In this research, the returns of four cryptocurrencies (Bitcoin, Litecoin, Ripple and Ethereum) were analyzed in order to answer the following research question: “How do the returns of Bitcoin and other altcoins behave over time, and what can we say about extreme values for losses and profits?” With respect to volatility, cryptocurrencies can still be considered extremely volatile. For Bitcoin, the least volatile of the four, we found an annual volatility of approximately 70% based on daily exchange rates. For Ethereum, the most volatile of all four, this percentage was closer to 130%. Also, several distributions were fitted on the returns. It is shown that the Generalized Hyperbolic Distribution is the best fit for all four cryptocurrencies, apart from the tails in some cases.<br/>The tails were investigated seperately by using Extreme Value Analysis and by looking into both empirical and theoretical risk quantities (the Value at Risk and Expected Shortfall). Bitcoin appears to be the least risky of all four cryptocurrencies, but also the least profitable, whereas Ripple appears to be the most risky and also the most profitable.<br/>Compared to previous research, Bitcoin has also become less risky, showing a less fat tail for the losses than before. For Litecoin and Ripple, the reverse is true, as they appear to have become riskier. For Ethereum, no comparisons could be made, as this is a relatively new cryptocurrency that has not been investigated much yet. When tested for Paretianity, the left tails of Litecoin and Ripple appear to Pareto distributed: the losses seem to exhibit heavy tail behavior. For the profits, the tails turned out to be even heavier and can therefore also be considered Paretian. These results were confirmed by Maximum to Sum ratio plots, indicating infinite third and fourth moments for the losses and profits of Litecoin and Ripple, but not for Bitcoin and Ethereum. The results have implications for investment and risk management purposes.
At least since the first Bitcoin futures were launched in December 2017, quantitative risk management on Bitcoin is no longer indispensable. This paper provides methodology and fundamental findings on approximations of intraday bitcoin returns through both symmetric and non-symmetric probability distributions. Different time frequencies of Bitcoin returns were analysed, and their non-Normal behaviour is shown. Their exchange rates versus the US Dollar, between April 14, 2017 until August 7, 2017, were considered by fitting parametric distributions to them. The nonnormality changes with the size of the timesteps, where standard heavy-tailed distributions give good fits of the data. These results are a first attempt to characterize intraday risk of the Bitcoin.
Digital currencies and cryptocurrencies have hesitantly started to penetrate the investors, and the next step will be the regulatory risk management framework. We examine the Value-at-Risk and Expected Shortfall properties for Bitcoin and Ethereum, using GARCH methodology and filtered historical simulation. We find the both Bitcoin and Ethereum are subject to a higher risk, therefore, to higher sufficient buffer and risk capital to cover potential losses.
Afees A. Salisu, Aviral Kumar Tiwari, Ibrahim D. Raheem
This study exploits several conditional heteroskedasticity models with various supported distributions in order to find the best distribution as well as the best GARCH-type model that may be used to model volatility of Bitcoin returns. Innovatively, the study is able to establish that pre-testing the residuals of Bitcoin returns for the best distribution can help to identify the appropriate distribution when modelling with GARCH-type models regardless of the data frequency.
We investigate the cross‐correlations of return‐volume relationship of the Bitcoin market. In particular, we select eight exchange rates whose trading volume accounts for more than 98% market shares to synthesize Bitcoin indexes. The empirical results based on multifractal detrended cross‐correlation analysis (MF‐DCCA) reveal that (1) the nonlinear dependencies and power‐law cross‐correlations in return‐volume relationship are found; (2) all cross‐correlations are multifractal, and there are antipersistent behaviors of cross‐correlation for q = 2; (3) the price of small fluctuations is more persistent than that of the volume, while the volume of larger fluctuations is more antipersistent; and (4) the rolling window method shows that the cross‐correlations of return‐volume are antipersistent in the entire sample period.
Purpose This paper aims to present a methodology for constructing cointegrated portfolios consisting of different cryptocurrencies and examines the performance of a number of trading strategies for the cryptocurrency portfolios. Design/methodology/approach The authors apply a series of statistical methods, including the Johansen test and Engle–Granger test, to derive a linear combination of cryptocurrencies that form a mean-reverting portfolio. Trading systems are designed and different trading strategies with stop-loss constraints are tested and compared according to a set of performance metrics. Findings The paper finds cointegrated portfolios involving four cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Bitcoin Cash (BCH) and Litecoin (LTC), and the corresponding trading strategies are shown to be profitable under different configurations. Originality/value The main contributions of the study are the use of multiple altcoins in addition to bitcoin to construct a cointegrated portfolio, and the detailed comparison of the performance of different trading strategies with and without stop-loss constraints.
Leopoldo Catania, Stefano Grassi, Francesco Ravazzolo
Cryptocurrencies have recently gained a lot of interest from investors, central banks and governments worldwide. The lack of any form of political regulation and their market far from being “efficient”, require new forms of regulation in the near future. From an econometric viewpoint, the process underlying the evolution of the cryptocurrencies’ volatility has been found to exhibit at the same time differences and similarities with other financial time-series, e.g. foreign exchanges returns. This short note focuses on predicting the conditional volatility of the four most traded cryptocurrencies: Bitcoin, Ethereum, Litecoin and Ripple. We investigate the effect of accounting for long memory in the volatility process as well as its asymmetric reaction to past values of the series to predict: 1 day, 1 and 2 weeks volatility levels.
