Capturing Tail Risks in Cryptomarkets: A New Systemic Risk Approach

Abstract

Using daily returns of Bitcoin, Litecoin, Ripple and Stellar, we introduce a novel risk measure for quantitative-risk management in the cryptomarket that accounts for the significant co-movements between cryptocurrencies. We find that our model has a lower error margin when forecasting the extent of future losses than traditional risk measures, such as Value-at-Risk and Expected Shortfall. Most notably, we observe this in Litecoin’s results, where Expected Shortfall, on average, overestimates the potential fall in the price of Litecoin by 8.61% and underestimates it by 3.92% more than our model. This research shows that traditional risk measures, while not necessarily inappropriate, are imperfect and incomplete representations of risk when it comes to the cryptomarket. Our model provides a suitable alternative for risk managers, who prioritize lower error margins over failure rates, and highlights the value in exploring how risk measures that incorporate the unique characteristics of cryptocurrencies can be used to supplement and complement traditional risk measures.

1. Introduction

Cryptocurrencies are digital currencies that rely on cryptographic algorithms in order to provide users a secure medium of exchange (Baek and Elbeck 2015); they are controlled by a mathematical algorithm (the so-called mining) and can be transferred completely between users’ digital addresses (combining private and public keys). The highly secure payment system of cryptocurrencies, which eliminates the need for a central authority to check the details of every transaction (Grant and Hogan 2015), has attracted much attention by institutional investors (Sun et al. 2021) and by retail-size investors (López-Cabarcos et al. 2021). Watters (2023) discusses the distinct characteristics and legal considerations of various cryptocurrencies, emphasizing that individuals often hold cryptocurrencies as a form of investment diversification rather than with the intent to use them, further highlighting the diversity and attraction within this asset class. Since the introduction of Bitcoin as the first decentralized digital currency, over 2237 cryptocurrencies have been introduced in the last decade, with a current market valuation of approximately USD 2.57 trillion (CoinMarketCap 2024). Hence, cryptocurrencies have become a “trending topic” in financial research and risk management analysis.

While cryptocurrencies like Bitcoin were originally created as an alternative currency, previous research has proven that cryptocurrency is mainly used as an asset for speculative investments in the developed world (Baur et al. 2018), or as a hedging instrument. Bartos (2015) found that the Bitcoin price follows the efficient market hypothesis and may be considered as an asset. Other studies document that Bitcoin acts as an asset and has hedging capabilities against inflation (Conlon and McGee 2020; Mariana et al. 2021; Choi and Shin 2022), against precious metals (Dyhrberg et al. 2018), and against traditional assets such as bonds and stocks (Dyhrberg 2016; Kjærland et al. 2018; Urquhart and Zhang 2019; Chan et al. 2019). In contrast, more recent studies provide strong evidence that cryptocurrency markets are too speculative and risky; hence, cryptocurrencies could not be considered as assets (Bouri et al. 2017; Baur et al. 2017, 2018). Regarding hedging capabilities, recent studies found that Bitcoin markets do not support the efficient market hypothesis (Lahmiri et al. 2018; Klein et al. 2018), concluding that they are too risky and volatile and could not act as a safe haven for hedging purposes. The speculative behavior is also strongly evident in smaller cryptocurrency markets such as Ethereum, Litecoin and Ripple (Gandal et al. 2018; Corbet et al. 2018); hence, cryptocurrencies cannot act as hedging instruments.

Moreover, the recent literature provides evidence of a volatility spillover effect between cryptocurrency returns, in which time-varying correlation is evident between cryptocurrency markets. For example, Beneki et al. (2019) document a delayed positive response of Bitcoin’s volatility to Ethereum’s volatility shock; Kyriazis (2019) finds that Ethereum, Litecoin and Ripple returns have a strong and significant returns interlinkage with Bitcoin; Xu et al. (2021) document a significant tail-risk spillover effect between Bitcoin’s returns among 23 cryptocurrencies. These results suggest that extreme negative changes in one cryptocurrency often lead to similar negative changes in other cryptocurrencies, highlighting the interconnectedness of these markets. Therefore, investors need to identify and mitigate risks associated with regime switching in cryptocurrency markets to make more informed decisions and develop effective trading strategies.

We argue that if institutional and retail-size investors invest in cryptocurrencies or use them for hedging purposes, they need to consider the effects of extreme volatility and unexpected market movements to prevent economic loss. Sudden price changes, often caused by market shocks or irregular trading activities, can significantly impact investment returns if not accounted for in risk management strategies. Additionally, the strong positive correlations and volatility spillover effects between cryptocurrency markets emphasize the potential risks to portfolios, which cannot be easily mitigated through diversification alone.

