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.
Bitcoin and other similar digital currencies on blockchains are not ideal means for payment, because their prices tend to go up in the long term (thus people are incentivized to hoard those currencies), and to fluctuate widely in the short term (thus people would want to avoid risks of losing values). The reason why those blockchain currencies based on proof of work are unstable may be found in their designs that the supplies of currencies do not respond to their positive and negative demand shocks, as the authors have formulated in our past work. Continuing from our past work, this paper proposes minimal changes to the design of blockchain currencies so that their market prices are automatically stabilized, absorbing both positive and negative demand shocks of the currencies by autonomously controlling their supplies. Those changes are: 1) limiting re-adjustment of proof-of-work targets, 2) making mining rewards variable according to the observed over-threshold changes of block intervals, and 3) enforcing negative interests to remove old coins in circulation. We have made basic design checks and evaluations of these measures through simple simulations. In addition to stabilization of prices, the proposed measures may have effects of making those currencies preferred means for payment by disincentivizing hoarding, and improving sustainability of the currency systems by making rewards to miners perpetual.
A peer-to-peer system of blockchain, originally started for a cryptocurrency Bitcoin, has caused major disruptions in the stock market. It has affected many businesses if not all, but its significance in the financial world is magnanimous. Historical data (daily rates) for the past 23 months are analyzed to understand the market size, market capitalization and price volatility for Bitcoin. Time series data and financial model are applied to realize the shocks. Monte Carlo simulation is applied to assess the dynamic structure of Bitcoin. With greater volume and activity, the banks and financial intermediaries may become outdated, and the middleman will have no place. It seems like a distant thought, but the facts are pointing toward its reality.
We present a dynamic Rational Expectations (RE) bubble model of prices with the intention to evaluate it on optimal investment strategies applied to Bitcoin. Our bubble model is defined as a geometric Brownian motion combined with separate crash (and rally) discrete jump distributions associated with positive (and negative) bubbles. The RE condition implies that the excess risk premium of the risky asset exposed to crashes is an increasing function of the amplitude of the expected crash, which itself grows with the bubble mispricing: hence, the larger the bubble price, the larger its subsequent growth rate. We use the RE condition to estimate the real-time crash probability dynamically through an accelerating probability function depending on the increasing expected return. We examine the optimal investment problem in the context of the bubble model by obtaining an analytic expression for maximizing the expected log of wealth (Kelly criterion) for the risky asset and a risk-free asset. Using our bubble model on Bitcoin from 8-Jul-2013 until 19-Dec-2017 would have generated a CAGR of 140% with a maximum drawdown of 69% giving a Calmar Ratio of 2.03. It would have moved out of Bitcoin gradually since 25-Apr-2017 to be completely out on 19-Dec-2017, three days before the crash. The outperformance of the Efficient Portfolio over just investing in Bitcoin was 265%, accomplished over 117 rebalances from 08-Jul- 2013 to 20-Dec-2017. This strategy could thus afford a cost of 2.27% at each rebalancing period and still outperform investing only in Bitcoin.
Digital currencies, such as Bitcoin, have emerged as an alternative form of money, untethered to traditional money and largely unregulated. As such, digital currency represents a wild frontier for investors who might otherwise be shopping for gold or foreign currencies, with serious risks. The present work considers digital currency from a traditional asset pricing perspective. Setting aside risks of seller fraud or currency theft, we examine fluctuation and systematic risk in the price of Bitcoin. From this perspective, Bitcoin does not appear to carry much systematic risk -- despite its high volatility -- and so is a reasonable candidate for inclusion in investors’ portfolios. Some illustrative examples suggest that the optimal amount of Bitcoin to include in investor portfolios may be tiny or instead substantial - as high as 21 percent of total financial assets.
Daniel Traian Pele, Miruna Mazurencu-Marinescu-Pele
In this paper we investigate the statistical properties of cryptocurrencies by using alpha-stable distributions. We also study the benefits of the Metcalfe's law (the value of a network is proportional to the square of the number of connected users of the system) for the evaluation of cryptocurrencies. As the results showed a potential for herding behaviour, we used LPPL models to capture the behaviour of cryptocurrencies exchange rates during an endogenous bubble and to predict the most probable time of the regime switching.
