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# Bitcoin market efficiency

Is Blockchain Making the Cryptocurrency Market More Efficient?Read the Privacy Policy to learn how this information is used. Listen to an audio version of this summary. Frequent and sizable arbitrage opportunities exist to exploit price differences for bitcoin across cryptocurrency exchanges. Do professional arbitrage traders have opportunities to profit in the bitcoin markets? The market for bitcoin has grown in size from negligible a little over a decade ago to USD0.

The authors suspected that because the bitcoin market is relatively new and is dominated primarily by individual investors, inefficiencies in trading might exist that institutional traders could exploit. Other researchers had found that opportunities to profit from this type of inefficiency decreased over time.

Such inefficiencies would typically manifest in price discrepancies between identical assets in different bitcoin exchanges. If such price differences were present for long enough periods, then professional investors would be able to profit by purchasing the cheaper-priced bitcoin and selling those priced higher in an arbitrage. The authors analyzed price data from many of the major bitcoin exchanges around the world over the period — The data included volume, price, and timestamp information for each trade or tick.

The authors took a three-pronged approach:. Two exchanges stood out as consistently offering lower prices for bitcoin for quotes in US dollars: Bitfinex and Bitstamp. The spread data show that arbitragers would benefit from operating primarily outside of US working hours.

The authors found that when a new bitcoin exchange opens, the spreads across the industry increase. However, this difference tended to get smaller over time. When bitcoin exchanges are hacked or robbed, the market spreads tend to increase for a period of approximately five weeks following the malfeasance.

Our findings also imply that a first-mover advantage would accrue to institutional money that acts to capture profits before arbitrage trading in bitcoin markets gains further mainstream attention. Original Research Article. Audio Summary. We were not able to record your PL credits.

Recently, cryptocurrencies have received substantial attention by investors given their innovative features, simplicity and transparency. We here analyze the increasingly popular Bitcoin and verify pertinence of the efficient market hypothesis.

Recent research suggests that Bitcoin markets, while inefficient in their early days, transitioned into efficient markets recently. We challenge this claim by proposing simple trading strategies based on moving average filters, on classic time series models as well as on non-linear neural nets.

Our findings suggest that trading performances of our designs are significantly positive; moreover, linear and non-linear approaches perform similarly except at singular time periods of the Bitcoin; finally, our results suggest that markets are becoming less rather than more efficient towards the sample end of the data. Recently, cryptocurrencies have received substantial attention by investors given their innovative features, simplicity, transparency and their increasing popularity.

The number of Bitcoin wallet owners is estimated to have quadrupled from about 1 million in to about 4 million in and the average daily number of trades has approached , To some extent, these peculiarities can be attributed to market liquidity which cannot compete with classic securities exchanges and which varies across Bitcoin exchanges, see Loi In this context, given the rising importance of Bitcoin as well as its non-standard price dynamics, we propose to verify pertinence of the so-called efficient market hypothesis EMH , as proposed by Fama In essence, the EMH postulates that efficient markets reflect all past information weak-form , public information semi-strong form , or public and private information strong form in market prices.

Verification of the EMH is important for market particpants as it implies that such information cannot be used to make persistent profits on trading on the market. In summary, recent research on the topic is inconclusive as to whether Bitcoin markets are efficient under the EMH or not. Some findings suggest that Bitcoin markets, while inefficient in their early days, transitioned into efficient markets recently. Others find support for the adaptive market hypothesis AMH , an alternative theory that builds on evolutionary principles and assumes markets and market efficiency evolve over time.

We here add to this growing body of literature by analyzing effective as opposed to theoretical market efficiency. While previous work focused on the latter approach by verifying theoretical features of Bitcoin prices in efficient markets, we here evaluate whether such features could, in fact, be consistently exploited for economic profit.

Therefore, we test performance of various trading strategies which under the weak form of market efficiency should be not statistically different from zero or even negative when accounting for trading cost.

After a review of related literature and a presentation of the used data, we start our analysis by unfolding serial dependence in log returns of Bitcoin. Based on these findings, we then challenge the previous body of research by applying simple trading strategies based on moving average filters, on classic time series models as well as on non-linear neural nets.

We account for costs by crossing the bid-ask spread at each trade so that positive net performances would be indicative of effective market inefficiency.

