.0425 –0.1685 0.1322 –0.0026 –0.2119 1.7405 0.0008 BTC_Ret_2019 0.0013 0.0356 –0.1409 0.1736 0.0023 0.5648 4.6202 0.0012 BTC_Ret_2020 0.0014 0.0377 –0.3717 0.1819 0.0046 –2.1970 27.9693 0.0027 BTC_Ret_2021 0.0018 0.0421 –0.1377 0.1875 0.0022 0.1127 1.5231 0.0013 By analysing descriptive statistics of bitcoin (BTC), ripple (XRP) and ethereum (ETH) we can see that the first year of analysis was the early stage of the crypto market and it followed big variations (Tables 1–3). Another high-intensity period was 2017 booming at the end of the year. We can see that 2017 was extremely high in daily returns for ripple which had the biggest loss in daily returns and a lot of larger positive returns (Table 2). Returns were positively skewed with the biggest positive value and it had an extremely high kurtosis value. 534 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies Table 2. Descriptive statistics of ripple daily returns per all analysed period and different years from 2013 to 2021 Variance SD Min Max Mean Skew Kurt Median XRP_Price 0.1 0.317 0.003 3.38 0.189 3.932 24.818 0.015 XRP_Ret_all 0.007 0.082 –0.46 1.794 0.004 6.339 109.457 –0.003 XRP_Ret_2013 0.022 0.148 –0.338 0.81 0.02 1.811 7.254 0.008 XRP_Ret_2014 0.004 0.065 –0.401 0.291 0.002 –0.041 6.6 –0.001 XRP_Ret_2015 0.002 0.045 –0.151 0.258 –0.003 0.952 5.797 –0.004 XRP_Ret_2016 0.001 0.037 –0.103 0.393 0.001 4.344 37.406 –0.004 XRP_Ret_2017 0.021 0.144 –0.46 1.794 0.024 6.262 65.955 0 XRP_Ret_2018 0.005 0.068 –0.298 0.38 –0.003 0.698 5.259 –0.005 XRP_Ret_2019 0.001 0.037 –0.126 0.257 –0.001 0.959 7.707 –0.003 XRP_Ret_2020 0.006 0.080 –0.327 0.560 0.007 1.557 10.048 0.002 XRP_Ret_2021 0.002 0.047 –0.195 0.211 –0.004 0.166 3.785 –0.004 Table 3. Descriptive statistics of ethereum daily returns per all analysed period and different years from 2015 to 2021 Variance SD Min Max Mean Skewness Kurtosis Median ETH_Price 58257.01 241.36 0.43 1396.42 203.34 1.82 3.62 149.02 ETH_Ret_all 0.0042 0.065 –0.2706 0.5103 0.0054 1.1909 7.5799 –0.0008 ETH_Ret_2015 0.0129 0.1137 –0.728 0.5103 0.0006 –0.4891 15.02 –0.009 ETH_Ret_2016 0.0048 0.0693 –0.2633 0.3536 0.0082 0.7657 4.253 –0.0025 ETH_Ret_2017 0.0053 0.0731 –0.2706 0.3366 0.0151 1.0223 3.8806 0.0039 ETH_Ret_2018 0.0031 0.0561 –0.1869 0.1807 –0.0032 –0.0244 1.1324 –0.0026 ETH_Ret_2019 0.0017 0.0411 –0.1674 0.156 0.0006 –0.1169 3.2202 –0.0008 ETH_Ret_2020 0.003 0.056 –0.272 0.259 0.006 0.009 3.418 0.006 ETH_Ret_2021 0.002 0.041 –0.148 0.114 –0.004 –0.283 0.886 0.000 Another common thing seen from the results about all analysed cryptocurrencies is that the mean of analysed cryptocurrencies was negative (Tables 1–3). Even though bitcoin had more than half positive daily returns, data was negatively skewed and maximum return was the lowest in all periods analysed. All these points show that after booming at the end of 2017, traders lost their trust in bitcoin. However, another common point highlighted for those cryptocurrencies is that all of them became more stable in 2019 as price fluctuations for all of them had the lowest values and the minimum loss value was the lowest, as well. Bitcoin, ethereum and ripple had a higher mean of returns value in 2019 compared with 2018 (Tables 1–3). Almost in all periods ethereum and ripple had 50% values of negative daily returns while bitcoin results were positive (Tables 4–6). Even though half of the returns of ripple and ethereum were negative almost in all periods but 75% quantile showed that ripple an ethereum tend to reach higher positive returns, for example, bitcoin’s 75% quantile value is 0.184, ripple’s is 0.0197 and ethereum’s is 0.0276. Given findings lead to the conclusion that it is necessary to evaluate periods in which prices are changing separately as daily closing prices do not show the exact returns of market participants. Journal of Business Economics and Management, 2023, 24(3): 527–550 541 per 1 point, another reacts to that change and moves the same direction after about 17 and more than 35 days. Also, it reacts negatively after one day. When evaluating the correlation coefficient between bitcoin and ethereum there is only reaction after 17 days and a negative reaction after 1 day. After measuring cross-correlations for ripple and ethereum it could be easily visually seen that cross-correlation usually occurs after a few days as cross-correlation values breach the given tolerance interval from –0.05 to 0.05. 