Intraday Predictability of Market Microstructure Statistics and
Technical Trading Rules
Lawrence Kryzanowski
Faculty of Commerce and Administration
Concordia University
Montreal, Quebec, Canada
Tel: (514) 848-2782, Fax: (514) 848-8645
E-mail: [email protected]
Feng Liu
Nanyang Business School (B2b-77)
Nanyang Technological University
Nanyang Avenue
Singapore 639798
Tel: (65) 799-1305, Fax: (65) 792-4217
E-mail: [email protected]
March 1997
Centre for Research in Financial Services
Working Paper No. 97-04
Financial support from FCAR (Fonds pour la formation de chercheurs et l'Aide à la
Recherche), and SSHRC (Social Sciences and Humanities Research Council of Canada) are
gratefully acknowledged. We are grateful for the research assistance provided by Pei Shuo
Chen. All remaining errors are the authors' responsibility.
Comments are welcomed.
Intraday Predictability of Market Microstructure Statistics and Technical Trading Rules
Abstract
The short-run predictability of price changes and quote revisions, using market
microstructure statistics and three popular technical trading rules, is examined using
intraday data. The average level and quality of traders' information is captured by price and
other microstructure variables (particularly volume and number of trades), respectively.
Historical trade information is useful in predicting current stock price movements and quote
revisions, and technical trading signals based on past price patterns have predictive ability
only for quote revisions. Very little incremental predictive power from adding technical
trading rule signals (such as moving average crossings, trading range breaks and relative
strength) to the prediction equation containing the market microstructure effects. Simulated
program trading based on technical trading rules is not profitable in the short-term.
Intraday Predictability of Market Microstructure Statistics and Technical Trading Rules
1. Introduction
Market statistics based on historical trades are found to be useful in predicting
future stock price movements. For example, Brown and Jennings (1989) and Grundy and
McNichols (1989) show that traders can discover the private information held by others by
using current and past prices in a rational expectations framework with aggregate supply
uncertainty, and Blume, Easley and O'Hara (1994) demonstrate that price and volume
together reveal all relevant information. Stickel and Verrecchia (1994) find that large price
changes tend to reverse on days with relatively weak volume support. This suggests that
higher volume reflects a greater likelihood that the demand originated from informed rather
than uninformed trades.1 Although Huang and Stoll (1994) find that five-minute quote and
transaction returns are more predictable when historical market microstructure statistics are
used instead of naive alternatives, most investors can not exploit this predictive power
because of transaction costs. Some other studies show that by capturing the characteristics
of the historical price path alone, various momentum indicators may play a significant role
in the formulation of potentially profitable trading strategies. For instance, Neftci (1991)
finds that the moving average method used by many technical analysts has some predictive
value for forecasts of the Dow-Jones Industrial Index beyond its own lags. Brock,
Lakonishok and LeBaron (1992) find strong support for technical strategies such as the
moving average and trading range break for the Dow Jones Index for the period from 1897
to 1986. The findings of these studies appear to be inconsistent with the efficient market
hypothesis.2 Discussions with professional traders on the exchange floor suggest that the
1
As Stickel and Verrecchia (1994) suggested, an interesting extension is to examine whether intraday volume
can predict subsequent intraday price changes, and yield profitable arbitrage opportunities.
2
The recent literature on market efficiency also suggests that stock returns may not be explained fully by
fundamentals and are predicable to a certain degree [e.g., see Shiller (1979, 1981), LeRoy and Porter (1981), De
Bondt and Thaler (1985), Fama and French (1986), Poterba and Summers (1988), Jegadeesh (1990), Lo and
MacKinlay (1990), Lehmann (1990), and French and Roll (1986)]. One potential explanation is market
inefficiency in which prices deviate from their fundamental values [Poterba and Summers (1988), Summers
(1986), and Shiller (1984)]. Another potential explanation is that markets are efficient, and the predictable
variation is due to time-varying equilibrium returns [Fama (1991) and Ferson and Harvey (1991)].
-1-
value of any exploitable market momentum is small and generally dissipated by the end of
a trading session (i.e., short-lived).
Technical analysis and market microstructure are related in at least four ways. First,
many investment professionals are technicians. All the major brokerage firms publish
technical commentary on the market and individual securities, and many newsletters are
technically oriented [Brock, Lakonishok, and LeBaron, (1992)]. Second, market quotations
are sensitive to irregular trading behaviors [Hasbrouck (1991a,b)]. Third, some stock price
changes are caused by "internal" news, which occurs when the market does an imperfect
job of revealing relevant information possessed by different investors, and when market
developments cause more information revelation [Romer (1993)]. Fourth, some traders use
technical analysis to update beliefs, especially for small, less-widely-followed stocks about
which they are relatively less well informed.
Given the paucity of published research on intraday performance of technical
analysis and the contradictory evidence on the predictability of intraday returns, this paper
examines the intraday predictability of price changes and quote revisions by using publicly
available information on quotation and trading history for individual stocks, and technical
trading rules on historical intraday price movements. The studied sample consists of the 35
stocks that constitute the Toronto Stock Exchange (TSE) 35 Index. The data are
summarized into 30-minute intervals over a one year period (1990.7 - 1991.6). We extend
previous work by using a more comprehensive information set of market microstructure
statistics to capture the quotation and trading behaviors of market makers and public
investors. Unlike previous studies, we assess the predictive power of market statistics, and
the addition of technical trading rules. To this end, we first formulate econometric
prediction models for quote revision and transaction price changes that reflect various
microstructure theories. The information set of market statistics includes the most
frequently used measures in the literature such as signed trading volumes, changes in the
number of trades, effective bid/ask spread, depth imbalance, heavy and thin trading
indicators, variables to examine the change in trading mechanism and week-end effect,3
3
The TSE opens with batch auction and switches to continuous trading for the reminder of the trading session.
The weekend effect is due to information gathering during this period of no trading.
-2-
and the 30-minute returns on TIPS to capture the co-movement of individual stock prices.4
The predictive ability of technical trading rules is investigated in isolation from
microstructure effects by using a market model plus the technical buy/sell indicators. The
incremental usefulness of technical trading rules is assessed by adding the technical buy/sell
indicators to the right-hand-side (RHS) of the basic prediction models that incorporate the
microstructure variables. We examine three popular technical rules; namely, the moving
average, trading range break, and relative strength.
Another interesting issue examined in this paper is the relationship between the
market microstructure variables and the technical trading rules based on historical price
series, i.e., what market momentum looks like at the time point when the buy or sell
signals are triggered from the price series. This is important since the technicians and most
of the professional traders use the trading activity measures such as trading volumes,
number of trades, bid-ask spreads and depths as support or confirmation to the buy or sell
indicators. A cross-sectional analysis of intraday changes in microstructure variables around
technical buy or sell signals is conducted. If the studied trading rules lack predictive power,
no significant changes in market momentum are expected in the pre- and post-signal
periods. The returns on a simulated program trading strategy based on technical trading
rules for 1, 2 or 5 day “round-trip” trades are tested to determine if they are significantly
differently from zero and market return, respectively. The tests examine the validity of the
popular market saying: "long-term fundamental, short-term technical".
The empirical results indicate that an examination of market statistics is better for
predicting quote revisions than transaction price changes. Quote revisions are affected
significantly by previous trading activities and the trend in market co-movement, which
implies an adverse selection effect. In contrast, transaction price changes are due mainly to
the bid-ask bounce effect of previous trades and the information effect of previous quotes.
These findings are consistent to with those of Huang and Stoll (1994) for U.S. data. The
impact of the trading mechanism switch and the weekend effect are not significant on
average, although some stocks exhibit significantly negative quote revision and transaction
price changes. When microstructure effects are ignored, the three technical trading rules
4
TIPS (TSE 35 Index Participations) is a traded security on the Toronto Stock Exchange, whose price is the
weighted average of the market values of the stocks comprising the TSE 35 Index. The units (or shares) of TIPS
-3-
appear to have certain short-term predictive ability for quote revisions. The results are
consistent with the theoretical predictions of Brown and Jennings (1989) and Grundy and
McNichols (1989), and with the empirical findings of Neftci (1991) and Brock et al (1992)
for U.S. market. When microstructure effects are considered, the addition of technical
trading rules has limited incremental predictive power over the very short term. This
implies that the historical market statistics of market momentum are more important than
the past price pattern for capturing future stock price movements.
Based on the cross-sectional analyses for buy and sell signal “events”, technical
analysis consistently and accurately reveals what has happened in the market, but has very
limited power in predicting future short-run stock price movements. This supports the
conjecture of Blume, Easley and O’Hara (1994) that technical analysis of only price
statistics cannot reveal all the relevant information, and that other microstructure statistics
such as trading volume may improve the information quality and may help in explaining
stock price changes. The simulated program trading strategy based on the technical buy and
sell recommendations are found not to be profitable. Since one-, two- and five-day returns
and abnormal returns for both limit- and market orders after buy signals are less than 1%,
they are not economically significant given reasonable transaction cost estimates.
While technical analysis extracts information from historical trading price changes,
the public traders and market makers react quickly to reflect that information. Since the
market is very efficient in response to whatever information is generated and technical
analysis only reveals what has happened, profits are not earned by exploiting technical buy
and sell signals. In fact, technical trading signals are not true information events and are
generated only when the prices break certain limits, since they are triggered by price
changes caused by information or liquidity trading. Therefore, real information events
precede (not follow) technical trading signals. It might be true that the practitioners who
claim they rely on the technical analysis maybe in fact rely on market microstructure effects.
The remainder of this paper is organized as follows: In the next section, the market
structure and the data are described. In section 3, the empirical models are specified, the
estimation methodology is discussed and the empirical results are presented and analyzed.
Section 4 concludes the paper.
can be converted proportionally into the shares of the 35 stocks under certain regulations.
-4-
2. The Market Structure and The Description of the Data
The TSE is a continuous auction market where the Registered Traders function like
specialists on the NYSE, but have less monopoly power and face more restrictions.
Compared to pure dealership markets, such as NASDAQ or the International Stock
Exchange (London) where public investors submit orders to and trade with multiple
competitive market makers directly and immediately, traders on the TSE can submit their
limit orders to the Limit Order Trading System (LOTS) to compete with the Registered
Traders' quotations. Unlike the NYSE where only the specialist has monopolistic access to
the limit order book, all market participants on the TSE have access to LOTS, market
quotes and to transaction information on a real-time basis. The orders to buy and sell stocks
from the investing public are "matched" with the best market quotes or with other
concurrently arriving market orders. The best market quotations are the result of
competition of public limit orders of traders (entered through the LOTS) with Registered
Trader's quotations. Each stock listed on the TSE is assigned to a Registered Trader, who
has the responsibility to maintain an orderly and continuously liquid market at minimum
spread in return for the privilege of trading for his own account. The Registered Trader
also posts the sizes for each quoted price on an ongoing basis to provide investors with an
indication of market depth. This kind of market structure is similar to a “free entry” market
making dealership market [Madhavan (1992)].
For each stock in the TSE 35 index, time-stamped trades (to the nearest second),
trade size, and bid/ask quotes are drawn from the TSE transaction database for the period 1
June 1990 to 30 June 1991. (See Table 1 for details about the TSE 35 Index composition
for July 1990.) During the sample period, four of these stocks (CAE Industrials, Sears
Canada, Southam Inc. and The Thomson Corporation) traded on the Computer Assisted
Trading System (CATS), and the rest traded on the floor.5 Stock prices are adjusted for
dividend distributions at the openings of the ex-dividend dates.6 Since data for the first
5
The TSE was the first exchange to offer fully automated stock trading through CATS in 1977 and has been
exported to Paris, Madrid, Brussels, Sao Paulo and Tokyo. The CATS has been developed in parallel to the
existing floor system and has been used primarily for less actively traded securities on the TSE (about 1/3 of all
listed stocks currently trade on CATS).
6
None of the 35 stocks split during the sample period from 1990.6.1 to 1991.6.30.
-5-
month are used to generate the technical signals, the sample for estimation and test is from
1990.7.1 to 1991.6.30 (a total of 3276 intervals).
[Insert Table 1 About Here.]
Similar to Lee, Mucklow and Ready (1993) and McInish and Wood (1992) where
30-minute intervals are used for NYSE stocks, the data are summarized into 13 30-minute
intervals for each trading day (9:30 AM to 4:00 PM). This is based on an examination of
the trading and quotation frequencies for the sample stocks, and the proportion of no
trading periods for various calendar time interval lengths. Based on Table 2, 14.7% of the
intervals are still no trading periods on average for the 30-minute intervals. The range is
from 0.31% for B to 52.35% for SCC. 7
[Insert Table 2 About Here.]
The transactions for each interval are aggregated as if they were one trade at a
transaction price ( Pt ) equal to the average price of all trades within the interval, and at a
trade size ( VOLt ) equal to the total trading volume of all trades within the interval.
Average price is statistically superior for reflecting price information for all trades than
any single point price such as the closing price. Total volume is a superior proxy of trade
size than average volume because total volume reflects the total number of shares traded
during the interval, and trading frequency is measured by the number of trades in each
interval ( NTt ). Thus, the measures of three dimensions of trade activity (average price,
total trading volume, and number of trades) reflect more information than the two
dimensions commonly used in the literature (namely, average or close price and volume).
The last rather than the average quotation is used to capture the most recent
information about quote behavior, because quotes reflect information only from one side of
the market (the market maker or the limit orders). Bt and At are the last bid and ask prices
for interval t, respectively. DBt and DAt are the quoted depth (size) of the last bid and the
last ask for interval t, respectively. Since quoted orders become trades once crossed with
market orders, information contained in the quotes within an interval are reflected in the
trade measures. Thus, the last quote is the most updated quote immediately after the last
trade within the interval.
-6-
A sequence of trades and quotes is characterized as follows: If the transaction at t
occurs after the closing quotation at t-1 or the opening quotation at t, then the quotation at t
is adjusted after the transaction at t. Therefore, a trade occurs ahead of a quote for the same
subscript t for all periods. If no transaction occurs in the interval t, VOLt = NTt = 0. Also,
since Pt = Pt-1 , the price change ∆Pt = Pt - Pt-1 = 0, based on the assumption that the
absence of trading implies an unchanged price. If no new quotations occur in the interval t,
Bt = Bt-1, At = At-1, DBt = DBt-1, DAt = DAt-1, and their respective changes are all equal to
zero.
After opening with a batch auction, the TSE like the NYSE switches to continuous
trading for the remainder of the trading session. French and Roll (1986) find that stock
prices are more volatile when the market is open. Amihud and Mendelson (1987) find that
opening returns exhibit greater dispersion, greater deviations from normality, and a more
negative and significant autocorrelation pattern than closing returns. These results suggest
that the no trading overnight period increases uncertainty or price volatility, while trading
reduces price volatility. Three dummy variables (TOt, TCt and QOt ) are used to measure
differential effects at the opening, and in closing trades and opening quotes, respectively.
Two dummy variables (MTOt and MQOt ) are used to measure differential effects on
Monday opening trades and quotes, respectively.
Basic statistics about the trade and quote variables are given in Table 2. The average
transaction price for 35 stocks is C$22.36, which is very close to average quote mid-point
price of C$22.37. The 30-minute average transaction return is -0.0004%, which is higher
than the average quote mid-point return of -0.0015%.8 The average trading volume is
16,720 and the average number of trades is 10.22 trades. The no trading periods average
483 out of the 3276 intervals.9 The average depth is 396 board lots (where one board lot
equals 100 shares) and the average quoted bid-ask spread is C$0.1546. The spread tends to
7
Trading frequencies of even actively traded stocks on the TSE are not as smoothly continuous as is assumed
in most of the theoretical models. When too many no trading periods exist in a time series, difficulties occur in
extracting the real relationship among variables.
8
The differences between quote and transaction returns are not statistically significant (t-value of 0.5461).
