Download Order Characteristics, Uncertainty and Price Formation in the

Order Characteristics, Uncertainty and Price Formation
in the Foreign Exchange Market
Aditya Kaul, Blake Phillips and Stephen Sapp*
Abstract
In this paper, we study the contribution to price discovery of market orders and limit
orders with differing degrees of aggressiveness, focusing on how these contributions
change with the level of volatility. Using intraday data from the Deutsche Mark – U.S.
dollar foreign exchange market, we find significant price effects of market orders and
both proximal and distant limit orders, with the relative contribution of limit orders,
especially distant limit orders, to price formation increasing with volatility. Our analysis
provides support for recent dynamic order submission models suggesting that both
market and limit orders are used by informed traders, especially in periods of price
uncertainty.
JEL Classification: G12, G14, G15
Keywords: market microstructure; foreign exchange; order flow; volatility
* The authors are from the School of Business, University of Alberta, the School of Accounting and
Finance, University of Waterloo and the Richard Ivey School of Business, University of Western Ontario.
Corresponding Author: Aditya Kaul; email [email protected]. We thank SSHRC for financial support,
and Laurence Lescourret, Patrice Poncet, Tanseli Savaser, and seminar participants at ESSEC Paris and
FMA Europe 2012 for helpful comments.
Abstract
In this paper, we study the contribution to price discovery of market orders and limit
orders with differing degrees of aggressiveness, focusing on how these contributions
change with the level of volatility. Using intraday data from the Deutsche Mark – U.S.
dollar foreign exchange market, we find significant price effects of market orders and
both proximal and distant limit orders, with the relative contribution of limit orders,
especially distant limit orders, to price formation increasing with volatility. Our analysis
provides support for recent dynamic order submission models suggesting that both
market and limit orders are used by informed traders, especially in periods of price
uncertainty.
1. Introduction
Financial markets perform the important functions of aggregating and
incorporating information into asset prices.
Theoretical and empirical research has
studied the role of the net volume of executed buy and sell orders in this process.1 One
justification for this focus is the assumption that informed traders submit market orders
for immediate execution; thus, these orders are thought to contain the most price relevant
information.
However, recent theoretical work, e.g. Goettler, Parlour and Rajan
(henceforth GPR, 2005, 2009) and Rosu (2009, 2011), suggests that informed traders
optimally choose strategies involving both market and limit orders. Market orders are
used when informed traders are willing to accept an uncertain price in return for
immediate execution, whereas limit orders are used when informed traders seek price
certainty and are willing to forgo execution immediacy.
This theoretical research
therefore suggests that the analysis of market orders alone may lead to an incomplete
view of the price formation process.
Our paper contributes to the price formation literature in several ways. First, we
examine the effects of different order types on prices in the foreign exchange (FX)
market. We compare the price informativeness of not only market orders but also limit
orders, as well as proximal relative to more distant limit orders. Second, our main
contribution is to test the pricing implications of an important prediction of the abovementioned theoretical work, namely that an informed trader’s choice between market and
limit orders depends on the level of price uncertainty. We proceed by examining the
1
See, for example, Brandt and Kavajecz (2004), Green (2004) and Pasquariello and Vega (2007) for bond
market evidence, Evans and Lyons (2002) for foreign exchange market evidence, and Chordia, Sarkar and
Subrahmanyam (2005) and Boehmer and Wu (2008) for equity market evidence.
1
contribution of each order type to price formation during periods of high and low price
uncertainty.
Our analysis is based on a short, but high quality, dataset of orders submitted in
the Deutsche Mark – U.S. dollar (DM – USD) foreign exchange market over a 5-day
period in October 1997. Our selection of this older dataset is motivated by its rare
availability of all market and limit orders submitted and either executed or cancelled in
the Reuters D2000-2 electronic broker system. Thus, the dataset is uniquely suited for
the purposes of addressing questions related to order type and price formation, which
cannot be examined with most recent datasets. We consider three hypotheses by relating
returns to aggregate market and limit order flow (constructed as the difference between
market and limit buy and sell orders) in 5- minute intervals through the trading day
(market orders include marketable limit orders that execute immediately upon
submission). To examine hypotheses related to price uncertainty, we sort the sample into
volatility terciles and compare effects in the high and low terciles.
The first hypothesis, based on the earliest market microstructure models (e.g.
Copeland and Galai, 1983), asserts that traders with short-lived private information will
submit market orders to ensure order execution and benefit from their information. We
expect the information content of market orders to increase in periods of high price
uncertainty as traders condition on executed transactions.
Consistent with existing
research (e.g. Evans and Lyons, 2002), we find that market orders contain important price
relevant information. Using volatility as a proxy for uncertainty, we extend existing
research by documenting that the permanent price effect of market orders is larger in
periods of high volatility.
2
The second hypothesis builds on more recent theoretical models which suggest
that informed traders use a mixed strategy of submitting both market and limit orders
(e.g. see GPR, 2009; Rosu, 2009). They submit market orders to benefit from short-lived
information, and limit orders to benefit from long-lived information. We find that,
although market orders convey more information than limit orders, the price effects of
both market and limit orders are significant. Comparing high and low volatility periods,
we find that the information content of both market and limit orders is higher in the high
volatility state, but the increase is larger for limit orders. This supports theoretical
predictions that informed traders employ mixed submission strategies, and use more limit
orders as uncertainty increases.
The final hypothesis we examine suggests that informed traders prefer to submit
less aggressive limit orders when uncertainty is high (e.g. Foucault, Kadan and Kandel,
2005; GPR, 2009). To evaluate this hypothesis, we examine the information content of
limit orders with varying degrees of aggressiveness, where aggressiveness is measured by
the proximity of the limit price to the best price in the limit order book. On average, the
price effect of market orders is larger than that of proximal limit orders (placed 1-3 pips
behind the best price) which, in turn, is larger than the effect of distant limit orders
(placed 4-5 pips or more than 5 pips behind the best price); all these price effects are
significant. The price effect of every order type is stronger in the high volatility state but
the largest increase occurs for the more distant (least aggressive) limit orders. This is
consistent with the hypothesis that less aggressive limit orders are increasingly used by
informed traders as price uncertainty increases.