3.2.6.2. Rolling correlation Finally, another type of correlation is a rolling correlation which measures the volatility of returns through all periods. Figure 7 shows the rolling correlations of the cryptocurrencies log-returns series available at each period. Rolling correlations are calculated over a backwards-looking window of 30 days. Despite that rolling correlation between bitcoin and ethereum was unstable until 2018, there is a unique change from the well-known spike at the end of 2017. We can see that after big bitcoin price movements in the end of 2017, 2018 Figure 6. Cross-correlation of bitcoin, ripple and ethereum with 50 lag Figure 7. Rolling correlation for ethereum and ripple, bitcoin and ethereum, bitcoin and ripple pairs 542 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies started with strong correlation between all analysed cryptocurrency pairs and it remains until the beginning of 2022. Only correlation between ethereum and ripple started to weaken in the end of 2020 but it continue to be strong from the middle of 2021. These results show that cryptocurrencies are strongly related to each other. According to De Pace and Rao (2022), correlations are natural to understand because cryptocurrencies are, in general, independently created and are based on slightly different platforms, technologies, and protocols. Thus, they exhibit different features, characteristics, and limitations. Findings based on correlation analysis lead to the conclusion that cryptocurrencies are related to each other. Extreme values on the main bitcoin cryptocurrency may tend to affect other cryptocurrencies with a delayed effect. Also, correlations are changing over time, so in order to achieve the best results and make predictions, it is necessary to evaluate how they change. 3.2.7. Comparison with tech-stocks By looking at rolling correlations between tech-stocks and bitcoin we can see that it follows some cycles (Figure 8). However, even if in some periods correlation coefficient shows medium strength linear dependency with coefficient value of 0.5 or 0.6, soon correlation goes to zero, or even negative value and cycles changes. Overall, by looking at the graph we can see that there is no correlation between tech-stocks and bitcoin as correlation coefficient between them usually fluctuates around zero. As bitcoin, ripple and ethereum are not correlated with tech-stocks, they can be used together with tech-stocks in a diversified portfolio. Figure 8. Rolling correlation for Amazon and bitcoin, Tesla and bitcoin, Meta and bitcoin pairs 4. Evaluation of risk measures A further empirical sensitivity analysis follows with the best-known risk estimation measures of Value-at-Risk (VaR) and Expected Shortfall (ES). VaR modelling determines the potential for loss in the entity being assessed and the probability of occurrence for the defined loss. The empirical analysis included nonparametric methods for VaR estimation as logarithmic returns are non-stationary, there is no normal distribution and outliers exist. There were used historical, modified and gaussian methods. VaR gives the maximum loss on a portfolio over a specific time period for a certain level of confidence. Journal of Business Economics and Management, 2023, 24(3): 527–550 543 4.1. Bitcoin, ethereum and ripple– VaR, ES Sensitivity analysis for Value-at-Risk and Expected Shortfall shows that results are almost the same for bitcoin in all exchanges using historical, modified and gaussian methods (Figure9). However, in all cases, the modified method gives not reliable results as with increasing confidence level risk measures steadily go down until some point after