The minor differences for some individual stocks is probably due to various microstructure effects such as bid/ask
bounce and asymmetrical trade direction. No reason exists to believe that this is due primarily to the data
aggregation procedure.
9
Based on an examination of trading volume, number of trades and no trading periods, four stocks traded on
CATS are less actively traded compared to the others in the sample.
-7-
be positively related to transaction price. An average of 104 out of 3276 intervals have
transaction prices equal to the prior mid-point quote.
The intraday patterns of price changes, quote revisions, depth imbalance, trading
volume, number of trades, and signed trading volume are similar to those reported in the
literature.10 For example, price changes and quote revisions have similar intraday patterns,
with a significantly negative average return in the first 30-minute interval of each day and a
positive average return in the last 30-minute interval of each day. Depth imbalances are
negative in all 30-minute intervals of a day, and gradually increase during the day. This
suggests that depth in bid dominates depth in ask on average, and that the differences
decline over the day for the sample studied herein. Both trading volume and number of
trades show a intraday U-shape, which indicates that trading is more active during the
opening and the closing intervals (especially the opening). Average signed trading volume
is positive for the opening interval, and negative for the closing interval. This suggests
that, on average, buy-initiated trades dominate at the open and sell-initiated trades dominate
at the close.
3. Model Specification and Empirical Findings
3.1 The Empirical Market Microstructure Models
The basic model is a simple conditional expectation model for returns, ~r t , given
by:
~
~ = E( ~ |
rt
r t Φ t -1 ) + ε t .
(1)
where E( ~
r t | Φ t -1 ) is the expected return at t conditional on all available public information,
~
~
Φt-1 ; and ε t is the error term such that ε t ~ N(0, σ2). In the random walk model, market
efficiency implies that the best forecast (or expectation) of the current return rt is rt-1; that
is, E( ~
r t | Φ t -1 ) = rt-1. Any information not included in Φt-1 is redundant because rt-1 already
reflects all the information available at t-1.
Versions of this model can be specified for various information sets of historical
information. If the set is confined to historical transaction prices, then (1) becomes the
10
The plots of the intraday patterns of the microstructure variables are available upon request.
-8-
autoregression (AR) model used by De Bondt and Thaler (1985), Fama and French (1986),
Poterba and Summers (1988), Jegadeesh (1990), Lo and MacKinlay (1990), Lehmann
(1990), French and Roll (1986), among others, to test the serial correlation in returns of
individual stocks and portfolios over periods with daily, weekly, monthly, annual, and
multi-year intervals. If Φt-1 includes additional information about historical trading activities
(such as trading volume, number of trades, bid/ask quotations and depths), then (1) can be
specified as a multi-autoregression model. E( ~r t | Φ t -1 ) is more accurate in predicting price
changes, if such information is not perfectly correlated. Versions of this model can also
incorporate the regularity of trading activity. Large stock price changes may be due to
information events which can be proxied by unexpected trading volume, heavy or thin
trading, switch of trading mechanism (e.g. from auction at market open to dealership
thereafter), and market momentum.
Madhavan and Smidt (1991) use a Bayesian model to test intraday security price
movements on the NYSE. They find strong evidence for information asymmetry as
perceived by the specialist, and that prices respond differently for large-block trades
relative to smaller trades, and for buyer-initiated trades relative to seller-initiated trades.
Huang and Stoll (1994) develop a two-equation econometric model of quote revisions and
transaction returns to identify the relative importance of different microstructure theories,
and to make predictions on the short-run behavior of stock returns. They find that fiveminute transaction returns react negatively to trade price deviations from the quote
midpoint in the prior period, which reflects an attenuated bid-ask bounce to compensate
market makers for order processing costs. Quote revisions react positively to the same
variable, which reflects the adjustment of quotes to the private information contained in the
prior trade. Quote and price returns tend to be negatively related to prior depth imbalance
(i.e., ask depth greater than bid depth). Huang and Stoll argue that since their model is
successful in making out-of-sample predictions compared to naive alternatives, it is
inconsistent with the efficient market hypothesis. However, the predictive power of their
model may be due to the use of past stock index futures returns in their model.
Furthermore, most investors would have difficulty exploiting this predictive power because
of transaction costs.
Similar to Huang and Stoll (1994), the first variant of (1) can be specified as:
-9-
rq,t = a0 + a1 rTIP,t + a2 zt + a3 SXt + a4 RNTt + a5 RHTt + a6 RTTt
+ a7 rq,t-1 + a8 DIt-1 + a9 QOt + a10 MQOt + ut.
(2)
where rq,t is the quote mid-point return (revision); rTIP,t is the 30-minute return on TIPS
designed to capture cross-stock (market) price co-movement; zt is one-half of the effective
spread as given by pt - qt-1;11 SXt is the signed square-root trading volume at time t based
on the transactions immediately before the quote revision at time t; RNTt is the change in
total number of trades in interval t; RHTt (RTTt ) is the indicator of Relative Heavy (Thin)
Trading;12 DIt is the imbalance of depth (the immediate market supply at ask over bid) as
measured by DAt - DBt; QOt is a dummy variable for the open quote; MQOt is a dummy
variable for the open quote on Monday in order to capture the weekend effect; and ut is the
disturbance term which measures the public information unreflected in the trade and quote
revision history.
The quote mid-point is normally taken as the market consensus price because of the
impact of transaction costs on transaction price. The lagged returns on TIPS account for
market co-movement to public information. One-half the effective spread captures the
location of transaction price at t relative to the prior quote mid-point. A positive (negative)
value of this measure indicates a trade closer to the ask (bid) than the bid (ask). According
to Huang and Stoll (1994), the influence of zt-1 on quote revision reflects the impact of the
preceding price deviation, which is the expected value of the private information revealed
through trading [Glosten and Milgrom (1985)]. RHTt and RTTt are used to measure the
impacts of extreme trading activities on quote revision, where revision is upwards if heavy
trading reflects private information, and insignificant otherwise. The specification is
restricted to one lag because experimentation indicates that more distant lags provide little
additional explanatory power [as in Huang and Stoll (1994)].
The second variant of (1) is based on the transaction price change prediction model:
pt = qt-1 + zt,
rp,t = rq,t-1 + zt - zt-1.
11
The term pt is the log transaction price of ln Pt and qt is the log quote mid-point given by ln[(Bt+At )/2].
RHTt (RTTt ) = 1 if VOLt is among the top (bottom) 10% trading volumes over the past month (260
intervals of 30 minutes), and RHTt (RTTt ) = 0, otherwise. RTTt also equals 1 when VOLt = 0 (a no trading
interval).
12
- 10 -
If zt is serially dependent and zt = ρ zt-1 + et captures inventory effects, where et is the
order arrival shock, then:
rp,t = rq,t-1 +(ρ - 1) zt-1 + et.
(3)
Combining (2) and (3) yields:
rp,t = a0 + a1 rTIP,t-1+ (a2 + ρ - 1) zt-1 + a3 SXt-1 + a4 RNTt-1 + a5 RHTt-1 + a6 RTTt1
+ a7 rq,t-2 + a8 DIt-2 + a9 QOt + a10 MQOt + et + ut-1.
(4)
Adding the observable rq,t-1 and DIt-1, and dummy variables of market open (TOt ), close
(TCt ) and Monday Open (MTOt ) to the RHS of (4) gives:
rp,t = b0 + b1 rTIP,t-1 + b2 zt-1 + b3 SXt-1 + b4 RNTt-1 + b5 RHTt-1 + b6 RTTt-1
+ b7 rq,t-1 + b8 DIt-1 + b9 TOt + b10 TCt + b11 MTOt + vt.
where vt is the disturbance term to capture the public information unreflected in the trade
and quote revision history.
Equations (2) and (5) cannot be jointly tested because there is a time lag between
quote and trade variables. Microstructure theory predicts that rq,t is positively related to zt-1
because it captures the information effect associated with trade, that rp,t is negatively related
to z t-1 due to the bid-ask bounce effect designed to compensate market makers for incurred
trading costs; that rq,t and rp,t are positively related to the information effects of trading SXt
or SXt-1, RNTt or RNTt-1, and RHTt or RHTt-1, and not significantly related to RTTt and RTTt-1
due to the lack of information [Easley and O'Hara (1992a,b)]; and that rq,t or rp,t should be
negatively related to DI t-1 to reflect an information effect from previous quote depth. An
inventory effect predicts a positive impact of DIt-1 on rq,t or rp,t, based on the assumption
that both quote level and depth are adjusted to facilitate transactions that equilibrate
inventory. The probability of a positive return from t-1 to t increases if a market maker
who has a large inventory at t-1 simultaneously lowers quote level and raises depth at ask
- 11 -
(5)
to attract buyers [Huang and Stoll (1994)].
Equations (2) and (5) are estimated using OLS with White (1980) heteroscedasticconsistent standard errors and variance. As reported in Tables 3 and 4, respectively.13
Their average adjusted R2 are 44.68% and 27.43%, respectively. The predictive powers
improve significantly for both quote revision and price changes when information contained
in market microstructure statistics is considered. In contrast, for a simple market model,
the average adjusted R2 is 2.4% for quote revision and 0.4% for price changes. The past
returns on TIPS are significantly and positively related to both current quote revisions and
price changes. On average, 7% of quote revisions and 3.5% of price changes are explained
by the previous returns on TIPS. This indicates that quote revisions are more highly related
to market co-movements than transaction prices (due to transaction costs).
[Insert Tables 3 and 4 About Here]
The past effective spread measure zt (or zt-1 ) is significantly and positively related to
current quote revision rq,t, and significantly and negatively related to the current transaction
price change rp,t [as in Huang and Stoll (1994)]. On average, 48.41% of the deviation of a
transaction price from the quote mid-point is reflected in a change in the quote mid-point in
the next interval. This suggests an information effect of prior transaction price to the next
quote revision. The average coefficient of -0.7114 indicates that 71.14% of the price
deviation from the quote mid-point in this interval is reversed in the next interval. This
reflects an attenuated bid-ask bounce effect since a coefficient of -1 reflects a full reflection
of the bid-ask bounce.
The information effect of prior trade is much stronger on current quote revisions
than on current price changes. Past signed square-root trading volume is significantly and
positively related to rq,t and insignificantly related to rp,t on average. Past changes in
number of trades are insignificantly related to both rq,t and rp,t on average. Of the 35
stocks, 15 exhibit a significantly positive relationship in the quote revision models. This
implies that trading volumes are more dominant in affecting quote revisions than number of
trade changes. Past relatively heavy (thin) trading indicators are not significantly related to
both rq,t and rp,t on average. This suggests that irregular trading activities have very
limited information content for both quote revision and price changes. Thirteen out of the
13
The estimation results for the four CATS traded stocks are not reported separately since they are not
significantly different from the rest of the sample.
- 12 -
35 stocks have a significantly positive relationship between RTTt and rq,t and 10 have a
significantly negative relationship between RTTt-1 and rp,t. This implies that quote levels
tend to be raised and transaction price tends to increase if no or thin trading occur in the
previous period.
Past quote revisions are insignificantly related to current rq,t (but significantly and
negatively related for 12 stocks), and significantly and positively related to current rp,t on
average. The former indicates a reverting behavior for quote revisions so that market
makers can recoup their inventory and trading costs. The latter indicates a strong impact of
quote revision direction on the next transaction. This implies strong predictive power for
prior quote revisions in tracking stock price movements (about 72.5% of price changes are
explained by past quote revisions on average). Previous depth imbalances are significantly
and negatively related to both current rq,t and rp,t. This is consistent with the information
effect and not the inventory effect hypothesis. If depth at the ask exceeds depth at the bid,
declared sellers exceed declared buyers. This drives quote and price returns to be negative
over the next interval (i.e., selling pressure pushes prices down).
With regard to the impact of the trading mechanism and the weekend effect, both rq,t
and rp,t are not significantly different on average for daily openings or closings or Monday
openings. Nevertheless, 13 and 8 stocks for rq,t and rp,t, respectively, have significantly
lower returns at daily openings, and 13 stocks for rp,t have significantly higher returns at
daily closings. These results suggest that both trading mechanism and weekend effects have
a weak average effect on both rq,t and rp,t.
3.2 The predictive Ability of Technical Trading Rules
Technicians study historical trading patterns because they believe that the current
stock price does not immediately reflect all information shocks (unexpected events). Given
that different investors react differently to news due to their different time horizons, a news
event may not be absorbed by the market instantaneously. In such cases, prediction is
possible for as long as the market takes time to absorb the event and its secondary effects.
Brown and Jennings (1989) and Grundy and McNichols (1989) use rational expectations
models in which a single price does not reveal the underlying information but a price
sequence does. Both papers show that traders can discover private information held by
others by using current and past prices. Some empirical support also exists for the technical
- 13 -
analysis of prices. Neftci (1991) finds that the moving average method has some predictive
value for changes in the value of Dow-Jones industrials beyond its own lags. Brock,
Lakonishok and LeBaron (1992) find strong support for technical strategies such as the
moving average and trading range break for the Dow Jones Index from 1897 to 1986. They
obtain non-consistent results from these strategies with four popular null models: random
walk, the AR(1), the GARCH-M, and the Exponential GARCH.
Only a few of the methodologies frequently used by technical analysts are pure
"Markov time" efficient, and most signals cannot be fully determined from historical
information [Neftci (1991)]. Three technical indicators of market sentiment, which can be
mathematically formulated and give clear signals, are used herein to test their ability to
forecast future price movements. They are the moving average, trading range break, and
relative strength index.
Buy and sell signals for the moving average method are generated by searching for
crossings in two moving averages; one for a longer period (n), and one for a shorter period
(m), where n > m. Let:
Zt =
1
n
n -1
Σ
s= 0
P t -s−
1
m
m -1
Σ
s= 0
P t - s = P n,t - P m ,t
Then, signals: τi = inf {t: t > τi-1, ZtZt-1 < 0}, where τ0 = 0, Pt-s is the 30-minute stock
price at period t-s.
Three pairs of moving average (MA) crossing buy (B) and sell (S) indicator
variables are used herein.14 MAkjt refers to a moving average crossing buy signal if k = B
and sell signal if k = S based on a comparison of a daily (m = 13) and a weekly (n = 65)
price average if j = 1, on a comparison of a daily (m = 13) and a monthly (n = 260)
price average if j = 2, and on a comparison of a 30-minute (m = 1) and a monthly (n =
260) price average if j = 3. The dummy variables for the moving average crossing buy and
sell indicators are set as follows ( j = 1,2,3 ):
- 14 -
MABjt = 1 when Pm,t > Pn,t 1and Pm,t -1 < Pn,t -1 2,
= 0 otherwise ;
MASjt
= 1 when Pm,t < Pn,t 3and Pm,t -1 > Pn,t -1 4,
= 0 otherwise.
The buy and sell signals for the two pairs of Trading Range Break indicators are
generated as stock prices hit local highs or lows by setting the locals as weekly and
monthly, respectively. The dummy variables for these buy (sell) indicators are set as:
TRBBjt (TRBSjt ) = 1
=0
if Pt > Max ( Pt-1 , ..., Pt-s ) [Pt < Min ( Pt-1 , ..., Pt-s )],
otherwise .
TRBB1t (TRBS1t ) is the weekly ( j = 1 ) indicator if s = 65 ; and TRBB2t (TRBS2t )
is the monthly ( j = 2 ) indicator if s = 260 .