3
Our paper makes three contributions. First, we find that significant price relevant
information is contained not only in market orders, but also in limit orders, including
limit orders at prices well behind the best price in the market. The fact that market orders
move FX prices is consistent with research focusing on order flow (e.g. Evans and Lyons,
2002). Market orders can have a mechanical impact on prices as they ‘walk the book’
and remove liquidity from the limit order book. However, limit orders, especially limit
orders well behind the best price, do not have such mechanical effects on prices because
they do not automatically execute against standing orders. Rather, the effects of limit
orders on prices are more likely to reflect pure information transmission. Our results
therefore indicate that the empirical literature’s focus on market orders misses substantial
and intriguing sources of price relevant information. This is especially relevant given the
prevalence of limit order markets in recent years.
Second, we find that the informativeness of market and limit orders is related to
the level of volatility in the market. Market orders always have the highest impact, but
the relative informativeness of limit orders (especially those further behind the best price)
increases as volatility increases.
These results point to an important role for the
information environment (notably uncertainty) in driving price formation by affecting the
order submission strategies of informed traders. Finally, our results provide some of the
first empirical support for the predictions of recent theoretical work (e.g. Foucault, Kadan
and Kandel, 2005; GPR, 2005, 2009; Rosu, 2009, 2011), in particular the suggestion that
informed investors employ mixed submission strategies and increase their use of limit
orders as uncertainty increases. The fact that such effects are strong in the inter-dealer
4
FX market lends further weight to the notion that private information is an important
influence in this market, as originally suggested by Lyons (1995).2
The rest of the paper is organized as follows. Section 2 summarizes our research
questions and related work. Section 3 describes the data set, variable construction and
modelling strategy. Section 4 discusses our results. Section 5 concludes.
2. Research questions and related literature
Despite the increasing presence of order driven markets over the past decade, the
role of limit orders in the price discovery process has received relatively little attention in
academic research. Most research focuses on the information content of executed orders
(i.e. market orders or marketable limit orders, together termed order flow). This section
outlines the hypotheses we study and summarizes related research.
The earliest microstructure models assume that informed traders submit market
orders to take advantage of their information before it loses value (e.g. Glosten and
Milgrom, 1985).
Consequently, our first hypothesis assumes that informed traders
submit market orders.
H1: Market orders convey price relevant information.
While this hypothesis has been examined in prior empirical research, we consider
it both to provide a benchmark for our main models and to confirm that relations
2
See also Lyons (2001) for an extensive discussion. Bjønnes, Osler and Rime (2008) provide interesting
evidence of private information in the interdealer FX market.
5
documented elsewhere also exist in our dataset. As discussed, previous studies show that
executed orders contain price relevant information.3
In line with more recent theoretical models suggesting that price uncertainty
affects informed traders’ order submission decisions (e.g. see Foucault, Kadan and
Kandel, 2005; GPR, 2009; Rosu, 2009), we also examine how the price effects of order
flow vary with volatility. Volatility is a measure of investor uncertainty about underlying
asset value, which has received relatively little attention in the empirical literature on
price formation.4 We extend Hypothesis 1 by comparing the price effects of market
orders in times of high relative to low volatility. Based on the theoretical literature we
expect investors to learn more from submitted market orders as volatility increases.
H1a: More price relevant information is conveyed by market orders when
volatility is high.
The second hypothesis extends the first to consider the price effects of both
market and limit orders. Recent microstructure models such as Foucault, Kadan and
Kandel (2005), GPR (2005, 2009) and Rosu (2009, 2011) suggest that informed traders
optimally use both market and limit orders. Market orders allow impatient traders with
short-lived information to demand immediacy and exploit stale orders in the limit order
book. Conversely, limit orders allow traders to supply liquidity while locking in prices to
3
Footnote 1 lists examples of this order flow literature. Marketable limit orders are limit orders where the
limit price is better than or equal to the best limit price on the opposite side of the market (e.g. for a
submitted buy limit order the price the trader is willing to pay is at least as high as the lowest ask price in
the book at the time). These orders execute almost immediately and are thus similar to market orders.
4
Research documenting a relation between order flow and volatility includes Easley, Hvidkjaer and
O’Hara (2002) in the equity market and Faust, Rogers, Wang and Wright (2007) and Berger, Chaboud,
Chernenko, Howorka and Wright (2008) in the foreign exchange market. Studies that show a relation
between market conditions and order type include Hasbrouck and Saar (2002), Hollifield, Miller, Sandas
and Slive (2006), Hall and Hautsch (2006) and Lo and Sapp (2010).
6
benefit from longer-lived information. Experimental studies by Bloomfield, O’Hara and
Saar (2005) and Anand, Chakravarty and Martell (2005) document that informed traders
use market and limit orders in equilibrium. Hautsch and Huang (2012) find that the price
impact of individual market orders is higher than that of limit orders, although both
effects are significant. Consequently, we expect both market and limit orders to convey
price relevant information. The interesting perspective provided by limit orders is that
they can only influence prices by signalling informed traders’ views on the future value
of the asset and not by directly influencing transaction prices as market orders do.5 This
leads to the second hypothesis:
H2: Price relevant information is conveyed by both market and limit orders. The
information content of market orders is greater than that of limit orders.
Kaniel and Liu (2006) suggest that informed traders will prefer limit orders during
periods of increased uncertainty to protect against price risk and camouflage their orders.
Rosu (2009, 2011) and GPR (2009) predict that informed traders submit market orders,
limit orders or a combination of the two depending on market conditions, such as the
level of price uncertainty. Specifically, GPR (2009) suggest that informed traders submit
limit orders in preference to market orders as uncertainty increases, so as to lock in the
value of their private information.6 We therefore expect to see an increased informational
role for both market and especially limit orders as volatility increases.
5
Limit order submissions can influence the price impact of market orders by increasing depth in the limit
order book. This will reduce the price impact of market orders.
6
As uncertainty regarding asset value increases, informed traders will submit both market orders, to hit
potentially stale limit orders, as well as limit orders to benefit from liquidity provision and their information
while avoiding the price risk associated with market orders (e.g. GPR, 2009; Foucault, Moinas and
Theissen, 2007). See, also, the empirical studies of Ahn, Bae and Chan (2001), Coppejans, Domowitz and
7
H2a: More price relevant information is conveyed by market and limit orders
when volatility is high. There is a larger increase in the informativeness of
limit orders relative to market orders when volatility is high.