Fama suggested three categories of informational efficiency: i weak efficiency, if current prices reflect the information contained in past prices, ii semi-strong efficiency, if prices reflect all public information and iii strong efficiency, if prices reflect all public and private information. Recently, the topic has also gained increased interest in the crypto-community and in particular for Bitcoin markets.

Urquhart analyzes the weak-form efficiency of Bitcoin by verifying pertinence of a random-walk hypothesis. While his results reject efficiency on the whole sample, from to , Bitcoin returns seem to be random from onward. In a subsequent study, Nadarajah and Chu use the same daily Bitcoin price data and apply a power transformation to the returns.

More recently, Brauneis and Mestel extend the study of weak-form efficiency to 73 cryptocurrencies and link efficiency to market liquidity and size of the respective cryptos. In addition, results suggest that market liquidity as well as market capitalization positively affects efficiency.

Along the same lines, Sensoy use intraday data on Bitcoin prices expressed in USD and EUR and find that both markets have become more efficient since beginning of , that the USD market is more efficient than the EUR market during the period observed, informational efficiency decreases for higher data frequency, and efficiency is positively negatively affected by market liquidity volatility. A parallel stream of work approaches informational efficiency by testing weekday effects on Bitcoin prices which, again, would contradict the EMH.

In a first study, Kurihara and Fukushima indeed find statistically significant weekday effects and conclude that Bitcoin markets are not efficient. On the other hand, separating the observation period into two parts they also find proof for Bitcoin markets transitioning to efficient markets. In an extended analysis Caporale and Plastun , the authors find similar results for Bitcoin but do not find consistent return anomalies for other crypto-currencies.

A third workstream focuses on an analysis of long-range memory in Bitcoin prices which, if existing, would point to rejection of the weak-form EMH. However, while Urquart suggested that Bitcoin markets have become more efficient the efficiency index computed over time in Tiwari seems to indicate decreasing efficiency towards the end of the sample.

Kristoufek b uses the same efficiency index and extends the analysis to Bitcoin prices expressed in Chinese Yuan. Results do not confirm earlier findings of increasing efficiency but suggest that Bitcoin markets remain largely inefficient throughout the observation period. Long memory is found in both the markets individually and the system of markets confirming informational inefficiency of Bitcoin. Another workstream has focused on the semi-strong form of efficiency.

For instance, Bartos analyzes the semi-strong form of the EMH for Bitcoin markets by correlating price to news events. Therefore, Bartos uses daily Bitcoin prices expressed in USD and aggregated across several exchanges over the period of March to July Hence, Bartos concludes that Bitcoin markets are, indeed, efficient.

Their data include 50 events 28 negative events and 22 positive expressing monetary policy and Bitcoin-related regulation announcements across the globe. The results of this study indicate that Bitcoin does not respond to monetary policy news which, according to the authors, confirms that Bitcoin is detached from the real economy. The results reviewed above are inconclusive as to whether Bitcoin markets are weak-form or semi-strong form efficient or not.

Generally, the authors observe times during which markets are efficient and for other periods they are not. In fact, Khuntia and Pattanayak confirm these patterns of efficiency and argue that these findings support the adaptive market hypothesis AMH introdcued in Lo In analogy to evolutionary principles, the AMH assumes that markets evolve and adapt and that, as a consequence, market efficiency varies in degree along time.

We here propose to challenge the EMH for Bitcoin by proposing simple univariate trading strategies, based on straightforward signal extraction and forecasting principles, whose performances appear remarkably consistent and resilient over time, beyond the singular breakdown of the currency in early Therefore, we believe that these data provide a good representation for Bitcoin market activity.

Further, it should be noted that the start of our data sample is different from other samples used in previous work. For instance, Urquhart uses Bitcoin price data starting at August 10, accessed through www. These data, however, represent a Bitcoin price index constructed as the volume-weighted average Bitcoin price from all available Bitcoin exchanges worldwide. Therefore, while the latter source provides a wider time window our sample is reproducible as it originates in a single market place and can be straightforwardly accessed.

As shown in the figure, the price of 1 Bitcoin moved below USD 1, from the start of the observed period until beginning of and skyrocketed up to almost USD 20, on December 17 in the same year. In the last period, the price then steadily decreased again to a level of about USD at the end of the observed period. Since both the drift as well as the volatility of the series are unusually large, when compared to classic assets, we compute the Sharpe ratio, which is a measure that balances drift and volatility aspects.