The relative strength indicator (RSI) measures the relationship between the sum of
the price increases during a given period (for example a day or a week) and the sum of the
price decreases during the same period. This momentum measure examines the relative
strength of positive over negative price changes rather than providing clear-cut buy or sell
signals. The measure is formulated as ( j = 1, 2 ):
RSIjt = 100 −
200

1 +  ∑ ∆Pt +− s
 s=0
S −1
S −1
∑ ∆P
s= 0
−
t −s



where Σ∆P+t-s (∆Pt-s = Pt-s - Pt-s-1 > 0 ) is the sum of the positive price changes and Σ∆P -t-s
(∆Pt-s = Pt-s - Pt-s-1 < 0 ) is the sum of negative price changes over one day ( S = 13 and s
= 0, ..., 12 ) or one week ( S = 65 and s = 0, ..., 64 ). If Σ∆P -t-s = 0, RSIjt is set to
100; RSIjt = -100 if Σ∆P+t-s = 0; and RSIj t = 0 if Σ∆P+t-s = Σ∆P -t-s ≠ 0.
14
There are no well established industry standards in choosing n and m. The most popularly used moving
average signals by public traders for the short-term are generated by daily/weekly or daily monthly moving
average price crossings.
- 15 -
Therefore, -100 ≤ RSIjt ≤ 100. No relative strength of positive over negative price changes
occurs over the past specified period if the indicator equals 0. It is expected that positive
(negative) RSI should be followed by positive (negative) price changes.
The predictive ability of the technical trading rules for future price movements is
tested by using a market model plus a series of lagged dummy buy and sell indicators
formulated by each of the three trading rules for several past periods ( j = 1, 2, 4, 6, 13. ).
Both rq,t and rp,t are expected to be positive and negative with past buy and sell indicators,
respectively.
The empirical results are reported in Tables 5 and 6. Almost all the technical
trading rules have significant predictive powers for quote revisions, but do not have
significant predictive ability for price changes (the trading range break indicator is an
exception). The adjusted R2 for the market model plus technical indicators are significantly
improved (from 2.4% to 7% on average for quote revisions, and from 0.4% to 1.85% for
price changes on average). The first lagged moving average (half-hour/monthly crossings),
trading range break buy (sell) indicators and relative strength indicators are significantly
and positively (negatively) related to current quote revisions. The first lagged moving
average buy (sell) indicators and relative strength indicators are negatively (positively) and
insignificantly related to current price changes. The first lagged trading range break
indicators are positively (negatively) related to current price changes, but are only
significant for 16 out of 35 stocks on average. These results suggest that the information
revealed from past price patterns has strong predictive ability for quote revisions but not
transaction price changes. Trading range break appears to be promising of the trading rules
examined herein. These results support Brown and Jennings (1989) and Grundy and
McNichols (1989) that traders can discover the private information held by others by using
current and past prices, and are consistent with the empirical results by Neftci (1991) and
Brock et al (1992) for the Dow Jones Index.
[Insert Tables 5 and 6 About Here]
3.3 The Prediction Models with Microstructure Effects and Technical Trading Rules
Kyle (1985) using an auction model and Glosten and Milgrom (1985) using a
sequential model for a dealership market argue that, since long-lived information is
gradually incorporated into prices, past prices or order flow are informative. Blume, Easley
- 16 -
and O'Hara (1994) show that in a standard rational expectations framework with aggregate
supply uncertainty, price and volume together reveal all relevant information. If price is not
revealing, then volume may provide information not incorporated in price. This suggests
that various momentum indicators may capture the characteristics of the historical price
path, and therefore play a significant role in formulating potentially profitable trading
strategies.
The joint effects of microstructure statistics and technical trading rules are tested by
adding the technical indicators to the RHS of equations (2) and (5). If buy (sell) signals can
still reveal good (bad) news after controlling for the information revealed by the market
statistics, then quote revisions and price changes should react positively (negatively) to
these buy (sell) indicators. Based on the results reported in Tables 7 and 8, the technical
trading indicators generally are not significant in predicting quote revisions and price
changes beyond the microstructure variables already considered. Exceptions include four
first lagged trading range break indicators for predicting quote revisions. A significant and
positive (negative) relationship exists between TRBB1t or TRBB2t (TRBS1t or TRBS2t ) and
current quote revisions. This implies that only the trading range break signals capture
information not reflected in other past trading activity measures for price movement. This
suggests that the predictive ability of technical trading rules based on historical price series
disappears after controlling for the information revealed by the microstructure variables.
These variables appear to already reflect the information that technical analysis tries to
reveal. The sole exceptions are the trading range break signals for predicting quote
revisions.
[Insert Tables 7 and 8 About Here]
3.4 Cross Sectional Analysis of the Technical Signals
By treating the technical buy and sell signals as events, event study methods are
used to investigate the significance of such technical signals on subsequent stock price
movements and six microstructure variables: VOLt, NTt, rp,t, rq,t, RSt and DIt. The means
and standard deviations of each variable in the pre- and post- signal panes of the two days
(26 half-hour intervals) are compared and tested using t- and sign-tests (the total window
- 17 -
length is 53 half-hour intervals).15 Trading volumes and numbers of trades are expected to
increase after both buy and sell signals are triggered, if traders believe that such signals
reveal information. Price changes and quote revisions are expected to be higher (lower)
after buy (sell) signals are triggered, if traders and market makers believe that such signals
reveal good (bad) news. The relative spread is expected to be smaller (larger) after buy
(sell) signals are triggered, if market makers believe that such information is now public.
Depth imbalances are expected to decrease (increase) if market makers believe such buy
(sell) signals reveal good (bad) news based on an adverse selection motive. Depth
imbalances are expected to increase (decrease) if market makers believe such buy (sell)
signals result in more buy- (sell-) initiated trading based on liquidity needs.
Table 9 presents the results of a cross sectional analysis of the behavior of six
microstructure variables around technical signals.16 The signals are generated for the 35
stocks over the one year time period. The 26-interval (two trading day) mean transaction
price returns and mean quote returns post-buy (sell) signals are significantly lower (higher)
than the 26-interval mean price returns and quote returns pre-buy (sell) signals for all
indicators but MAB3 and MAS3. The 26-interval accumulated transaction price returns and
quote returns pre- and post-signal exhibit a similar pattern. This suggests that the technical
signals give contrarian recommendations. Lower average (or total) two-day returns occur
post-buy signal than pre-buy signal if stocks recommended by the buy signals are
purchased. Higher average (total) two-day returns occur post-sell signal than pre-sell signal
if stocks recommended by the sell signals are not sold.
Panels A and C in Figure 1 give the plots of the intraday distributions of mean
price changes and quote mid-point returns around buy and sell signals, respectively. The
four-day accumulated returns are also plotted on the same diagram. Significant breaks
occur for both rq,t and rp,t in the intervals four hours before and three hours after the buy
or sell signals are generated. The mean transaction price changes and quote returns are
higher (lower) during this period than other periods. The plots confirm the results of the
previous statistical tests, since higher (lower) returns for both trades and quotes appear
15
The t-test requires a normal distribution, while the nonparametric sign-test is distribution free assuming the
median is zero.
16
The tests are conducted only for those technical analysis methods which generate clear-cut buy or sell
signals (i.e., moving average crossings and trading range breaks in this study). The relative strength index, which
is scaled from -100 to 100, measures relative market momentum, and does not give clear-cut buy or sell signals.
- 18 -
before the buy (sell) signals rather than after the signals. This is as expected since technical
analysis is just a study of historical patterns of price movements. While its underlying
premise is that recent historical abnormal price changes reveal information, and that the
future direction of such changes is expected to be unchanged, this does not hold in an
efficient stock market.
[Insert Table 9, and Figure 1 About Here]
The volatility of price and quote returns in the post-signal periods are significantly
higher than in the pre-signal periods for all buy and sell signals, with the peaks occuring
about three hours post-signal (Panels B and D of Figure 1). The volatility around sell
signals is higher than around buy signals, probably due to the sensitivity of investors to
price decreases. The 26-interval means and standard deviations of trading volumes and
number of trades post-signal are significantly higher than those pre-signal for most buy and
sell signals (see Table 9).17 The heavy trading volume and number of trades occur most
frequently around the signal intervals, and peak about 2.5 hours post-signal (see Panels A
and B in Figure 2). This is consistent with the information hypothesis in which the market
reacts to the information that triggers the technical signals.
[Insert Figure 2 About Here]
The quote variables react differently to buy and sell signals. The 26-interval means
of relative quoted spreads post-signal tend to be significantly narrower (wider) than presignal for most buy (sell) signals.18 The volatility of relative spreads post-signal are
significantly lower (higher) than those pre-signal for only trading range break buy (sell)
signals TRBB1, TRBS1 and TRBS2. This suggests that market makers react differently to
the good and bad news revealed by technical analysis. Since good news is less risky, they
increase the spread after a sell to protect themselves from trading against the public, and
decrease the spread after a buy signal to stimulate trading. This is shown by the distribution
plots in Panel A of Figure 3.
[Insert Figure 3 About Here]
The means and standard deviations of depth imbalance are not significantly different
17
Means and standard deviations of trading volume post-signal are not significantly different from those presignal for MAS1, MAS2 and TRBS1. Means and standard deviations of number of trades post-signal are not
significantly different from those pre-signal for MAS1 and MAS2 (standard deviation only for TRBS2).
18
The differences for MAB3 and MAS3 are not significant.
- 19 -
in the post- and pre-signal periods for most indicators (see Table 7).19 Based on Panel B in
Figure 3, the mean depth imbalances are negative (positive) for most periods except around
signals where they change sign. This weakly supports the liquidity hypothesis that market
makers increase depth in ask (bid) relative to depth in bid (ask) after the buy (sell) signals
to ease the public buy (sell) pressure.
3.5 Test of Programed Trading Strategies
In this section, we formulate and test a program trading strategy based on technical
trading rules using the same data set. Suppose a buy signal triggers a stock purchase for
both limit and market orders. An investor, who places a limit order triggered at the closing
price of that period, purchases one unit of that stock, and then sells it at the prevailing bid
price 1, 2 or 5 days thereafter. An investor, who places a market order crossed at the
outstanding ask price of that period, purchases one unit of that stock, and then sells it at the
prevailing bid price 1, 2, or 5 days thereafter. If technical analysis is useful, the one-, two, or five-day returns will be positive. Tests are conducted to determine if these active
returns are significantly greater than zero and significantly greater than market returns over
identical holding periods.20 Using similar logic, the one-, two-, or five-day active returns
for a sell signal are expected to be negative.
The simulated program trading strategy results based on the technical buy and sell
recommendations are reported in Table 10. They are consistent with those reported in
Table 9. One-, two- and five-day returns and abnormal returns for both limit- and market
orders after buy signals MAB1, MAB2 and MAB3 are significantly lower than zero.21 Most
one-, two- and five-day returns and abnormal returns after buy signals TRBB1 and TRBB2,
and after all sell signals MAS1, MAS2, MAS3, TRBS1 and TRBS2 are significantly higher
than zero. Since all of these returns are less than 1%, they are not economically significant
19
The exceptions are MAB1 and MAS1, where the mean depth imbalances are significantly higher and lower
post-signal than pre-signal. Only t-test values show that the mean depth imbalances are significantly higher postsignal than pre-signal for MAB1, MAB3 and TRBB1. The standard deviation of depth imbalance tends to be
lower post-signal than pre-signal for all buy and sell indicators, but only is significant for TRBB1 and TRBS1.
20
The market return is proxied by using the return on TIPS for the same period as the stock tested after a
technical signal is triggered.
21
The one- (or two- or five-) day return for each stock is the real return for that stock, while the abnormal
return is the real return net of the market return as proxied by the return on TIPS for the same period. Table 8
reports average returns and abnormal returns for the 35 stocks during the one year period from 1990.7.1 to
1991.6.30.
- 20 -
given reasonable transaction cost estimates. Thus, technical indicators are not helpful in
predicting and exploiting short-term future stock price movements of one, two and five day
durations.
[Insert Table 10 About Here]
While technical analysis extracts information from historical trading price changes,
the public traders and market makers react quickly to reflect that information. Since the
market is very efficient in response to whatever information is generated and technical
analysis only reveals what has happened, profits are not earned by exploiting technical buy
and sell signals. In fact, technical trading signals are not true information events and are
generated only when the prices break certain limits, since they are triggered by price
changes caused by information or liquidity trading. Therefore, real information events
precede (not follow) technical trading signals.
4. Conclusion
Information about historical trading (especially volume and number of trades) is
relatively less useful in predicting current stock price movements than market quote
revisions. While price impounds information about the average level of traders' private
information, other microstructure variables capture important information about the quality
of traders' information signals. Quote revisions are more predictable than transaction price
changes, and are related more to market co-movement as proxied by TIPS.
Current quote revisions are significantly related to the information revealed by
historical market microstructure effects such as past effective spread, signed square-root
trading volume, and depth imbalance, which is consistent with the adverse selection
information hypothesis. Transaction price changes are mainly due to the bid-ask bounce
effect of previous trade, and the information effect of prior quote revision and depth
imbalance. Price changes and quote revisions are not influenced by the changes in number
of trades and abnormally heavy or thin trading behaviors.
While technical analysis reveals the causes of significant changes in stock prices,
most technical trading rules examined herein have significant predictive power for quote
revisions if based solely on the historical price patterns. Trading range break indicator is a
more reliable technical trading rule than moving average of prices and relative strength
indicators. The incremental predictive power of the moving average and relative strength
- 21 -
indicators vanishes after accounting for the various microstructure measures of historical
trade activity, such as trading volume, number of trades, effective spread, and depth
imbalance. Thus, these technical trading rules reveal no additional information to that
revealed by various market microstructure statistics about the short-term direction of future
stock price movements. Based on the cross-sectional analyses, technical analysis can
consistently and accurately reveal what has happened in the market, but has very limited
power in predicting future short-term stock price movements.
These results imply that the current stock price is efficient in reflecting the
information gleanable from the historical transaction price series. While relying only on
historical price patterns is not very helpful, the study of the historical patterns of other
market statistics is somewhat more useful in tracking future price movements. Our evidence
supports the theoretical work of Blume, Easley and O’Hara (1994) that technical analysis of
only price statistics cannot reveal all relevant information, and that other microstructure
statistics (such as trading volume) can improve information quality and may be helpful in
explaining future stock price changes.
Traders using technical analysis to extracts information from historical price
changes. Technical trading signals are not true information events and are generated only
when the prices break certain limits, since they are triggered by price changes caused by
information or liquidity trading. Therefore, real information events precede (not follow)
technical trading signals. In this study we shave shown that the practitioners who claim they
rely on the technical analysis might be in fact rely on market microstructure effects.
- 22 -
References
Amihud, Y. and H. Mendelson (1987), "Trading Mechanisms and Stock Returns: An Empirical
Investigation," Journal of Finance 42, 533-553.
Blume,L., D. Easley and M. O'Hara (1994), "Market Statistics and Technical Analysis: The Role of
Volume," Journal of Finance 49, 153-181.
Brown, D.P. and R.H. Jennings (1989), "On Technical Analysis," Review of Financial Studies 2, 527-552.
Brock, W.A., J. Lakonishok and B. LeBaron (1992), "Simple Technical Trading Rules and the Stochastic
Properties of Stock Returns," Journal of Finance 47, 1731-1764.
De Bondt, W.F.M. and R. Thaler (1985), "Does the Stock Market Overreact?," Journal of Finance 40, 793805.
Easley, D. and M. O'Hara (1992a), "Adverse Selection and Large Volume," Journal of Financial and
Quantitative Analysis 22, 229-252.
Easley, D. and M. O'Hara (1992b), "Time and the Process of Security Price Adjustment," Journal of
Finance 47, 577-605.
Fama, E.F. (1991), "Efficient Capital Markets: II," Journal of Finance 46, 1575-1617.
Fama, E.F. and K.R. French (1986), "Permanent and Temporary Components of Stock Prices," Journal of
Political Economy 98, 246-274.
Ferson, W.F. and Harvey, C.A. (1991), "The Variation of Economic Risk Premiums," Journal of
Political Economy 99, 385-415.
French, K.R. and R. Roll (1986), "Stock-Return Variances: The Arrival of Information and the Reaction of
Traders," Journal of Financial Economics 17, 5-26.