The third hypothesis examines the relation between information content and limit
order aggressiveness. GPR (2009) suggests that informed traders optimally choose a
combination of market orders and limit orders at different price levels. Berber and
Caglio (2005) and Foucault, Moinas and Theissen (2007) find that the volume of orders
at different price levels in the limit order book contains information about future price
movements. Cao, Hansch and Wang (2008) and Hautsch and Huang (2012) find that
market orders and aggressive limit orders have significant price impacts. Cao, Hansch
and Wang (2009) and Eisler, Bouchard and Kockelkoren (2010) document differences in
the price impact of market orders, limit orders at the best price and limit orders behind
the best price. This leads to the hypothesis:
H3: Price relevant information is conveyed, not just by market orders, but also by
limit orders at all price levels in the limit order book. Price informativeness
drops for less aggressive orders, i.e. going from market orders to limit orders
at the best price to limit orders behind the best price.
We also examine the informativeness of limit orders of varying aggressiveness
conditional on price uncertainty. Ellul, Holden, Jain and Jennings (2007) and Lo and
Sapp (2006) provide evidence that uncertainty generally lowers the aggressiveness of
subsequent orders submitted by traders. GPR (2009) suggest that, when uncertainty is
Madhavan (2001) and Pascual and Veredas (2010), which find that volatility affects investor preferences
for market versus limit orders.
8
high, informed traders place limit orders, especially less aggressive limit orders, because
the insurance-like features of these orders enable them to capture more of the value of
their information. Thus, we expect a larger increase in the information content of less
aggressive orders when volatility is high.
H3a: More price relevant information is conveyed by all orders when volatility is
high. However, the increase in price informativeness is smaller for market
orders than aggressive limit orders and largest for limit orders further
behind the best price.
3. Data and variable summary
3.1. The dataset
To test these hypotheses on the relevance of market and limit orders, we use a rich
dataset containing market and limit order submissions by foreign exchange dealers. The
data come from the DM-USD spot market for the first full week in October 1997. The
trading platform is the Reuters D2000-2 system, which is an electronic limit order book
for interdealer trading.
Due to Reuters’ strong position in this currency and the
importance of electronic trading platforms in this market, the dataset captures a
significant proportion of global interdealer spot trading for this currency pair.7
Dealers can submit market orders and submit or cancel limit orders to buy or sell
DM for USD at any time during the day (quotes are in DM/USD). Order sizes are $1
million (USD) or greater. The system allows all dealers to observe the best bid and ask
7
Such order-driven electronic markets represent around 85% of all interdealer trading in major currencies
(e.g. see Sager and Taylor, 2006).
9
prices and the associated depth, as well as the price required to clear a $10 million order
on either side of the book. Information on the rest of the limit order book, while
unobservable, may be inferred by dealers using sources such as Reuters’ EFX page or
their customer order flow.8 Dealers may also estimate market depth by submitting orders
at or behind the best price in the market and observing the prices at which these orders
are filled, and the delay in their order fill.
The dataset covers activity from the evening of October 5, 1997 until midnight on
October 10, 1997. Although a longer time span would be preferable, this is one of very
few datasets with complete limit order book information. It contains all of the market
and limit orders submitted and cancelled over this period, and thus provides a nice
complement to the less detailed data used in most studies of the currency and equity
markets. By studying the DM-USD currency pair (the most heavily traded pair over the
sample period), we sidestep potential problems resulting from thin trading and errors in
the measurement of high frequency variables. Thus, the dataset is well-suited to shed
light on the price effects of different types of orders.
The dataset includes information on order type (market order or limit order and
the corresponding price), whether the order is on the bid or ask side of the book, the entry
and execution or cancellation time of the order, and the quantity to be traded. There are a
total of 266,723 submitted orders, of which 15% are market orders and 85% are limit
orders; of the limit orders, 20% are marketable. Figure 1 displays the total value of
orders submitted in each hour of the day, sorted by order type and summed across all five
8
For instance, see Danielsson and Payne (2002), who find that the shading of the indicative quotes in the
EFX system can provide useful information about depth in the Reuters D2000-2 book. Lo and Sapp (2010)
suggest that dealers have information about order book depth behind the best prices and use it in their order
submission decisions.
10
days. Figure 1a shows a clear seasonality in order submissions, with the greatest value of
orders submitted around the market openings in Europe and North America (roughly 8:00
GMT and 13:00 GMT).
Figure 1b shows time variation in order aggressiveness over the course of the
trading day. Traders typically use more aggressive limit orders during times of high
market activity. Proximal orders, with limit prices within 3 pips of the best price, account
for 60% of the non-marketable limit orders placed during the peak trading hours of 07:00
- 16:00 GMT. Less aggressive limit orders are employed during off peak hours, with 7080% of orders placed more than 5 pips away from the best price.
We use the sequence of submitted market and limit orders to reconstruct the limit
order book, i.e. the quantity offered for purchase or sale at each price. Specifically,
following the submission, execution or cancellation of each order, we use the associated
volume and price to update the quantities at all prices on both sides of the book. The
state of the book when the dataset starts is unknown, so we assume that there were no
standing limit orders at that time. For three reasons, we are confident that this does not
impair our ability to accurately reconstruct the book: (a) the dataset commences at 19:30
GMT (after the U.S. markets close and before the Asian markets open), a period of thin
trading; (b) few trades carry over from one day to the next; and (c) only limit orders are
placed during the first four hours and the majority of these orders are cancelled.
To limit the influence of thin trading, we study orders submitted between 07:00
and 16:00 (GMT), the most active period in the market (see Figure 1a), and analyze data
measured over 5-minute intervals.
11
3.2. Variable definitions
The key variables in our analysis are returns, volatility, and order flow. Log
(continuously compounded) returns are computed using the midpoint of the best bid and
ask prices at the end of adjacent 5-minute intervals. We measure volatility as the natural
logarithm of the ratio of the high and low prices at which orders are executed in a given
5-minute interval t (Parkinson, 1980).9
(
)
(1)
Following Evans and Lyons (2002), we define market order flow as the difference
between the volume of immediately executable buyer and seller initiated trades:
OFMt = VBt – VSt
(2)
where OFMt is market order flow in interval t, and VBt and VSt are the volumes of all
buyer initiated and seller initiated marketable trades executed in interval t.10 A positive
value of OFMt indicates an excess of buyer-initiated trades in interval t.
We similarly construct OFLt as the difference between buy and sell volumes of all
non-marketable limit orders. We also calculate order flow for limit orders partitioned
according to their aggressiveness: OFL1-3,t, OFL4-5,t and OFL6+,t are order flow for limit
orders placed 1-3, 4-5 and 6 or more pips from the best price on the other side of the
book. For example, OFL1-3,t is the volume of limit orders to buy less the volume of limit
orders to sell, where the buy limit prices are between 1 and 3 pips below the lowest ask in
9
Alizadeh, Brandt and Diebold (2002) show that this measure of volatility is more efficient and more
robust than alternative candidates.
