Price Discovery of a Speculative Asset: [623017]
Price Discovery of a Speculative Asset:
Evidence from a Bitcoin Exchange
Eric GhyselsyGiang Nguyenz
September 27, 2019
Abstract
We examine price discovery and liquidity provision in the secondary market for
bitcoin|an asset with a high level of speculative trading. Based on BTC-es full limit
order book over the 2013{2014 period, we nd that order informativeness increases with
order aggressiveness within the rst 10 tiers, but that this pattern reverses in outer
tiers. In a high volatility environment, aggressive orders seem to be more attractive to
informed agents, but market liquidity migrates outward in response to the information
asymmetry. We also nd support to the Markovian learning assumption often made in
theoretical models of limit order markets.
Keywords: Bitcoin; cryptocurrency; price discovery; liquidity; price impact; limit order
book market; adverse selection; learning
JEL Classi cation: G10, G12, G14, G19
We are grateful to Jacob Sagi for providing the data used in this paper. We thank Ekkehart Boehmer,
Pab Jotikasthira, Stefan Lewellen, Duane Seppi, Kumar Venkataraman, Mao Ye, and participants at the
2018 NBER Big Data and High Performance Computing for Financial Economics workshop, Penn State
University, Southern Methodist University, UC Louvain, and 2018 SFS Cavalcade Asia-Paci c for helpful
comments. We also thank Joseph Pate for excellent research assistance. This paper was previously titled
\Bitcoin Price Discovery".
yDepartment of Economics and Kenan-Flagler Business School, University of North Carolina{Chapel Hill.
Email: [anonimizat].
zSmeal College of Business, Pennsylvania State University. Email: [anonimizat].
Bitcoin is currently the most prominent cryptocurrency with a market capitalization
of approximately $116 billion (as of August 26, 2018). It was created in 2009 by Satoshi
Nakamoto (whose identity remains unknown) with the purpose of having \a system for
electronic transactions without relying on trust". However, the nascent literature on bitcoin
seems to nd converging evidence that people use bitcoin and other cryptocurrencies more as
a speculative asset rather than as a medium of exchange (see e.g., Cermak, 2017; Baur and
Dimp
, 2018; Glaser, Zimmermann, Haferkorn, Weber, and Siering, 2014; Baur, Hong, and
Lee, 2017). Notwithstanding, Dimp
(2017) nds that the adverse selection component of the
spread in bitcoin trading is high. This raises an intriguing question about what constitutes
private information in the bitcoin market and whether the price discovery process here di ers
from that of other asset classes.
For equities and xed income assets, we have the notion of a fundamental price process.
What about bitcoin? Reasonable arguments have been put forward questioning the intrinsic
value of the cryptocurrency|even claiming it features a purely speculative price bubble
process.1Yet, there is information that should a ect the price of bitcoin. For example, the
hacking of Mt Gox clearly impacted the notion that bitcoin is immune to cyber attacks.2
Likewise, the ban of bitcoin in countries such as China and South Korea (major hubs for
bitcoin mining and trading activities) should matter as well, because it a ects the future value
of bitcoin as a borderless medium of exchange. How does such information get impounded
in the price process of bitcoin? The answer to this question ultimately boils down to how
informed agents trade in this market.
The purpose of our paper is to shed light on the microstructure of one of the major bitcoin
exchanges|BTC-e. Based on a rich dataset o ering a full view of BTC-e's limit order book
1A number of recent papers have proposed equilibrium price models for cryptocurrencies, including Garratt
and Wallace (2018), Schilling and Uhlig (2018), Sockin and Xiong (2018), among others. Many prominent
business leaders, including Carl Icahn, Warren Bu ett, JP Morgan CEO Jamie Dimon, and Goldman Sachs
CEO Lloyd Blankfein, characterized bitcoin as a bubble or even a fraud.
2To be more precise, while the cryptography of distributed ledgers is designed to withstand malicious
attacks, the so-called wallets are not. Hackers attacked Mt Gox's wallets and stole coins owned by the
exchange's participants.
1
across 150 price levels on each side of the market at the sub-second frequency, we are able
to measure the extent to which information shows up at the various layers in the book (in
addition to trades). The data also allows us to see how liquidity is shifting across the book and
to test important implications of adverse selection on market liquidity, di erentiating di erent
theories of limit order book markets. With over nearly ten months of trading from December
7, 2013 to September 24, 2014, we are able to characterize the intraday behavior and time
series variation of volume, volatility, and liquidity on this important bitcoin exchange.3
Our empirical analysis is based on the Ricco, Rindi, and Seppi (2018) model of a dynamic
limit order market with asymmetric information and non-Markovian learning (that is, traders
condition their trading and quoting decision on not only the current state of the limit order
book but also the history leading to the current state). The bitcoin market is a great
laboratory to test this model given the high level of adverse selection as documented by
Dimp
(2017). In addition, the non-Markovian learning feature of the model appears tting
for the bitcoin market, especially when fundamental information is not present or multiple
price equilibria may occur (see Sockin and Xiong 2018 for further discussion). That leaves
trade and order history being even more important as the possible source for information
extraction. Based on this model, we develop and test three main hypotheses.
The rst hypothesis explores the link between orders' informativeness and aggressiveness,
which can then shed light on order strategies pursued by informed traders in this market.
Traditional microstructure theories such as Kyle (1985) assume that informed traders exploit
their information advantage through market orders|the most aggressive type of orders|,
while recent work such as O'Hara (2015) argue that informed traders might prefer to hide
information in various layers of the limit order book (i.e., less aggressive orders). The Ricco,
Rindi, and Seppi (2018) model suggests that the relationship between order informativeness
and aggressiveness is more nuanced: it depends on the size of the information shock. For large
information shocks, informed traders are more likely to trade and quote more aggressively to
3During this period, BTC-e's market share is roughly 20% of the global trading volume of bitcoin against
the USD.
2
realize the value of the information quickly. On the other hand, the value of small information
shocks might not be sucient to o set the cost of crossing the spread, thereby inducing them
to use less aggressive orders for price improvement.
We nd that on average, there is a positive relationship between order informativeness and
aggressiveness up to the 10th level in the book. Beyond this level, however, the information
content of an order is greater the deeper it is in the book, a nding that would be consistent
with the action of informed traders with noisy signals. We then test how this relationship
changes in large value shock and small value shock environments. Our hypothesis states that
in the former, the relationship between informativeness and aggressiveness becomes more
positive (or less negative for the outer region of the book with negative relationship). The
parallel hypothesis for low value shock environment is that the positive (negative) relationship
between informativeness and aggressiveness lessens (strengthens) as informed traders resort
to less aggressive orders for the price improvement.
Our results support these hypotheses. Limit orders at or near the market (most aggressive
limit orders) become signi cantly more informative, whereas limit orders farther away from
the market (less aggressive limit orders) become signi cantly less informative, on days with
large information shocks. In a low volatility environment, however, the most aggressive order
types, namely marketable orders and inside limit orders, become less informative while the
less aggressive limit orders residing between level 6 through 50 become signi cantly more
informative. Our ndings support the idea that the size of the information shock matters for
informed traders' order strategies.
The second hypothesis is concerned with how adverse selection a ects market liquidity.
If the rst hypothesis uncovers the strategies of the informed traders, market liquidity
as examined in the second hypothesis is the outcome of the interaction of informed and
uninformed traders, given that this is a limit order market in which liquidity is supplied by
the participants themselves. How adverse selection in
uences this outcome is an empirical
question. Ricco, Rindi, and Seppi (2018) di erentiate between whether adverse selection
3
is due to an increased fraction of informed traders (holding the shock size xed) or the
occurrence of a large shock. In the former case, the increased fraction of informed traders
does not change the informed traders' strategies but drive uninformed liquidity away from
the market, resulting in a liquidity reduction. The latter is more complex, because a large
value shock can induce informed traders to trade and quote aggressively, namely an inward
migration of informed liquidity. At the same time, due to increased pick-o risk, uninformed
liquidity is expected to move outward. Accordingly, the net outcome could be either an
increase or decrease in market liquidity.
To test the second hypothesis, we use the measure developed by Cont, Kukanov, and
Stoikov (2014) to proxy for the amount of adverse selection at the hourly frequency. We use
the slope of the limit order book to capture market liquidity along both the quantity and
price dimensions. Most importantly, the slope can capture the migration of liquidity toward
or away from the market and allows us to test the theory discussed above as close as possible.
This is a novel feature of our exercise, which is possible only with the full limit order book
data used in this paper. We nd that in a normal environment, increased adverse selection is
associated with a
atter slope, as limit orders migrate to more conservative prices. In a large
value shock environment, the slope becomes even
atter, suggesting a signi cant reduction in
liquidity. In contrast, the limit order book slope steepens signi cantly in low value shock
environment, making it easier and less costly to trade. These results contribute empirical
evidence to further our understanding of Ricco, Rindi, and Seppi (2018)'s model.
The third hypothesis directly tests Ricco, Rindi, and Seppi (2018)'s assumption of non-
Markovian learning in nancial markets. If price discovery is non-Markovian, lagged market
variables should have incremental explanatory power, over and above that of the current
state variables. In other words, traders learn from not only the current state of the limit
order market, but also the path leading to the current state. Based on predictive regressions
of current state variables and their 24-hour histories on hourly price impact measure, we nd
no concrete evidence of the order book history having a signi cant predictive power over that
4
by the current state variables. One important caveat of this exercise is that we examine only
the linear form of dependency, and thus our evidence permits only a quali ed conclusion that
there is no linear dependency of price discovery on the history of the individual state variable.
