Emmanouil Platanakis, Charles Sutcliffe, Andrew Urquhart
This paper contributes to the literature on cryptocurrencies by examining the performance of naïve (1/N) and optimal (Markowitz) diversification in a portfolio of four popular cryptocurrencies. We employ weekly data with weekly rebalancing and show there is very little to select between naïve diversification and optimal diversification. Our results hold for different levels of risk-aversion and an alternative estimation window.
Due to conclusion could not rely on only one test, in this study, we apply various approaches to verify the actuary of VaR model to find out whether VaR model, especially historical VaR and delta normal VaR model, can provide the accurate risk measurement results for cryptocurrencies risk, especially CRIX, BTC, ETH and XRP. We use Kupiec’s POF test, Independence Test - Christoffersen (1998) and Joint Test that widely use for backtesting VaR model. Performance test results for risk measurement by historical VaR provide a fairly accurate over delta normal VaR when we use Kupiec’s POF-test for the accuracy of VaR model. Christoffersen (1998) independence test, the exceptions (failures) of historical VaR and delta normal VaR model show independence exceptions in accordance with an only high confidence level of critical values (0.99). Otherwise, the low confidence level of critical values (0.90 and 0.95) appears dependence exceptions. For the Joint test, we combine POF-test and independence test because each model has different advantages and disadvantages. The results show that historical VaR model is suitable for measuring cryptocurrency risk over delta normal VaR only high confidence level of critical values.
Leopoldo Catania, Stefano Grassi, Francesco Ravazzolo
This paper studies the predictability of cryptocurrencies time series. We compare several alternative univariate and multivariate models in point and density forecasting of four of the most capitalized series: Bitcoin, Litecoin, Ripple and Ethereum. We apply a set of crypto–predictors and rely on Dynamic Model Averaging to combine a large set of univariate Dynamic Linear Models and several multivariate Vector Autoregressive models with different forms of time variation. We find statistical significant improvements in point forecasting when using combinations of univariate models and in density forecasting when relying on selection of multivariate models.
Stjepan Begušić, Zvonko Kostanjčar, H. Eugene Stanley, Boris Podobnik
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation distributions. Motivated by the rise of novel digital assets based on blockchain technology, we study the distributions of cryptocurrency price fluctuations. We consider Bitcoin returns over various time intervals and from multiple digital exchanges, in order to investigate the existence of universal scaling behavior in the tails, and ascertain whether the scaling exponent supports the presence of a finite second moment. We provide empirical evidence on slowly decaying tails in the distributions of returns over multiple time intervals and different exchanges, corresponding to a power-law. We estimate the scaling exponent and find an asymptotic power-law behavior with 2 < α < 2.5 suggesting that Bitcoin returns, in addition to being more volatile, also exhibit heavier tails than stocks, which are known to be around 3. Our results also imply the existence of a finite second moment, thus providing a fundamental basis for the usage of standard financial theories and covariance-based techniques in risk management and portfolio optimization scenarios.
Bitcoin is one of the most prominent decentralized digital cryptocurrencies. Ability to understand which factors drive the fluctuations of the Bitcoin price and to what extent they are predictable is interesting both from the theoretical and practical perspective. In this paper, we study the problem of the Bitcoin short-term volatility forecasting based on volatility history and order book data. Order book, consisting of buy and sell orders over time, reflects the intention of the market and is closely related to the evolution of volatility. We propose temporal mixture models capable of adaptively exploiting both volatility history and order book features. By leveraging rolling and incremental learning and evaluation procedures, we demonstrate the prediction performance of our model as well as studying the robustness, in comparison to a variety of statistical and machine learning baselines. Meanwhile, our temporal mixture model enables to decipher the time-varying effect of order book features on volatility. It demonstrates the prospect of our temporal mixture model as an interpretable forecasting framework over heterogeneous Bitcoin data.
Cryptocurrencies return cross-predictability yields information on risk
propagation and market segmentation. To explore these effects, we build a
dynamic network of cryptocurrencies based on the evolution of return
cross-predictability and develop a dynamic covariate-assisted spectral
clustering method to consistently estimate the latent group membership of
cryptocurrencies. We show that return cross-predictability and
cryptocurrencies' characteristics, including hashing algorithms and proof
types, jointly determine the cryptocurrencies market segmentation. Portfolio
analysis reveals that more centred cryptocurrencies in the network earn higher
risk premiums.
Elie Bouri, Mahamitra Das, Rangan Gupta, David Roubaud
This paper contributes to the embryonic literature on the relations between Bitcoin and conventional investments by studying return and volatility spillovers between this largest cryptocurrency and four asset classes (equities, stocks, commodities, currencies, and bonds) in bear and bull market conditions. We conducted empirical analyses based on a smooth transition VAR GARCH-in-mean model covering daily data from July 19, 2010 to October 31, 2017. We found significant evidence that Bitcoin returns are related quite closely to those of most of the other assets studies, particularly commodities, and therefore, the Bitcoin market is not isolated completely. The significance and sign of the spillovers exhibited some differences in the two market conditions and in the direction of the spillovers, with greater evidence that Bitcoin receives more volatility than it transmits. Our findings have implications for investors and fund managers who are considering Bitcoin as part of their investment strategies and for policymakers concerned about the vulnerability that Bitcoin represents to the stability of the global financial system.