Accordingly, standard risk measures such as the Value-at-Risk (VaR) and Expected Shortfall (ES), which are widely used in the financial industry to estimate economic capital and market risk, are not suitable measures for an estimation of the risk associated in cryptocurrencies. First, the VaR measure, which quantifies the potential portfolio loss using a high quantile of the loss distribution, does not have the subadditivity property and hence does not quantify the tail risk associated with outlying cryptocurrency returns, as noted by Trucíos et al. (2020) and Jiménez et al. (2020).

Second, although the ES measure, which quantifies the average expected loss when it exceeds the VaR, is better at capturing tail risks than VaR (Artzner et al. 1999; Acerbi and Tasche 2002; Tasche 2002; Yamai and Yoshiba 2005; Embrechts and Wang 2015; Landsman et al. 2016), it has several limitations. Specifically, the ES measure is highly sensitive to extreme events, which are frequent in cryptocurrency markets (Ji et al. 2020; López-Cabarcos et al. 2021). This sensitivity is evidenced by the large fluctuations in ES values during periods of market stress, leading to potentially exaggerated risk estimates. Jiménez et al. (2020) show that the ES measure can lead to significantly higher capital requirements during periods of extreme volatility. Hence, the ES measure may lead to incorrect investment decisions and transactions involving cryptocurrencies.

Third, since cryptocurrency returns are heavily skewed (Osterrieder and Lorenz 2017; Gkillas and Katsiampa 2018; Trucíos et al. 2020; Jiménez et al. 2020), diversification does not effectively mitigate the VaR and ES, as noted by Ibragimov and Prokhorov (2016). This skewness and heavy tails in cryptocurrency returns mean that investors are exposed to high, indistinguishable risks, which refer to the inability to differentiate between regular market fluctuations and extreme, unexpected events. The implications of these risks are significant as they can lead to substantial financial losses that are not adequately captured by traditional risk measures, thereby providing a false sense of security and potentially resulting in poor investment decisions.

Fourth, and most importantly, we argue that even extreme-value-theory-based VaR and ES measures (Longin 2005) may not properly capture the risk for cryptocurrency investors since they do not take into account the strong time-varying correlation between cryptocurrency markets and their idiosyncratic risks (Borri 2019; Xu et al. 2021).

In this paper, we propose a novel risk measure designed to capture the unique risk features of the cryptocurrency markets. The risk measure is based on the Epsilon Drawdown Method proposed by Johansen and Sornette (2001), which captures the loss from the last local maximum to the next local minimum and intuitively offers a more realistic measure of real market risks. This method has been applied by Gerlach et al. (2019), who employed a robust automatic peak detection method on Bitcoin prices to predict regime switching between market growth (drawups) and market decline (drawdowns). Gerlach et al. (2019) demonstrated that this method provides useful information to warn of imminent economic crash risks, proving its effectiveness in capturing the risks inherent in cryptocurrencies. We extend this method by considering multivariate risks between four cryptocurrencies, capturing excess economic loss for a diversified cryptocurrency portfolio. We apply a modified ES risk measure with a dynamic quantile variable that is sensitive to cryptocurrency market behavior. This novel approach provides a superior alternative to traditional risk measures, better capturing the tail risks and interdependencies unique to cryptocurrency markets. Our findings significantly contribute to the literature on financial risk management and offer practical tools for investors and portfolio managers, demonstrating the method’s robustness and reliability.

To this end, the objectives of this research are to examine the following: (1) if traditional financial risk measures, namely, VaR and ES, are appropriate risk measures for the cryptocurrency market; (2) if the novel risk measure can provide a superior alternative risk measure for cryptocurrency investors. We have analyzed the volatility and time-series correlation of the daily returns of Bitcoin, Litecoin, Ripple and Stellar, which are four prominent cryptocurrencies in terms of market capitalization size, and applied our modified dynamic quantile ES measure in order to forecast the risk of market drawdowns. The results show that our model is more accurate in capturing future economic losses than traditional VaR and ES measures and hence offers a better alternative method for risk managers.

The rest of this paper is organized as follows: Section 2 provides a review of the existing literature pertaining to the risk management of cryptocurrencies. In Section 3, we outline the framework for our novel dynamic-quantile-modified ES risk measure, and we provide a basis for the econometric model. Section 4 presents the results and reviews the performance of our risk measure against the traditional risk measures, namely, VaR and ES. Section 5 presents our conclusion.

2. Literature Review

An immense body of literature highlights the extreme volatility of cryptocurrency markets (Dyhrberg 2016; Conrad et al. 2018; Katsiampa 2017), especially in comparison to other assets. Osterrieder and Lorenz (2017), Klein et al. (2018) and Panagiotidis et al. (2019) found that Bitcoin returns exhibit high volatility, strong non-normal characteristics and heavy tails and have an asymmetric response to market shocks. Baek and Elbeck (2015) found that Bitcoin volatility is much higher relative to the S&P 500 and that Bitcoin returns are internally driven by buyers and sellers, making them highly speculative and subject to much higher risk for investors. Phillip et al. (2018) also compared the volatility of Ethereum, Ripple, Nem and Dash to Bitcoin and found that these cryptocurrencies exhibit much larger volatility and are heavily skewed, concluding that they are riskier for investors.