The recent evolution of cryptocurrencies has been characterized by bubble-like behavior and extreme volatility. While it is difficult to assess an intrinsic value to a specific cryptocurrency, one can employ recently proposed bubble tests that rely on recursive applications of classical unit root tests. This paper extends this approach to the case where volatility is time varying, assuming a deterministic long-run component that may take into account a decrease of unconditional volatility when the cryptocurrency matures with a higher market dissemination. Volatility also includes a stochastic short-run component to capture volatility clustering. The wild bootstrap is shown to correctly adjust the size properties of the bubble test, which retains good power properties. In an empirical application using eleven of the largest cryptocurrencies and the CRIX index, the general evidence in favor of bubbles is confirmed, but much less pronounced than under constant volatility.
This paper aims to select the best model or set of models for modelling volatility of the four most popular cryptocurrencies, i.e. Bitcoin, Ethereum, Ripple and Litecoin. More than 1000 GARCH models are fitted to the log returns of the exchange rates of each of these cryptocurrencies to estimate a one-step ahead prediction of Value-at-Risk (VaR) and Expected Shortfall (ES) on a rolling window basis. The best model or superior set of models is then chosen by backtesting VaR and ES as well as using a Model Confidence Set (MCS) procedure for their loss functions. The results imply that using standard GARCH models may yield incorrect VaR and ES predictions, and hence result in ineffective risk-management, portfolio optimisation, pricing of derivative securities etc. These could be improved by using instead the model specifications allowing for asymmetries and regime switching suggested by our analysis, from which both investors and regulators can benefit.
This paper aims to elucidate the connectedness between major forex currencies and cryptocurrencies using the quantile cross-spectral approach recently proposed by Baruník and Kley (2015). The sample covers six forex currencies and six cryptocurrencies over the period of 1 September 2015 to 29 December 2017. Compared with the results obtained from standard correlations and detrended moving-average cross-correlation analysis (DMCA), the quantile cross-spectral approach provides richer information on the dependence structure across different quantiles and frequencies. The most interesting result is that the intra-group dependencies are positive in the lower extreme quantiles, while inter-group dependencies are negative. This result holds in both the short- and long-term perspectives. Thus, it is worth diversifying between these two currency groups.
Cryptocurrencies such as Bitcoin are establishing themselves as an investment asset and are often named the New Gold. This study, however, shows that the two assets could barely be more di?erent. Firstly, we analyze and compare conditional variance properties of Bitcoin and Gold as well as other assets and ?nd di?erences in their structure. Secondly, we implement a BEKK-GARCH model to estimate time-varying conditional correlations. Gold plays an important role in ?nancial markets with ?ight-to-quality in times of market distress. Our results show that Bitcoin behaves as the exact opposite and it positively correlates with downward markets. Lastly, we analyze the properties of Bitcoin as portfolio component and ?nd no evidence for hedging capabilities. We conclude that Bitcoin and Gold feature fundamentally di?erent properties as assets and linkages to equity markets. Our results hold for the broad cryptocurrency index CRIX. As of now, Bitcoin does not re?ect any distinctive properties of Gold other than asymmetric response in variance.
This paper is the first to forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the generalised autoregressive conditional heteroscedasticity (GARCH) (1,1), the exponentially weighted moving average (EWMA), and the exponential generalised autoregressive conditional heteroscedasticity (EGARCH) (1,1). Models' parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realised volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behaviour of the Bitcoin, results might change in the future.
This paper examines the movement of cryptocurrencies’ return based on price. This volatility can spread to others of the same kind. Currently, the more cryptocurrencies are traded in market, the more chances are available for investors. The author wonders whether contagion risk among these cryptocurrencies happens or not in the event of crashing. We also introduce one empirical evidence of the mutual influence on these cryptocurrencies using Copulas approach. The findings show that all pairs have the structure dependence with Kendall-plots, particularly strong left tail dependence with Chi-plots. It also means the existence of contagion risk among these cryptocurrencies. The three methodologies namely Kendall-plots, Chi-plots and Copulas estimation produce consistent results. Therefore, the investors should carefully perform portfolio diversification to avoid contagious phenomenon.
The emergence of Bitcoin in 2009 has received considerable attention surrounding the validity of cryptocurrencies as a viable and, in some jurisdictions, a legal currency alternative. Despite widespread concern that these cryptocurrencies are fostering the environment within which a substantial bubble can occur, it is important to analyze whether these new assets are behaving similarly to major international currencies. This paper investigates the effects of international monetary policy changes on bitcoin returns using a GARCH (1.1) estimation model. The results indicate that monetary policy decisions based on interest rates taken by the Federal Open Market Committee in the United States significantly impact upon bitcoin returns. After controlling for international effects, we find significant evidence of volatility effects driven by United States, European Union, United Kingdom and Japanese quantitative easing announcements. These results show that, despite its nature and ideals, bitcoin seems to be subject to the same economic factors as traditional fiat currencies, and is not entirely unaffected by government policies. This result has implications for investors using bitcoin as a hedging or diversification tool. In addition, we contribute to the existing debate regarding the classification of bitcoin as an asset class, by illustrating that bitcoin volatility exhibits various reactions that bear resemblance to both currency pairs and store-of-value assets.