Our ndings do not rule out the possibility that the dependency could be of a non-linear
form, or on some combination of the state variables. That said, the lack of evidence for
non-Markovian learning in the linear form suggests that the Markovian learning assumption
typically adopted in limit order book models might not be unreasonable. This assumption
is important because it allows theorist to simplify the state space signi cantly. Our results
here provide some initial empirical support for this assumption in modeling limit order
markets. Furthermore, as noted earlier, some bitcoin pricing models suggest that multiple
price equilibria may occur, see in particular Sockin and Xiong (2018). In their model, multiple
equilibria occur endogeneously and relate to future trading bene ts of the cryptocurrency.
Although this is one of several theoretical bitcoin pricing models that have been proposed, our
empirical analysis suggests that such pricing behavior might potentially be well approximated
by a Markovian regime-switching model.
Our study contributes, rst and foremost, to the nascent literature on bitcoin in general
and the microstructure of secondary market trading in this cryptocurrency in particular.
Bitcoin is traded around the clock on many exchanges globally, all of which operate as limit
order markets. As in any limit order market, the key question of interest is how informed
traders choose their strategies and how the uninformed learn value relevant information from
market observables. Even though this question is relatively well researched across many asset
markets, bitcoin is an interesting and unique asset in part because the asset pricing theory is
still in
ux. It is not clear what constitutes fundamental information underlying the intrinsic
value of bitcoin. Furthermore, as argued by Zimmerman (2018), bitcoin is extremely volatile
and attracts speculative trading due to the unique blockchain structure. Accordingly, it is
possible that the price dynamics are sentiment-driven and that traders' strategies might di er
from what we know based on prior theories and empirical work. It is an interesting question
5
whether these unique features of bitcoin could upend the predictions from current theories of
limit order markets.
The paper also contributes to the literature on limit order markets. Our paper is based
on the full limit order book data, which permits a study of the information content and
liquidity across the whole book, not just those pertaining to the top tier or the top few
tiers as is commonly done in the literature. With the bene t of observing a more complete
state space and action space, the obtained evidence provides a more complete view of order
strategies of informed agents and market liquidity. Our evidence therefore can be helpful for
the development of theoretical models aimed at capturing more realistically the dynamics of a
limit order market, as well as for the interpretation of such models. An additional advantage
of using the bitcoin market as an empirical lab for testing limit order market models is that it
is relatively free from market frictions (e.g., free entry, no minimum order size or tick size)|a
common assumption that usually does not hold in more traditional asset markets.
The paper proceeds as follows. We review the literature on the microstructure of the
bitcoin market and derive testable hypotheses in Section 1. We then describe our data
and provide summary statistics in Section 2. Section 3 examines the link between order
aggressiveness and informativeness in relation to the size of the information shock, providing
evidence on order strategies of informed traders. Section 4 analyzes the relationship between
adverse selection and market liquidity. In Section 5, we discuss our tests of the non-Markovian
learning property. Finally, Section 6 concludes.
1 Related literature and testable hypotheses
Our paper belongs to the small but growing literature that focuses on the microstructure of
the secondary market for bitcoin and determinants of bitcoin returns. We review some of the
relevant papers in the rst subsection. In the second subsection, we state the hypotheses of
direct interest that are subsequently tested in our empirical analysis.
6
1.1 Related Literature
Balcilar, Bouri, Gupta, and Roubaud (2017) analyze the relationship between trading volume
and bitcoin returns and nd that volume can predict returns except in bear and bull markets,
but cannot predict volatility. Eross, McGroarty, Urquhart, and Wolfe (2017) nd that volume,
bid-ask spread, and volatility all have n-shaped patterns, and conclude that European and
North American traders are the main driver of trading activity in this market. Polasik,
Piotrowska, Wisniewski, Kotkowski, and Lightfoot (2015) show that bitcoin returns are driven
primarily by its popularity, public sentiments, and the total number of transactions. Dimp
(2017) nds that the adverse selection component of the spread is high. Caporale and Plastun
(2017) examine the day-of-the-week e ect in cryptocurrency markets and nd no evidence
of this anomaly in most crypto currencies except bitcoin, whose returns on Mondays are
signi cantly higher than on other days. They view this nding as evidence against eciency
of the bitcoin market. Detzel, Liu, Strauss, Zhou, and Zhu (2018) nd that bitcoin returns
are predictable by the 5- to 100-day moving averages of its prices but largely unpredictable
by macroeconomic variables. They explain this nding with an equilibrium model of rational
learning in the absence of fundamental cash
ow information. Makarov and Schoar (2018)
document large and persistent arbitrage opportunities across cryptocurrency exchanges, a
result they attribute to capital controls that prevent arbitrage capital from moving freely
across borders.
Also related are studies that focus on measuring volatility and understanding the dynamics
of jumps in bitcoin prices. Conrad, Custovic, and Ghysels (2018) use the GARCH-MIDAS
model to extract the long- and short-term components of bitcoin's volatility and explore
potential macroeconomic determinants of bitcoin's long-term volatility. Out of the many
macroeconomic variables considered, only four have signi cant e ects on bitcoin's long-term
volatility (i.e., U.S. stock market volatility, U.S. volatility risk premium, global economic
activity, and bitcoin's own trading volume). Scaillet, Treccani, and Trevisan (2017) nd
that jumps occur frequently on Mt. Gox, a major bitcoin exchange before its bankruptcy in
7
March 2014. They show that order
ow imbalance and the widening of the bid-ask spread
can predict jumps, which in turn have a short-term positive impact on market activity and
induce persistent price changes.
With bitcoin being viewed as an asset (albeit a speculative one) and traded on exchanges
that operate as limit order markets, its secondary market is similar in many respects to that of
other nancial instruments. Thus, our study also belongs to the large literature that models
and studies price discovery, liquidity provision, and order strategies in limit order markets.
The di erences between bitcoin and other nancial assets, however, can deliver important
insights as to the key drivers of market dynamics. We draw upon the theoretical model by
Ricco, Rindi, and Seppi (2018) (henceforth RRS2018) to empirically study the link between
information asymmetry and order strategies, which in turn has important implications for
the price discovery process. We discuss this model and derive our testable hypotheses in the
next subsection.
Finally, it is important to note that alongside the literature on cryptocurrency trading is a
more established literature on blockchain technology, smart contracts underlying the working
of distributed ledgers, and the organization and economics of mining and verifying transactions
(see Malinova and Park 2017 for a thorough discussion of this literature). Pagnotta and
Buraschi (2018) develop the rst equilibrium model of bitcoin value in a decentralized
nancial network, based on the interaction of agents' demand for the censorship-resistance of
transfers and the ability to engage in trustless exchanges, with miners' endogeneous supply
of harshing power. Thus, the model provides important insights into what can serve as the
\fundamentals" of bitcoin value. Zimmerman (2018) provides a model to explain how the
limited blockchain capacity gives rise to the extreme price volatility and the disproportionate
extent of speculative trading in bitcoin, linking the \primary market" to important secondary
market features of cryptocurrencies. Our paper is on the microstructure of the secondary
market where bitcoin is traded, focusing more instead on the interaction of liquidity providers
and demanders and how such interaction a ects bitcoin returns.
8
1.2 Testable Hypotheses
The main objective of this paper is to study the extent to which limit order book activities
contribute to the dynamics of bitcoin price. Our empirical analysis is built upon RRS2018's
model that extends the framework developed in Kyle (1985) for a limit order market in which
informed traders can exploit their information advantage through either market or limit orders
at varying prices. Featured in their model are informed traders who have perfect information
on the value shock that is eventually realized in the nal trading round, and uninformed
traders who use Bayes' rule and observable market dynamics over time to learn about the
value shock. RRS2018 characterize the optimal order-submission strategy of informed and
uninformed traders at each point in time, conditioning on the path of the limit order book
up to that point. As in other theories of limit order markets, the key trade-o is between
price improvement and trading immediacy. Whether the information asymmetry arises from
a large value shock or a greater fraction of informed traders can result in di erent e ects of
adverse selection on market liquidity and price discovery. The model provides three important
empirical predictions.
First, when information asymmetry arises from a large value shock, informed traders are
more likely to increase their trading and quoting activities at or near the market, because those
orders have a higher execution probability and the magnitude of the private information is
suciently large that such executions are pro table. However, this substantially increases the
picked-o risk for the uninformed, inducing them to refrain from trading or quoting too close
to the market. Accordingly, in this environment, the informativeness of more aggressive orders
is higher. On the other hand, in a low volatility environment, the information advantage is
too small to outweight the costs of trading or quoting aggressively. Hence, it is more likely
that informed traders post orders further out in the book for the price improvement. In an
experimental study, Bloom eld, O'Hara, and Saar (2005) also nd that informed traders are
more likely to take liquidity when the value shock is large, but switch to providing liquidity
when the value shock is small.