which risk measures become smaller. This shows that the modified method is not suitable for evaluating ES. In order to check if the results are accurate, we used well-known back-testing technique. Figure 9. Risk confidence sensitivity for bitcoin, ripple, ethereum Value-at-Risk and Expected Shortfall An analysis is based on evaluation with confidence levels of 95%. We determined one-day VaR for bitcoin in 2021 is equal to 6.4% with historical method (Table 10). This means that with a 95% confidence level the worst daily loss will not exceed 6.4% for bitcoin. Ripple and ethereum experience larger VaR values of 9.8% and 7.9% accordingly. It is clear that with a 95% confidence level gaussian method gives larger VaR values while the historical method shows the smallest VaR value. Bitcoin is still considered the least risky cryptocurrency as VaR values with all methods are smaller than for other cryptocurrencies. Back-testing determines the exceedance amount of a VaR model by involving the comparison of the calculated VaR measure to the actual losses (or gains) achieved. Value shows how many times values exceeded the expected VaR level (Table 10). In this case, the smaller the exceedance amount the better and we can see that most of the time best results are achieved using the historical method. 544 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies Table 10. VaR for bitcoin, ripple, ethereum with 95% confidence levels using Historical, Modified and Gaussian methods BTC XRP ETH Historical Modified Gaussian Historical Modified Gaussian Historical Modified Gaussian 2016 0.027 0.036 0.039 0.042 0.023 0.052 0.081 0.084 0.105 Exceed 11 20 19 10 16 22 17 23 30 2017 0.073 0.063 0.073 0.094 0.030 0.162 0.083 0.077 0.105 Exceed 28 29 33 6 21 18 13 23 23 2018 0.077 0.073 0.072 0.099 0.094 0.115 0.099 0.094 0.095 Exceed 16 20 16 14 19 20 22 23 20 2019 0.047 0.047 0.056 0.057 0.056 0.058 0.066 0.066 0.067 Exceed 13 22 24 17 24 19 17 22 19 2020 0.045 0.041 0.046 0.073 0.065 0.097 0.065 0.058 0.065 Exceed 18 27 22 12 31 28 17 26 21 2021 0.064 0.066 0.066 0.098 0.070 0.125 0.079 0.082 0.086 Expected Shortfall is defined as the average of all losses which are greater or equal than VaR. It gives the expected value of an investment in the worst case (Table 11). For bitcoin, using historical method this value with a 95% confidence level is equal to 9.4% and for ripple is equal to 16.4%. It shows that in the worst-case loss in bitcoin would be 9.4% which is less than 16.4% for ripple. The difference between VaR and ES for bitcoin is equal to 3 % and for ripple this difference is 6.6%. That means that in worst case ripple is more likely to evidence losses. Table 11. ES for bitcoin, ripple, ethereum with 95% confidence levels using Historical, Modified and Gaussian methods BTC XRP ETH Historical Modified Gaussian Historical Modified Gaussian Historical Modified Gaussian 2016 0.061 0.089 0.050 0.059 0.109 0.072 0.146 0.138 0.134 2017 0.107 0.107 0.094 0.170 0.091 0.190 0.135 0.109 0.132 2018 0.111 0.117 0.092 0.161 0.166 0.145 0.141 0.143 0.121 2019 0.081 0.070 0.071 0.087 0.054 0.077 0.104 0.120 0.085 2020 0.064 0.049 0.060 0.144 0.205 0.127 0.094 0.092 0.084 2021 0.094 0.097 0.085 0.164 0.100 0.155 0.127 0.163 0.111 Finally, graphs for predicted values and backtesting results for bitcoin, ripple and ethereum are presented in Appendix A.1, A.2, A.3 given in the external Mendeley Data repository (Bruzgė, 2023). Journal of Business Economics and Management, 2023, 24(3): 527–550 545 4.2. Amazon, Tesla and Meta– VaR, ES As explored in literature analysis, scientists find some significant relationships between cryptocurrency and the stock market. In our empirical research, we decided to compare cryptocurrency results with traditional financial assets. As cryptocurrencies are usually compared with tech-stocks, we picked 3 of the best-known tech-stocks such Tesla, Amazon and Meta. We did the same sensitivity analysis for tech-stocks (Tables 12–13). Table 12. VaR for Tesla, Meta and Amazon with 95% confidence levels