Glosten, L. and P. Milgrom (1985) "Bid, Ask, and Transaction Prices in a Specialist Market with
Heterogeneously Informed Traders," Journal of Financial Economics 14, 71-100.
Grundy, B.D. and M. McNichols (1989), "Trade and Revelation of Information through Prices and Direct
Disclosure," Review of Financial Studies 2, 495-526.
Hasbrouck, J. (1991a), "Measuring the Information Content of Stock Trades," Journal of Finance 46, 179207.
Hasbrouck, J. (1991b), "The Summary Informativeness of Stock Trade: An Econometric Analysis," Review
of Financial Studies 4, 571-595.
Huang, R.D. and H.R. Stoll (1994), "Market Microstructure and Stock Return Predictions," Review of
Financial Studies 7, 179-312.
Jegadeesh, N. (1991), "Evidence of Predictable Behavior of Security Returns," Journal of Finance 45, 881898.
Lee, C.M.C., B. Mucklow, and M.J. Ready (1993), "Spread, Depths and the Impact of Earnings
Information: An Intraday Analysis," Review of Financial Studies 6, 345-374.
Lehmann, B.N. (1990), "Fads, Martingales and Market Efficiency," Quarterly Journal of Economics 105, 128.
Lehmann, B.N. and D.M. Modest (1994), "Trading and Liquidity on the Tokyo Stock Exchange: A Bird's
Eye View," Journal of Finance 49, 951-984.
Lo, A. and C. MacKinlay (1990), "When are Contrarian Profits Due to Stock Market Overreaction?"
Review of Financial Studies 3, 175-205.
Kyle, A.S. (1985), "Continuous Auctions and Insider Trading," Econometrica 53, 1315-1336.
- 23 -
Le Roy, S.F. and R.D. Porter (1981), "The Present-Value Relation: Tests Based on Implied Variance
Bounds," Econometrica 49, 555-574.
Madhavan, A. (1992), "Trading Mechanisms in Securities Markets," Journal of Finance 47, 607-641.
Madhavan, A. and S. Smidt (1991), "A Bayesian Model of Intraday Specialist Pricing," Journal of Financial
Economics 30, 99-134.
McInish, T.H. and R.A. Wood (1992), "An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE
Stocks," Journal of Finance 47, 753-764.
Neftci, S.N. (1991), "Naive Trading Rules in Financial Markets and Wiener-Kolmogorov Prediction
Theory: A Study of 'Technical Analysis'," Journal of Business 64, 549-571.
Poterba, J.M. and L.H. Summers (1988), "Mean Reversion in Stock Prices: Evidence and Implications,"
Journal of Financial Economics 22, 27-60.
Romer, D. (1993), "Rational Asset-Price Movements Without News," American Economic Review 83, 11121130.
Shiller, R.J. (1979), "The Volatility of Long Term Interest Rates and Expectations Models of the Term
Structure," Journal of Political Economy 87, 1190-1209.
Shiller, R.J. (1981), "The Use of Volatility Measures in Assessing Market Efficiency," Journal of Finance
36, 291-304.
Shiller, R.J. (1984), "Theories of Aggregate Stock Price Movements, " Journal of Portfolio Management
10, 28-37.
Stickel, S.E. and R.E. Verrecchia (1994), “Evidence that Trading Volume Sustains Stock Price Changes,”
Financial Analysts Journal, November - December, 57-67.
Summers, L. (1986), "Does The Stock Market Rationally Reflect Fundamental Values?," Journal of Finance
41, 591-600.
White, H. (1980), "A Heteroskedasticity-consistent Covariance Matrix Estimator and a Direct Test for
Heteroskedasticity," Econometrica 48, 817-838.
- 24 -
Table 1:
Toronto 35 Index Composition for July 1990
No.
Company
Ticker
Shares
Price ($)
Weight (%)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
Alcan
BCE Inc.
Bank of Montreal
Bank of Nova Scotia
Bow Valley Industrial
CAE Industrials
Canadian Imperial Bank
Canadian Pacific Ltd
Canadian Tire Class A
Echo Bay Mines
Gulf Canada Resources
Imperial Oil Class A
IMASCO Ltd
Lac Minerials
Laidlaw Class B
Macmillan Bloedel
Moore Corp
Inco Limited
National Bank
Noranda Inc.
Northern Telecom
Nova Corp of Alberta
Placer Dome
Power Corp
Ranger Oil
Royal Bank
Sears Canada
Stelco Series A
Southam Inc.
Transalta Utilities
Toronto-Dominion Bank
Teck Corp Class B
The Thomson Corporation
Transcanada Pipelines
Seagram
AL
B
BMO
BNS
BVI
CAE
CM
CP
CTR.A
ECO
GOU
IMO.A
IMS
LAC
LDM.B
MB
MCL
N
NA
NOR
NTL
NVA
PDG
POW
RGO
RY
SCC
STE.A
STM
TAU
TD
TEK.B
TOC
TRP
VO
1500
1500
1000
1000
1000
1500
1500
2000
2000
1000
1000
500
1000
750
1500
1000
1000
1000
1000
1000
1000
3000
2100
1000
3000
2000
1500
500
750
2000
2000
1000
2000
1000
500
27.875
37.625
27.000
14.625
13.750
6.250
27.250
20.000
20.250
15.000
16.000
61.375
36.500
12.000
25.250
18.125
33.125
36.125
10.000
20.000
31.250
8.625
19.375
14.875
7.875
24.125
11.375
16.375
22.375
11.625
19.250
25.875
14.375
15.625
97.000
4.38
5.92
2.83
1.53
1.44
0.98
4.29
4.19
4.25
1.57
1.68
3.22
3.83
0.94
3.97
1.90
3.47
3.79
1.05
2.10
3.28
2.71
4.27
1.56
2.48
5.06
1.79
0.86
1.76
2.44
4.04
2.71
3.01
1.64
5.08
Total
Basket Quoted Market Value (QMV) = $953,906.25
Index=193.54
P/E = 14.70
Base = 4928
100
Yield = 3.73
Table 2: Transaction and Quotation Statistics
TSE 35 Index Stocks, 1990.7 - 1991.6. Total of 3276 observations (30-minute interval)
Transaction
Quote
Transaction
Quote
Trade
Number
Depth
Spread
No
Price C$
Mid-point
Return (%)
Return (%)
Volume
of Trades
(DA+DB)
C$
Trading
Ticker
Price C$
(# of Shares)
(board lot)
NT
at MQ
Periods
1
AL
24.09
24.08
-0.0019
-0.0031
27,583
14.86
357.20
0.1482
150
125
2
B
39.61
39.62
0.0037
0.0017
23,058
29.68
507.37
0.1389
10#
22
3
BMO
30.94
30.95
0.0082
0.0061
20,961
14.74
341.54
0.1384
70
64
4
BNS
14.03
14.03
0.0072
0.0050
33,125
33.22*
860.45
0.1294
18
15#
5
BVI
14.13
14.14
0.0015
0.0016
3,593
1.66
183.83
0.1679
1662
109
6
CAE
5.81#
5.81*
0.0025
0.0017
12,164
4.89
514.53
0.1118#
631
58
7
CM
27.75
27.76
0.0044
0.0031
15,309
9.48
305.80
0.1409
162
78
8
CP
19.81
19.81
-0.0008
-0.0021
35,327
22.78
754.85
0.1371
35
61
9
CTR.A
22.10
22.11
0.0072
0.0068
6,621
5.88
185.60
0.1631
451
145
10
ECO
11.59
11.59
-0.0104
-0.0106
9,153
4.97
274.22
0.1597
753
236*
11
GOU
12.00
12.00
-0.0158
-0.0169
6,065
3.02
194.00
0.1675
1090
126
12
IMO.A
58.93
58.93
0.0002
-0.0006
5,364
6.11
83.83
0.2258
276
123
13
IMS
30.15
30.15
-0.0042
-0.0054
5,904
4.03
131.12
0.1808
683
172
14
LAC
9.52
9.52
-0.0030
-0.0038
20,630
9.20
513.55
0.1406
335
131
15
LDM.B
19.39
19.39
-0.0245
-0.0250
60198*
30.67
577.00
0.1415
50
71
16
MB
17.98
18.00
0.0056
0.0041
8,023
6.97
232.40
0.1521
328
101
17
MCL
28.58
28.58
-0.0030
-0.0037
9,661
5.71
174.19
0.1643
404
172
18
N
34.05
34.05
0.0079
0.0068
23,691
10.03
209.52
0.1609
256
185
19
NA
9.17
9.16
0.0056
0.0032
10,892
7.97
559.07
0.1371
421
98
20
NOR
17.62
17.63
0.0015
0.0000
12,195
6.42
275.96
0.1547
382
155
21
NTL
33.53
33.53
0.0084*
0.0080*
13,833
8.39
221.84
0.1526
244
157
22
NVA
8.44
8.45
-0.0006
-0.0028
31,041
16.19
1402.38*
0.1296
74
26
23
PDG
17.38
17.38
-0.0029
-0.0035
29,749
18.37
507.20
0.1417
104
113
24
POW
15.99
16.01
0.0040
0.0024
3,858
3.61
233.81
0.1454
811
107
25
RGO
8.01
8.02
0.0037
0.0030
20,100
4.65
698.00
0.1316
1113
49
26
RY
23.65
23.65
0.0020
0.0006
19,761
12.90
389.81
0.1373
96
71
27
SCC
11.28
11.30
0.0056
0.0044
3,763
1.37#
151.52
0.1886
1715*
97
28
STE.A
11.26
11.26
-0.0292#
-0.0297#
4,743
4.68
158.29
0.1584
695
169
29
STM
19.40
19.40
-0.0094
-0.0094
3,177#
1.94
93.65
0.1871
1249
131
30
TAU
12.35
12.34
0.0023
0.0000
12,311
13.32
640.63
0.1329
182
58
31
TEK.B
22.42
22.42
-0.0017
-0.0020
8,076
3.03
170.37
0.1757
1185
146
32
TD
17.61
17.62
0.0017
0.0004
25,466
18.33
506.56
0.1339
48
40
33
TOC
15.72
15.72
0.0013
0.0001
12,391
4.64
432.58
0.1361
462
69
34
TRP
16.79
16.79
0.0034
0.0022
17,851
9.61
983.40
0.1319
271
59
35
VO
101.59*
101.59*
0.0070
0.0064
3,957
4.29
37.91#
0.2682*
489
103
Ave
22.36
22.37
-0.0004
-0.0015
15,988
10.22
396.11
0.1546
483
104
S.D.
TIPS
17.43
18.79
17.43
18.74
0.0086
-0.0010
0.0083
-0.0002
12,173
18,438
8.39
2.63
290.67
814.28
0.0295
0.1270
462
1,048
52
48
Notes: (1) Transaction price is the average price of all trades; Quote mid-point price is the the average of last bid and ask price;Transaction
return is the log difference of transaction price at t and t-1; Quote return is the log difference of quote mid-point price at t and t-1;
Trade volume is the total number of shares; Number of trades is the total number of transactions; Depth is the sum of last
quoted size at bid and at ask; Spread is the difference between the bid and ask prices; no trading periods are the number of
no transaction intervals in the sample period; and NT at MQ is the number of intervals where the transaction price equals
the previous quote mid-point price in the sample period.
(2) "*" indicates the maximum in the category; and "#" indicates the minimum in the category.
(3) CAE, SCC, STM and TOC are traded on CATS during the sample period.
Table 3: Quote Revision Model (Equation 2)
(2)
RQ(t) = a0 + a1*TRP(t) + a2*Z(t) + a3*SX(t) + a4*RNT(t) + a5*RHT(t) + a6*RTT(t)
+ a7*RQ(t-1) + a8*DI(t-1) + a9*QO(t) + a10*MQO(t) + u(t)
coefficient x 1000
Constant
TRP(t)
Z(t-1)
SX(t)
RNT(t)
RHT(t)
RTT(t)
RQ(t-1)
DI(t-1)
QO(t)
MQO(t)
adj-R-sq
71.629
3.3545*
30
484.09
13.681*
35
0.0091
5.6512*
33
0.0102
0.6840
15
0.0533
0.2084
7
0.0765
0.6911
13
-11.2238
-0.5961
12
-0.0024
-6.7287*
33
-0.3415
-0.8925
14
0.0477
0.1508
6
0.4468
314.00~*
35
With Microstructure Effects
Ave. Coeff.
Ave. t-stat
No.signif.
0.0480
0.7856
19
Without Microstructure Effects
Ave. Coeff.
Ave. t-stat
No.signif.
0.0229
175.96
-0.4245
-0.1058
0.0240
0.3042
7.3161*
-1.0730
-0.4296
27.125~*
3
31
23
14
35
Notes: (1) The results for equation (2) are reported under With Microstructure Effects. The results for a market model are reported under Without Microstructure Effects.
(2) The "*" indicates significance at a level of 90% or above. The "~" indicates F-statistics.
(3) Number significant indicates that the coefficient is significant for the stated number of stocks out of the sample of 35 stocks.
Table 4: Price Changes Prediction Model (Equation 5):
(5)
RP(t) = b0 + b1*TRP(t-1) + b2*Z(t-1) + b3*SX(t-1) + b4*RNT(t-1) + b5*RHT(t-1) + b6*RTT(t-1)
+ b7*RQ(t-1) + b8*DI(t-1) + b9*TO(t) + b10*TC(t) + b11*MTO(t) + v(t)
coefficient x 1000
Constant
TRP(t-1)
Z(t-1)
SX(t-1)
RNT(t-1)
RHT(t-1)
RTT(t-1)
RQ(t-1)
DI(t-1)
TO(t)
TC(t)
MTO(t)
adj-R-sq
34.796
1.3745*
18
-711.36
-23.604*
35
0.0001
0.5277
13
-0.0024
-0.0408
4
0.0945
0.3738
5
-0.1490
-0.8309
10
725.44
23.311*
35
-0.0025
-6.3189*
33
-0.5274
-0.6411
9
0.1901
0.6911
17
0.0225
-0.0860
6
0.2743
115.61~*
-0.4487
-0.9630
13
0.0283
0.4040
10
-0.1551
-0.2201
10
0.0040
3.2826~*
22
With Microstructure Effects
Ave. Coeff.
Ave. t-stat
No. Signif.
-0.1000
-0.9951
24
35
Without Microstructure Effects
Ave. Coeff.
Ave. t-stat
No. Signif.
0.0326
0.2277
3
56.6471
1.9378*
21
Notes: (1) The results for equation (5) are reported under With Microstructure Effects. Also see the notes to Table 3.
Table 5: Prediction of Quote Revisions with Technical Analysis Indicators (Microstructure Effects Ignored)
RQ(t) = a0 + a1*TRP(t) + a9*QO(t) + a10*MQO(t)
+ bo*BSi(t) + B1*BSi(t-1) + B2*BSi(t-2) + B4*BSi(t-6) + B5*BSi(t-13)
+ s0*SSi(t) + S1*SSi(t-1) + S2*SSi(t-2) + S4*SSi(t-6) + S5*SSi(t-13) + e(t)
where BSi and SSi indicate buy and sell signals, respectively, i = 1, 2, 3, ...,7. BS1 , BS2 and BS3 are MAB1, MAB2 and MAB3, respectively, SS1, SS2 and SS3 are MAS1, MAS2
and MAS3, respectively. They are buy and sell indicators based on daily-weekly, daily-monthly and 30-minute-monthly average price crossings; BS4 and BS5 are TRBB1 and TRBB2,
and SS4 and SS5 are TRBS1 and TRBS2, respectively. They are buy and sell indicators based on 30-minute to weekly and 30-minute to monthly maximum or minimum price breaks.