9
If the channel discussed above re
ects informed traders' behavior in this bitcoin market,
we expect to nd:
Hypothesis 1A : the information content of limit orders at or near the market
increases, while the information content of limit orders at outer tiers decreases, in
a high volatility environment.
Hypothesis 1B : the information content of limit orders at or near the market
decreases, while the information content of limit orders at outer tiers increases, in
a low volatility environment.
Second, while the prediction on the informativeness of market and limit orders at the
inside and outside tiers is unambiguous, the e ect of adverse selection on market liquidity is
more nuanced. Theoretical work in this area provide di erent predictions, depending on how
adverse selection is de ned and which measure of liquidity is used. For example, in Rosu
(2016), adverse selection is de ned by the fraction of informed traders in the market; the
higher this fraction, the faster is information incorporated in prices and thus the higher the
market liquidity as measured by a narrower bid-ask spread. In Goettler, Parlour, and Rajan
(2009), adverse selection arises due to innovations in the asset's fundamentals. It reduces
liquidity at the best quote but increases liquidity behind the best quote, because informed
agents use marketable orders while other agents submit more conservative limit orders.
The RRS2018 model considers both types of adverse selection: one driven by the value
shock size and the other by the fraction of informed traders in the market. However, their
results are based on numerical analysis and could depend on the speci c parameters adopted.
They nd that when adverse selection increases due to an increase in the fraction of informed
traders while holding the value shock size xed, the liquidity provision strategy of the informed
does not change, while uninformed traders reduce their trading and quoting activities near
the market in response to the increased level of adverse selection. This situation results in
an unambiguous net reduction in liquidity at or near the market, but increased liquidity at
more conservative price levels|a result opposite that of Rosu (2016). RRS2018's numerical
10
results for the case in which adverse section increases due to a large value shock indicate that
liquidity at or near the market could improve. This is because informed traders are likely to
increase their trading and aggressive limit order activities, thereby raising liquidity provision
at more aggressive price levels, which in turn could outweigh the reduction in uninformed
liquidity. It remains an empirical question whether the net change is an increase (decrease)
in liquidity
owing toward the market, implying a steepening (
attening) of the order book
slope. The above discussion gives rise to the second set of hypotheses:
Hypothesis 2A : adverse selection due to large value shock can improve liquidity
and be associated with a steeper slope of the limit order book.
Hypothesis 2B : adverse selection due to increased fraction of informed traders
reduces liquidity, i.e., is associated with a
atter slope of the limit order book.
Finally, the model predicts that order history carries information beyond that conveyed
by the current state of the limit order book. This arises because uninformed traders is using
Bayesian updating to learn about the value shock. The path that leads the market to its
current state therefore has important implications on the price impact of order
ow. If so,
we expect that lagged limit order book variables have incremental explanatory power on the
price impact of order
ow after controlling for the most current state of the limit order book.
We thus have the third hypothesis:
Hypothesis 3 : Lagged order book variables have signi cant explanatory power
on price impact of order
ow over and beyond the most current state of the limit
order book.
We focus speci cally on testing for the linear form of history dependence, that is, lagged
order book variables enter a linear regression linking price impact with current order book
state. It is important to note that a failure to reject the null does not invalidate the non-
Markovian property of learning as featured in this model. All we can conclude from this test
11
is whether price discovery in this market is linear non-Markovian. It is still plausible that
the history dependency takes on some non-linear form, or that the history of the variables
considered is not the one that matters. The RRS2018 model is still under development with
respect to which types of histories are important. Nevertheless, studying one set of order
book variables and one speci c form of history dependence is the rst important step toward
understanding the nature of learning in the market, and provides useful empirical evidence
for further theory development.
2 Data
We use data from BTC-e, which is a digital currency trading platform founded in July 2011.
It operated as a limit order market in which users can trade with one another via market or
limit orders. The platform allowed trading between several cryptocurrencies (bitcoin, litecoin,
namecoin, novacoin, peercoin, dash and ethereum) and three at currencies (U.S. dollar
(USD), Russian ruble and Euro), but in this paper, we focus on the bitcoin{USD pair. The
platform charged a
at fee of 0.2% on all transactions. It was seized by the U.S. authorities
in July 2017 on international money laundering charges. During its time of operation, BTC-e
was one of the largest cryptocurrency exchanges in the world, serving approximately 700,000
users including a large customer base in the U.S.4BTC-e was operated by a complex web of
entities located in Russia, Bulgaria, and elsewhere, but its servers were located in the U.S.
2.1 The data
The data was collected through direct API access provided by BTC-e to query transaction
history and limit order book snapshots.5Data collection began on 12/6/2013 and ended on
9/25/2014 (we exclude these two end dates from the sample due to incomplete data on the
full 24-hour day.) This period encloses several major events in the cryptocurrency world,
4See United States of America v. BTC-E, A/K/A Canton Business Corporation, and Alexander Vinnik.
5We are grateful to Jacob Sagi for providing us with this data.
12
most notably the collapse of Mt. Gox in February and March of 2014. Appendix A provides
the list of news articles covering important events in the cryptocurrency world in general,
and bitcoin in particular.
During the sample period, two computers simultaneously pinged BTC-e's servers approxi-
mately every 0.1 seconds, took snapshots of the limit order book, and downloaded the most
recent 150 transactions. The two computers ran in parallel, so that if one computer was
down, the other was still available for the downloading to ensure completeness. We unify
these two separate datasets and clean them as follows.
For transaction history data, each trade record has a unique order ID, so it is straightfor-
ward to merge the two transaction histories and eliminate duplicates. Transaction history
data contain the following variables: transaction date-time stamp (one-second resolution),
transaction price, quantity transacted, trade type (\ask" for seller-initiated and \bid" for
buyer-initiated trades), and the order number. It is important to note that a large market
order, upon arrival, might execute against multiple limit orders, each of which appears as
a separate record in the transaction history data and is given an order number. As in the
literature, we aggregate multiple records that likely belong to the same market order as one
single trade. We identify a sequence of trade records as belonging to a \parent" market
order if the following apply: 1) they span at most two consecutive seconds, 2) have the
same trade type (i.e., buy or sell), 3) they occur in non-decreasing prices (for buys) or
non-increasing prices (for sells), re
ecting the fact that as a market order walks deeper into
the book, the prices are sequentially worse, 4) their order numbers are sequential and there
is no gap between adjacent orders' numbers (e.g., 12345678L, 12345679L, 12345680L).6We
then aggregate each identi ed sequence of trade records to the parent order level by summing
up the traded quantities and aggregating the prices in two ways: 1) the price of the last trade
6BTC-e order numbers are assigned based on when an order takes place on the platform, regardless of in
which coin pairs. That is, BTC-e does not assign a separate order ID series to each coin pair traded on the
exchange. Thus, there can be a gap in order numbering of adjacent market orders if in between which there
are transactions in other coin pairs. The fourth requirement is very important in identifying the sequence of
orders belonging to the same market order execution.
13
record in the sequence, and 2) the volume-weighted average price. We refer to aggregated
orders as trades and this is the unit of analysis of trading activity in the rest of the paper.
As reported later in the paper, the trade size is still very small, which is likely due to traders
slicing their large orders into multiple smaller ones to send to the exchange. The data we
have do not contain trader IDs to allow for the identi cation and aggregation to this level.
The merging and cleaning of the two limit order book snapshot datasets is more involved.
It is important to ensure the correct time sequencing of snapshots, which is a challenging
task because the latency between each downloading computer and BTC-e's servers can vary
and time stamps are only up to the one-second resolution. The data downloading algorithm
captures the start time of a request and the time it takes to nish the downloading of a
snapshot. Thus, each snapshot in each dataset has a lower and upper time bounds, based on
which we can conservatively supplement gaps in one dataset with available snapshots from
the other. After this step, we obtain a combined dataset containing snapshots of the limit
order book with 150 price levels on each side of the market at an ultra-high frequency.7We
remove duplicate snapshots when there is no change in any of the price nor quantity in the
book. We refer to the resulting dataset as the tick-frequency limit order book data.
To see the extent to which the price on BTC-e di ers from that on other exchanges, we
plot in Figure 1 the evolution of the best mid-quote on BTC-e at the one-minute frequency
and the daily closing price collected by CoinMarketCap, a cryptocurrency market tracking
company. Except for the earlier part of the sample period, the price on BTC-e aligns quite
closely with the general price level in the market. In fact, Brandvold, Molnar, Vagstad, and
Valstad (2015) nd that BTC-e, together with Mt. Gox, leads in price discovery in a study of
seven bitcoin exchanges that collectively make up 90% of bitcoin trades over the period from
April 2013 to February 2014. Dimp
(2017) also nds that BTC-e is the most liquid market
for trading bitcoin in U.S. dollar based on data from November 2016 to January 2017.
7After merging the two parallel datasets, there remains a very small number of gaps for when data from
both computers are not available due to the servers' downtime or random shutdowns of both computers. The
longest gap is roughly 1.5 hours, and is an isolated incidence. Most gaps are for only a few minutes.