For the Bitcoin data, the annualized Sharpe ratio is 0. At the same time, the h trading volume seems to exhibit some cyclical pattern with the year showing low trading volume, year a steady increase in volume building up to the almost USD 20, best price mark at the end of and trading activity comparable to pre levels, while the trading activity decreased again sharply after that and continuously throughout most of the year , increasing again for a short period at the end of Historical bid price top panel , log price second panel , log returns third panel , and log volumes bottom panel for Bitcoin in USD sourced from the Bitstamp exchange.

The autocorrelation function acf of the log returns is displayed in Fig. Autocorrelation function Acf up to lag 30 for log returns left panel and of standardized model residuals right panel for Bitcoin. The MA 6 coefficient is largest, as expected, and strongly significant with a p value of 0.

Furthermore, the autocorrelation structure of the standardized model residuals in the right panel of Fig. The empirical significance level of the Ljung Box statistic of the standardized model residuals at lag six amounts to 0.

We note, also, that the peak of the autocorrelation at lag 6 seems persistent across time, so for example this number amounts to 0. We infer that the log returns of the series are subject to systematic and significant positive autocorrelation, which points towards a possible market inefficiency that could be exploited by suitable trading strategies. The question whether the observed dependency structure is sufficient for balancing trading costs and to outperform the already impressive passive buy-and-hold strategy under these circumstances will be analyzed below.

The above data analysis has revealed dependency structures which contradict the weak form EMH and which could be exploited by suitable forecast techniques. We propose three variants: moving-average filters, frequently found in momentum trading strategies, ARMA time series models and neural nets. Whereas the former two can exploit the statistically significant linear dependency structure of the log returns, the latter can account for possible non-linearity in the data, additionally. Momentum trading is a technique in which traders buy or sell an asset according to the direction of its trend.

Given the different characteristics of these filters, we are faced with the problem of selecting a pertinent design and we propose to base our decision upon signal extraction principles. For that purpose, consider the following simple local linear level model:. Harvey This model-based perspective justifies heavy smoothing in the case of noisy data, which would suggest applications to first differences or log returns of the original prices.

We infer that the usage of EqMAs, as applied to log returns of Bitcoin data, could be justified based on signal extraction principles and use this design for our momentum trading strategy.

The previous EqMA-designs apply equal weights to current and past observations. A potentially more refined weighting scheme, at least in terms of forecasting, could be obtained by relying on the MA 6 -model 1 proposed in the previous section.

The model can be inverted into its infinite autoregressive representation. For simplicity of exposition, we here restrict the analysis to feedforward nets with two hidden layers of dimensions six and three, see Fig.

Their outputs. The decision for the above net configuration is based on our data analysis input layer accounts for the first six lags of the data as well as on a suitable compromise between flexibility and simplicity requirements classic mean-square loss function as well as traditional sigmoid activation function : the results obtained by the above structure are representative for a fairly broad range of alternative net specifications or software implementations.

Feedforward net with two hidden layers applied. The six dimensions of the first hidden layer correspond to the first six lags of the Bitcoin log returns.

As we have discussed above, under the EMH none of the above trading strategies could be persistently profitable and in fact they should all lead to systematic losses when accounting for the bid-ask spread at the corresponding trading time points. We will now challenge these claims, equipped with linear and non-linear filter techniques.

The previous analysis of prices, log prices, and log returns in Sect. In particular, the autocorrelation function in Fig. Therefore, we propose to apply a simple EqMA 6 filter.

Top panel: log returns black and filtered series red. Bottom panel: cumulated log- performances of the momentum strategy based on EqMA 6 for Bitcoin color figure online. Note that trading costs are ignored here for simplicity see below for corresponding results.

The empirical significance level of a test for whether the two Sharpe ratios differ significantly amounts to 6.

Continuing our performance analysis, we compute in Fig. First of all, our results show strictly positive returns over the entire period which itself is impressive. This points to the fact that the Bitcoin market inefficiency becomes more accentuated in the last period of our sample, which contrasts with previous findings in Urquhart , Kurihara and Fukushima , and Bariviera stating increased efficiency after around though it is fair to mention that our data sample stretches two years further to the right than theirs.

A test of the hypothesis that the drift of the resulting performance is larger than zero Footnote 2 leads to a value of the corresponding t statistic of 3. To conclude, we note that the above results may claim out-of-sample validity since the only freely determined parameter, namely the filter length, was obtained from a straightforward analysis of the autocorrelation function whose main feature, the peak at lag 6, is pretty stable over time as shown in Sect.