BS6 and BS7 are RSI1 and RSI2, and SS6 = SS7 = 0, respectively. They are relative strength scale measures (from -100 to 100 by definition) based on daily sums or weekly sums of
positive or negative price changes.
coefficient x 1000
BSi(t)
BSi(t-1)
BSi(t-2)
BSi(t-6)
BSi(t-13)
SSi(t)
SSi(t-1)
SSi(t-2)
SSi(t-6)
SSi(t-13)
adj-R-sq
0.9118
1.1219
10
0.1629
0.1083
1
0.1235
0.2019
2
0.3203
0.4082
6
0.1148
0.2507
3
-0.5484
-0.7265
8
-0.6053
-0.6789
5
-0.0241
0.0576
4
0.0171
-0.0158
3
-0.2257
-0.3574
3
0.0331
3.3897~*
33
1.0513
0.7316
10
0.3780
0.3833
4
0.5417
0.4872
6
-0.1082
0.0087
2
0.4152
0.4967
4
-1.8033
-1.3669*
11
-0.2716
-0.2680
3
-0.5952
-0.5711
4
-0.0288
-0.1905
2
-0.2448
-0.3206
4
0.0338
3.4676~*
33
3.2516
4.7283*
35
1.3594
2.1817*
21
0.9429
1.4556*
15
0.2335
0.3749
7
0.5948
1.0347
9
-2.9159
-4.2041*
34
-1.3332
-2.0932*
25
-0.9537
-1.5014*
9
-0.4358
-0.7069
3
-0.1723
-0.4371
5
0.0439
4.5628~*
35
-0.9410
-1.9765*
24
-0.3724
-0.8755
10
0.1813
0.3233
4
-0.0707
-0.2851
6
-4.5873
-10.169*
35
0.6496
1.6745*
21
0.3593
0.7087
10
-0.0444
-0.2776
2
0.0269
0.1825
7
0.1000
11.034~*
35
5.3453
8.3631*
35
-1.0384
-1.9532*
24
-0.4935
-1.0325
13
0.1691
0.3148
4
-0.0390
-0.1211
3
-5.3457
-8.1433*
35
0.9167
1.8609*
23
0.5269
0.8874
11
-0.0544
-0.1132
3
0.3377
0.5014
10
0.0754
8.0707~*
35
0.0672
14.543*
35
-0.0461
-7.9497*
35
-0.0073
-1.2361
12
0.0022
0.3393
4
-0.0028
-0.3432
6
0.0921
18.925~*
35
0.3687
16.088*
35
-0.2749
-9.3318*
35
-0.0418
-1.4505*
13
0.0107
0.3672
4
0.0107
0.4000
7
0.1077
22.523~*
35
MAB1 and MAS1
Ave. Coeff.
Ave. t-stat
No. Signif.
MAB2 and MAS2
Ave. Coeff.
Ave. t-stat
No. Signif.
MAB3 and MAS3
Ave. Coeff.
Ave. t-stat
No. Signif.
TRBB1 and TRBS1
Ave. Coeff.
Ave. t-stat
No. Signif.
4.7864
10.720*
35
TRBB2 and TRBS2
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI1
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI2
Ave. Coeff.
Ave. t-stat
No. Signif.
Notes: (1) The table reports only the results of the coefficients for technical indicators.
(2) More complete results are available upon request from the authors.
(3) See Table 3 for other notations.
Table 6: Prediction of Price Changes with Technical Analysis Indicators (Microstructure Effects Ignored)
RP(t) = a0 + a1*TRP(t-1) +a2*TO(t) + a3*TC(t) + a4*MTO(t)
+ b1*BSi(t-1) + b2*BSi(t-2) + b3*BSi(t-4) + b4*BSi(t-6) + b5*BSi(t-13)
+ s1*SSi(t-1) + s2*SSi(t-2) + s3*SSi(t-4) + s4*SSi(t-6) + s5*SSi(t-13) + e(t)
where all the variables are as defined in Table 5.
coefficient x 1000
BSi(t-1)
BSi(t-2)
BSi(t-4)
BSi(t-6)
BSi(t-13)
SSi(t-1)
SSi(t-2)
SSi(t-4)
SSi(t-6)
SSi(t-13)
adj-R-sq
-0.0596
-0.0722
4
0.2815
0.2027
3
0.1581
0.2868
6
-0.2427
-0.0599
2
0.1732
0.1507
6
0.2510
0.2019
2
0.0986
0.0192
3
0.1978
0.0338
3
-0.3568
-0.3125
2
0.0122
1.1757~
14
0.5693
0.3701
4
0.0467
0.1317
3
0.1447
0.2043
2
-0.7083
-0.5098
3
0.4345
0.4496
7
-0.5673
-0.4625
4
-0.1056
-0.0680
5
-0.0141
-0.1219
1
0.4577
0.2861
6
0.0123
1.1874~
11
-1.5695
-1.9250*
17
-0.4545
-0.5231
9
-0.2815
-0.3974
4
0.0179
0.1096
3
2.2787
3.0614*
22
1.2815
1.5525*
16
0.4982
0.6394
9
0.2554
0.3546
6
-0.1111
-0.4083
7
0.0182
1.7754~*
24
0.2361
0.5384
7
-0.1246
-0.1612
4
0.5318
0.5501
4
-0.0374
0.0165
2
0.3586
0.5962
16
0.1004
0.0426
4
0.0400
-0.0667
5
-0.1120
-0.2905
5
-0.2239
-0.1805
7
0.0166
1.6134~*
21
0.1789
0.2017
18
0.0057
0.0140
2
0.0496
0.1823
6
0.4986
0.4591
4
-0.2779
-0.3763
6
-0.3199
-0.3688
16
0.1270
0.0117
7
-0.2420
-0.3444
5
-0.1875
-0.2164
5
0.0439
0.0043
7
0.0149
1.4418~*
21
-0.0409
-6.5761*
29
0.0227
3.0433*
25
0.0042
0.5099
6
0.0010
0.0550
7
-0.0026
-0.3186
5
0.0282
5.0344~*
35
-0.1983
-6.2811*
30
0.1181
2.9971*
23
0.0126
0.3144
5
0.0120
0.3181
1
-0.0275
-0.5927
8
0.0268
4.7878~*
35
MAB1 and MAS1
Ave. Coeff.
Ave. t-stat
No. Signif.
-0.4709
-0.3532
7
MAB2 and MAS2
Ave. Coeff.
Ave. t-stat
No. Signif.
-0.5675
-0.4741
5
MAB3 and MAS3
Ave. Coeff.
Ave. t-stat
No. Signif.
-2.0792
-2.9207*
20
TRBB1 and TRBS1
Ave. Coeff.
Ave. t-stat
No. Signif.
0.0599
0.1498
13
TRBB2 and TRBS2
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI1
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI2
Ave. Coeff.
Ave. t-stat
No. Signif.
Notes: See Table 5.
Table 7: Prediction of Quote Revisions with Microstructure Effects and Technical Analysis Indicators
RQ(t) = a0 + a1*Z(t) + a2*TRP(t) + a3*SX(t) + a4*RNT(t) + a5*RHT(t) + a6*RTT(t) + a7*RQ(t-1) + a8*DI(t-1) + a9*QO(t) + a10*MQO(t)
+ bo*BSi(t) + B1*BSi(t-1) + B2*BSi(t-2) + B4*BSi(t-6) + B5*BSi(t-13)
+ s0*SSi(t) + S1*SSi(t-1) + S2*SSi(t-2) + S4*SSi(t-6) + S5*SSi(t-13) + e(t)
where BSi and SSi indicate buy and sell signals, respectively, i = 1, 2, 3, ...,7. BS1 , BS2 and BS3 are MAB1, MAB and MAB3, respectively, SS1, SS2 and SS3 are MAS1, MAS2
and MAS3, respectively. They are buy and sell indicators based on daily-weekly, daily-monthly and 30-minute-monthly average price crossings; BS4 and BS5 are TRBB1 and
TRBB2, and SS4 and SS5 are TRBS1 and TRBS2, respectively. They are buy and sell indicators based on 30-minute to weekly and 30-minute to monthly maximum or minimum
price breaks. BS6 and BS7 are RSI1 and RSI2, and SS6 = SS7 = 0, respectively. They are relative strength scale measures (from -100 to 100 by definition) based on daily sums or
weekly sums of positive or negative price changes.
coefficient x 1000
BSi(t)
BSi(t-1)
BSi(t-2)
BSi(t-6)
BSi(t-13)
SSi(t)
SSi(t-1)
SSi(t-2)
SSi(t-6)
SSi(t-13)
adj-R-sq
-0.0729
-0.1708
3
0.1138
0.2769
7
0.0210
-0.1190
4
0.1340
0.2768
3
0.1230
0.1692
4
-0.0604
-0.0908
5
-0.1279
-0.2875
13
0.1215
0.2760
9
-0.2206
-0.4372
7
0.4466
143.18~*
35
0.0549
0.0491
5
0.0409
0.0647
9
-0.0720
-0.2026
4
0.0676
-0.0197
6
-0.3003
-0.1121
6
-0.1365
-0.3193
5
-0.0713
-0.0827
10
0.0629
0.1758
5
-0.0552
0.0304
6
0.4469
143.35~*
35
-0.1896
-0.5090
10
0.0705
0.2491
7
0.0032
0.0928
9
0.0166
0.0179
7
0.2793
0.5722
11
0.1250
0.2966
9
-0.0718
-0.2030
10
-0.0640
-0.2833
7
0.0317
0.1111
7
0.4473
143.54~*
35
-0.2442
-0.6973
9
-0.1020
-0.3889
3
0.0569
0.1499
6
-0.0343
-0.1129
2
-1.3889
-2.9023*
32
0.1935
0.6536
10
-0.0059
0.0629
7
-0.0488
-0.1625
4
0.1450
0.2627
10
0.4541
146.56~*
35
1.5492
2.5505*
30
-0.3612
-1.0172
16
-0.0776
-0.3059
8
-0.0253
-0.1248
8
-0.1094
-0.0655
2
-1.7156
-2.2549*
31
0.3084
0.8098
8
0.0197
0.1164
6
0.0187
0.1153
8
0.1274
0.1214
4
0.4522
145.89~*
35
-0.0007
0.0557
9
-0.0004
-0.2760
12
0.0011
0.4197
8
-0.0008
-0.2892
9
0.0000
0.1189
6
0.4478
197.38~*
35
0.0247
1.1997
16
-0.0258
-1.2041
17
0.0044
0.2785
7
-0.0054
-0.4776
12
-0.0019
-0.2102
9
0.4484
197.57~*
35
MAB1 and MAS1
Ave. Coeff.
Ave. t-stat
No. Signif.
0.0349
0.0146
5
MAB2 and MAS2
Ave. Coeff.
Ave. t-stat
No. Signif.
0.1848
0.0288
10
MAB3 and MAS3
Ave. Coeff.
Ave. t-stat
No. Signif.
0.0073
-0.0192
9
TRBB1 and TRBS1
Ave. Coeff.
Ave. t-stat
No. Signif.
1.3971
3.1706*
33
TRBB2 and TRBS2
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI1
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI2
Ave. Coeff.
Ave. t-stat
No. Signif.
Notes: See Table 5.
Table 8: Prediction of Price Changes with Microstructure Effects and Technical Analysis Indicators
RP(t) = a0 + a1*Z(t-1) + a2*TRP(t-1) + a3*SX(t-1) + a4*RNT(t-1) + a5*RHT(t-1) + a6*RTT(t-1) + a7*RQ(t-1) + a8*DI(t-1)
+ a9*TO(t) + a10*TC(t) + a11*MTO(t) + b1*BSi(t-1) + b2*BSi(t-2) + b3*BSi(t-4) + b4*BSi(t-6) + b5*BSi(t-13)
+ s1*SSi(t-1) + s2*SSi(t-2) + s3*SSi(t-4) + s4*SSi(t-6) + s5*SSi(t-13) + e(t)
where all the variables are as defined in Tables 4 and 7.
coefficient x 1000
BSi(t-1)
BSi(t-2)
BSi(t-4)
BSi(t-6)
BSi(t-13)
SSi(t-1)
SSi(t-2)
SSi(t-4)
SSi(t-6)
SSi(t-13)
adj-R-sq
0.1679
0.3079
10
0.2178
0.3447
8
0.2868
0.2779
7
0.2080
0.2432
8
-0.0276
0.0115
4
-0.3104
-0.4889
9
-0.2319
-0.2912
5
-0.0171
-0.1911
7
-0.1476
-0.2360
9
-0.1990
-0.2774
6
0.2743
55.823~*
35
0.1269
0.2502
8
0.4449
0.4459
11
0.1588
0.0634
5
0.1890
0.2032
4
0.2056
0.3174
6
-0.0666
-0.0287
7
-0.4362
-0.4614
12
-0.0303
0.1218
8
-0.3520
-0.4617
7
-0.1763
-0.2466
7
0.2744
55.844~*
35
-0.1606
-0.4319
11
-0.0388
0.0392
10
0.2441
0.5269
7
-0.0719
-0.2222
5
0.1129
0.1903
1
0.1899
0.3709
5
0.0103
-0.0227
7
-0.1140
-0.2110
6
-0.0854
-0.1415
2
-0.0871
-0.1168
3
0.2748
56.030~*
35
0.3802
0.8161
9
0.0222
0.2234
10
0.2332
0.4908
8
-0.0020
-0.0623
5
-0.0948
-0.1654
8
-0.0335
-0.0813
4
-0.1548
-0.3733
5
-0.1051
-0.3929
10
0.0471
0.2368
6
0.2762
56.327~*
35
0.1956
0.4069
8
0.1600
0.3346
7
0.1690
0.4381
5
0.0250
-0.0315
6
-0.0563
-0.2078
9
-0.2082
-0.2314
11
-0.0264
-0.0884
4
-0.1144
-0.2182
3
-0.1575
-0.3880
2
0.0682
0.2668
7
0.2754
56.106~*
35
-0.0010
-0.0910
15
0.0037
0.6801
15
0.0006
0.0637
8
0.0018
0.4160
9
-0.0006
-0.1159
10
0.2763
75.886~*
35
-0.0181
-0.5809
13
0.0308
1.0100
11
0.0024
0.0811
5
0.0020
0.0420
6
-0.0126
-0.9219
11
0.2759
75.770~*
35
MAB1 and MAS1
Ave. Coeff.
Ave. t-stat
No. Signif.
MAB2 and MAS2
Ave. Coeff.
Ave. t-stat
No. Signif.
MAB3 and MAS3
Ave. Coeff.
Ave. t-stat
No. Signif.
TRBB1 and TRBS1
Ave. Coeff.
Ave. t-stat
No. Signif.
0.2716
0.5620
7
TRBB2 and TRBS2
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI1
Ave. Coeff.
Ave. t-stat
No. Signif.
RSI2
Ave. Coeff.
Ave. t-stat
No. Signif.
Notes: See Table 5.
Table 9: Cross-Sectional Tests of the Behavior of Microstructure Variables Around Technical Signals
T-test gives the t-statistics for the differences between pre-signal 10 day (130 period) and post-signal 10 day mean, standard deviation and cumulative average return for each of the microstructure variables. Sign-test gives the Z-scores for
the numbers of increased over numbers of decreased post-signal compared to those pre-signal for each of the microstructure variables.
Price Return
Mean
S.D.
Volume
CAR
Mean
Signed Volume
S.D.
Mean
Number of Trades
Quote Return
Relative Spread
Depth Imbalance
S.D.
Mean
S.D.
Mean
S.D.
CAR
Mean
S.D.
Mean
S.D.
MAB1
Difference
0.0004
-0.0001
0.0091
-3,066
-7,700
1,627
-8,334
-0.7359
-0.8537
0.0003
-0.0003
0.0082
0.0002
0.0001
-0.0641
-0.0055
(1206 obs.)
