The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies

doi:10.1016/j.frl.2018.04.002

Finance Research Letters

Volume 28, March 2019, Pages 68-73

https://doi.org/10.1016/j.frl.2018.04.002 Get rights and content

Highlights

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Weak-form efficiency of high frequency BTCUSD and BTCEUR is analyzed.
•
Pricing efficiency has been improving in the last few years at the intraday level.
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BTCUSD is slightly more efficient that BTCEUR
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Higher the return frequency, lower the informational efficiency is.
•
Strong positive (negative) relation between liquidity (volatility) and high frequency Bitcoin efficiency exists.

Abstract

We compare the time-varying weak-form efficiency of Bitcoin prices in terms of US dollars (BTCUSD) and euro (BTCEUR) at a high-frequency level by using permutation entropy. We find that BTCUSD and BTCEUR markets have become more informationally efficient at the intraday level since the beginning of 2016, and BTCUSD market is slightly more efficient than BTCEUR market in the sample period. We also find that higher the frequency, lower the pricing efficiency is. Finally, liquidity (volatility) has a significant positive (negative) effect on the informational efficiency of Bitcoin prices.

Introduction

Since the first time it was introduced by Nakamoto (2008), Bitcoin has received considerable attention among policymakers, investors and regulators. Due to its unique nature, Bitcoin can be traded any time online and exchanged into major currencies at a low cost (Fry and Cheah, 2015). The market for Bitcoin, which was created in 2009 but active trading started only in 2013, is rather young. However, its innovative features, simplicity, transparency; and the late exponential growth in its value made Bitcoin more popular than ever.

One of the key issues that is of interest to market participants is whether the pricing behaviour of Bitcoin is predictable, which would be inconsistent with the Efficient Market Hypotheses (Fama, 1970). In the past couple of years, a few academics have produced significant results on this subject via tests on the weak and semi-strong form of EMH. For instance, Urquhart (2016) uses many tests to analyse the efficiency of Bitcoin market and concludes that it becomes more efficient in the latter time sample. Nadaraj and Chu (2017) utilize eight different tests on an odd integer power transformation of Bitcoin returns and show that returns are weakly efficient. Bariviera (2017) studies the dynamics of long-range dependence properties of the Bitcoin price and finds a trend towards efficiency via Hurst exponent analysis. Similar results are found by Tiwari et al. (2018). On the other hand, using daily data with a Hurst exponent analysis, Yonghong et al. (2018) show that the Bitcoin market does not become more efficient over time. From a different perspective, Al-Yahyaee et al. (2018) compare the efficiency of Bitcoin with other assets such as gold, stock and currency. They show that Bitcoin market is the least efficient.¹

Whether it is a static or a dynamic analysis, the above-mentioned studies use daily data to perform their main empirical tests. However, in today’s modern financial markets, computers took over the trading scene through algorithmic (especially high-frequency) trading activities. These automated computers are programmed to take certain actions in response to varying market data in real time. The estimated percentage of the algorithmic trading volume in the total volume in US equities was 85% in 2012, where the big part of this value was attributed to high frequency trading strategies (Glantz and Kissell, 2013). Today, several Bitcoin exchanges provide algorithmic trading platforms to their customers which makes it essential to analyse the Bitcoin market efficiency at the intraday level. In this study, we aim to fill this gap by testing the weak-form efficiency of Bitcoin markets through high frequency returns, which has not been covered by previous studies as far as we know.

In addition to the data frequency, we also test Bitcoin’s pricing efficiency in terms of not only US dollar (BTCUSD) but also euro (BTCEUR), which is the second most traded currency in the world after US dollar. In this way, we will be able to see if it is possible to create more profitable strategies by using an alternative currency.

Previous studies use Bitcoin price data from a single exchange or a weighted price index from several exchanges. In this study, we use a tick-by-tick dataset that comes from all exchanges where USD and/or EUR can be directly used in Bitcoin trading, which is a massive extension of the previous datasets.

Our methodological framework also differs from prior studies on the weak-form efficiency of the Bitcoin markets in two ways. First, prior studies generally estimate a fixed level of market efficiency for the entire sample period. In contrast, we employ a time-varying approach by using rolling samples, giving us the flexibility of not being forced to impose cut-off dates which are usually subject to criticism in empirical studies. Second, we employ a relatively new methodology, permutation entropy, introduced by Bandt and Pompe (2002). This methodology has not been used in this context before and has several advantages over the common methodologies as explained in Section 2.

Our findings can be summarized as follows: (i) BTCUSD and BTCEUR markets have become more informationally efficient at the intraday level since the beginning of 2016, however this improvement has a cyclical pattern for BTCUSD, whereas it is a gradual increase for BTCEUR; (ii) BTCUSD market is slightly more efficient than BTCEUR market at the intraday level in the sample period; (iii) higher the frequency, lower the pricing efficiency is; and (iv) liquidity (volatility) has a significant positive (negative) effect on the informational efficiency of Bitcoin prices.

Section snippets

Methodology

Permutation entropy considers market efficiency as a dependency concept and translates the problem of dependency into a symbolic dynamic. A special entropy measure is associated with these symbols to test the dependency in the time series. This approach has four advantages as explained by Sensoy et al. (2015). First, the measure depends only on ordinal patterns of time series, therefore it is unaffected by the data’s volatility and can detect non-linear temporal dependencies in contrast to

Data and results

Bitcoin can be traded 24 hours a day and 7 days a week and our data comes from all exchanges where USD and/or EUR can be directly used in Bitcoin trading.²

Conclusion

The analysis above is the first to study the weak-form efficiency of the Bitcoin prices at high-frequency and in terms of euro in addition to the US dollar. We employ permutation entropy with a rolling window approach to test for the weak-form of market efficiency of intraday Bitcoin prices. There are four principal findings.

First, BTCUSD and BTCEUR markets have become more informationally efficient at the intraday level since the beginning of 2016, supporting the findings of Urquhart (2016)

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The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies

Highlights

Abstract

Introduction

Section snippets

Methodology

Data and results

Conclusion

Econ. Lett.

Econ. Lett.

Econ. Lett.

Reg. Sci. Urban Econ.

J. Econom.

N. Am. J. Econ. Finance

Econ. Lett.

Econ. Lett.

Econ. Lett.

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Finance Res. Lett.

Permutation entropy - a natural complexity measure for time series

Phys. Rev. Lett.