14
2.2 The microstructure of BTC-e
2.2.1 The limit order book
We plot in Figure 2 the average shape of the limit order book, indicating the percentage of
cumulative depth up to the 150th tier. The x-axis shows the distance (in cents) from each
price level to the mid-quote. For reference, the plot includes a solid line showing cumulative
depth in an equally-distributed book. The distribution is convex on both sides, suggesting
that there is relatively more depth available the further out the price level. The plot also
reveals the di erence in how depth is distributed on the two sides. On the ask side, depth
is more concentrated at or near the market than that on the bid side. To supplement this
plot, Panel A of Table 1 reports some speci c depth statistics at select tiers. These statistics
further indicate that depth is quite spread out across the book, totaling about 320 coins
across 150 price levels on each side, or averaging slightly above 2 coins per tier. At the inside
tier, there are about 4.1 bitcoins on the ask and only 2.6 on the bid.
We report the average cost of immediacy as measured by the relative spread at various
price tiers in Panel B of Table 1. The spread at a select tier is computed as the di erence
between the price at that tier and the best price on the opposite side, standardized by the
mid-quote. The inside bid-ask spread averages to 19.5 bps, comparable to the bid-ask spread
of a large stock. Adding the
at transaction fee of 20 bps charged by BTC-e, the total
transaction cost is at least 40 bps.
We also report the volume-weighted spread, computed as the di erence between the
depth-weighted average of prices up to a given tier and the best price on the opposite side.
The simple spread statistics on the bid side up to the 20th tier are smaller, indicating that
these bid orders are placed slightly closer to the market than their ask counterparts. However,
taking into account their lower quantities (as shown in Panel A), the volume-weighted spread
on the bid side is equal to or greater than that on the ask side. Furthermore, beyond the
50th tier, bid limit orders are placed at a further distance as compared to the corresponding
15
ask limit orders. Taken together, the summary statistics presented here indicate that the cost
of immediacy for a bitcoin buyer (who takes the asks) is slightly lower than that for a seller
(who hits the bids), i.e., it is easier to immediately buy than sell, especially a large quantity.
We examine the time series variation of depth over the sample period (plot available upon
request) and nd that ask depth appears to
uctuate more than bid depth. Furthermore,
there are several spikes in ask depth not accompanied by similar spikes in bid depth, especially
at the top 5 price levels. This indicates that most occasions of signi cant market imbalances
are due to excessive selling pressure on the ask side of the book. Perhaps most interestingly,
bid depth often leads ask depth. Granger-causality tests with up to 10 lags on the daily
average bid and ask depth at the top ve tiers and across the whole book all indicate that
depth on the bid side systematically leads depth on the ask side. However, this lead-lag
relationship prevails only at the daily frequency and not at intraday frequencies.
2.2.2 Trading Activities and Market Volatility
As reported in Table 2, trades on the BTC-e platform occur frequently with nearly 13,000
trades per 24-hour trading day on average, for a total of 5,626 coins bought and 5,752
coins sold. On average, the total dollar volume transacted each day is roughly $7 million.
Buyer-initiated trades generally occur more frequently than seller-initiated trades, but with a
slightly smaller trade size: 0.84 versus 0.93 coins per average trade (or in the $500 range in
dollar trade size). The median of 0.1 coin and the tail statistics (5th and 95th percentiles)
indicate that the trade size distribution is highly skewed to the right. 95% of trades are for 4
coins or less, which can be easily absorbed by limit orders at the top tiers in the book.
We nd that trading volume is highly correlated with volatility, as shown in Figure 3. We
compute daily realized volatility from 5-minute mid-quote returns.8The sample correlation
between volume and volatility is nearly 0.68, and they both exhibit multiple spikes around
major events in the cryptocurrency world. December 2013 appears to be the most volatile
8We annualize daily realized volatility by a factor ofp
365because the bitcoin market operates 24/7
throughout the year, unlike most other nancial assets that are traded only during weekday trading hours.
16
month in the sample period, and includes the biggest spike of over 500% in volatility. Analysis
of news events in December points to China Central Bank's decision on 12/5/2013 to ban
nancial institutions from handling bitcoin transactions as the catalyst. The collapse of Mt.
Gox in late February 2014, the IRS's decision to tax bitcoin as property in late March 2014,
and the closure of bank accounts of Chinese bitcoin exchanges also see volatility shooting
up. Interestingly, volatility does not appear a ected by Dell's and Paypal's announcements
to accept bitcoin. This evidence seems consistent with earlier research that bitcoin is used
more as an asset than as a currency. The high level of volatility, averaging to about 63%
during the sample period, also supports earlier studies' conclusion that bitcoin is too volatile
to serve as a store of value and medium of exchange.
2.2.3 Intraday Patterns
Even though the market operates continuously 24/7, intraday patterns of key market variables
in Figure 4 indicate that the most liquid and active time is between 3:00 and 12:00 ET. After
12:00, depth, trade volume, and volatility all trend down. The bid-ask spread stays narrow
for a few more hours and only widens signi cantly after 18:00. We also check if liquidity
exhibits any day-of-week pattern widely documented in U.S. equity markets, by regressing
di erent daily liquidity variables on day-of-week dummies. We nd that these dummies are
rarely signi cant, providing little evidence for the day-of-week pattern in either depth or
trading volume. There is some mild evidence that the bid-ask spread is narrower mid-week
(Tuesday through Thursday).
3 Adverse selection and order strategies
In this section, we measure and analyze the information content of market and limit orders,
in order to test the hypothesis that the link between order informativeness and order
aggressiveness depends on the size of the value shock. Thus, it is important to identify when
17
there is likely a large value shock, and compare the information content of orders of varying
degree of aggressiveness in such an environment with that in a normal environment. To
strengthen the analysis, we also test if the reverse is true in a low value shock environment.
3.1 Identi cation of large value shock environment
As the rst step, we partition the sample period into three subsamples corresponding to
large value shock, low value shock, and average value shock environments. We use both
realized volatility and the high-low range of the midquote to determine these partitions.9
Speci cally, for each day, the high-low range is computed as the di erence between the log
of the highest and lowest mid-quote of the day, based on the raw snapshot data available
at the tick frequency. Essentially, this measure captures the return that can be achieved by
an informed trader with perfect information who buys at the lowest price and sells at the
highest price. Thus, it is a reasonable proxy for the asset value shock signal.
The use of realized volatility to supplement the high-low range is to ensure that a large
high-low range reasonably re
ects an environment with a large value shock and not one
that is otherwise a tranquil day but for a
eeting price outlier. We compute the daily
realized volatility by the square root of the sum of squared log returns based on the midquote
sampled every ve minutes.10The large (low) value shock days are those days when both the
realized volatility and the high low range are in the top (bottom) quartile of their respective
distributions. The average environment is de ned as the rest of the days in the sample on
which the value shock size is neither too large or too small. This exercise results in 62 days
in the large value shock subsample, 58 days in the low value shock subsample, and 172 days
in the average value shock subsample.
We verify that the procedure above delivers a reasonable partition of the data by conducting
9Unlike in other markets, the absence of observable fundamentals presents a challenge to identifying when
there might be an information shock. We take an ex-post approach here in an attempt to infer on which days
during the sample period that new information might have arrived.
10The empirical analysis in Liu, Patton, and Sheppard (2015) suggests that the ve-minute frequency is
the optimal sampling frequency for the computation of daily realized variance.
18
a comprehensive news search of important crypto market events from major news outlets,
including Bloomberg, Reuters, and popular cryptocurrency news websites CCN and CoinDesk.
We then classify these news articles into three broad categories: cybersecurity threats,
regulatory changes, or market acceptance. The table below shows the count of each news type
that falls into the high value shock, average value shock, and low value shock subsamples:11
News Type High Average Low
Market Acceptance 2 4 1
Regulatory 14 14 0
Security/Hack 15 16 1
Total days with news 31 34 2
It is clear that a disproportionately large number of important news are in the high
volatility subsample, while there is almost no news on low volatility days. This provides
further assurance that the high and low value shock subsamples do indeed re
ect the di erence
in their information environment. It is also important to point out that the major type of
news during the sample period relates to hacking incidences that expose the security risk of
owning and trading bitcoin. Regulatory actions of various governments also seem relevant,
much more so than does market acceptance. News of bitcoin being accepted by retailers as a
method of payment (e.g., Overstock, Dell, and eBay) does not occur as frequently, and does
not seem to be informationally relevant, as indicated in Figure 3 by the muted response of
trading volume and volatility upon such events.
3.2 Information content of the limit order book
An important task in testing Hypotheses 1A and 1B is measuring the information content
of limit orders at di erent price levels in the book. For this, we use Hasbrouck (1995)'s
information shares, similar to Cao, Hansch, and Wang (2009). With 150 price levels on
11If an event date was not given in the article, a di erent source with a listed event date was used. The list
of the collected news articles is in Appendix A.
19
each side of the market, it is not econometrically feasible to model their dynamics without
some data summarizing and dimension reduction. To keep the exercise manageable, we
partition the 150 levels of the order book into six categories: tier 1, tiers 2-5, tiers 6-10,
tiers 11-50, tiers 51-100, and tiers 101-150, ranging from the most aggressive limit orders
to the least aggressive ones. Together with the trade price series, they are all some noisy
representation of the true price of one common asset and thus cannot deviate too much from
the common underlying price process. Thus, we model their dynamics with a vector error
correction (VEC) model based on which to compute their respective information shares. The
information share of a price series re
ects its contribution to the variance of the permanent
price updates: the higher the information share, the more informative a price series is and
the more it contributes to price discovery.