In this context, Longin (2005) argued that the choice of the distribution of asset returns plays a central role in financial modeling and risk management. Therefore, if cryptocurrencies exhibit extreme price changes, risk managers need to examine the tail behavior of these returns and select an appropriate distribution that captures the underlying patterns. Stavroyiannis (2018) examined the VaR measure for Bitcoin returns and found that the high volatility of returns persistently violated the VaR measure, indicating higher risk for Bitcoin. According to Basel committee regulations, which relate capital requirements to the size of financial buffers based on assumed risk, Stavroyiannis (2018) concluded that Bitcoin investors are subject to higher capital requirements and capital allocation ratios to cover potential losses. Osterrieder and Lorenz (2017) studied the tail-risk characteristics of Bitcoin returns and found that the returns distribution exhibits strong non-normal characteristics and heavier tails than traditional G10 currencies. Charles and Darné (2019) studied the volatility of Bitcoin returns in the presence of outliers and found that they are characterized with high volatility and by the presence of jumps. The tail-risk behavior of Bitcoin returns distribution may affect the VaR and ES drastically, as mentioned by Boudt et al. (2013) and Trucíos and Hotta (2015), and hence has broad implications for risk management, both from the investors’ and regulators’ points of view.

More recent studies use extreme value theory to examine the vulnerability of several cryptocurrencies to tail risk compared to Bitcoin. Gkillas and Katsiampa (2018) use the generalized Pareto Distribution to study the tail behavior of the returns of Ethereum, Ripple, Bitcoin Cash and Litecoin compared to Bitcoin and found that all cryptocurrencies exhibit higher VaR and ES values as a result of the extremely heavy tails of the returns distributions. Silahli et al. (2021) employed Chen and Gerlach’s (2013) approach to model cryptocurrency portfolio tail risk using the Weibull distribution, capturing the time-series characteristics of cryptocurrencies such as extreme volatility, volatility clustering, very heavy tails and skewness. Similarly, Osterrieder and Lorenz (2017) applied the Generalized Extreme Value (GEV) distribution (Jenkinson 1955) to Bitcoin returns to model its tail-risk behavior. Borri (2019) used the Conditional Value-at-Risk (CoVaR) measure (Adrian and Brunnermeier 2016) to examine the co-movements and exposure of Bitcoin, Ethereum, Ripple and Litecoin to tail-risk events; they found that these cryptocurrencies are highly exposed to tail risk within the cryptocurrency markets and that cryptocurrency returns are highly correlated. Zhang et al. (2019) also documented the tail-risk behavior of Bitcoin, Ethereum, Litecoin and Ripple’s hourly log returns by estimating VaR and ES at various quantile thresholds and found that Bitcoin is the least risky cryptocurrency, while all other cryptocurrencies exhibit higher volatility with heavy tails, indicating a higher risk of exposure. Nevertheless, although extreme value theory might be useful for risk management purposes (Longin 2005), the investigation of the extreme tail behavior of cryptocurrencies is rather limited, and, to the best of our knowledge, most previous studies do not take into account the time-series correlations and the spillover effects between cryptocurrencies.

Few recent studies have tried to assess the linkage between cryptocurrency tail-risk events. Fry (2018) introduced a bespoke model for bubbles in cryptocurrency markets that combines both heavy tails and the probability of a complete collapse in asset prices. This model suggests that liquidity risks may generate heavy tails in Bitcoin and other cryptocurrency markets, and that dramatic boom–bust cryptocurrency price patterns can occur and may cause a complete price collapse. Fry (2018) also provides empirical evidence of a bubble in Bitcoin and Ethereum. Bouri et al. (2019) documented empirical evidence of multidirectional bubble behavior, where a price boom in one cryptocurrency can lead to price booms in other cryptocurrencies and vice versa, creating a ripple effect across the market. This interconnectedness implies that the rise or fall in the price of one cryptocurrency can significantly influence the prices of others. Koutmos (2018) studied returns and volatility spillovers among 18 major cryptocurrencies and found that Bitcoin is the dominant contributor of return and volatility spillovers. Xu et al. (2021) also studied tail-risk interdependence among 23 cryptocurrencies and found significant risk-spillover effects in cryptocurrency markets. Ahelegbey et al. (2021) explored the relationships among crypto-asset markets during stressful times using the extreme downside hedge (EDH) and the extreme downside correlation (EDC) for tail-do a methodology to estimate tail risk within cryptocurrencies by decomposing return series into positive and negative components and using negative outliers for the tail index and extreme dependence correlation matrix. This methodology improved portfolio risk measurement and allowed for a better estimation of extreme dependence among cryptocurrencies. Hence, these recent studies suggest total interconnectedness among cryptocurrencies and highlight the potential risk for cryptocurrency investors.