10
Evans and Lyons (2002) and much of the extant research refers to this simply as order flow. Because of
our extension of this measure to limit orders, we use a more precise definition of market orders as the sum
of market orders and marketable limit orders.
12
the book at the time and the sell limit prices are between 1 and 3 pips above the highest
bid in the book.11
Our tests include controls for market volatility (as defined above) and illiquidity.
To measure illiquidity, we follow Hasbrouck and Seppi (2001) and construct the slope of
the limit order book at the end of interval t as the difference between the best ask and bid
quotes divided by the sum of the logarithms of the total buy and sell volume in the book:
[
]
(3)
This measure, which combines spread and depth information, is richer than pure spread
based measures, as it increases when either the spread increases or overall depth
decreases, both changes indicating reduced trader willingness to participate in the market.
In Table I we present statistics summarizing the data. The mean 5-minute return
in the sample period is close to zero (the median is zero) with a relatively symmetric
distribution. Comparing order flow from market and limit orders, we see net buying
pressure from both types of orders, though the magnitudes are significantly different
(mean 0.9 and median 3.0 for OFM, mean 5.6 and median 4.0 for OFL). The large
values of OFL6+ (mean 5.4, median 3.0) relative to OFL1-3 (mean 0.6, median 2.0) imply
that the net buying pressure in the case of limit orders is mainly due to distant limit
orders.
The order flow measures are highly variable: the quartile values are -$29 million
and +$31 million for OFM, and -$24 million and +$35 million for OFL. Thus, the
11
Note that marketable limit orders, which are limit orders submitted at the best price on the opposite side
of the market or better, will execute immediately and are included in market order flow. Orders 1-3 pips
away from the best price on the opposite side of the market do not execute immediately, though they may
improve the bid-ask spread and will then be at the front of the queue for execution against subsequent
orders.
13
dataset has periods of both strong buying and strong selling pressure. The range for the
less aggressive limit orders is smaller, though still appreciable. The large variability of
each order flow series suggests that our data have the power to identify effects of order
flow on prices.
The mean and median values of Volatility, which measures uncertainty, are
0.0006 and 0.0005. The mean and median values of Slope, which measures limit order
book illiquidity, are 0.00006 and 0.00003. Their large interquartile range values (78% of
the median value for Volatility and 150% for Slope) again point to substantial variation in
both variables over the sample period.
In unreported tests, we calculate the pairwise correlations between the key
variables. The correlation between order flow from market and limit orders is low,
suggesting that the information content of each order type is distinct. Likewise, the order
flow correlations among the limit order categories are always below 0.20, indicating that
the order flow series convey unique information.
3.3. Model definitions
To examine price formation in the DM-USD market, we estimate the following
model for continuously compounded 5-minute returns:
∑
∑
(4a)
Here Rt is the return in 5-minute interval t, and Dj,t are dummy variables corresponding to
the hours (j) of 7:00 through 15:00 (15:00 to 16:00 is the base hour). DThurs,t is a dummy
variable for the hours of 9:00 through 12:00 on October 9, 1997, which corresponds to
14
the period surrounding an unanticipated interest rate increase by the Bundesbank. The
use of these dummy variables controls for well-known intraday seasonalities in the
foreign exchange market (e.g. Dacrogna et al., 2001) and the effects of an announcement
known to have had a major effect on the market (e.g. Carlson and Lo, 2006). To study
the informativeness of orders with differing degrees of aggressiveness, we estimate
models with the net volumes of market orders (OFM), limit orders (OFL), and proximal
and distant limit orders (OFL1-3, OFL4-5 and OFL6+, respectively):
∑
∑
(4b)
∑
∑
(4c)
The models are estimated after standardizing the values of the dependent and independent
variables to have a mean value of zero and standard deviation of one. Consequently,
there are no intercept terms in the models and we can assess economic significance (the
effects of a one standard deviation shock) directly from the coefficients.
Note that each specification includes measures of volatility and illiquidity, as
defined by equations (1) and (3). There are two reasons for including these variables.
First, both return and order submissions could be driven by prevailing volatility or
illiquidity.
The inclusion of these variables addresses such simultaneity concerns.
15
Further, both variables serve to control for mechanical order flow effects, e.g. market
orders could have more pronounced effects in less liquid or more volatile markets.12
To examine whether volatility affects price formation, we sort the sample into
terciles based on the volatility in 5-minute period t-1. We then estimate the above models
using the observations corresponding to the high volatility (volatility in the top tercile)
and low volatility (volatility in the bottom tercile) states. This tercile sort sharpens the
gap between the high and low volatility states while providing a reasonable number of
observations (182 and 181, respectively) for model estimation. Both features increase the
power of the hypothesis tests related to the effects of uncertainty.
4. Results
4.1. The price informativeness of market order flow
Since the original market microstructure models suggest that market orders are
the most significant source of price relevant information, we start by examining the price
effects of market order flow in Hypothesis 1. The model is described in equation (4a),
which includes a set of time dummy variables (to control for intraday seasonalities), 12
lags of returns (to control for high frequency return autocorrelation), lagged volatility and
illiquidity (to control for market conditions), and contemporaneous market order flow
12
Note that we study the price effects of new order submissions in period t, whereas the volatility and
illiquidity controls are from period t-1. However, the stated concerns are relevant because volatility and
illiquidity are persistent. Mechanical effects of limit order flow stemming from volatility or illiquidity are
less of a concern. If higher volatility leads to the execution of more distant limit orders, the coefficient on
limit order flow should be negative (e.g. as prices rise, limit orders to sell will execute and limit order flow
will be negative). In fact, our analysis shows that the coefficient on limit order flow is positive, so that
negative limit order flow is associated with lower, not higher, prices.
16
(OFM) to capture the immediate price effect of order flow. This model is estimated over
the entire dataset.
Model 2 in Table II reports the results. Of the 12 coefficients on lagged returns,
only that on the first lag is statistically significant. Its negative sign is consistent with
high frequency foreign exchange studies such as Dacrogna et al. (2001). The coefficients
on the dummy variables are not significant at conventional levels.13 The coefficient on
the lagged illiquidity control is positive but not significant, while that on lagged volatility
is negative and significant. We discuss these coefficients later.