using Historical, Modified and Gaussian methods TSL META AMZN Historical Modified Gaussian Historical Modified Gaussian Historical Modified Gaussian 2016 0.039 0.043 0.039 0.026 0.010 0.026 0.028 0.027 0.028 Exceed 15 11 11 15 15 9 11 10 8 2017 0.035 0.036 0.035 0.016 0.017 0.016 0.016 NA 0.019 Exceed 12 13 12 14 10 10 13 8 9 2018 0.052 0.051 0.060 0.032 0.034 0.034 0.042 0.037 0.036 Exceed 12 13 9 18 18 18 18 8 21 2019 0.050 0.050 0.050 0.024 0.023 0.027 0.023 0.023 0.023 Exceed 12 10 10 14 12 10 10 9 10 2020 0.077 0.089 0.084 0.043 0.048 0.047 0.038 0.035 0.037 Exceed 12 11 8 11 11 7 12 11 12 2021 0.051 0.048 0.054 0.032 0.030 0.030 0.026 0.026 0.025 Exceed 12 11 9 14 13 11 12 10 12 Table 13. ES for Tesla, Meta and Amazon with 95% confidence levels using Historical, Modified and Gaussian methods TSL META AMZN Historical Modified Gaussian Historical Modified Gaussian Historical Modified Gaussian 2016 0.060 0.069 0.050 0.038 0.010 0.036 0.044 0.038 0.037 2017 0.050 0.051 0.044 0.025 0.029 0.020 0.024 0.008 0.025 2018 0.078 0.061 0.075 0.052 0.053 0.043 0.056 0.057 0.046 2019 0.079 0.095 0.063 0.036 0.027 0.034 0.033 0.034 0.029 2020 0.136 0.153 0.108 0.068 0.084 0.059 0.049 0.047 0.046 2021 0.071 0.062 0.069 0.041 0.040 0.037 0.033 0.041 0.031 Value-at-Risk sometimes was couple of times lower for tech-stocks than for cryptocurrencies. However, still, chosen stocks experienced some shocks and were sensitive for big news. As historic prices show losses could be even bigger in practice but still lower than in the cryptocurrency market. 546 R. Bruzgė et al. Stylized facts, volatility dynamics and risk measures of cryptocurrencies Graphs for predicted values and back-testing results for Tesla, Meta and Amazon are presented in Appendix A.4, A.5, A.6 given in the external Mendeley Data repository (Bruzgė, 2023). Discussion Almeida etal. (2022) found that cryptocurrencies may have safe haven properties. Their empirical research of cryptocurrency market show that during the pandemic uncertainty increased but risk decreased. Additionally, extensive systematic literature review performed by Almeida and Gonçalves (2022) indicated that cryptocurrencies can be used as a hedge against stocks, fiat currencies and geopolitical risks. Our research confirms the safe haven properties as we showed that cryptocurrencies can be used as a hedge as they are not correlated with tech stocks. We explored the same cryptocurrencies as Melki and Nefzi (2022) for the same purpose as they did but additionally from Almeida etal. (2022), Almeida and Gonçalves (2022) and Melki and Nefzi (2022) our research was broadened by including analysis of stylized facts and value at risk measures from which we gave novel results about the existing volatility clustering in the cryptocurrency market. Value at risk were mainly used by scientist as source to increase the accuracy of forecasting (Jiang etal., 2022; Görgen etal., 2022; Müller etal., 2022). However, in our paper we did not forecast the returns of cryptocurrencies. We used this risk measures additionally with stylized facts analysis to determine the volatility clusters and we found that there exists volatility clustering in the cryptocurrency market when active and highly volatile periods are followed by minimal activity periods. Conclusions Literature analysis showed that the cryptocurrency market is inefficient compared with gold and stock markets. Stronger deviations, uncertainty, and volatility are the results of the irrational behaviour of investors. Inefficiency leads to arbitrage potential, however big returns and losses, as well. An investor must be educated about the risk that he takes before investing in financial instruments with less efficiency, naming cryptocurrency and tech-stocks. Literature analysis shows that cryptocurrencies offer diversification benefits and can work as a hedge in the investment portfolio. Scientific research explores volatility clustering and seasonal patterns in the cryptocurrency market, however, still there is a lack of empirical research