We here rely on the forecast filter derived from the MA 6 -model 1. Specifically, we buy or sell the Bitcoin depending on the sign of the forecasts. Cumulated performances of the resulting strategy are displayed in Fig.

Except for a short contraction, coinciding with the drawdown of Bitcoin in early , model-performances are fairly regular over the observed time span. The time series model beats buy-and-hold on all accounts, but the extent is less marked than for the previous simpler EqMA 6 strategy.

The trading strategy applied in this section builds on a return forecast through a neural net time series model outlined in Sect. Analogously to the previous strategy, which used a classic time series model for return forecasting, the sign of our Bitcoin return forecast again indicates whether we buy or sell.

In contrast to the previous linear approaches, fitting of unknown parameters is generally more challenging for neural nets because the numerical optimization tends being trapped into local minima. Therefore, parameter estimates ordinarily depend upon suitable initial values for these parameters.

In this context, it is common to rely on random initializations of biases and weights: each random seed thus generates a new random net whose parameters may differ substantially from realization to realization. In order to illustrate the extent of this problem on trading outcomes, we compare cumulated in-sample left panel and out-of-sample right panel performances of random nets in Fig.

Cumulated performances of random nets applied to log returns of Bitcoin: in-sample left panel and out-of-sample right panel. A quick glance at both graphs illustrates the effect of the random seed on trading performances: for example annualized Sharpe ratios vary in a range from 0.

In-sample performances are overly optimistic due to overfitting, as expected. Interestingly, out-of-sample gains seem to be quite substantial, in the mean over all realizations, even after the breakdown of the Bitcoin in early The out-of-sample results in Fig. At this stage of the analysis, we may be interested in finding out if in-sample numbers trading performances or forecast performances are informative about future out-of-sample performances.

Specifically, the correlation between in-sample and out-of-sample Sharpe ratios amounts to 0. Overcoming these conflicting evidences, we could rely on a simple ensemble average, the cross-sectional mean, of all performances as shown in Fig.

Average cumulated out-of-sample performances across random nets for the neural net forecast model red versus MA 6 forecast model blue strategies for Bitcoin color figure online. Indeed, a quick glance at both curves suggests fairly similar performances, except perhaps for the heavier drawdown of the classic model at the beginning of Buy-and-hold and the MA 6 -model are systematically outperformed by the other two strategies for the considered time span. To verify significance of the above out-of-sample performances, we compute the t test for positive trading performances: the empirical significance levels are 0.

We may infer from Fig. To conclude, we briefly analyze the effects of trading costs, by crossing the spread between bid and ask prices at each trade.

We here restrict the analysis to EqMA filters, since results are similar across all three approaches. Effect of trading costs crossing the bid-ask spread on performances of the momentum strategy based on EqMA 6 for Bitcoin. We may infer that the effect of the spread is negligible even for filters with relatively short holding periods, such as the EqMA 6. Our aim was to check pertinence of the EMH for the Bitcoin.

Data analysis suggested evidence for a violation of this assumption by revealing systematic significant positive serial correlation of the log returns, which unfolded after accounting for volatility clustering.

We then proposed three different trading strategies relying on simple equally weighted moving average filters, derived from signal extraction principles, as well as on classic ARMA forecast models and non-linear neural nets.

Our trading results confirmed the previous data analysis, by highlighting a filter of length 6, or an EqMA 6 , as the most effective momentum strategy.

Its performances were strongly statistically significant and the course of the yearly return series suggested increasing market inefficiency towards the sample end Januar 10, Similar results were obtained for the two forecast approaches with a slight edge in favor of the ensemble average of random neural nets. A comparison of their trading performances out-of-sample suggested only modest departure from linearity, possibly during the drawdown of the Bitcoin at the beginning of Statistical significance could be established for all but the MA 6 -model which marginally missed the mark due to the aforementioned drawdown.

Finally, we extended our performance analysis to the inclusion of trading costs by crossing the spread between bid and ask prices at each trade. Confirming the overall positive cumulative performances, our results were only marginally affected by accounting for trading costs. In summary, our findings strongly reject the EMH for the Bitcoin market throughout the entire sample period and in particular in recent times.

Departures from linearity appear marginal, possibly confined to the drawdown of Bitcoin in early Quandl is a general data market place that collects and makes available public as well as commercial data sets through a unified API.

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