The positive coefficient on OFM implies that returns are positively related to
contemporaneous market order flow (t-statistic of 27.5). This is consistent with previous
work documenting a positive price impact of order flow: net buying (selling) pressure
leads to positive (negative) returns. In untabulated specifications, we include 3 through
12 lags of order flow as additional regressors and find that the coefficients on the lagged
order flow terms are not significant.
Thus, we find a strong and permanent
contemporaneous effect of order flow on prices. The rapid and accurate incorporation of
order flow related information into prices is consistent with highly active trading in the
DM-USD market, with the Bank for International Settlements (BIS, 1998) reporting daily
trading volume of USD 309 billion. The coefficient on order flow is 0.757, implying that
a one standard deviation increase in 5-minute order flow (51.7 million USD) corresponds
to a return that is higher by 0.757 standard deviations (or 3.73 bps). This effect is
economically significant, and sets the stage for the subsequent hypotheses that are our
13
For robustness we also estimate the model excluding the hourly dummies. Our results on the importance
of order flow are unchanged. However, since intraday foreign exchange return seasonalities are welldocumented, we choose to retain these dummies in subsequent models.
17
focus. As can be seen from the estimates under Model 1, the remaining coefficients are
similar when we exclude Slope and Volatility.
The second part of this hypothesis, Hypothesis 1a, examines the influence of
uncertainty on the price effects of order flow. This builds on theoretical models (e.g.
GPR, 2009) which propose that order submission behavior changes as volatility changes.
Panel A of Table III reports the key coefficients from a simplified version of model (4a)
which relates the 5-minute return to its first lag, contemporaneous order flow, lagged
volatility and illiquidity, the hourly dummies and the dummy for the Bundesbank
announcement (the dummies are suppressed to conserve space). The coefficients in the
unconditional (base) model are similar to those in Table II. In the low volatility state, the
coefficient on OFM drops by 34% relative to its unconditional value (i.e. from 0.76 to
0.50), whereas in the high volatility state the coefficient increases by 16% (i.e. from 0.76
to 0.88).
The difference of 0.38 between the high and low volatility order flow
coefficients is statistically significant (t-statistic of 3.97). Further, the model’s R2 value is
almost 75% higher (0.70 vs. 0.41) in the high relative to the low volatility state. These
results confirm the hypothesis that in times of increased uncertainty, counterparties
condition on (or learn more from) order flow.
The coefficient on the lagged return is not significantly different from zero in the
low and high volatility states. The coefficients on the dummy variables (not reported) are
similar to those in Table II.
The coefficients on lagged volatility and illiquidity display interesting differences
across states. While the coefficient on illiquidity is positive and significant in the low
volatility state but not in the high volatility state, the coefficient on lagged volatility is
18
negative and significant in the high volatility but not the low volatility state. The positive
coefficient on illiquidity is consistent with increasing demand for U.S. dollars (often
regarded as a safe haven currency) when the DM-USD market becomes more illiquid.
However, it is somewhat surprising that this effect arises when volatility is relatively low.
The negative coefficient on volatility in the high volatility state is consistent with
carry trade effects, documented in e.g. Menkhoff, Sarno, Schmeling and Schrimpf
(2012). The carry trade involves borrowing low interest rate currencies and investing the
proceeds in high interest rate currencies. As volatility rises, investors tend to unwind
their positions and this leads to depreciation of the high interest rate currency.
Annualized U.S. interest rates in the years leading up to our sample period were 1%-4%
higher than those in Germany (depending on maturity).
This would have created
incentives for investors to borrow DM and invest the proceeds in USD, and subsequently
to sell USD for DM as volatility rose. Such unwinding transactions should be especially
pronounced in the high volatility state.
4.2. The price informativeness of market and limit orders
Panel B of Table III presents the results of tests examining the relative importance
of market and limit orders. The coefficients on market and limit order flows (OFM and
OFL) are positive and statistically significant for the full sample. Thus, both market and
limit orders contribute to price formation.
This supports the prediction in recent
microstructure models that informed traders submit both market and limit orders. Note
that the coefficient on OFL is 30% that on OFM (0.23 versus 0.84). The smaller effect of
limit order flow is consistent with informed traders generally having a preference for
19
immediacy, e.g. to take advantage of short-lived information. These results support
Hypothesis 2.
To evaluate Hypothesis 2a, we examine the price effects of market and limit
orders in the high and low volatility states. In the low volatility state, the price effects of
both OFM and OFL, while smaller than in the unconditional case, are still significantly
above zero. The price effects of OFM and OFL increase substantially in the high
volatility state.
However, the relative increase from the low volatility to the high
volatility state is larger for limit orders than for market orders. Specifically, there is a
three-fold increase in the price effect of OFL (from 0.180 to 0.531), compared to a lessthan-doubling in the price effect of OFM (from 0.607 to 1.014). Paralleling the increases
in the coefficient values, we find that the adjusted R2 is strikingly higher in the high
volatility state.14
These results confirm the importance of both market and limit orders in price
formation, unconditionally and across volatility states. They also suggest that the relative
informativeness of limit orders increases with price uncertainty. Thus, traders submitting
limit orders when uncertainty is high appear more likely to be informed. It is important
to recognize that the channel by which limit orders affect prices is not mechanical.
Unlike market orders, limit order submissions do not directly impact prices. Rather, their
submission affects market-clearing prices by conveying information about the demands
of informed investors, and thereby altering the demands of other investors for immediacy.
14
We add (up to six) lags of market and limit order flows to this model and find that the lagged order flow
coefficients are all insignificant. Thus, the contemporaneous price effects of market and limit order flow
appear to be permanent.
20
Our results therefore provide strong evidence that there is information not only in
executed transactions (the focus of the extant literature) but also in submitted but not-yetexecuted limit orders. Consistent with the hypotheses proposed by GPR (2009), we also
find that the information content of these different order types changes with the level of
uncertainty.
4.3. The informativeness of near versus distant limit orders
Given our previous evidence that limit orders contain price relevant information,
Hypothesis 3 considers the information content of limit orders submitted at different price
levels. We compare the informativeness of market orders to the informativeness of
proximal limit orders, defined as limit orders with prices 1-3 pips behind the best price on
the opposite side of the market (OFL1-3,), and of more distant limit orders, submitted at
prices 4-5 pips or at 6 or more pips behind the best price (OFL4-5 and OFL6+).15
Panel C of Table III presents the results. Not reported, the coefficients on the
dummy and control variables are similar to those in the previous panels.