which performs sensitivity analysis of both cryptocurrencies and tech-stocks and gives valuable insights into the volatility clustering and the risk in these markets. Scientific literature confirm that cryptocurrency market is a unique laboratory for studying due to its’ unique features and arising opportunities because of existing volatility clustering. The overall analysis covered in this empirical research confirms that there exists some volatility clustering in bitcoin, ethereum and ripple returns. Descriptive statistics showed that bitcoin, ethereum and ripple developed through the analysed period as all of them became more stable in 2019, but were still very sensitive to shocks and were heavily influenced by the Covid-19 pandemic shock. Despite that, price fluctuations decreased and the mean for all of them remained positive. Bitcoin looks the most stable compared with ripple and ethereum. Despite that ripple was introduced earlier than ethereum, it remains less predictable as there were some periods with a high level of price shocks. Journal of Business Economics and Management, 2023, 24(3): 527–550 547 Stylized facts analysis showed that there are many outliers or extreme deviations, data is not normally distributed. After evaluation of extreme values, it was confirmed that there exists some tail dependency between different cryptocurrency pairs. Autocorrelation results confirmed that there exists higher-order dependency on squared logarithmic and absolute returns that can be modelled in predicting volatility clustering. Following that, it was confirmed existing ARCH effects for all cryptocurrencies in all analysed periods which confirms the existence of volatility clusters. The further work provided a comprehensive and detailed analysis of the correlation between cryptocurrencies and confirmed that cryptocurrencies are strongly correlated. Comparison of rolling correlations with tech-stocks showed that there is no correlation between cryptocurrencies and tech-stocks. It confirms that cryptocurrencies can be used as a hedge in a diversified portfolio as they are not correlated with stocks. Sensitivity analysis by evaluating key risk measures of VaR and ES showed that cryptocurrencies are riskier than tech-stocks, however both cryptocurrencies and tech-stocks are sensitive to shocks in the market. While being one of the riskiest financial instruments cryptocurrencies represent a unique financial asset class which has an anti-inflationary mechanism and other advantages when comparing them with stocks. Our results confirmed the existence of volatility clusters and showed that tech-stocks are not correlated with cryptocurrencies so based on these findings there are possible implications for businesses and policymakers. Businesses could create some diversified cryptocurrency/tech-stock high risk indexes for risk prone investors. As cryptocurrencies are decentralized, policymakers cannot regulate cryptocurrencies, but they can regulate cryptocurrency exchanges with the indirect effect for cryptocurrencies. New regulations should indicate that exchanges must maintain given requirements in order to offer trading opportunities. More requirements would lower the emergence of new exchanges as well as fraudulent ones. As a result risk coming from the high frequency trading and fraudulent activity would be minimized. Volatility clustering showed us periods of high volatility which increase risk. Policymakers could add requirements for exchanges to keep investors informed when risk in the market increases as market goes into the bigger volatility period. Research gave a broad view and analysis of the volatility clustering topic but the main limitation is a lack of detailed analysis of volatility clusters. That’s why our future direction is to expand the analysis of volatility clusters even further by finding the factors which indicates when the volatility period starts or ends and explore periods of high and low volatility more in detail. 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