T-test
11.23*
-1.17
11.06*
-3.84*
-2.11*
2.08*
-2.29*
-4.71*
-5.62*
10.44*
-4.31*
10.34*
3.25*
1.60
-4.08*
-0.62
Sign-test
11.57*
-1.34
11.18*
-4.61*
-3.34*
2.74*
-3.71*
-5.41*
-5.38*
10.35*
-3.68*
10.95*
4.38*
1.40
-3.43*
0.37
MAB2
Difference
0.0006
0.0002
0.0153
-568
784
1,551
770
-0.5915
-0.3412
0.0006
0.0001
0.0513
0.0001
0.0001
-0.0721
0.0040
(2475 obs.)
T-test
23.22*
5.13*
23.11*
-1.75
0.63
4.63*
0.62
-6.39*
-2.95*
23.36*
2.99*
23.20*
2.24*
2.10*
-6.08*
0.68
Sign-test
19.41*
3.15*
19.09*
-3.90*
2.89*
5.71*
-3.50*
-8.23*
-4.90*
19.46*
3.48*
19.62*
7.52*
0.74
-1.69
0.88
Difference
0.0000
-0.0002
-0.0004
-1,795
-4,064
-353
-4,226
-0.6556
-0.7341
0.0000
-0.0002
0.0005
0.0000
0.0000
-0.0312
-0.0410
-0.60
-3.60*
-0.72
-3.91*
-3.05*
-1.02
-3.07*
-6.10*
-5.84*
1.04
-3.89*
0.88
0.99
0.34
-2.45*
-1.89
1.00
-2.34*
1.11
-4.44*
-3.42*
-1.52
-2.76*
-5.89*
-5.50*
2.57*
-3.15*
3.22*
1.40
0.05
-1.17
-1.04
MAB3
(2054 obs.)
T-test
Sign-test
TRBB1
Difference
0.0009
-0.0002
0.0235
-2,888
-2,752
4,414
-4,186
-1.9488
-0.9135
0.0010
-0.0002
0.0253
0.0002
0.0000
-0.0248
-0.0104
(5770 obs.)
T-test
50.79*
-8.55*
50.44*
-8.05*
-2.33*
12.15*
-3.55*
-22.58*
-11.68*
54.86*
-7.41*
54.54*
9.38*
2.19*
-3.82*
-3.15*
Sign-test
43.12*
-7.15*
42.97*
-10.60*
-5.42*
19.94*
-7.54*
-19.67*
-7.37*
46.21*
-6.03*
47.16*
17.41*
5.89*
-1.90
-3.08*
TRBB2
Difference
0.0010
-0.0003
0.0259
-2,183
876
5,718
-1,131
-2.4259
-0.7228
0.0011
-0.0001
0.0280
0.0002
0.0000
-0.0145
-0.0138
( 2782 obs.)
T-test
39.21*
-7.12*
38.90*
-6.28*
0.94
15.85*
-1.21
-17.26*
-5.74*
42.29*
-3.93*
42.05*
6.92*
1.76
-1.65
-2.91*
Sign-test
31.96*
-4.66*
31.88*
-6.81*
-1.97*
17.27*
-4.57*
-14.89*
-1.73
34.20*
-2.46*
34.97*
13.10*
4.87*
-0.47
-1.78
MAS1
Difference
-0.0003
-0.0001
-0.0091
54
-13
-1,293
-37
0.2245
0.0132
-0.0003
-0.0002
-0.0078
-0.0001
0.0000
0.0546
-0.0005
(2434 obs.)
T-test
-16.95*
-2.30*
-17.16*
0.07
0.00
-1.61
-0.01
2.11*
0.14
-14.96*
-3.36*
-15.17*
-2.89*
-0.24
4.89*
-0.08
Sign-test
-13.48*
-0.97
-12.34*
-1.32
-1.32
-4.24*
-1.16
0.96
-0.79
-11.21*
-2.08*
-9.33*
-5.24*
-1.57
3.51*
1.16
MAS2
Difference
-0.0005
0.0001
-0.0136
1,910
8,874
-4,002
8,874
-0.1671
-0.0510
-0.0005
0.0001
-0.0134
-0.0002
-0.0001
0.0232
-0.0098
(992 obs.)
T-test
-13.83*
0.74
-13.86*
1.57
1.96
-2.82*
1.98*
-0.73
-0.21
-13.74*
0.87
-13.96*
-3.77*
-1.14
1.20
-0.97
Sign-test
-11.10*
0.16
-11.19*
0.48
0.00
-3.65*
0.60
-0.35
-0.10
-10.87*
0.88
-10.16*
-5.63*
-3.47*
1.81
-1.62
-0.0112
MAS3
Difference
0.0001
-0.0002
0.0013
-1,921
-5,032
1,126
-5,230
-0.4749
-0.5756
0.0000
-0.0002
-0.0006
-0.0001
0.0000
0.0122
(2054 obs.)
T-test
2.26*
-4.66*
2.14*
-3.43*
-2.90*
2.89*
-2.92*
-3.87*
-4.20*
-0.93
-4.48*
-1.08
-1.93
-0.94
0.95
-1.51
Sign-test
2.35*
-2.71*
2.95*
-2.65*
-2.41*
2.01*
-1.96*
-3.30*
-3.16*
-0.40
-2.90*
-0.05
-2.82*
-1.11
1.02
-1.94
TRBS1
Difference
-0.0009
-0.0005
-0.0225
-1,288
-1,863
-4,023
-2,650
-1.0059
-0.4243
-0.0010
-0.0002
-0.0245
-0.0003
-0.0001
0.0087
-0.0173
(5688 obs.)
T-test
-44.66*
-13.62*
-45.13*
-1.75
-0.53
-5.29*
-0.76
-7.33*
-3.04*
-47.83*
-5.32*
-48.06*
-15.47*
-4.90*
1.27
-5.10*
Sign-test
-43.28*
-13.77*
-42.40*
0.20
0.54
-21.89*
-0.08
-3.70*
2.75
-47.73*
-7.47*
-44.72*
-17.23*
-8.79*
0.28
-3.81*
-0.0073
TRBS2
Difference
-0.0011
-0.0006
-0.0281
-4,221
-15,374
-2,286
-16,520
-1.6406
-0.4619
-0.0012
-0.0003
-0.0304
-0.0003
-0.0001
0.0024
( 2423 obs.)
T-test
-30.33*
-9.66*
-30.67*
-3.35*
-2.64*
-1.83
-2.84*
-6.44*
-1.89
-32.26*
-3.67*
-32.38*
-9.91*
-2.46*
0.23
-1.51
Sign-test
-30.28*
-10.74*
-29.98*
-1.50
-0.77
-16.17
-1.50
-5.09*
1.83
-32.97*
-5.55*
-30.96*
-11.30*
-6.38*
-0.75
-0.93
Notes: (1) The difference is pre- minus post- signal average; t-test is t-stat; sign-test is the Z-score. CAR is the cumulated average return.
(2) Negative Z-score means that the cases of post-signal variable mean greater than pre-signal one are more than the cases of post-signal variable mean smaller than pre-signal one.
(3) The "*" indicates significance at a level of 95% or above.
Table 10: Results of Simulated Program Trading Tests of Predictability
MAB1
MAS1
MAS2
MAS3
TRBS1
TRBS2
-0.0032
-0.0024
-0.0066
0.0041
0.0045
0.0070
-0.0003
-0.0004
0.0021
0.0015
-3.3100*
5.7104*
-0.0068
2.2400*
1.6995
-18.070*
19.690*
-0.0020
-5.7100*
5.5131*
8.9100*
9.4117*
0.0028
6.2100*
5.8580*
5.4900*
7.1919*
0.0024
3.0400*
3.9796*
19.540*
19.335*
0.0051
14.300*
4.6256*
-1.2300
5.4880*
0.0029
12.630*
1.4412
-1.0700
3.5869*
0.0025
7.7200*
6.8260*
7.1300*
14.544*
0.0007
2.6000*
6.6412*
2.7300*
7.8582*
-0.0001
-0.2400
3.1203*
Market
Order
R
T-test
Sign-test
AR
T-test
Sign-test
-0.0076
-0.0025
-0.0097
0.0076
0.0081
0.0095
-0.0041
-0.0043
0.0060
0.0060
-14.710*
15.725*
-0.0014
-2.9700*
3.1381*
-9.2300*
10.691*
-0.0069
-0.8500
1.4360
-27.460*
27.738*
-0.0028
-8.3500*
8.8702*
16.530*
16.609*
0.0015
3.3600*
2.0490*
10.420*
11.727*
0.0015
1.9500*
2.3883*
26.540*
27.155*
0.0027
7.6300*
7.8162*
-16.810*
20.213*
0.0016
7.0500*
6.4659*
-12.220*
14.058*
0.0011
3.4700*
3.1100*
20.510*
28.197*
-0.0001
-0.4400
1.7815*
10.860*
17.518*
-0.0004
-0.7800
1.8953*
Limit
Order
R
T-test
Sign-test
AR
T-test
Sign-test
-0.0027
-0.0049
-0.0068
0.0033
0.0041
0.0066
-0.0003
0.0004
0.0018
0.0019
-3.7900*
5.7551*
0.0014
2.1300*
1.3717
-2.3200*
3.6543*
-0.0093
1.9300*
2.5052*
-13.400*
16.391*
-0.0020
-4.3700*
2.6419*
4.9600*
5.5027*
0.0026
4.1800*
3.2563*
3.7800*
3.7059*
0.0024
2.3800*
2.8876*
13.100*
14.080*
0.0049
10.320*
11.888*
-0.9000
5.1355*
0.0024
7.7600*
8.1481*
0.7400
1.9764*
0.0020
4.5200*
4.6766*
4.4900*
11.302*
0.0008
2.1300*
7.8314*
2.5800*
6.3959*
0.0000
0.0400
3.4812*
Market
Order
R
T-test
Sign-test
AR
T-test
Sign-test
Y
S
Limit
Order
V
E
D
Market
A
Y
Order
S
TRBB2
-6.2900*
7.6065*
0.0008
1.7300
2.0810*
T
W
O
F
I
TRBB1
R
T-test
Sign-test
AR
T-test
Sign-test
Y
D
A
MAB2
Limit
Order
O
N
E
D
A
MAB2
-0.0070
-0.0066
-0.0099
0.0068
0.0077
0.0090
-0.0041
-0.0036
0.0057
0.0063
-9.8400*
12.302*
-6.4300*
7.5889*
-19.810*
22.446*
10.310*
10.947*
7.2400*
8.1888*
18.020*
20.294*
-12.220*
15.163*
-7.4100*
8.9266*
14.350*
21.743*
8.8000*
13.543*
-0.0008
-0.0097
-0.0029
0.0013
0.0014
0.0025
0.0011
0.0006
-0.0001
-0.0002
-1.2500
0.9648
-0.2400
0.1843
-6.2400*
6.1057*
2.1000*
1.1481
1.4500
1.9519*
5.2700*
6.8095*
3.5500*
5.4630*
1.3900
2.9665*
-0.1600
3.4701*
-0.3700
2.2738*
R
T-test
Sign-test
AR
T-test
Sign-test
-0.0031
-2.8200*
3.5964*
-0.0068
-2.8900*
3.2383*
-0.0071
-8.5200*
9.9824*
0.0023
2.0400*
1.8485*
0.0019
1.0000
2.4378*
0.0062
7.2600*
6.6439*
-0.0024
-4.6000*
4.4525*
0.0003
0.4300
0.5354
0.0030
4.8700*
7.6073*
0.0043
4.3300*
5.4470*
0.0016
-0.0099
-0.0026
0.0026
0.0005
0.0042
0.0001
-0.0002
0.0014
0.0007
1.6800
2.0969*
-0.0500
0.7759
-3.4800*
2.9822*
2.5200*
2.6123*
0.2700
2.1018*
5.4600*
5.7827*
0.1500
3.9546*
-0.3800
1.6892
2.5300*
8.4523*
0.7200
3.8608*
R
T-test
Sign-test
AR
T-test
Sign-test
-0.0074
-6.7800*
8.0193*
-0.0071
-5.4700*
6.2594*
-0.0102
-12.280*
14.287*
0.0058
5.1200*
4.8608*
0.0055
2.9800*
4.3383*
0.0087
10.120*
10.803*
-0.0062
-12.110*
11.296*
-0.0037
-5.0700*
4.9617*
0.0068
11.300*
13.731*
0.0087
8.8300*
9.9546*
-0.0006
-0.6400
0.7559
-0.0102
-1.3900
0.4560
-0.0035
-4.6000*
3.6699*
0.0012
1.2300
0.8203
-0.0005
-0.3200
1.1955
0.0019
2.3900*
2.6062*
-0.0012
-2.7300*
2.3970*
-0.0016
-2.5400*
0.0762
0.0006
0.9800
5.3548*
0.0004
0.4200
2.9449*
Notes: (1) R and AR are return and abnormal return (net of the return on TIPS) after technical signals, respectively.
(2) The "*" of t-test and sign-test (Z-score) indicates significance at a level of 95% or above.