In addition to volatility-spillover effects, other studies have documented conditional correlations among cryptocurrency returns. Kumar and Anandarao (2019) studied spillover effects among the returns of Bitcoin, Ethereum, Ripple and Litecoin by employing an integrated generalized autoregressive conditional heteroscedasticity-dynamic conditional correlation specification (IGARCH(1,1)-DCC(1,1)) and found significant volatility spillovers from Bitcoin to Ethereum and Litecoin and evidence of co-movement behavior among cryptocurrency returns. Luu Duc Huynh (2019) also highlighted the potential collapse of cryptocurrency markets via spillover effects that Granger-cause a negative change in other cryptocurrencies in terms of extreme value. While these studies suggest a time-series correlation among cryptocurrency returns, only a few risk management studies on cryptocurrencies take into account the dependencies among cryptocurrency returns and their effects on the entire portfolio (Katsiampa 2019).

Given the recent evidence of spillover behavior in digital currency markets, appropriate cryptocurrency risk management needs to account for the tail-risk interdependence among cryptocurrency returns. Risk managers must pay attention to negative news in cryptocurrency markets and be aware of moving patterns among cryptocurrencies to mitigate potential risks. Following Gerlach et al. (2019), our model aims to capture the potential formation of bubbles in cryptocurrency markets and intuitively provides a more accurate estimation of the underlying risk to cryptocurrency investors. Our model extends Gerlach et al.’s (2019) and includes several cryptocurrencies while also considering the tail-risk interdependence among cryptocurrency returns.

3. Data and Methodology

To establish the tail-risk interdependence between different cryptocurrencies and their potential risk effect, we gathered daily closing prices of the four largest cryptocurrencies (in terms of market capitalization), namely, Bitcoin, Litecoin, Ripple and Stellar. We created a sample of closing prices for all cryptocurrencies, dating from 5 August 2014 to 5 March 2019, extracted from the Coin Metrics website.

We began by calculating discrete daily log returns, $r_t^i$,

$$r_t^i=ln{(P}_t^i)-{ln(P}_{t-1}^i), i=1, 2, 3 , 4$$

(1)

where $P_t^i$ is the extracted price of the i-th cryptocurrency at time t. Next, following Gerlach et al. (2019), we adapted and applied an extension of the Epsilon Drawdown Method to each time series of returns to diagnose the present state for the i-th cryptocurrency. This method functions by breaking a time series into periods of drawups and drawdowns. Drawups can be described as low-risk market periods characterized by predominantly positive returns, while drawdowns denote market periods of predominantly negative returns and thus higher risk.

To capture the bubble size between the bubble start and peak for each bubble, we calculated the cumulative return dates within a period of peaks and crashes. Let $t_{d1}$ indicate the first day of a given period, such that a cryptocurrency return, $r_{t_{d1}}^i,$ represents the beginning of a drawup (drawdown) period if ${ r}_{td1}^i>0 (r_{td1}^i<0)$. For each subsequent day in the given period, the cumulative return, $c_{t_{d1},t_{dn}}^i,$ is calculated until the period comes to an end, with $t_{dn}$ indicating the end of a period:

$$c_{t_{d1},t_{dn}}^i={\sum }_{k=t_{d1}}^{t_{dn}}{r}_{k.}^i$$

(2)

Furthermore, the current period remains active as long as there is no deviation—a return in the opposite direction—greater than a predefined tolerance level, $\epsilon$. The tolerance level is cryptocurrency-dependent and is determined by identifying, at each point in time, the threshold that optimally divides the past one hundred days of returns into drawup and drawdown periods. A time series of returns will be optimally divided such that the sum of positive returns is maximized during drawup periods and minimized during drawdown periods, while the sum of negative returns is maximized during drawdown periods and minimized during drawup periods.

At each point in time, we need to verify whether the current drawup or drawdown period is still active. We calculated the deviation ${\delta }_{t_{d1},t_{dn}}^i$ as follows:

$${\delta }_{t_{d1},t_{dn}}^i=\left\{\begin{array}{c}max\left\{c_{t_{d1},t_{dk}}^i,d1\le k\le dn\right\}-c_{t_{d1},t_{dn}}^i drawups\\ c_{t_{d1},t_{dn}}^i-min\left\{c_{t_{d1},t_{dk}}^i,d1\le k\le dn\right\} drawdowns\end{array}\right.$$

(3)

We define a period to end when ${\delta }_{t_{d1},t_{dn}}^i$ > $\epsilon$. The end of a period may occur suddenly due to a significant event or due to an aggregation of smaller deviations over a longer time.

Further, to capture underlying risks between cryptocurrencies within drawup and drawdown periods, a specific cryptocurrency was selected and provided with multiple daily risk factors—one from each cryptocurrency, including the chosen cryptocurrency. This risk factor, denoted ${ w}_{t,}^i,$ reflects the likely lower limit of a fall in price for the following day for the $i$-th cryptocurrency.