More
importantly, the coefficients measuring the price effects of order flow from each order
type are significant in the unconditional model. The effect of market orders (0.864) is
larger than that of all the limit orders. The price effect of limit orders declines as the
limit orders become less aggressive. The estimated price effect of limit orders 1-3 pips
behind the best price is 0.243, compared to 0.166 for orders 4-5 pips behind, and 0.085
15
We use this definition of proximal and distant limit orders based on the fact that typical spreads in the
DM-USD market are 2-3 pips. Consequently, orders within: (a) 1-3 pips of the best price on the opposite
side are placed inside or close to the typical spread; (b) 4-5 pips are placed outside the spread; and (c) 6+
pips are substantially away from the spread. For robustness we replicate the models with alternative and
finer partitions and find that partition placement does not affect our conclusions.
21
for orders 6 or more pips behind, the best price (t-statistics in excess of 3 for all three
coefficients). These results support Hypothesis 3: there is price relevant information in
all limit orders, including limit orders submitted behind the best price. This is consistent
with GPR (2009), who suggest that informed traders submit not only market and limit
orders close to the best price but also limit orders further behind the best price.
The results for the tests of Hypothesis 3a are also found in Panel C of Table III.
The information content of orders changes with volatility. In the low volatility state, the
price effects of all orders decrease relative to their unconditional values. However, the
effect of market orders declines less than that of limit orders. In fact, the coefficient on
the most distant limit order flows (4-5 or 6 or more pips behind the best price) are no
longer significant. In the high volatility state, the price effect of each order type increases
and the increase is larger for limit orders. Relative to its unconditional value, the effect
of the most distant limit orders increases the most, by 300%, compared to increases of
15-30% for market and more proximal limit orders.
This is consistent with the
predictions of the GPR (2009) model. GPR suggest that, as volatility increases, informed
traders exploit the potential gains to supplying liquidity further away from the best prices,
and other investors rationally infer some of their information and impound it in prices.
5. Conclusions
Empirical microstructure research has focused on the price effects of market
orders.
However, recent theoretical work (e.g. GPR, 2009; Rosu, 2009, 2011) has
modeled the decision to submit market versus limit orders. This work suggests that the
22
choice between market and limit orders depends on both traders’ private information and
market conditions, and that both order types can contain price relevant information. The
goal of our study is to evaluate these predictions. We examine the contribution of order
flow from market and limit orders as well as from limit orders of varying aggressiveness
to price formation in the foreign exchange market, both unconditionally and across
volatility states.
Using a short, but high quality, dataset of all submitted orders in the interdealer
DM-USD spot market, we find that, while the price effects of order flow from executed
market orders are largest, order flow from unexecuted limit orders also contains
significant price relevant information. Further, while proximal limit order flow has a
larger effect on prices than more distant limit order flow, the latter also significantly
moves prices. Finally, the relative importance of each order type depends on market
volatility. The price effects of all orders increase when volatility is high, but the effect of
limit orders, and especially of distant limit orders, increases by more than that of market
orders. As a sidelight, we document a negative relation between volatility and future
returns, one that is confined to the high volatility state and is consistent with carry trade
effects.
Thus, our results confirm the predictions from recent theoretical work. Informed
traders appear to use not only market orders but also all types of limit orders. Further,
they increasingly use limit orders, and less aggressive limit orders, as price uncertainty
rises and the insurance-like features of less aggressive limit orders become more
23
valuable.
Consistent with recent theoretical work, our analysis suggests that the
information environment influences informed traders’ order submission decisions.
24
References
Ahn, H., K. Bae and K. Chan, 2001, Limit Orders, Depth, and Volatility: Evidence from
the Stock Exchange of Hong Kong, Journal of Finance 56, 769-790.
Alizadeh, S., M. Brandt and F. Diebold, 2002, Range-based Estimation of Stochastic
Volatility Models, Journal of Finance 57, 1047-1089.
Anand, A., S. Chakravarty and T. Martell, 2005, Empirical Evidence on the Evolution of
Liquidity: Choice of Market Versus Limit Orders by Informed and Uninformed
Traders, Journal of Financial Markets 8, 289-309.
Bank for International Settlements, 1998, Triennial Central Bank Survey of Foreign
Exchange and Derivatives Market Activity.
Berber, A. and C. Caglio, 2005, Orders Submission Strategies and Information: Empirical
Evidence from the NYSE, unpublished working paper, University of Pennsylvania.
Berger, D., A. Chaboud, S. Chernenko, E. Howorka, and J. Wright, 2008, Order flow and
Exchange Rate Dynamics in Electronic Brokerage System Data, Journal of
International Economics 75, 93–109.
Bjønnes, G., C. Osler, and D. Rime, 2008, Asymmetric Information in the Interbank Foreign
Exchange Market, Norges Bank Working Paper 2008/25.
Bloomfield, R., M. O’Hara and G. Saar, 2005, The “Make or Take” Decision in an
Electronic Market: Evidence on the Evolution of Liquidity, Journal of Financial
Economics 75, 165–199.
Boehmer, E. and J. Wu, 2008, Order Flow and Prices, unpublished working paper,
University of Georgia.
Brandt, M. and K. Kavajecz, 2004, Price Discovery in the U.S. Treasury Market: The
Impact of Orderflow and Liquidity on the Yield Curve, Journal of Finance 59,
2623-2654.
Carlson, J. and M. Lo, 2006, One Minute in the Life of the DM/US$: Public News in an
Electronic Market, Journal of International Money and Finance 25, 1090–1102.
Cao, C., O. Hansch and X. Wang, 2009, The Informational Content of an Open Limit
Order Book, Journal of Futures Markets 29, 16-41.
Chordia, T., A. Sarkar and A. Subrahmanyam, 2005, An Empirical Analysis of Stock and
Bond Market Liquidity, Review of Financial Studies 18, 85-130.
25
Copeland, T. and D. Galai, 1983, Information Effects on the Bid-Ask Spreads, Journal of
Finance 38, 1457–1469.
Coppejans, M., I. Domowitz and A. Madhavan, 2001, Liquidity in an Automated
Auction, Unpublished working paper, Pennsylvania State University.
Dacorogna, M., R. Gençay, U. Muller, R. Olsen, and O. Pictet, 2001, An Introduction to
High-frequency Finance, Academic Press.
Dannıelsson, J. and R. Payne, 2002, Real Trading Patterns and Prices in Spot Foreign
Exchange Markets, Journal of International Money and Finance 21, 203–222.