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
mab1
-0.0004
-0.0003
-0.0004
-0.0002
-0.0001
-0.0001
-0.0003
-0.0003
-0.0002
-0.0004
0
-0.0001
0.0002
0.0001
-0.0004
-0.0001
0
-0.0001
-0.0009
0.0017
0.0012
0.0008
0.0009
0.0009
0.0011
0.001
0.0011
0.0014
0.0009
0.0012
0.0015
0.0017
-0.0004
0.0001
0.0002
0.0003
0.0001
mab2
-0.0001
0.0002
0
-0.0002
0
-0.0002
-0.0003
-0.0001
-0.0002
0.0002
-0.0002
0.0001
0.0001
-0.0002
0.0001
0.0005
0.0003
0.0004
-0.0006
0.0021
0.0018
0.0011
0.0017
0.0015
0.0012
0.0013
0.0015
0.0013
0.0011
0.0015
0.0015
0.0019
-0.0001
0.0003
0.0004
-0.0001
0.0002
mab3
trbb1
trbb2
0.0002 0.0004 0.0006
0 0.0004 0.0006
-0.0001 0.0005 0.0006
0.0001 0.0005 0.0006
0 0.0006 0.0008
-0.0002 0.0006 0.0009
0 0.0005 0.0006
-0.0002 0.0007 0.0008
0.0001 0.0006 0.0007
-0.0001 0.0006 0.0007
-0.0002 0.0007 0.0007
0.0001 0.0006 0.0006
0 0.0006 0.0006
0 0.0006 0.0007
-0.0001 0.0007 0.0008
0.0001 0.0008 0.0009
-0.0002 0.0009
0.001
0
0.001 0.0011
0.0001 0.0012 0.0014
0.0002 0.0012 0.0012
0 0.0011 0.0012
0 0.0011 0.0012
0.0001 0.0011 0.0012
0 0.0011 0.0012
0.0001 0.0011 0.0012
0.0001 0.0012 0.0013
0 0.0012 0.0013
0.0001 0.0014 0.0015
0 0.0017 0.0018
-0.0003 0.0022 0.0024
-0.0017
0.003 0.0031
0.008 0.0059 0.0057
-0.0015 0.0004 0.0006
-0.0004 0.0004 0.0004
0 0.0003 0.0003
0 0.0003 0.0003
0 0.0003 0.0003
mas1
0
0.0003
0.0003
0.0002
0.0003
0
0.0003
0.0001
0.0003
0.0001
0.0003
0
-0.0001
0.0001
0
0.0003
0.0003
0
0.0011
-0.0017
-0.0015
-0.0009
-0.0007
-0.0008
-0.0008
-0.001
-0.0008
-0.0009
-0.0014
-0.0012
-0.0013
-0.0016
0.0003
0
0.0003
-0.0002
-0.0003
mas2
-0.0005
0.0001
0
0.0001
-0.0007
-0.0001
-0.0002
-0.0001
0.0002
0.0001
0.0002
-0.0002
0
0.0001
-0.0001
0.0003
0
0
0.0008
-0.002
-0.0011
-0.0013
-0.0011
-0.0017
-0.0011
-0.0012
-0.0011
-0.0009
-0.0013
-0.0012
-0.0013
-0.003
0.0008
-0.0002
-0.0003
0.0001
-0.0001
mas3
-0.0002
0
0
0.0002
-0.0002
0.0001
-0.0001
-0.0001
-0.0002
0
0.0001
-0.0002
-0.0001
-0.0001
0
-0.0001
0.0003
0.0001
0.0001
-0.0003
-0.0001
0.0003
-0.0002
0.0002
0
0.0001
0
0.0002
-0.0001
0.0004
0.0018
-0.0081
0.0016
0.0003
0
0
0.0001
trbs1
-0.0005
-0.0005
-0.0004
-0.0005
-0.0007
-0.0006
-0.0006
-0.0005
-0.0006
-0.0005
-0.0004
-0.0006
-0.0006
-0.0007
-0.0007
-0.0007
-0.0008
-0.0009
-0.0011
-0.001
-0.001
-0.0009
-0.001
-0.001
-0.0011
-0.0011
-0.0012
-0.0013
-0.0015
-0.002
-0.003
-0.0067
-0.0001
-0.0001
-0.0001
-0.0003
-0.0003
trbs2
-0.0007
-0.0006
-0.0005
-0.0008
-0.0008
-0.0008
-0.0007
-0.0008
-0.0008
-0.0007
-0.0006
-0.0006
-0.0006
-0.001
-0.0009
-0.0009
-0.0008
-0.0011
-0.0015
-0.0014
-0.0013
-0.0012
-0.0012
-0.0012
-0.0013
-0.0012
-0.0015
-0.0015
-0.0016
-0.0024
-0.0037
-0.0075
-0.0003
-0.0001
-0.0001
-0.0004
-0.0003
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
Buy
Sell
Buy-CR
0.00014 -0.00038
0.00018 -0.00014
0.00012 -0.00012
0.00016 -0.00016
0.00026 -0.00042
0.0002 -0.00028
0.0001 -0.00026
0.00018 -0.00028
0.0002 -0.00022
0.0002
-0.0002
0.0002 -0.00008
0.00026 -0.00032
0.0003 -0.00028
0.00024 -0.00032
0.00022 -0.00034
0.00044 -0.00022
0.0004
-0.0002
0.00048 -0.00038
0.00024 -0.00012
0.00128 -0.00128
0.00106
-0.001
0.00084
-0.0008
0.001 -0.00084
0.00094
-0.0009
0.00094 -0.00086
0.00098 -0.00088
0.00102 -0.00092
0.00114 -0.00088
0.0011 -0.00118
0.0014 -0.00128
0.00148
-0.0015
0.00464 -0.00538
-0.0002 0.00046
0.00016 -0.00002
0.00024 -0.00004
0.00016 -0.00016
0.00018 -0.00018
0.00014
0.00032
0.00044
0.0006
0.00086
0.00106
0.00116
0.00134
0.00154
0.00174
0.00194
0.0022
0.0025
0.00274
0.00296
0.0034
0.0038
0.00428
0.00452
0.0058
0.00686
0.0077
0.0087
0.00964
0.01058
0.01156
0.01258
0.01372
0.01482
0.01622
0.0177
0.02234
0.02214
0.0223
0.02254
0.0227
0.02288
Sell-CR
-0.00038
-0.00052
-0.00064
-0.0008
-0.00122
-0.0015
-0.00176
-0.00204
-0.00226
-0.00246
-0.00254
-0.00286
-0.00314
-0.00346
-0.0038
-0.00402
-0.00422
-0.0046
-0.00472
-0.006
-0.007
-0.0078
-0.00864
-0.00954
-0.0104
-0.01128
-0.0122
-0.01308
-0.01426
-0.01554
-0.01704
-0.02242
-0.02196
-0.02198
-0.02202
-0.02218
-0.02236
11 0.0001 0.0003
0 0.0003 0.0003 -0.0002 -0.0001
12 0.0001 0.0003 0.0001 0.0003 0.0002 0.0001 -0.0004
13 0.0001
0 0.0001 0.0003 0.0002 -0.0001 0.0002
14 0.0001
0 -0.0001 0.0003 0.0003 -0.0005 -0.0004
15 0.0003 0.0001 -0.0001 0.0002 0.0002 0.0003
0
16 0.0004 0.0007 0.0002 0.0003 0.0002 -0.0002 -0.0002
17 -0.0002 0.0002 0.0001 0.0003 0.0003 0.0001
0
18
0 0.0003 0.0001 0.0001 0.0001 -0.0003 0.0001
19 -0.0002
0 0.0001
0
0 -0.0004 -0.0004
20 0.0002 0.0002 -0.0001
0 0.0001
0 -0.0001
21 0.0001 -0.0001 0.0003 0.0001 0.0001
0 -0.0002
22 0.0001 0.0002 -0.0001
0 -0.0001
0
0
23 0.0001 0.0003 0.0002 0.0001 0.0001
0 0.0003
24
0 -0.0005 -0.0001
0
0 -0.0001 -0.0002
25 0.0001 -0.0001 -0.0001
0
0
0 0.0003
26 -0.0001
0 -0.0001 -0.0001
0 -0.0002 -0.0003
0
-0.0001
-0.0001
-0.0001
-0.0001
0
-0.0003
-0.0001
0
0.0001
-0.0001
0.0003
0
-0.0001
-0.0001
0
-0.0003
-0.0002
-0.0002
-0.0001
-0.0002
-0.0002
-0.0001
-0.0001
0
0
-0.0001
0
0
0.0001
0
0
rasq
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
0.0053 0.0056 0.0055 0.0053 0.0049 0.0051 0.0056 0.0056 0.0054
0.006 0.0051 0.0056 0.0049 0.0045 0.0055 0.0052 0.0055 0.0051
0.0053 0.0055 0.0055
0.005 0.0046 0.0054
0.005 0.0053 0.0053
0.0057
0.005 0.0057 0.0052 0.0049 0.0052 0.0053 0.0051 0.0053
0.0057
0.006 0.0056 0.0053 0.0052 0.0055 0.0051 0.0055 0.0055
0.0058
0.007 0.0056 0.0054 0.0054
0.005 0.0048 0.0059 0.0054
0.0057 0.0058 0.0057
0.005 0.0048 0.0055 0.0057 0.0056 0.0053
0.0054 0.0056 0.0057
0.005 0.0049 0.0055 0.0052 0.0056
0.005
0.0053 0.0059 0.0057 0.0049 0.0046 0.0053 0.0056 0.0055 0.0053
0.0053 0.0056 0.0054 0.0048 0.0047 0.0057
0.005 0.0054 0.0053
0.0058 0.0054 0.0053 0.0048 0.0047 0.0053 0.0054 0.0056 0.0053
0.0055 0.0049 0.0057 0.0048 0.0045 0.0051 0.0051 0.0053 0.0053
0.0057 0.0059 0.0055 0.0049 0.0046 0.0051 0.0049 0.0058 0.0049
0.0057 0.0066 0.0056 0.0051 0.0048 0.0053 0.0057 0.0054
0.005
0.006 0.0057 0.0056 0.0051 0.0051 0.0049 0.0053 0.0053 0.0053
0.0056 0.0057 0.0058 0.0051 0.0049 0.0051 0.0048 0.0052 0.0054
0.0051
0.005 0.0058 0.0052 0.0051 0.0054
0.005 0.0057 0.0055
0.0051 0.0058 0.0056 0.0054 0.0054 0.0055 0.0056 0.0056 0.0059
0.005 0.0052 0.0057 0.0056 0.0054 0.0053 0.0062 0.0058 0.0062
0.0053 0.0064 0.0056 0.0051 0.0049 0.0051 0.0055 0.0057 0.0058
-0.0004
11 0.0002
-0.0002
-0.0003
12 0.0002 -0.00018
-0.0003
13 0.00014
-0.0001
0
14 0.00012 -0.00022
-0.0004
15 0.00014 -0.00008
-0.0004
16 0.00036
-0.0002
-0.0001
17 0.00014 -0.00008
-0.0001
18 0.00012
-0.0001
-0.0001
19 -2E-05 -0.00018
0
20 0.00008
0
-0.0002
21 0.0001 -0.00012
0.0001
22 0.00002 0.00008
0
23 0.00016 0.00006
0.0001
24 -0.0001 -0.00004
0
25 -2E-05 0.00004
0.0001
26 -6E-05 -0.00008
ra
rasq
trbs2
Buy
Sell
0.0059
-26 0.00532 0.00552
0.0053
-25 0.00522 0.00532
0.0057
-24 0.00518 0.00534
0.0057
-23 0.0053 0.00532
0.0058
-22 0.00556 0.00548
0.0056
-21 0.00584 0.00534
0.0054
-20 0.0054
0.0055
0.0054
-19 0.00532 0.00534
0.0059
-18 0.00528 0.00552
0.0061
-17 0.00516
0.0055
0.0061
-16 0.0052 0.00554
0.006
-15 0.00508 0.00536
0.0054
-14 0.00532 0.00522
0.0053
-13 0.00556 0.00534
0.006
-12 0.0055 0.00536
0.0057
-11 0.00542 0.00524
0.0057
-10 0.00524 0.00546
0.0066
-9 0.00546 0.00584
0.0072
-8 0.00538 0.00614
0.0069
-7 0.00546
0.0058
0.02308
0.02328
0.02342
0.02354
0.02368
0.02404
0.02418
0.0243
0.02428
0.02436
0.02446
0.02448
0.02464
0.02452
0.0245
0.02444
-0.02256
-0.02274
-0.02284
-0.02306
-0.02314
-0.02334
-0.02342
-0.02352
-0.0237
-0.0237
-0.02382
-0.02374
-0.02368
-0.02372
-0.02368
-0.02376
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
0.0055
0.0051
0.0055
0.0056
0.0052
0.0056
0.0055
0.0062
0.0057
0.0061
0.0058
0.0059
0.0058
0.0053
0.0054
0.006
0.0055
0.007
0.0056
0.0054
0.0064
0.0065
0.0058
0.0062
0.0058
0.0056
0.0049
0.0056
0.0067
0.0052
0.0057
0.0058
0.0058
0.0056
0.0054
0.007
0.006
0.0058
0.0052
0.0063
0.0061
0.0063
0.0063
0.006
0.0058
0.0055
0.0061
0.006
0.0057
0.0053
0.0052
0.0058
0.0056
0.0054
0.005
0.0058
0.0056
0.0063
0.0049
0.0051
0.0051
0.0058
0.0056
0.0076
0.0056
0.0057
0.0056
0.0056
0.0058
0.0054
0.0055
0.0055
0.0053
0.0053
0.0055
0.0058
0.0059
0.0067
0.0065
0.0058
0.0062
0.0056
0.0055
0.0057
0.0058
0.0058
0.0065
0.0057
0.0058
0.0062
0.0062
0.006
0.0057
0.0067
0.0061
0.0055
0.0056
0.006
0.0053
0.0049
0.0049
0.0048
0.0048
0.0049
0.0049
0.0048
0.0048
0.005
0.0052
0.0056
0.0063
0.0066
0.0056
0.0053
0.0052
0.0052
0.0055
0.0051
0.0052
0.0054
0.0055
0.0055
0.0055
0.0057
0.0054
0.0052
0.0051
0.0049
0.0049
0.0048
0.0051
0.0052
0.0047
0.0046
0.0047
0.0048
0.0046
0.0048
0.0047
0.0049
0.0051
0.0054
0.0056
0.0062
0.0064
0.0056
0.0051
0.0049
0.0051
0.0053
0.0049
0.0053
0.0056
0.0055
0.0055
0.0055
0.0059
0.0054
0.0051
0.0049
0.0048
0.0049
0.0047
0.005
0.0052
0.0052
0.0056
0.0051
0.0052
0.0054
0.0052
0.0056
0.0057
0.0076
0.0056
0.0066
0.0058
0.0058
0.0057
0.0056
0.0057
0.0059
0.0058
0.0053
0.0051
0.0055
0.0054
0.0061
0.0052
0.0056
0.006
0.0057
0.0054
0.006
0.0053
0.0053
0.0055
0.006
0.006
0.0065
0.0057
0.0092
0.0057
0.0059
0.0053
0.0058
0.0062
0.0062
0.0063
0.0098
0.0074
0.0056
0.0055
0.0056
0.0051
0.0052
0.0058
0.0063
0.006
0.0053
0.0058
0.0057
0.0057
0.0067
0.0057
0.0063
0.0055
0.0058
0.0055
0.0053
0.0052
0.0055
0.0054
0.0056
0.0055
0.0053
0.0055
0.0053
0.0053
0.0054
0.0057
0.0063
0.0078
0.0065
0.0061
0.0056
0.0057
0.0057
0.0059
0.0059
0.0063
0.0057
0.006
0.0057
0.0062
0.0065
0.0063
0.0057
0.0054
0.0061
0.0059
0.0055
0.0059
0.0054
0.006
0.0052
0.0052
0.005
0.0054
0.0055
0.0058
0.0055
0.0054
0.006
0.0067
0.0082
0.0073
0.0062
0.0061
0.0061
0.0059
0.006
0.006
0.0062
0.006
0.006
0.0062
0.0064
0.0066
0.0058
0.0056
0.0055
0.0056
0.0055
0.0056
0.0058
0.006
0.0073
0.0057
0.0057
0.0054
0.006
0.0061
0.0066
0.006
0.0058
0.007
0.008
0.0094
0.0084
0.0069
0.007
0.007
0.0066
0.0066
0.0065
0.007
0.0067
0.0068
0.0068
0.0071
0.0074
0.0064
0.0061
0.0058
0.0061
0.0064
0.0065
0.0068
0.0063
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
0.00526
0.00512
0.00556
0.00532
0.0052
0.0052
0.00532
0.00546
0.00552
0.00576
0.00578
0.00618
0.00616
0.00568
0.0056
0.00548
0.00532
0.00574
0.00544
0.00546
0.00586
0.00564
0.00568
0.0058
0.00598
0.00546
0.0052
0.00548
0.00566
0.00522
0.00568
0.0055
0.00544
0.006
0.00568
0.00546
0.00606
0.00556
0.00564
0.00572
0.00566
0.00608
0.0061
0.00678
0.0082
0.00708
0.0061
0.00596
0.00602
0.00584
0.0059
0.0059
0.00618
0.00598
0.0059
0.00612
0.00612
0.00636
0.00624
0.00576
0.00568
0.00586
0.00578
0.00568
0.00586
0.00578
Figure 1: Mean and Standard Deviation of Price Changes and Quote Revisions Around Buy and Sell Signals on Interval 0.
Panel C: Quote Revisions
Panel A: Price Changes
0.03
0.03
0.02
0.02
0.01
0.01
-0.01
-0.01
-0.02
25
22
19
16
13
10
7
4
1
-2
Buy-CR
Buy-CR
Sell-CR
Sell-CR
-0.03
-0.03
Panel B: Price Change Volatilities
Panel D: Quote Revision Volatilities
0.008
0.008
0.007
0.007
0.006
0.006
0.005
0.005
0.004
0.004
19
16
13
10
7
4
1
-2
-5
-8
-1
1
-2
6
25
22
19
16
13
10
7
4
1
-2
-5
-8
1
-1
-1
-1
-2
-2
4
0
7
0
0
0.001
3
0.001
Note : Buy-CR and Sell-CR are four day cumulative returns around buy and sell signals, respectively.