We modeled the risk factors using a modified version of the traditional ES risk measure, with a dynamic quantile variable that varies depending on the current active period and the daily difference between the tolerance level and deviation. This process is depicted in Equations (4)–(6):

$$Drawup period \left\{\begin{array}{c}\epsilon -\delta >0, w_t^i={ES}_{q+}\left(X_t^i\right)\\ \epsilon -\delta \le 0, w_t^i={ES}_{q-}\left(X_t^i\right)\end{array}\right.$$

(4)

$$Drawdown period \left\{\begin{array}{l}\epsilon -\delta =\epsilon , w_t^i={ES}_{q^{+}}\left(X_t^i\right)\\ \epsilon -\delta \le 0, w_t^i={ES}_{q-}\left(X_t^i\right)\\ 0<\epsilon -\delta <\epsilon , w_t^i=rho\left(X_t^i\right)\end{array}\right.$$

(5)

where

$$\rho \left(X_t^i\right)={\displaystyle \frac{{ES}_{q+}\left(X_t^i\right)-{ES}_{q^{-}}\left(X_t^i\right)}{\epsilon }}\ast \left(\epsilon -\delta \right)+{ES}_{q^{-}}\left({ X}_t^i\right) .$$

(6)

In the above equations, the ES and $\rho$ measures represent the loss for the chosen $i$-th cryptocurrency, determined by a one-hundred-day historical calculation. $q^{+}$ and $q^{-}$ are upper and lower quantile levels, respectively, that determine the magnitude of ES during higher and lower risk periods. These quantile boundaries are determined by an analyst’s risk preference and are thus local parameters that vary from case to case. We assume that ${q^{-}<q}^{+}.$

During a drawup period, when the difference between the tolerance level and deviation is greater than zero, returns are predominantly positive and thus the lower limit quantile $q^{-}$ is used. This ensures a more conservative loss forecast during times of low risk. On the other hand, shortly after local maxima in cryptocurrency prices, when the deviation surpasses the tolerance level, $q^{+}$ is used to account for the current higher risk period by forecasting a more severe potential loss. Similarly, loss values are calculated during drawdown periods, with the exception of days when the difference between the tolerance level and deviation lies between zero and the tolerance level. In such a circumstance, quantile $q$ is used, which is determined by the upper and lower limits and ranges between these values, as portrayed in Equation (6).

To evaluate the influence of each of other $j$-th cryptocurrency on a selected $i$-th cryptocurrency, we utilized the square correlation, denoted ${\rho }^2$. This metric measures the proportion of the price movement of the $i$-th cryptocurrency that can be explained by the movements of the $j$-th cryptocurrency, serving as a robust measure of influence. Squaring the correlation ensures a clearer representation of the strength of the relationship, independent of its direction. This approach allows stronger correlations to exert greater influence in our model, enhancing its sensitivity to significant relational dynamics between cryptocurrencies.

We defined the risk factor $W_t^i$ as the aggregate risks of the influences of all other cryptocurrencies:

$$W_t^i={\sum }_{j=1,j\ne i}^4{w}_t^j({\displaystyle \frac{{{\rho }^2}_t^{ij}}{{\displaystyle {\sum }_{j=1,j\ne i}^4}{{\rho }^2}_t^{ij}}}).$$

(7)

To prevent the cryptomarket risk factor weighing too heavily on the chosen cryptocurrency (which will naturally have a ${\rho }^2$ of 1 with itself), we used the sum j = 1, 2, 3, 4 where j $\ne i$ in our calculations. This approach avoids self-correlation dominance and provides a more balanced risk measure. Additionally, this formula adjusts based on the direction of correlation—positive or negative. For negative correlations, a rise in returns is treated as a drawdown, and a fall as a drawup, reflecting the inverse relationship in risk assessment.

Finally, we forecasted the risk-adjusted price for the $i$th cryptocurrency at $t+1$, denoted $P_{t+1}^{adj,i}$, as a function of the risk factor ${ W}_t^i$ and the present price $P_t^i$ at time $t$:

$$P_{t+1}^{adj,i}=P_t^i{(1+W}_t^i).$$

(8)

Equation (8) depicts our final risk measure, which attempts to forecast a day-ahead risk-adjusted price as a function of the present price and as a function of the risk factor ${ W}_t^i$. Hence, this process ensures that the $i$th cryptocurrency will have a unique risk factor, which is dependent on its own historic losses and correlations with all cryptocurrencies. By incorporating $W_t^i$ into our model, we effectively captured the tail-risk dependencies among cryptocurrency returns and the potential spillover effects between cryptocurrency markets, providing a more accurate risk assessment for each cryptocurrency. We call the proposed measure the systemic risk model.