In this thesis, an analysis of Bitcoin, Monero price and volatility is conducted with respect to S&P500 and the VIX index. Moreover using Python, we computed correlation coefficients of nine cryptocurrencies with two different approaches: Pearson and Spearman from July 2016 -July 2018. Moreover the Pearson correlation coefficient was computed for each year from July2016 - July 2017 - July 2018. It has been concluded that in 2016 the correlation between the selected cryptocurrencies was very weak - almost none, but in 2017 the correlation increased and became moderate positive. In 2018, almost all of the cryptocurrencies were highly correlated. For example, from January until July of 2018, the Bitcoin - Monero correlation was 0.86 and Bitcoin - Ethereum was 0.82.
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.
We examine the predictions of the resale option hypothesis (Scheinkman and Xiong, 2003) in cryptocurrency markets. The resale option hypothesis yields testable implications on the relationship between the level and volatility of mispricing, and the degree of heterogeneous beliefs. Using turnover as a proxy for heterogeneity, we find evidence supporting the resale option hypothesis. These findings are persistent across various types of cryptocurrencies, and support the notion that cryptocurrencies trade above intrinsic value. Futhermore, we conduct two backtests to show that portfolios with higher turnover or resale option characteristics underperform portfolios with lower turnover or resale option characteristics. This supports the theory that disagreement is negatively related to future returns for positive biased assets (see Atmaz and Basak, 2018).
From positions, attained by modern theoretical physics in understanding of the universe bases, the methodological and philosophical analysis of fundamental physical concepts and their formal and informal connections with the real economic measuring is carried out. Procedures for heterogeneous economic time determination, normalized economic coordinates and economic mass are offered, based on the analysis of time series, the concept of economic Plank's constant has been proposed. The theory has been approved on the real economic dynamic's time series, related to the cryptocurrencies market, the achieved results are open for discussion. Then, combined the empirical cross-correlation matrix with the random matrix theory, we mainly examine the statistical properties of cross-correlation coefficient, the evolution of average correlation coefficient, the distribution of eigenvalues and corresponding eigenvectors of the global cryptocurrency market using the daily returns of 15 cryptocurrencies price time series across the world from 2016 to 2018. The result indicated that the largest eigenvalue reflects a collective effect of the whole market, practically coincides with the dynamics of the mean value of the correlation coefficient and very sensitive to the crisis phenomena. It is shown that both the introduced economic mass and the largest eigenvalue of the matrix of correlations can serve as quantum indicator-predictors of crises in the market of cryptocurrencies.
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.
Natália Diniz Maganini, Antônio Carlos da Silva Filho, Eduardo Fonseca de Almeida
O surgimento e crescimento do uso de criptomoedas baseadas na tecnologia Blockchain, em tempos recentes, aumenta o interesse pelo estudo da sua dinâmica econômica e características financeiras.O Bitcoin é, atualmente, a criptomoeda mais conhecida e disseminada, com maior volume de transações, valor de mercado e aceitação em serviços de câmbio.Com o objetivo de contribuir para a análise do comportamento de preços do mercado do Bitcoin, este estudo analisa se a série histórica dos preços desta moeda, cotadas de 12 em 12 horas no período de 14 de setembro de 2011 a 20 de novembro de 2017, possui características multifractais.Os resultados da pesquisa foram positivos.Além disso, percebe-se que tanto correlações de longo alcance como a distribuição das caudas gordas, contribuem para o comportamento multifractal do Bitcoin.
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.
The old school -which consists largely of middle-aged and elderly men- tend to claim that bitcoin is a "bubble", and seize on every downturn in the price of bitcoin as evidence that the bubble has burst or is about to burst. The bubble only gets fatter, and all of the anti-crypto arguments -notably the argument that currencies need themselves to possess, or to be based on something with "intrinsic" value, and cryptocurrencies lack intrinsic value- are fallacious. Here we propose that there are deep mathematical reasons why the conservatives are mistaken, and why cryptocurrencies will increasingly replace their traditional counterparts.
This paper studies the efficiency of the cryptocurrency market by looking at the distribution of bitcoin prices over time and across exchange-currency pairs. We document persistent differences in relative bitcoin prices (or discounts), with a half-life of 1 day, and a distribution which is leptokurtic, skewed to the right, with a standard deviation of 3.9%. The variability of discounts is larger in countries with tighter capital controls due to the combined effect of market segmentation and local supply and demand shocks, which we relate to location-specific mining activities and investor attention.