Purpose The purpose of this paper is to examine the value-at-risk and related measures for the Bitcoin and to compare the findings with Standard and Poor’s SP500 Index, and the gold spot price time series. Design/methodology/approach A GJR-GARCH model has been implemented, in which the residuals follow the standardized Pearson type-IV distribution. A large variety of value-at-risk measures and backtesting criteria are implemented. Findings Bitcoin is a highly volatile currency violating the value-at-risk measures more than the other assets. With respect to the Basel Committee on Banking Supervision Accords, a Bitcoin investor is subjected to higher capital requirements and capital allocation ratio. Practical implications The risk of an investor holding Bitcoins is measured and quantified via the regulatory framework practices. Originality/value This paper is the first comprehensive approach to the risk properties of Bitcoin.
Cryptocurrencies are known as unpredictable due to their highly volatility. In time series, the forecasting accuracy is strongly affected by the methodologies that are used in identifying the pattern of a nonstationary stochastic realization. The purpose of the present study is to develop an algorithm that is capable of efficiently identifying the pattern of cryptocurrencies. A brief summary of the algorithm is given. To illustrate the quality of our proposed algorithm, we study the pattern of ten different reputable cryptocurrencies and use their daily closing prices to constitute a time series. The comparison between our proposed forecasting algorithm versus the autoregressive integrated moving average (ARIMA) process will be demonstrated.
Cryptocurrencies as an investment have received increasing attention by media and international governments over the last years.However, little is known yet about the dynamics that drive these highly volatile alternative assets.This thesis studies the dynamic interdependencies between the volatility of Bitcoin, Litecoin, Ripple, Dogecoin and Feathercoin via the Dynamic Conditional Correlation model by Engle (2002) with the multivariate Student-t distribution.The main question is whether a multivariate approach improves the Value at Risk forecasting accuracy for the conditional heteroscedasticity in comparison to univariate GARCH-type models.Results show that there is a high interconnectedness between the volatility of the currencies.However, the Dynamic Conditional Correlation model can not deliver better forecasting results than the univariate GARCH-type models for the individual cryptocurrency return series. Contents List of Figures iv List of Tables vList of Tables 1 Summary Statistics for daily log returns 100 of cryptocurrencies.Log returns are calculated using: r t = 100ln(P t /P t-1 ).Returns are observed until 14 th of March 2018.Market cap is captured at 14 th of March 2018.Jarque-Bera-Test checks for deviation from normality (skewness S different from zero and kurtosis K different from 3): JB = T (S/6 + (k -3) 2 /24), is distributed as X 2 (2) with 2 degrees of freedom.Its critical value at the five-percent level is 5.99 and at the one-percent it is 9.21. . . . . . . . . . . . . . . . . . . . . . . . . 2 AIC and BIC for the estimated GARCH-type models. t is modelled via an ARMA-(1,1) process. t is modelled via a GARCH-type process of order (1,1).T=1544.Lowest AICs and BICs per group are written in bold letters. . . . . . . . . . . . . . . . . . . . . . . . . . 3 1%-and 5%-Value at Risk results for the univariate GARCH-type models.1-day-ahead rolling forecast with recursive window, model parameters refitted every 300 observations.Model is built on a training data set of 800 observations, which leaves 744 out-of-sample forecasts.% Viol: Percentage of VaR violations at = 1% and = 5%.L uc : p-value for test of unconditional coverage; L cc : p-value for test of conditional coverage.Values printed bold if p < 0.05. . . . . . . 4 Model parameters of the selected GARCH models. t is modelled via an ARMA-(1,1) process.T=1544.*** p-value < 0.001; ** pvalue < 0.01; * p-value < 0.05.Q(10): p-value of Ljung-Box test on squared standardized residuals for lag = 10; ARCH(5): p-value for weighted ARCH LM test for lag = 5. . . . . . . . . . . . . . . . . 5 Lag = 0 sample correlation matrix 0 (Pearson) of the five crypto currency log return series.T = 1554. . . . . . . . . . . . . . . . . .6 Model parameters for the estimated DCC models.T=1544, k=5, *** p-value < 0.001; ** p-value < 0.01; * p-value < 0.05.Model parameters for univariate volatility series are listed in table (4). . .7 Mean and (standard deviation) of the lag = 0 correlations in the multivariate volatility of the currencies estimated by the DCC model in equation (57).T=1544. . . . . . . . . . . .
Cel – Celem artykułu jest prezentacja koncepcji systemu informatycznego umożliwiającego prognozowanie kursu kryptowaluty bitcoin (BTC) w odniesieniu do waluty euro. Metodologia badania – Na potrzeby realizacji tak sformułowanego celu opracowano model sztucznej sieci neuronowej – perceptronu wielowarstwowego. W ramach badań dobrano zmienne wejściowe, od których uzależniono kurs BTC. Pozyskano także odpowiednie dane, pochodzące z dziennych notowań kursów wybranych walut i metali. Dane poddano stosownej obróbce matematycznej w celu ich dostosowania do wykorzystania podczas uczenia, walidacji i testowania sztucznej sieci neuronowej. Oryginalność/wartość – Oryginalny był dobór wektora zmiennych wejściowych, umożliwiających prognozowanie kursu BTC. Wyniki przeprowadzonych eksperymentów potwierdziły wysoką skuteczność prognozowania w perspektywie jedno- i dwudniowej. Wysokie wartości współczynnika regresji (R) i mały błąd średniokwadratowy (MSE) świadczą o tym, że opracowany system predykcyjny prawidłowo przewiduje kursy analizowanej kryptowaluty nie tylko w odniesieniu do danych historycznych, lecz także dla wartości bieżących i przyszłych.
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.
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.