Easley, D., S. Hvidkjaer, and M. O'Hara, 2002, Is Information Risk a Determinant of
Asset Returns?, Journal of Finance 57, 2185-2221.
Eisler, Z., J. Bouchaud and J. Kockelkoren, 2010, The Price Impact of Order Book
Events: Market Orders, Limit Orders and Cancellations, Unpublished working
paper, Capital Fund Management.
Ellul, A., C. Holden, P. Jain, and R. Jennings, 2007, Order Dynamics: Recent Evidence
from the NYSE, Journal of Empirical Finance 14, 636-661.
Evans, M. and R. Lyons, 2002, Order flow and Exchange Rate Dynamics, Journal of
Political Economy 110, 170-180.
Faust, J., J. Rogers, S. Wang and J. Wright, 2007, The High-Frequency Response of
Exchange Rates and Interest Rates to Macroeconomic Announcements, Journal of
Monetary Economics 54, 1051-1068
Foucault, T., O. Kadan and E. Kandel, 2005, Limit Order Book as a Market for Liquidity,
Review of Financial Studies 18, 1171-1217.
Foucault, T., S. Moinas, and E. Theissen, 2007, Does Anonymity Matter in Electronic
Limit Order Markets? Review of Financial Studies 20, 1707-1747.
Glosten, L. and P. Milgrom, 1985, Bid, Ask, and Transaction Prices in a Specialist
Market with Heterogeneously Informed Traders, Journal of Financial Economics
21, 123–144.
Goettler, R., C. Parlour and U. Rajan, 2005, Equilibrium in a Dynamic Limit Order
Market, Journal of Finance 60, 2149–2192.
Goettler, R., C. Parlour, and U. Rajan, 2009, Informed Traders and Limit Order Markets,
Journal of Financial Economics 93, 67-87.
26
Green C., 2004, Economic News and the Impact of Trading on Bond Prices, Journal of
Finance 59, 1201–1234.
Hall, A. and N. Hautsch, 2006, Order Aggressiveness and Order Book Dynamics,
Empirical Economics, 30, 973-1005.
Hasbrouck, J. and G. Saar, 2002, Limit Orders and Volatility in a Hybrid Market: The
Island ECN, Unpublished working paper, New York University.
Hautsch, N. and R. Huang, 2012, The Market Impact of a Limit Order, Journal of
Economic Dynamics and Control , 36, 501-522.
Hollifield, B., R. Miller, P. Såndas and J. Slive, 2006, Estimating the Gains from Trade in
Limit Order Markets, Journal of Finance 61, 2753-2804.
Kaniel, R. and H. Liu, 2006, So What Orders do Informed Traders Use, Journal of
Business 79, 1867-1913.
Lo, I. and S. Sapp, 2006, The Submission of Limit Orders or Market Orders: The Role of
Timing and Information in the Reuters D2000-2 System, Journal of International
Money and Finance 27, 1056–1073.
Lo, I. and S. Sapp, 2010, Order Submission: The Choice Between Limit and Market
Orders, Journal of International Financial Markets, Institutions and Money 20,
213-237.
Lyons, R., 1995, Tests of Microstructural Hypotheses in the Foreign Exchange Market,
Journal of Financial Economics 39, 321-351.
Lyons, R., 2001, The Microstructure Approach to Exchange Rates, The MIT Press,
Cambridge, Massachusetts.
Menkhoff, L., L. Sarno, M. Schmeling and A. Schrimpf, 2012, Carry Trades and Global
Foreign Exchange Volatility, Journal of Finance 67, 681-718.
Parkinson, M., 1980, The Extreme Value Method for Estimating the Variance of the Rate
of Return, Journal of Business 53, 61-65.
Pascual, R. and D. Veredas, 2010, Does the Open Limit Order Book Matter in Explaining
Informational Volatility?, Journal of Financial Econometrics 8, 57-87.
Pasquariello, P. and C. Vega, 2007, Informed and Strategic Order Flow in the Bond
Markets, Review of Financial Studies 20, 1975-2019.
27
Rock, 1996, The Specialist’s Order Book and Price Anomalies, Unpublished working
paper, Harvard University.
Rosu, I., 2009, A Dynamic Model of the Limit Order Book, Review of Financial Studies
22, 4601-4641.
Rosu, I., 2011, Liquidity and Information in Order Driven Markets, Unpublished working
paper, HEC Paris.
Sager, M. and M. Taylor, 2008, Commercially Available Order Flow Data and Exchange
Rate Movements: Caveat Emptor, Journal of Money, Credit and Banking 40, 583625.
28
Figure 1: Intraday patterns in order submissions
Figure 1 summarizes the orders submitted in the Deutschmark-U.S. dollar (DM-USD) interdealer spot
market for the week of October 6-10, 1997, obtained from Reuters. Orders are aggregated by hour to
illustrate time of day seasonalities in order submissions. Total submitted order volume is the total dollar
value of orders submitted in that hour across all five trading days. Market orders include market orders and
limit orders that are immediately executed. Panel A summarizes total submitted order volume by order
type and Panel B summarizes the proportion of submitted non-marketable limit orders according to
distance from the best price (in pips).