LetXi
PT; P1; P2; P3; P4; P5; P6T
i, wherePTis the last transaction price, and the
remainders are depth-weighted average prices corresponding to tier 1, tiers 2-5, tiers 6-10,
tiers 11-50, tiers 51-100, and tiers 101-150 (averaged across both sides and all relevant tiers).
The VEC model is:
Xi= zi 1+k 1X
i=j jXi j+i; (1)
wherezi 1is a 61 vector of correction terms, i.e.
zi 1=2
66664PT 2P1
:::
PT 6P63
77775:
In our implementation, we choose k= 10 and estimate the model separately for each day
using one-minute price data. Due to the high dimensionality of the VEC model (7 price
series with 10 lags), estimating information shares at intraday frequencies might compromise
the reliability of the estimates. The Hasbrouck (1995)'s information shares rely on two
20
ingredients derived from the model. The rst is the permanent impact of the shock vector
on all cointegrated prices in the system (i.e., the long-run multipliers based on the moving
average representation of the VEC model). The second is the vector of orthogonalized shocks,
which we obtain via a Cholesky decomposition of the covariance matrix of the residuals
=E[i0
i]. The information share of price series jis then computed as:
ISj=hPn
i=j
imiji2
[Pn
i=1
imi1]2+ [Pn
i=2
imi2]2+:::+ [
nmnn]2;
where
iis the permanent price impact of shock i, andmijis the (i;j) element of the lower
triangular matrix Msuch thatMM0=
. Thus, the information share of a given price series
is the contribution of its variation to the total variation of the ecient price updates. To
address the sensitivity of information shares to variable ordering in the model, we perform
the calculation for all possible orderings and then compute the average information shares
across all orderings. These are the information share estimates we use throughout the paper.
We plot the 7-day moving averages of our information share estimates in Figure 5, with
the legend indicating the average information share for each order category over the entire
sample period. It is clear that trades and limit orders posted at the top tier of the book
account for the largest portion of the total variation of bitcoin price updates, 31% and 28%
on average respectively. The remaining 41% average information shares come from the rest
of the limit order book. It is interesting to see that information shares do not monotonically
decrease the less aggressive the limit orders: they decrease through the 10th level but then
increase the further away the limit orders. This is surprising and contrasts with the common
belief that information content increases with order aggressiveness. Earlier research into the
information content of limit order books, such as Cao, Hansch, and Wang (2009), does not go
this far into the limit order book. Therefore, it is not clear if we would have seen the same
pattern had we examined equity market limit order books beyond the 10th tier, or if this is
a peculiar feature of the bitcoin market in which the extreme volatility might increase the
21
probability of execution for further-away orders, thereby inducing informed traders to post
more of such orders. This is similar to out-of-the-money options having a greater chance of
moving in-the-money the higher the volatility, which can be attractive to informed traders.
3.3 Order aggressiveness and information content
The RRS2018 model predicts that informed traders increase their trading and quoting at
the most aggressive price levels when the value shock is suciently large. In contrast, in low
value shock environment (i.e., the value of the private information is small), it might not be
pro table for them to trade and quote aggressively, and hence orders closer to the market
might become less informative.
Panels A1{A3 of Table 3 show the average information share of trades and limit orders
at varying degree of aggressiveness by the three information environments. Consistent with
Figure 5, we observe that trades carry the most information regardless of the information
environment, alone accounting for nearly one third of the total variation in price updates.
We continue to observe that very little information is conveyed by limit orders at tiers 6{10
(less than 3%). It seems that informed traders either trade or quote very aggressively, or
submit orders away from the market.
We then perform a di erence-in-mean t-test by comparing, for each order aggressiveness
category, the information share in a large (low) value shock environment with that in an
average volatility environment. Panels B1 and B2 contain the results of these tests, and they
both provide strong support for RRS2018's model. That is, when the value shock is large,
informed traders are more likely to trade and quote aggressively to exploit their information,
because the value of the information is more than o set the cost of trading or quoting
aggressively. Panel B1 shows that aggressive limit orders (i.e., those placed in the top 10 tiers
in the book) become statistically more informative than they normally would in an average
volatility environment, whereas limit orders posted beyond the 10th tier become statistically
less informative. The evidence provided in Panel B2 for the low value shock environment
22
reveals the opposite, which is that less aggressive orders are statistically more informative,
lending further support to the theory that informed traders in such an environment choose
to use limit orders deeper in the book, as trading and quoting aggressively is not pro table
when the value shock is small.
4 Adverse selection and liquidity provision
We next investigate how adverse selection a ects market liquidity through its impact on
order strategies of informed and uninformed traders. This exercise helps demonstrate that
whether adverse selection hurts market liquidity depends on the nature of the information
asymmetry. For this, we rst discuss how we construct the measure of adverse selection at
an hourly frequency, and the measure that summarizes the state of liquidity supply. Next,
we present and discuss our ndings.
4.1 Measuring adverse selection
Central to our empirical analysis is a measure of the degree of adverse selection in the market.
Previous studies traditionally measure adverse selection by the price impact of trades, which
re
ects the common assumption underlying many traditional microstructure theories that
informed traders use market orders to exploit their information advantage. O'Hara (2015)
argues that this assumption is increasingly detached from the reality of trading in today's
high frequency trading world. Recent work has argued that informed traders can also utilize
limit orders to exploit their information advantage (for theoretical work, see e.g., Boulatov
and George 2013, Ricco, Rindi, and Seppi 2018, and references therein; for empirical evidence,
see e.g., Fleming, Mizrach, and Nguyen 2018, Brogaard, Hendershott, and Riordan 2018, and
Cont, Kukanov, and Stoikov 2014, among others.) As Cont, Kukanov, and Stoikov (2014)
(CKS2014) argue, trades are not sucient to capture price movements given the sheer amount
of limit order book events between any two trades. Our earlier ndings on the information
23
composition of trade and limit order activities also con rm that trades, while accounting for
the largest share of price discovery, account for only 30%. The rest of price discovery is due
to movements in the limit orders. Accordingly, price impact of limit order book events, and
not just trades, is a better measure of adverse selection in a limit order market. Following
CKS2014, we estimate this price impact measure by the following regression model:
Pk;i=\Constant i+cPIiOFIk;i+bPI
k;i; (2)
where Pk;iis the change in the mid-quote over the sub-interval kof intervali, andOFIk;iis
the order
ow imbalance that aggregates limit order submissions, cancellations, and executions
at the inside tier over the same sub-interval. Estimating Equation 2 separately for each
intervali, we obtain the interval's price impact estimate dPIi. To ensure that there are
sucient observations within each interval to reliably estimate dPIi, we choose the interval
frequency to be hourly (i.e., i= 0;1;:::;23), and the sub-interval sampling frequency to be
one-minute (i.e., k= 1;2;:::;60). To compute OFIk;i, we accumulate changes at the top of
the book over the sub-interval kusing the raw snapshot data available at the tick frequency.
The net order
ow between ticks t 1 andtis
et=
qb
t1fPb
tPb
t 1g qb
t 11fPb
tPb
t 1g
qs
t1fPs
tPs
t 1g qs
t 11fPs
tPs
t 1g
;
wherePb
tandqb
tare the price and quantity of coins available at the best bid (similarly de ned
for the best ask). If price does not change, then the order
ow to the bid side is qb
t qb
t 1.
If there is an improvement in the best bid (i.e., Pb
t>Pb
t 1), the order
ow to the bid side
equals the size of the new price-improving orders. If there is a cancellation or trade execution
that completely wipes out the previous tick's rst tier and pushes the second tier forward
(i.e.,Pb
t<Pb
t 1), the order
ow is decreased by the quantity of the rst tier at the previous
tick. The same logic applies to the ask side. The net order
ow from one tick to the next is
therefore the di erence between the order
ow to the bid (in the rst parentheses) and that
24
to the ask (in the second parentheses). We aggregate this net order
ow to the sub-interval k
level, i.e.,OFIk;i=P
t2(k;i)et.
Panel A of Figure 6 provides summary statistics of cPIi. It is reassuring that the estimate
is correctly positive 95% of the time (i.e., excess buying pressure results in price increases
and vice versa). The distribution is right-skewed indicating the presence of extremely large
values, with a mean of 2.4 and a median of 1.65.
4.2 Measuring liquidity provision
Given the high dimensionality of the limit order book, the slope of the bid and ask schedules
is a useful measure of how willing liquidity providers supply their bids/o ers to ful ll trading
demand by more impatient traders. Ns and Skjeltorp (2006) examine the slope and show
that it is indeed very important for the trading and volatility relationship. Ns and Skjeltorp
(2006) rst measure the slope locally at each price level by the ratio of the increase in depth
over the increase in price, then average across all price levels and the two sides of the book
to obtain an average slope measure. Our full limit order book data allows us to estimate the
slope compactly with the following regression:
QP ;i=\Constant i+cSLid ;i+bSL
;i; (3)
whereQP ;iis the percentage of cumulative depth at tier ( = 1;:::;150) as of the end of
intervaliandd ;iis the distance between the price at tier and the best bid-ask midpoint
jP ;i Pmid;ij. We estimate the slope separately for the bid and the ask side and for each
intervali, and denote them by SLA
iandSLB
i.