Finally, to assess the performance of our novel risk management model in forecasting potential future losses, we back-tested the day-ahead forecasts for each cryptocurrency using the risk factor $W_t^i$, as well as back-tested the historical 99% VaR and ES risk measures, defined as the average of all losses that exceed the VaR. We set the back-testing procedure by setting $q^{-}$ to the median negative return over the last 100 days and $q^{+}$ equal to 0.99. The 100-day window is commonly used in risk management to keep models responsive to recent market shifts, which are prevalent in cryptocurrency markets. This period provides sufficient historical data while maintaining relevance to current conditions. In particular, $q^{-}$ functions as a safety-net price reduction imposed by the model during periods deemed low risk. Setting the quantile as the median negative return attempts to capture the majority of negative returns that may arise during low-risk periods without consistently decreasing the forecasted price by an unnecessarily large amount.

We measured the performance of our dynamic quantile ES risk measure in predicting future losses as a result of cryptocurrency price drops, in comparison to the 99% VaR and ES risk measures. We used two key measures to quantify the accuracy of the risk models in estimating the loss. First, we defined the “success” cases, in which the models underestimated the future loss. Specifically, success cases indicate that the cryptocurrency price forecast is below its real market price, suggesting an omission error in predicting the loss. Accordingly, we defined the Success Average Error (SAD) measure, calculated as the percentage average of errors of the model in success cases, where the error is defined as the difference between the price forecast and the real market price observed. We argue that better-performing models should generate lower SAD values, which suggest a better estimation of the risk associated with cryptocurrency price drops.

Second, in a similar manner, we defined the “failure” cases, in which the forecasted falling price was found to be higher than the actual market price observed, indicating an overestimation of the loss. We defined the Failure Average Error (FAD), calculated as the percentage average of errors of the model in failure cases. We calculated SAD and FAD values for all risk management models. We argue that the superior risk management model should be the one that has lower SAD and FAD values, suggesting a lower error margin in forecasting future losses.

4. Results and Discussion

4.1. Cryptocurrency Risk through Drawup and Drawdown Periods

We first analyze the tail risks and co-movements between cryptocurrencies to highlight the risk effect and the importance of our dynamic quantile ES risk measure.

Figure 1 depicts the scaled prices of Bitcoin, Litecoin, Ripple and Stellar between 5 August 2014 and 5 March 2019. To clearly illustrate the co-movement between the prices over time, the prices have been scaled as follows: Bitcoin is divided by 350, Litecoin is divided by 10, Ripple is multiplied by 10, and Stellar is multiplied by 10. The figure shows strong price co-movement between all four cryptocurrencies, suggesting high conditional correlation, as evident in Kumar and Anandarao (2019) and Luu Duc Huynh (2019).

Figure 2 depicts the number of returns, drawups and drawdowns that emerged between 5 August 2014 and 5 March 2019, for all cryptocurrencies in the sample, based on the adapted extension of the Epsilon Drawdown Method. The figure shows that Stellar has the largest number of drawup and drawdown periods among the four cryptocurrencies, with a total of 168. This suggests that Stellar is the cryptocurrency most prone to significant price movements in opposite directions and thus holds a higher level of investment risk. Regarding Bitcoin, we find 134 periods of drawups and drawdowns, suggesting a high presence of jumps in Bitcoin returns, as evident in Charles and Darné (2019). However, we find that Ripple and Litecoin displayed the lowest number of price movements, suggesting that these cryptocurrencies exhibit lower risk exposure compared to Bitcoin, contrary to Zhang et al. (2019), who consider Ripple the riskiest cryptocurrency (and Bitcoin the least).

Following Borri (2019) and Bouri et al. (2019), we also examine the vulnerability of cryptocurrencies to tail-risk events, where the trend of a cryptocurrency price time series experiences a significant negative change or critical event.

Table 1. Average and minimum number of days until local maxima.

	Bitcoin	Litecoin	Ripple	Stellar
Bitcoin Event	70 (28)	25 (14)	54 (14)	46 (14)
Litecoin Event	62 (28)	53 (28)	75 (28)	68 (14)
Ripple Event	48 (14)	63 (28)	50 (28)	53 (14)
Stellar Event	60 (28)	70 (42)	14 (14)	58 (42)

Notes: The table reports the average number of days until local maxima. The minimum number of days is reported in parentheses.

presents the average and minimum number of days until local maxima for all four cryptocurrencies.

The table demonstrates that if a cryptocurrency in the sample experiences a critical event, the minimum time before another cryptocurrency reaches a local maximum is almost always under a month and, in most cases, within two weeks. This suggests a strong negative price pattern among cryptocurrencies, as evident in Fry (2018) and Bouri et al. (2019), indicating potential risk for cryptocurrency investors. Moreover, we find that the average and minimum number of days until local maxima for Litecoin, Ripple and Stellar are at their lowest level after Bitcoin experiences a critical event. This finding suggests that Bitcoin has the most dominant tail-risk spillover effect among cryptocurrencies, as documented by Koutmos (2018).