Total Submitted Order Volume (Million USD)
Panel A: Total daily volume of market and limit orders
30000
25000
20000
15000
10000
5000
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour
Limit Orders
Market Orders
Panel B: Relative dollar value of non-marketable limit order submissions sorted by distance from
the best price
100%
90%
80%
70%
60%
50%
6+ PIPS
40%
4-5 PIPS
1-3 PIPS
30%
20%
10%
0%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Hour
Table I: Descriptive statistics
Table I presents descriptive statistics for key variables, computed over 5-minute intervals in the DM-USD
interdealer foreign exchange spot market. The data are from the Reuters electronic brokerage system for
the week of October 6-10, 1997 and cover the period from 7:00 to 16:00 GMT. Return is calculated using
the bid-ask midpoints at the end of adjacent intervals. We consider five order imbalance variables, each
calculated as the difference between buy and sell volumes in a given 5-minute interval. OFM includes only
market orders and marketable limit orders, and OFL includes all limit orders placed away from the best
price on the opposite side of the limit order book. We further partition OFL based on order aggressiveness:
OFL1-3, OFL4-5 and OFL6+ include limit orders 1 to 3, 4 to 5 and 6 or more pips from the best price in the
book. Volatility is calculated as the logarithm of the ratio of the highest and lowest transaction prices in
each interval. Slope is calculated as
Variable
[
]
Mean
Median
Std Dev
Lower Quartile
Upper Quartile
Return
-5.39E-06
0.00
4.93E-04
-2.57E-04
2.56E-04
OFM
0.906
3.000
51.670
-29.000
31.000
OFL
5.629
4.000
64.716
-24.000
35.000
OFL1-3
0.596
2.000
29.759
-15.000
17.000
OFL4-5
-0.380
-1.000
22.492
-13.000
13.000
OFL6+
5.413
3.000
51.875
-11.000
18.000
Volatility
6.12E-04
5.12E-04
5.83E-04
3.41E-04
7.39E-04
Slope
6.84E-05
3.45E-05
1.20E-04
1.74E-05
6.95E-05
Table II: The price effects of market order flow
Table II presents results from the base model (4a) estimated over 5-minute intervals between 7:00 to 16:00
GMT each day in the DM-USD interdealer foreign exchange spot market during the week of October 6-10,
1997. The dependent variable is Return, calculated using the bid-ask midpoints at the end of adjacent
intervals. The independent variables include lagged returns, hour fixed effects, an indicator variable for the
surprise rate announcement on October 9, 1997 (Thurs) defined as one for the three hour period bracketing
the announcement (and otherwise zero), a range-based volatility measure and a slope measure of illiquidity
(both from the previous period), and contemporaneous market order flow (OFM), defined as the difference
between buy and sell volume for market orders and marketable limit orders in each interval.
Model 1
Variable
Model 2
Parameter
Estimate
T-stat
Parameter
Estimate
T-stat
Return t-1
-0.070
2.48
-0.070
2.57
Return t-2
-0.023
0.82
-0.038
1.39
Return t-3
0.017
0.62
0.001
0.05
Return t-4
-0.041
1.46
-0.039
1.46
Return t-5
-0.012
0.43
-0.019
0.68
Return t-6
0.024
0.86
0.015
0.57
Return t-7
-0.026
0.92
-0.023
-0.84
Return t-8
-0.009
0.32
-0.007
0.24
Return t-9
-0.026
0.92
-0.038
1.40
Return t-10
0.027
0.95
0.017
0.61
Return t-11
-0.007
0.24
-0.011
0.41
Return t-12
-0.030
1.05
-0.035
1.30
Thurs
-0.054
1.80
-0.018
-0.62
hour7
-0.007
0.20
0.011
0.30
hour8
0.011
0.31
0.024
0.67
hour9
0.003
0.09
-0.007
0.20
hour10
0.032
0.87
0.021
0.57
hour11
-0.039
1.03
-0.006
0.17
hour12
0.008
0.22
0.037
0.99
hour13
-0.048
1.33
-0.008
0.23
hour14
0.036
0.98
0.058
1.65
OFMt
0.771
27.10
0.757
27.48
Slopet-1
0.037
1.32
Volatilityt-1
-0.184
6.36
2
Adj R
0.59
0.62
Table III: The price effects of order flow partitioned by order type and volatility
Table III presents results from models (4a)-(4c) estimated over 5-minute intervals between 7:00 to 16:00
GMT each day in the DM-USD interdealer foreign exchange spot market during the week of October 6-10,
1997. Volatility is calculated as the logarithm of the high and low transaction prices in each interval. The
low and high volatility states are defined as intervals when lagged volatility is in its bottom and top tercile,
respectively. The dependent variable is Return, calculated using the bid-ask midpoints at the end of
adjacent intervals. The independent variables include the first lag of return, hour fixed effects, an indicator
variable for the surprise rate announcement on October 9, 1997 (Thurs) defined as one for the three hour
period bracketing the announcement (and otherwise zero), volatility and a slope measure of illiquidity (both
from the previous period), OFM, which includes order flow for market orders and marketable limit orders,
and OFL, which includes all limit orders placed away from the best price on the opposite side of the limit
order book. We further partition OFL based on order aggressiveness: OFL1-3, OFL4-5 and OFL6+ are order
flow for limit orders 1 to 3, 4 to 5 and 6 or more pips from the best price in the book.
Panel A: Market order flow
Base Model
Variable
Low Volatility
High Volatility
T-stat
1.36
Coef.
Dif.
0.090
0.884
18.52
0.382
3.97
3.37
0.036
0.44
0.059
0.97
0.79
-0.251
4.91
-0.079
0.19
Coef.
T-stat
Coef.
T-stat
Coef.
T-stat
Return t-1
-0.076
2.80
0.028
0.57
0.062
OFMt
0.761
28.09
0.502
9.99
Slopet-1
0.036
1.30
0.095
Volatilityt-1
-0.178
6.27
-0.172
2
Adj R
0.62
High – Low
0.41
1.04
0.70
Panel B: Market and limit order flow
Base Model
Variable
Low Volatility
High Volatility
T-stat
2.09
Coef.
Dif.
-0.105
1.014
25.10
0.407
4.49
0.531
9.79
0.351
3.81
3.58
0.095
1.43
-0.005
0.22
0.87
-0.285
6.96
-0.102
0.28
Coef.
T-stat
Coef.
T-stat
Coef.
T-stat
Return t-1
0.077
3.05
0.029
0.60
-0.076
OFMt
0.836
31.25
0.607
10.28
OFLt
0.234
8.76
0.180
3.18
Slopet-1
0.049
1.87
0.099
Volatilityt-1
-0.181
6.78
-0.183
2
Adj R
0.67
0.44
High – Low
0.81
1.37
Panel C: Market and limit order flow partitions
Base Model
Variable
Low Volatility
High Volatility
High – Low
Return t-1
-0.087
3.55
0.008
0.16
-0.083
2.12
Coef.
Dif.
-0.091
OFMt
0.864
29.30
0.614
9.70
1.001
19.31
0.387
3.95
OFL1-3,t
0.243
10.17
0.124
3.64
0.284
6.39
0.160
2.68
OFL4-5,t
0.166
5.64
0.071
1.53
0.220
3.90
0.149
1.92
OFL6+,t
0.085
3.45
0.025
0.32
0.348
5.29
0.323
2.59
Slopet-1
0.052
2.12
0.099
3.65
0.089
1.33
-0.010
0.29
Volatilityt-1
-0.174
6.87
-0.210
1.00
-0.277
6.69
-0.067
0.16
2
Adj R
Coef.
T-stat
Coef.
T-stat
Coef.
0.70
0.45
T-stat
0.81
T-stat
1.14