Because we standardize cumulative depths by the total depth across all 150 tiers, QP 150;i
is always 100%. Therefore, the slope measure depends merely on how wide the 150-tier pricing
grid is (the intercept already takes care of QP 1;i). Accordingly, our slope measure captures
the tightness of prices in the book. A steeper slope indicates that limit orders are priced
25
closer to the market. Figure 7 illustrates how the slope captures the liquidity distribution in
the book. Another way of interpreting the slope is that it measures the elasticity of depth
with respect to price. A steeper slope implies that for one unit increase in price, there is
a greater increase in the quantity bid or o ered, implying a greater willingness of liquidity
providers to facilitate trading demand on each side of the market.
We plot the histogram of the slope estimates in Panels B and C of Figure 6. Both slopes
are strictly positive, re
ecting that liquidity supply is greater the better the price for the
liquidity providers. With zero being the lower limit, both distributions have long right tails.
The ask slope is steeper than the bid slope, as indicated by both the mean and the median,
and has more variability. This suggests a greater but also more volatile willingness to provide
liquidity on the ask side.
4.3 Does adverse selection worsen market liquidity?
To test hypothesis 2A and 2B, we run the following regression:
SLi=c+ PIi+ H(PIi1HiVol ) + L(PIi1LoVol) +
Zi+i; (4)
whereSLiis the slope of the order book at the end of hourly interval i,PIiis the measure
of adverse selection for interval i,1HiVol is an indicator for days with a large value shock,
1LoVol is an indicator for days with a low value shock, and Ziare control variables. Included
inZiare: 1) the slope on the opposite side (to see if liquidity provision on one side interacts
with that on the other), 2) the total number of coins bid and o ered in the book (to control
for the absolute amount of liquidity available at any given point in time), 3) the fraction of
depth residing at the top (to control for the possibility that a
at slope can also re
ects the
front-loading of depth at the top tier), 4) the current level of trading activity (to assess if
trading demand plays a role in shaping liquidity provision), and 5) the prevailing volatility
in the market (as volatility is well documented to a ect liquidity). Depth, trading volume,
26
and trade count are log-transformed. We also estimate a speci cation that includes hourly
dummies to account for any diurnal e ects on the order book shape and liquidity provision.
We use robust regression methodology to minimize the potential impact of outliers on the
results. We report the results in Table 4. The key estimates | , H, and L| appear on
the rst three rows.
Robust across side and speci cations is a signi cantly negative | the coecient for PI
| indicating that increased adverse selection is associated with a
atter order book slope.
Moreover, the signi cantly negative coecient on PI1HiVol indicates that the already
negative association of adverse selection and liquidity becomes even stronger on days when
large value shocks are likely present. On the other hand, in a low value shock environment,
the order book steepens signi cantly as shown by the signi cantly positive estimates of L,
suggesting a greater liquidity supply. Unreported tests indicate that the sum of and Lis
signi cantly positive, that is, on low volatility days, adverse selection is positively associated
with liquidity provision.
The
attening of the order book in the high value shock environment, compared with
the steepening of the order book in the low value shock environment, indicates that it is the
value shock size that matters for both informed and uninformed traders. In an environment
where adverse selection is due to a large value shock, informed traders are likely to trade
and quote more aggressively, resulting in informed liquidity moving toward the inside tier.
However, worried about the risk of being picked o , uninformed traders' liquidity moves away
from the market. Our ndings are consistent with the outward migration of uninformed
liquidity outweighing the inward migration of informed liquidity, resulting in the
attening of
the order book slope.
Within each information environment, the variation of adverse selection is likely due to
changes in the fraction of informed traders. However, the evidence only supports hypothesis
2B (that adverse selection due to increased fraction of informed traders worsens liquidity) in
the high value shock environment. In such an environment, the increased fraction of informed
27
traders heightens the picked-o risk and contributes to drive uninformed liquidity away from
the market. The opposite evidence obtained for the low value shock environment does not
support RRS2018's prediction, but is instead consistent with Rosu (2016)'s intuition that
the increased fraction of informed traders facilitates better learning by uninformed traders,
thereby improving liquidity.
5 Is price discovery history-dependent?
Another important implication of RRS2018's model is the non-Markovian property of in-
formation learning in a limit order market. It implies that the price impact of order
ow
depends not only on the current state of the limit order book, but also on the history of past
order actions leading up to the current state. Given that the history space is large, it would
be desirable to have some theoretical guidance as to what types of histories matter most for
price discovery. The theory is still under development in this regard. Here, we rely on the
data to tell us which part of the history that is important.
One important caveat is that, order history can enter the price discovery process in some
unknown form. Our empirical analysis below looks speci cally for linear e ects, recognizing
that the lack of evidence for the non-Markovian property in the linear sense does not imply
that price discovery is not non-Markovian. It could still well be, just not in a linear form.
Alternatively, the speci c elements in the history space we consider are not the ones that
matter. Nevertheless, it is still a very useful exercise to at least know that certain elements
and certain forms do not work. This would be especially helpful for the development of
theories with respect to the non-Markovian learning implication.
We test for the linear non-Markovian property by regressing the hourly price impact|the
measure of price discovery|on a set of variables that capture the current state of the limit
order book. These are: (a) the total depth on each side, (b) the concentration of depth at the
top tier on each side, (c) the concentration of depth at the top 5 tiers on each side, (d) the
28
slope of the order book on each side, (e) the level of buying and selling activity in the market,
and (f) the prevailing short-term volatility. Order book variables (a, b, c, d) are measured at
the beginning of each interval. Trading and volatility variables (e, f) are measured over each
interval, similar to the way the dependent variable is measured. We then add the history of
each of these variables, one by one, to the regression to determine if the lagged values of the
chosen variable have any incremental explanatory power over the price discovery measure.
We allow for a 24-hour history in these variables, that is, we include 24 lags of each covariate.
LetZibe the vector collecting all of the above 11 explanatory variables for the hourly interval
i, whileZ(j)idenotes the individual explanatory variable j. We run the following regression
for each explanatory variable j:
PIi=c+ 0
0Zi+24X
l=1j;lZ(j)i l+i: (5)
Panel A of Table 5 shows the baseline regression results that include only the explanatory
variables that capture the current state of the limit order book. The regression results are
consistent with intuition: 1) price impact is lower when trading is more active (regardless
of the side), 2) price impact is higher when the market is more volatile, 3) greater ask
depth (indicating increased selling pressure) dampens price impact while greater bid depth
(indicating increased buying pressure) increases it, and 4) a greater concentration of depth at
the top 5 tiers reduces price impact.
It is interesting to note that the concentration of depth at the top tier does not explain
price impact, nor does the slope. It seems that market participants care only about the total
amount of depth in the book and how much of that depth resides at the top 5 tiers. We also
include hourly dummies to control for the potential diurnal pattern of price discovery, but
nd that these dummies have little explanatory power, and that the coecients of order book
variables remain robust to the inclusion of the hourly dummies. Thus, for regressions that
include lagged explanatory variables, we use the baseline model without the hourly dummies.
Panel B of Table 5 documents the incremental explanatory power of each covariate's
29
24-hour history, as indicated by the number of lags with a signi cant coecient and the
adjustedR2of the regression. These lags are rarely signi cant. At the 1% signi cance level,
the history of most order book variables studied here is completely insigni cant (except the
total bid depth and the realize volatility, each of which has only 1 signi cant lag out of the
24-hour history). Even at the 10% signi cance level, the number of signi cant lags for most
variables is very small, at most 4 out of 24. In addition, the inclusion of the lags reduces the
adjustedR2, as opposed to increasing it. Overall, Panel B shows little support for the linear
history-dependence of price discovery.
6 Conclusion
Our paper provides an in-depth analysis of the information content and liquidity of the limit
order book on a major bitcoin trading platform. We nd several important results that
contribute to both the growing literature on bitcoin trading and the literature on limit order
book modeling.
First, trades and limit orders at the best bid and ask are most informative. The information
content then decreases the more conservative the price up to the 10th best level, and mildly
increases for orders posted at far-away tiers. In a high value shock environment, aggressive
orders become more informative, suggesting the increased use of such orders by informed
traders. On the other hand, in a low value shock environment, the informativeness of market
orders and best limit orders is reduced while that of mid-book orders increases. Second, we
nd that the information shock size matters for market liquidity. When asset volatility is high,
adverse selection worsens liquidity, in contrast to the improved liquidity in the low volatility
environment. Finally, we do not nd concrete evidence to support the linear dependency of
price discovery on the history of individual state variables. This result indicates that the
Markovian learning assumption typically adopted in limit order market models might not be
unreasonable after all.
30
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34
Table 1: Summary statistics of BTC-e limit order book: 12/7/2013 to 9/24/2014.