Lastly, we illustrate the bull–bear regime switching for all cryptocurrencies in our sample to provide insights for risk management. Figure 3 was derived using the drawup–drawdown method to identify bull and bear regimes within the time-series data of the cryptocurrencies in our sample. Figure 3 displays the dynamic time series of bear and bull regimes within the sample. The results indicate that 50.52% of the entire period analyzed comprises overlapping regimes shared by all cryptocurrencies, suggesting that these assets simultaneously experience bull or bear regimes. Notably, these overlapping periods are not evenly distributed over time, with 77.64% occurring between 30 July 2017 and 21 July 2019. In line with Xu et al. (2021), this asymmetry highlights the interlinkage of returns within the crypto markets, indicating that market events or major economic shifts impact all cryptocurrencies in a similar manner. The increase in regime overlap underscores the significant market co-movement among cryptocurrencies, emphasizing the increase in cryptocurrency tail correlation and the growing systemic risk in the market (Feng et al. 2018). These results underscore the necessity of exploring regime-switching behavior for effective risk management insights and investment decisions.

4.2. Risk Management Performances

Table 2. Econometric model versus traditional risk measures.

Cryptocurrency	Risk Measure	Failure Count	SAD	FAD
Bitcoin	Systemic Risk Model	59	0.0829	0.0297
	VaR q+	24	0.1017	0.0404
	ES q+	13	0.1348	0.0352
Litecoin	Systemic Risk Model	66	0.1189	0.0499
	VaR q+	18	0.1686	0.0784
	ES q+	14	0.2050	0.0891
Ripple	Systemic Risk Model	56	0.1223	0.0538
	VaR q+	17	0.1612	0.0674
	ES q+	12	0.1870	0.0757
Stellar	Systemic Risk Model	59	0.1329	0.0508
	VaR q+	13	0.1718	0.0509
	ES q+	11	0.1907	0.0367

Notes: Failure Count indicates the number of cases, out of the total 1473 days back-tested, in which the model forecasted a risk-reduced price that was higher than the real price. The Failure Average Difference presents the percentage average of the differences between the real and forecasted price for these failure cases. The Success Average Difference presents the average percentage difference when the forecasted price is lower than the actual price.

presents the risk management performance of the systemic risk model (SRM) alongside traditional VaR and ES measures, utilizing our comprehensive back-testing procedure. This table details the number of failures and the percentage average error of these failures (successes), highlighting cases where forecasted prices were either above (failure) or below (success) the actual market prices observed for each cryptocurrency.

Table 2 shows that the ES measure has the lowest number of failures for all cryptocurrencies, with an average failure rate of 0.88%. This is followed by VaR, with a failure rate of 1.22%, and then the SRM with a higher failure rate of 4.07%. By definition, ES will always have a lower failure count than VaR at the same quantile level.

However, it is crucial to understand the context of these metrics. Despite the higher failure count, the SRM demonstrates superior accuracy in predicting price falls, as indicated by significantly lower SAD values. The SRM’s design prioritizes responsiveness to market changes, which may result in a higher failure rate but ensures that risk is not underestimated. This approach provides a conservative safety buffer, essential in the highly volatile cryptocurrency market.

For example, the SAD values for Litecoin under the SRM are notably lower than those under ES, indicating a more accurate prediction of price drops. Specifically, the ES measure overestimates the potential price fall of Litecoin by 8.61% more than the SRM, suggesting that the SRM’s forecasts are closer to actual market outcomes. Additionally, the ES measure’s optimistic forecasts miss the actual market price by 3.92% more than the SRM, underscoring the SRM’s effectiveness in risk prediction.

To further illustrate the trend, we present the price forecasts for Litecoin. Figure 4 shows the price drop forecasts for Litecoin, revealing that the SRM lies closer to the real price on average compared to the other risk measures. This suggests that the SRM may provide more accurate forecasts, highlighting its effectiveness for risk management. These observations reinforce the SRM’s overall superior performance across various cryptocurrencies and market conditions, solidifying its role as a valuable tool for investors seeking to enhance their risk management strategies.

We acknowledge a significant regime change that occurred in the cryptocurrency market after 2017, which is evident in the figure. This period marked a substantial shift in market dynamics, characterized by increased volatility, greater market participation and more frequent and intense price swings. The post-2017 period introduced new market conditions that could challenge traditional risk measures due to the unpredictability and rapid fluctuations in prices. Notably, our SRM managed to provide good forecasts for Ripple during sharp price rise movements in mid-December 2017, outperforming the VaR and ES measures. This trend is also depicted during the sharp price drop between March 2018 and April 2018, where the systemic risk model forecasted price drops more accurately. This indicates the model’s robustness and adaptability in various market conditions, further emphasizing its value in accurately predicting significant market shifts and aiding in effective risk management.

A similar trend is depicted for Bitcoin, Ripple and Stellar, as shown in the Appendix A. The only case in which ES outperforms the systemic risk model in terms of Failure Average Difference is Stellar. In this instance, the systemic risk model, on average, underestimates the fall in price by 1.41% more than the ES model. These observations reinforce the systemic risk model’s overall superior performance across various cryptocurrencies and market conditions, solidifying its role as a valuable tool for investors seeking to enhance their risk management strategies.