Tier 1 Tier 5 Tier 10 Tier 20 Tier 50 Tier 100 Tier 150
Panel A: Distribution of Depth Across Price Tiers
Ask: Cum. Depth 4.1 17.5 30.0 51.3 108.3 203.5 322.3
Ask: % Cum. Depth 1.3 5.4 9.2 15.6 33.0 61.9 100.0
Bid: Cum. Depth 2.6 11.1 19.8 36.3 89.3 190.6 321.3
Bid: % Cum. Depth 0.8 3.5 6.2 11.3 27.2 58.1 100.0
Panel B: Spreads as Fraction of Bid-Ask Midpoint (bps)
Ask: Distance from Best Bid 19.5 36.7 47.3 61.8 94.2 139.2 181.4
Ask: Volume-weighted Spread 19.5 27.6 33.9 42.8 62.2 88.6 116.6
Bid: Distance from Best Ask 19.5 36.1 46.5 61.1 95.0 144.9 194.3
Bid: Volume-weighted Spread 19.5 27.7 33.9 43.2 64.2 94.4 126.2
35
Table 2: Descriptive statistics of daily trading activity. The reported statistics are based on BTC-e transaction history data
over the period from 12/7/2013 to 9/24/2014. Each day is de ned to be from 0:00:00 to 23:59:59 ET.
Buyer-initiated Trades Seller-initiated Trades
Mean P5th Median P95th Mean P5th Median P95th
Trade Frequency 6,710 1,712 4,413 15,220 6,197 1,179 3,648 15,427
Volume (# BTC) 5,626 873 3,321 18,584 5,752 795 3,065 18,808
Dollar Volume ($ m) 3.44 0.49 1.939 11.21 3.51 0.44 1.76 11.27
Trade Size (# BTC) 0.84 0.01 0.10 3.25 0.93 0.01 0.10 3.78
Dollar Trade Size ($) 512.62 5.13 56.11 2,007.58 566.87 5.50 59.93 2,291.98
36
Table 3: This table reports the information shares of trade and limit order prices. The
price vector consists of last trade price, and depth-weighted prices of limit orders at tier 1,
tiers 2-5, tiers 6-10, tiers 11-50, tiers 51-100, and tiers 101-150 on both sides of the market.
Their dynamics at the one-minute frequency are modeled with a vector error correction
model with 10 lags, and information shares are computed from the Cholesky decomposition
of the covariance matrix of the residuals. The model is estimated separately for each day.
Each day is de ned to be from 0:00:00 to 23:59:59 ET. Data are from BTC-e for the period
from 12/7/2013 to 9/24/2014. Panels A1, A2, and A3 report the means and standard
errors of information shares separately for the high volatility, average volatility, and low
volatility sub-samples partitioned as described in the text. Panel B1 reports the test statistics
of the di erence in mean information share of each order category on high-volatility days
versus average-volatility days. Panel B2 reports the test statistics of the di erence in mean
information share of each order category on low-volatility days versus average-volatility days.
Statistic Trade Tier Tiers Tiers Tiers Tiers Tiers
1 2-5 6-10 11-50 51-100 101-150
A1. High volatility days (N=62)
Mean 30.05 31.76 13.44 5.24 5.55 7.60 6.37
S.e. 1.11 1.03 0.70 0.39 0.51 0.90 0.88
A2. Average volatility days (N=172)
Mean 31.98 27.38 6.88 2.79 7.62 11.33 12.02
S.e. 0.90 0.79 0.37 0.22 0.63 0.92 0.94
A3. Low volatility days (N=58)
Mean 27.94 23.60 5.88 3.97 13.45 12.62 12.53
S.e. 1.72 1.50 0.71 0.54 1.76 1.88 1.45
B1. Test of hypothesis 1A
t-stat -1.357 3.366 8.303 5.496 -2.552 -2.910 -4.381
p-val 0.088 0.000 0.000 0.000 0.006 0.002 0.000
B2. Test of hypothesis 1B
t-stat -2.085 -2.225 -1.242 2.025 3.129 0.619 0.293
p-val 0.020 0.014 0.109 0.023 0.001 0.269 0.385
37
Table 4: Regression of limit order book slope on adverse selection and information environment indicators. The slope of the
order book on each side is estimated from order book snapshot prevailing at the end of each hour. Adverse selection (`PI') is
measured by the price impact of order book events over each hour, as described in the text. Days with large value shock (`hivol')
have both realized volatility and high-low range measures in the top quartile of their respective distributions. Days with low
value shock (`lovol') are similarly de ned using the bottom quartile. Controls include the percent of same-side depth at the
top tier, slope on the opposite side, the total quantity of all ask limit orders, the total quantity of all bid limit orders, total
trading volume and log trade count over each hour split into buyer-initiated and seller-initiated, and hourly realized volatility
computed from ve-minute returns. All depth and trading volume variables are in the number of coins and log-transformed.
Hourly dummies capture the time-of-day e ects. Data are from BTC-e for the period from 12/7/2013 to 9/24/2014.
Dep. Variable = Ask Slope Dep. Variable = Bid Slope
(1) (2) (3) (4) (5) (6) (7) (8)
PI 0:40 0:41 0:46 0:46 0:48 0:48 0:51 0:53
PI x hivol 0:68 0:68 0:69 0:68 0:99 1:05 1:05 0:99
PI x lovol 2 :242:232:272:252:402:432:442:39
Control Variables:
Realized Volatility 2:90 2:89 2:86 2:57 2:68 2:57 2:58 2:42
Opposite Slope 0 :320:320:320:320:180:180:180:18
% Depth at Top Tier 0:76 0:75 0:65 0:65
Total Ask Depth (logged) 1 :171.05 0.90 0.82 4 :394:154:023:82
Total Bid Depth (logged) 6:15 6:16 6:12 6:25 7:84 7:95 8:06 8:04
Buyer-initiated Trade Volume (logged) 2 :952:672:922:60 7:27 5:61 5:50 5:84
Buyer-initiated Trade Count (logged) 1.03 1.19 1.13 2:92 3:11 3:04
Seller-initiated Trade Volume (logged) 8:29 7:46 7:53 7:671:782:042:102:06
Seller-initiated Trade Count (logged) 1:62 1:96 1:710.52 0.63 0.65
Constant Yes Yes Yes Yes Yes Yes Yes Yes
Hourly Dummies No No No Yes No No No Yes
Nobs 7,007 7,007 7,007 7,007 7,007 7,007 7,007 7,007
AdjustedR20.39 0.39 0.40 0.38 0.41 0.41 0.42 0.40
38
Table 5: Regression of price impact on limit order book state. Panel A reports the baseline
regression of price impact on listed explanatory variables capturing the prevailing state of the
limit order book. We estimate the regression without (Model 1) and with (Model 2) hourly
dummies to account for possible diurnality of price impact.,, andindicate statistical
signi cance at the 1%, 5%, and 10% levels respectively. Panel B shows the incremental
explanatory power of the 24-hour history of each explatory power. Each row in Panel B is
based on the regression that augments baseline model 1 with 24 lags of the given explanatory
variable. Reported are the number of lags with signi cant coecient at the 1%, 5%, and
10% level, as well as the adjusted R2. Price impact (the dependent variable in all regressions
reported in the table) is the price impact of order book events over each hour, estimated as
described in the text. Data are from BTC-e for the period from 12/7/2013 to 9/24/2014.
Panel A: Baseline Regression of Price Impact
Explanatory Variable Model 1 Model 2
Ask Slope -0.000 -0.000
Bid Slope 0.001 0.000
Total Ask Depth (logged) 0:141 0:147
Total Bid Depth (logged) 0 :0990:095
Buy Volume (logged) 0:214 0:231
Sell Volume (logged) 0:064 0:067
Realized Volatility 0 :6420:659
% Ask Depth at Top Tier -0.007 -0.007
% Bid Depth at Top Tier -0.010 -0.010
% Ask Depth at Top 5 Tiers 0:008 0:008
% Bid Depth at Top 5 Tiers 0:011 0:010
Hourly Dummies No Yes
AdjustedR212.61 11.49
Panel B: Explanatory Power of 24-hour History
# Signi cant Lag Coecients
1% Level 5% Level 10% Level Adj. R2
Ask Slope 0 0 0 10.04
Bid Slope 0 0 1 10.08
Total Ask Depth (logged) 0 0 0 9.95
Total Bid Depth (logged) 1 1 3 10.27
Buy Volume (logged) 0 1 4 10.24
Sell Volume (logged) 0 1 1 10.27
Realized Volatility 1 2 3 9.69
% Ask Depth at Top Tier 0 2 3 10.15
% Bid Depth at Top Tier 0 1 2 10.08
% Ask Depth at Top 5 Tiers 0 0 1 10.07
% Bid Depth at Top 5 Tiers 0 0 0 9.98
39
Dec 2013 Jan 2014 Feb 2014 Mar 2014 Apr 2014 May 2014 Jun 2014 Jul 2014 Aug 2014 Sep 2014 Oct 20143004005006007008009001000Price of BTC in US$BTC-e 1-min Mid-Quote
CoinMarketCap Daily CloseFigure 1: Evolution of bitcoin price on BTC-e versus other exchanges over sample period.
40
-1200 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 1200
Distance from Mid-quote (in cents)102030405060708090% Cumulative Depth
Bid Side Ask SideFigure 2: Percentage share of cumulative depth up to the 150th price level. The gure
shows the percent of cumulative depth (y-axis) by the distance from the mid-quote in cents
(x-axis). Average cumulative depths and price distances are computed from one-minute
snapshots of BTC-e limit order book for the 12/7/2013 { 9/24/2014 period.