These findings show that the systemic risk model has a clear advantage over traditional risk measures in predicting market movements, especially during significant price changes. Traditional measures like VaR and ES are inadequate for the highly volatile and rapidly fluctuating cryptomarket. The systemic risk model offers a more nuanced and accurate risk assessment by incorporating a broader range of tail-risk events and considering the co-movements within cryptocurrencies and overall market dynamics.

During tail events, relying solely on traditional risk measures exposes investors to higher error margins regarding the extent of their losses. Error margins are more critical than failure rates in the cryptomarket, which is prone to bubbles, high volatility and greater exposure to tail events (Osterrieder and Lorenz 2017; Zhang et al. 2018). Moreover, traditional measures neglect the co-movements between cryptocurrency prices, highlighted by Katsiampa’s (2019) research on Bitcoin and Ethereum volatility and Borri’s (2019) conditional tail-risk study. In contrast, the systemic risk model adjusts risk forecasts based on market ripple effects, resulting in a better accuracy and lower error margin.

With rising investment levels and interest in cryptocurrencies, as shown by the proliferation of cryptocurrencies and the upcoming release of Facebook’s Libra (Telford 2019), it is crucial to establish reliable risk measures tailored to this market, given the shortcomings of traditional methods.

5. Conclusions

Recent research emphasizes the speculative nature of cryptocurrencies, highlighting their extreme volatility and interlinkage of returns. This makes traditional risk measures like Value-at-Risk (VaR) and Expected Shortfall (ES) inadequate for the cryptomarket due to their inability to capture tail risks and time-varying correlations between cryptocurrencies. These limitations pose significant challenges to investment decisions and trading strategies for investors and can potentially cause high losses, particularly given the substantial investments from both institutional and retail investors.

Our study proposes a novel systemic risk model tailored to the unique characteristics of cryptocurrencies by effectively capturing tail risks and considering the interdependencies between cryptocurrencies. By analyzing the daily returns of Bitcoin, Litecoin, Ripple and Stellar, we demonstrate that our model significantly outperforms traditional risk measures in predicting market drawdowns.

Back-testing results show that the systemic risk measure provides a more reliable forecast of potential losses, offering a more accurate and robust tool for managing cryptocurrency investment risks. For investors and portfolio managers, these findings underscore the necessity of adopting advanced risk measures specifically designed for the unique dynamics of the cryptocurrency market, providing a more reliable forecast of potential losses and allowing for better-informed investment decisions and more effective risk management strategies.

The economic implications of our findings are substantial. Improved risk management is achievable as the systemic risk model offers more accurate assessments, reducing exposure to extreme losses and enhancing portfolio stability. Informed investment decisions become possible by capturing tail risks and market interdependencies, potentially curbing speculative behavior. Our findings offer valuable regulatory insights, enabling the development of robust frameworks for cryptocurrency markets and advocating for more stringent risk management practices. Lastly, the application of advanced risk measures can drive innovation in risk management across the broader financial sector, fostering more resilient financial markets.

We believe that our novel risk measure is a preliminary step towards achieving better risk management in cryptocurrencies and may act as a reference point for future crypto-related risk measurement tools. Despite its promising results, our study has limitations, including a focus on only four cryptocurrencies and reliance on historical data, which may not capture future market conditions or external factors like regulatory changes and macroeconomic shifts. Additionally, our study did not include data from the pandemic and post-pandemic periods, which introduced significant market volatility and could provide valuable insights into the evolving dynamics of cryptocurrency markets.

Future research should expand the model to include a wider range of cryptocurrencies and asset classes, integrate real-time data and machine learning for better predictive accuracy and consider external influences to provide a more comprehensive risk assessment. Including data from the pandemic and post-pandemic periods would be particularly valuable in understanding how these unprecedented events affect the relationships between cryptocurrencies during business cycles. Such an expansion will allow for better testing and an explanation of the model under various market conditions and will enable a more robust comparison of the systemic risk model to traditional VaR and ES risk measures. Developing user-friendly tools to facilitate the adoption of advanced risk measures among investors and portfolio managers is essential for enhancing market stability and resilience.

Moreover, future research should also consider incorporating on-chain data, such as the number of active wallets, to provide a more intrinsic and fundamental understanding of cryptocurrency risks. By integrating both on-chain and off-chain factors, risk management models can offer a more holistic view, improving their effectiveness in capturing the full spectrum of risks associated with cryptocurrencies. This approach will bridge the gap between a priori (on-chain) and a posteriori (off-chain) risk factors, providing a more comprehensive framework for cryptocurrency risk management. Furthermore, it is important to recognize the different types of cryptocurrencies and how these differences can influence study results. Future research should consider these differences to provide a more nuanced understanding of risk across different types of digital assets.