41
12/13 01/14 02/14 03/14 04/14 05/14 06/14 07/14 08/14 09/14 10/14051015Daily #BTC Transacted104
(1) (2) (3) (4) (5) (6) (7)(a) Daily Trading Volume
12/13 01/14 02/14 03/14 04/14 05/14 06/14 07/14 08/14 09/14 10/140100200300400500600Daily Realized Volatility (Annualized %)(1) (2) (3) (4) (5) (6) (7)
(b) Realized Volatility
Figure 3: Daily trading activity and realized volatility. Realized volatility is computed from
5-minute returns, and annualized by a factor ofp
365. Data are from the BTC-e platform
for the period from 12/7/2013 to 9/24/2014. Vertical lines mark the following dates: (1)
12/17/2013: third-party payment rms cut o services to bitcoin exchanges in China; (2)
2/24/2014: Mt. Gox exchange collapsed; (3) 3/25/2014: the IRS declared bitcoin to be taxed
as property; (4) 4/10/2014: bank accounts of Chinese bitcoin exchanges were closed; (5)
6/13/2014: Mining pool GHash.io reached 51% harshing power; (6) 7/18/2014: Dell started
accepting bitcoin; and (7) 9/8/2014: Paypal subsidiary Braintree started accepting bitcoin.
42
0 3 6 9 12 15 18 21 24290300310320330340350Total Book Depth (# BTC)
Ask
Bid
0 3 6 9 12 15 18 21 24300350400450500550600Trade Volume (# BTC)
0 3 6 9 12 15 18 21 2418.51919.52020.521Bid-Ask Relative Spread (bps)
0 3 6 9 12 15 18 21 240.850.90.9511.051.1Hourly Realized Volatility (%)Figure 4: Depth, volume, spread, and volatility over 24-hour trading day (Eastern Time).
43
01/2014 02/2014 03/2014 04/2014 05/2014 06/2014 07/2014 08/2014 09/20140102030405060708090100
Tier 101-150 (11%)
Tier 51-100 (11%)
Tier 11-50 (8%)
Tier 6-10 (4%)
Tier 2-5 (8%)
Tier 1 (28%)
Trade (31%)
Figure 5: Information shares of trade and limit orders. They are computed daily from a vector error correction model on
one-minute data of trade price, and limit order prices at tier 1, tiers 2-5, tiers 6-10, tiers 11-50, tiers 51-100, and tiers 101-150.
For each limit order category, the price is the average price of all bid and ask orders in the relevant tiers, weighted by the
corresponding depth. Data are from BTC-e for the period 12/7/2013 { 9/24/2014. Each day is de ned to be from 0:00:00 to
23:59:59 ET. The gure shows the 7-day moving averages of daily information share series.
44
Mean = 2.4
Std. Dev. = 2.71
Median = 1.65
% Positive = 95%
0 10 20
A. PI ($/BTC)00.050.10.15
Mean = 78.05
Std. Dev. = 40.34
Median = 69.37
% Positive = 100%
0 100 200 300
B. Ask Slope00.020.040.060.080.1
Mean = 71.49
Std. Dev. = 34.81
Median = 64.69
% Positive = 100%
0 100 200 300
C. Bid Slope00.020.040.060.080.1
Figure 6: Summary statistics of adverse selection and liquidity provision measures. Panel A is the histogram of hourly price
impact of order book events (in $ per one-coin order
ow imbalance). Panels B and C are the slopes of the limit order book
on the ask and bid sides respectively. The y-axis shows the probability of each data bin. Data are from BTC-e for the period
12/7/2013 { 9/24/2014.
45
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
Distance from Mid-quote (in cents)0102030405060708090100% Cumulative DepthAsk
Bid
Figure 7: The gure plots the average slope of the bid and the ask side of the limit order book. The x-axis shows the price
distance from the best bid-ask midpoint in cents. The y-axis shows the percent of cumulative depth at each price increment.
Data are from BTC-e for the period 12/7/2013 { 9/24/2014.
46
Appendix A Cryptocurrency news articles
Date Title
12/05/2013 A Better Translation Of Peoples Bank Of Chinas First Ocial Statement
On Bitcoin
12/06/2013 People's Bank of China Issues a Regulatory Notice on Bitcoin
12/07/2013 BTC China now Requires ID Veri cation from All Users Upon Logging In
12/07/2013 The UK can Finally Have a Real Bitcoin Exchange
12/05/2013 China bans banks from handling Bitcoin trade
12/14/2013 Taiwan Bitcoin Exchange
12/16/2013 Norway Doesnt Consider Bitcoin a Legitimate Currency
12/17/2013 Peoples Bank of China Further Restricts Bitcoin
12/19/2013 Chinese Bitcoin Exchange Accepting Deposits
12/20/2013 Overstock.com Will Start Accepting Bitcoin In 2014
12/23/2013 Chinese Bitcoin Ban Driven by Chinese Banking Crisis?
12/23/2013 New Indonesian Bitcoin Exchange Could Help Spur its Economy
12/25/2013 HashCows Mining Pool Hacked
12/26/2013 Online Dogecoin Wallets Hacked
12/27/2013 Chinese Bitcoin Exchanges Find Workaround To Allow RMB Deposits,
Exchange Rate Rallies
12/28/2013 The US Department of Treasury issues a Bitcoin-Friendly ruling for Miners
12/30/2013 Bitcoins Uncertain Fate in India
01/06/2014 Indian Exchange Unocoin To Resume Operations
01/07/2014 Bitstamp is down
01/07/2014 Taobao.com (Chinas Ebay) Bans Bitcoin Payments
01/09/2014 Ghash.IO ocial statement on the 51% attack threat
01/12/2014 Warning: Huobi has closed their personal bank accounts system
01/13/2014 The Bitcoin Price Falls due to Concerns with China
01/14/2014 OpenEx Hacked
01/17/2014 Ebay will allow Bitcoin Trading
01/20/2014 Finland Decides To Treat Bitcoin As A Commodity
01/23/2014 Give Me COINS Litecoin Pool Hacked
01/27/2014 BitInstant CEO and Bitcoin Foundation Vice Chairman Charlie Shrem
Arrested in New York
01/28/2014 The Epic Fall Of Mt. Gox: The Increasingly Illiquid Bitcoin Exchange
01/28/2014 Central Bank of the Russian Federation Discourages Use of Bitcoin
continued on the next page…
47
Date Title
continued from the previous page…
02/01/2014 Bitcoin Now Accepted at Every 7-Eleven in Mexico
02/03/2014 Calm Down Internet, BTC-e is Not About to Be Shutdown
02/05/2014 Do Cryptocurrency Exchanges steal or are they just badly built? Keep
away from Bter.com
02/06/2014 Bitcoin Price Volatility Returns Alongside Exchange Problems
02/07/2014 Bitcoin Price Plunges as Mt. Gox Exchange Halts Activity
02/07/2014 Russia Uses Doublespeak to Ban Bitcoins and Cryptocurrencies
02/11/2014 Bitcoin Exchanges Under \Massive and Concerted Attack"
02/13/2014 Silk Road 2 Hacked, All Bitcoins Stolen { $2.7 Million
02/14/2014 Bitstamp to Resume Bitcoin Withdrawals Later Today
02/15/2014 Bank of Thailand Decides Bitcoin is OK for Now
02/17/2014 Mt. Gox Press Release
02/20/2014 Bitcoin investor fury at Mt. Gox delays
02/23/2014 Mt. Gox resigns from Bitcoin Foundation
02/24/2014 Bitcoin exchange Mt. Gox goes oine amid allegations of $350 million hack
02/25/2014 Mt. Gox les for bankruptcy, hit with lawsuit
02/28/2014 Mt. Gox Unable to Make a Surprise out of the Recovery of 200,000 BTC
03/03/2014 Flexcoin and Poloniex; Security Holes Exploited in Another Hack Attack
03/11/2014 CryptoRush support worker leaks inside info
03/11/2014 New York Financial Authorities Will Accept Applications for Virtual Cur-
rency Exchanges
03/14/2014 Bitcurex Targeted by Hacking Attack
03/17/2014 Blockchain Su ers Extended Downtime unscheduled maintenance
03/18/2014 As Promised, Bitcurex Resumes Operations on Tuesday
03/18/2014 CoinEX Hacked, All Coins Stolen
03/25/2014 IRS Virtual Currency Guidance
03/31/2014 Square Market Accepts Bitcoin
04/03/2014 Popular Chinese Bitcoin Exchange Huobi Halting Voucher Deposits
04/04/2014 eBay Adds Virtual Currency Category to U.S. Website
04/08/2014 Hacker Exploits Heartbleed Bug in BTCJam Heist
04/10/2014 Bitcoin Price Drops 10% as Chinese Exchanges Stop Bank Deposits
06/13/2014 Bitcoin currency could have been destroyed by \51%" attack
06/19/2014 Silk Road Bitcoins and the Current Price Trend
06/27/2014 Silk Road Auction Winners and Losers
07/13/2014 8 Million Vericoin Hack Prompts Hard Fork to Recover Funds
07/17/2014 New York Reveals BitLicense Framework for Bitcoin Businesses
07/18/2014 Dell Begins Accepting Bitcoin
07/29/2014 Cryptsy: Trades & Withdrawals Suspended Inde nitely, Claims Bitcoin
Theft
09/08/2014 Payments Processor Braintree Con rms Bitcoin Integration Rumors
48
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