Sell
0.002
-1
4
Sell
-1
7
0.002
Buy
0.003
-2
0
Buy
-2
3
0.003
25
0.009
22
0.009
6
-5
Sell
Sell
-2
-8
1
4
-1
Buy
Buy
-0.02
-1
0
7
-1
-2
6
-2
-2
25
22
19
16
13
10
7
4
1
-2
-5
-8
1
4
-1
7
-1
-1
0
3
-2
6
-2
-2
3
0
0
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
trbs2
15891 13765 12787 17165 20388 13844 12599 14488 15147 15989
14316 12826 11322 17818 21405 13378 14144 13383 15257 15464
13245 16223 13373 18434 21693 14472 14473 12736 16273 16672
15098 11676 13965 19082 22286 14965 13651 12771 21382 20015
13971 14813 12669 19008 22686 14923 13153 13191 22178 20975
14985 14098 13600 19953 24417 13878 12234 13454 22308 21641
12032 12600 14289 19157 23613 16152 15460 12865 20041 17074
12362 12091 12600 17008 20093 14344 12012 12838 16122 15914
11105 11941 13010 17559 20724 12058 13418 13168 15384 17241
12402 14766 14590 16416 19722 13377 13918 13158 14998 16279
13012 13069 11860 17379 19080 12415 13135 13339 14760 17072
12254 10928 12432 17301 18937 14883 11664 12326 15037 16523
12476 15784 12319 16184 19224 11677 11341 13420 15183 16358
11328 13289 12473 16864 19621 13149 13560 13048 16203 16961
12318 11477 12889 17997 21636 12709 13271 12534 16839 18956
14886 13017 14045 18297 22005 11498 13641 12032 17624 19438
12223 12687 12025 19026 23091 13426 14575 13915 21127 18702
10798 12020 13016 19341 23546 11767 12654 12048 22514 21105
10199 16205 12836 20218 24694 13448 12631 14958 22704 22014
11350 12565 13262 18706 22377 13762 17099 13335 18215 21295
11888 14325 13430 19088 23247 13318 14065 12526 18463 21192
11480 13757 13492 18801 22147 12674 12625 13658 18383 22863
11910 14218 13845 17945 20753 12475 15466 12250 17903 23430
11687 15794 11845 17983 21818 13200 16649 14038 23637 25827
12326 13955 11922 18395 22508 12849 15735 12216 17576 17813
12207 15304 11278 18538 23107 13519 38094 11936 22277 19710
13016 16037 12148 21450 25796 13207 11724 10915 24998 29235
14502 16701 11742 22460 26031 21656 13842 11711 27291 29127
15874 26763 12727 23116 28938 15381 33173 12522 21509 22437
20295 14960 13040 25877 32176 16688 14565 12191 23104 25781
13034 16607 13105 31437 40045 36515 32338 12607 32541 31088
15124 18108 16569 38212 45642 12948 15807 22609 41019 48498
13040 12492 15338 27636 33687 15304 20099 18102 27027 36079
15436 14260 13007 24042 29615 13589 13891 14101 24547 32494
21684 16954 14595 22519 27328 12966 13805 18235 24040 31057
14374 16400 16827 22429 27492 14413 14878 13426 23377 30628
14701 13893 13138 21227 25498 13978 16471 14059 21878 30263
14428 13486 13722 21460 24726 14024 13200 12984 19363 22292
29944 13742 13570 21259 24196 12222 14409 15191 20320 23290
12145 15583 13414 21879 25912 12335 13986 13073 23244 30853
15372 14062 13378 21983 26900 13182 19003 13267 23170 29958
15004 14846 20002 23231 26499 12746 12478 14150 23655 31134
15349 15211 13305 24518 29366 13807 15215 19822 23282 30517
17803 15785 14937 26152 30571 13503 14336 14094 20956 23299
14298 18311 14532 25204 29383 14771 16506 16120 20991 23700
16672 14756 17571 24316 25312 13324 17415 14520 18355 21626
13472 14856 13140 20600 22597 12981 12815 14434 20801 26470
18892 12816 14399 21030 22241 16761 14593 14644 21578 28674
13407 14353 15059 22483 21837 12412 11798 13840 19634 19148
12773 15250 14100 18708 21199 14463 12265 14761 16545 19189
16776 14109 14191 19476 20194 12916 15080 14413 15967 17757
14325 13876 14373 20287 21395 12625 12575 13252 16981 20664
13706 14707 14969 19556 22563 15143 10146 14407 17003 19258
mab1
-26
-25
-24
mab2
9
9
9
mab3
9
9
9
trbb1
9
9
9
trbb2
12
12
12
mas1
14
14
15
mas2
10
10
10
mas3
8
9
9
trbs1
8
9
9
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
trbs2
11
11
11
11
11
11
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-26
-25
-24
-23
-22
-21
-20
10
9
9
9
9
9
9
9
9
9
8
9
9
9
8
8
9
8
9
8
9
9
8
9
9
10
9
10
10
9
9
9
9
9
10
10
9
9
10
10
11
9
10
9
10
9
9
10
9
10
9
9
9
8
9
8
8
9
8
9
9
8
9
9
8
9
9
10
9
9
10
9
10
10
10
10
10
11
11
10
10
9
10
9
9
10
10
10
10
10
9
10
10
9
8
9
10
9
10
10
9
9
10
9
9
9
9
8
8
8
9
8
9
9
9
9
9
9
9
9
9
8
8
8
8
9
9
9
11
9
9
9
9
9
9
9
9
9
9
9
10
10
10
9
9
9
9
9
9
9
13
13
13
12
12
12
11
11
11
11
12
12
12
13
13
13
13
12
12
12
12
12
13
13
14
15
16
18
20
17
16
15
15
14
15
14
15
15
16
16
16
16
15
14
14
13
13
13
13
14
15
15
16
15
14
14
14
13
13
13
14
15
15
15
16
16
15
15
14
14
15
15
15
16
17
18
20
23
25
21
19
18
18
18
18
17
18
19
19
19
20
19
18
17
16
16
16
16
16
16
10
10
9
10
10
9
10
9
9
9
9
9
9
10
9
10
9
9
9
9
9
9
9
9
9
10
10
9
9
10
9
9
9
9
9
9
9
9
9
10
9
9
9
9
9
9
9
9
9
9
10
9
9
9
8
8
9
9
9
8
9
8
9
9
8
9
9
9
9
9
10
9
9
9
9
9
10
10
9
9
9
9
9
9
9
9
10
11
9
10
9
10
10
9
9
9
9
9
9
8
9
9
10
9
9
9
9
9
8
9
9
8
8
9
9
9
9
9
9
8
9
8
8
8
8
9
9
9
11
9
9
9
9
9
8
9
9
9
9
9
10
10
9
9
9
9
10
9
9
9
12
12
12
11
10
10
10
10
11
11
11
11
11
12
12
12
11
12
11
11
11
11
11
11
12
12
13
15
17
14
13
13
13
12
12
12
12
13
13
13
14
13
13
12
12
11
11
11
11
12
12
12
12
11
10
11
11
11
11
11
12
12
12
12
13
13
13
13
12
12
12
12
12
13
13
13
15
18
21
17
16
15
15
14
14
14
14
14
14
15
15
15
14
13
13
13
13
12
12
13
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
trbs2
-6629
-1851
379
2475
5481
1322
-4143
1364
-1892 -3610
-2576
-2484
-701
2735
4922
1359
1740
157
-2135 -2872
-3527
-1880
-2619
2703
4916
2738
1785
-204
-2071 -2655
-1557
-173
-268
3595
6306
-33
425
-327
-6790 -5725
-947
-4021
-345
4507
8027
1843
-2818
-645
-7212 -5492
663
-2530
-1152
4469
7955
1355
889
1023
-7197 -6134
-1933
-1671
491
3810
6874
822
-3645
991
-7049 -5823
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-2127
-1365
-4083
-2448
-1589
-701
-1215
-225
1422
-546
599
-1151
3638
3076
3188
2126
3271
1883
3682
6412
6529
5649
12483
3250
7207
578
812
8509
923
-665
-1002
-14110
-742
1729
3629
617
418
1211
-1994
751
-1272
1683
-264
-1770
1826
503
-3179
-412
-1396
236
2746
-1805
550
539
566
1729
1622
-5104
3715
5535
6738
4750
7908
4058
5466
2318
7099
16592
4521
8185
9357
2464
1416
7696
689
2032
435
1716
196
-2023
-2813
3844
260
1538
3711
1126
1354
1484
2606
-4576
-21
7
-1717
-166
-1082
-2307
63
-976
177
506
-1793
-941
-1472
-446
-1336
-357
-49
-617
-1503
441
-1362
-1015
-1261
-150
-1025
-2035
13993
604
229
124
3328
-1085
-1428
-1995
113
-2045
-4799
520
261
119
120
-441
460
-2074
-59
-872
1302
-2215
3359
3971
3303
4041
3457
3308
3541
4205
4077
3957
4974
6104
5553
6784
6648
5479
6574
6629
7485
8020
10110
10063
13807
19471
29103
5734
4720
4116
3317
3252
2898
2160
2332
2842
2983
3282
4612
1935
-423
2077
-654
-2214
2710
-853
-627
968
5531
7186
4928
4141
3366
4897
4846
5173
6039
6075
6898
8220
6885
8503
7960
7742
9184
9500
11051
9122
12204
12925
17656
24648
32703
5808
5864
4957
5362
3528
2692
1101
2247
3183
3741
4180
5001
1297
967
2195
1949
1564
2415
271
1675
1291
1732
991
200
3029
375
-94
941
-1813
573
2404
1163
-579
-4577
-3109
-3967
-3842
-4747
-5390
-6143
-4746
-11853
-5288
-4880
-28785
-4173
-3299
-1328
692
387
-1453
-4241
-379
-536
-863
-1165
162
665
-1169
230
-506
1024
-1499
297
-641
-1290
-2027
1324
-1602
1054
-2975
1497
-2700
2124
109
-608
1136
-1266
-604
-9293
-4062
-4635
-6081
-6733
-6539
-29425
-5002
-2953
-25297
-6174
-25789
-10446
-6410
-3878
-2137
30
-1947
-3918
-4463
-2582
-308
-54
-101
-2129
2855
-3169
599
-2063
-261
-561
-380
1158
-1365
-418
-1959
-155
280
-965
-7
390
-3062
210
9
959
-2871
-752
-1277
-1715
-1971
-378
-1614
-781
-1337
-749
-2303
1424
1245
-20933
-7348
-1816
-7239
-66
-329
-3258
-1677
-2196
-1813
-947
-5099
-2018
-151
-1597
-965
-1973
33
-490
-1448
-1819
757
-4052
-3420
-3082
-2409
-2863
-3052
-3895
-5382
-4501
-7010
-8755
-8471
-4866
-5749
-5886
-6826
-14088
-7589
-12361
-14396
-16042
-10040
-11671
-22549
-33107
-7349
-5804
-5559
-5793
-5045
-2862
-3864
-6538
-5449
-6025
-5318
-2518
-1610
-884
-3767
-4321
-4899
-1290
-846
-1533
-2087
-5015
-5878
-4390
-3544
-3809
-2994
-4663
-7445
-5307
-4608
-7272
-7015
-6980
-7545
-9734
-11043
-15466
-7181
-9025
-17625
-16606
-10089
-13122
-20957
-38268
-12309
-10780
-11423
-11564
-9590
-4996
-7456
-13472
-11579
-12605
-11233
-4191
-2449
-1866
-8961
-9403
-1750
-1619
-1162
-2845
-2394
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Figure 2: Cross-Sectional Means of Trading Volumes, Number of Trades and Signed Trading Volumes
Around Buy and Sell Signals on Interval 0.
35000
30000
20000
15000
Sell
5000
26
24
22
20
18
16
14
12
8
10
6
4
0
2
-2
-4
-6
-8
-1
0
-1
2
-1
4
-1
6
-1
8
-2
0
-2
2
-2
4
-2
6
0
18
14
12
8
6
Sell
2
20
20
26
18
18
24
16
16
22
14
14
12
10
8
6
4
2
0
-2
-4
-6
-8
0
2
-1
4
-1
-1
6
8
-1
-1
0
2
-2
-2
4
-2
-2
6
0
25000
15000
10000
Sell
26
24
12
10
8
6
4
2
0
-2
-4
-6
-8
0
-1
2
-1
4
-1
6
-1
8
-1
0
-2
2
-2
4
-2
-2
6
0
Buy
Sell
vol
15999.2 14413.4
15537.4 14325.2
16593.6 14925.2
16421.4 16556.8
16629.4
16884
17410.6
16703
16338.2 16318.4
14830.8
14246
14867.8 14253.8
15579.2
14346
14880 14144.2
14370.4 14086.6
15197.4 13595.8
14715 14584.2
15263.4 14861.8
16450 14846.6
15810.4
16349
15744.2 16017.6
16830.4
17151
15652 16741.2
16395.6 15912.8
15935.4 16040.6
15734.2 16304.8
15825.4 18670.2
15821.2 15237.8
16086.8 21107.2
17689.4 18015.8
18287.2 20725.4
21483.6 21004.4
21269.6 18465.8
22845.6 29017.8
26731 28176.2
20438.6 23322.2
19272 19724.4
20616 20020.6
19504.4 19344.4
17691.4 19329.8
17564.4 16372.6
20542.2 17086.4
17786.6 18698.2
18339
19716
19916.4 18832.6
19549.8 20528.6
21049.6 17237.6
20345.6 18417.6
19725.4
17048
16933 17500.2
17875.6
19250
17427.8 15366.4
16406 15444.6
16949.2 15226.6
16851.2 15219.4
17100.2 15191.4
Buy
Sell
10.6
10.6
10.8
nt
9.6
10
10
11.2
11
11.4
10.6
10.6
10.4
10.2
10
9.8
10
10.4
10.4
10.8
11
10.8
11
11
10.8
10.6
10.4
11
10.6
10.8
11.2
11.6
12.4
12.8
14.2
15.4
13.2
12.6
12
12.2
11.8
12.2
12
12.2
12.4
12.8
12.8
13.2
12.8
12.6
11.6
11.4
11.2
11.4
11.4
11.4
11.8
Buy
-29
379.2
-81.4
1580.6
1444.2
1881
1514.2
10.6
10.4
10.4
10
9.4
9.4
9.8
9.6
9.6
9.6
10
9.6
9.8
10.4
10.2
10.6
10.2
10.4
10
9.8
10.2
9.8
9.8
10
10.2
10.6
11.4
12.2
13.4
11.8
11.2
11
11
10.6
10.4
10.6
10.8
11.2
10.8
11.4
11.4
11.4
11
10.4
10.4
10.2
10.4
10
10
10.2
Sell
x
-1391.8
-350.2
-81.4
-2490
-2864.8
-2012.8
-2940.8
-1285.8
-2373.6
-1274.6
-1123.8
-1153
-1769.4
-1020.6
-3518.6
-1926.6
-1613.8
-3034.2
-3908
-5293.6
-4348.4
-5187.4
-5952.6
-8282.4
-5662.6
-11547
-8621.2
-9640.6
-10603.4
-6884.6
-19367
-21385.4
-7343
-4721.2
-5133.2
-3401.2
-3672.8
-3855
-2225.6
829.2
737.2
548.2
2488.6
2110.4
1220
476.2
1141.6
367.4
88.6
1481.6
-1560
831
110.8
-895.4
-1265.8
-1423.2
trbs2
0.0088
0.0088
0.0089
0.0088
0.0088
0.0089
0.0089
0.0088
0.0088
0.0088
0.0089
0.009
0.009
0.0091
0.009
0.0089
0.0091
0.0091
0.009
0.009
0.0091
0.009
0.009
0.0091
0.009
0.009
0.0092
0.0091
0.0093
0.0093
0.0096
0.0099
0.0095
0.0095
0.0095
0.0095
0.0094
0.0093
0.0095
0.0095
0.0094
0.0093
0.0094
0.0094
0.0094
0.0093
0.0093
0.0092
0.0093
0.0093
0.0094
0.0093
0.0094
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
trbs2
-26 -0.0965 0.0203 -0.0383 -0.0572
-0.04 -0.0515 -0.0161 -0.0498 -0.0102 -0.0037
-25 -0.099 -0.0167 -0.0304 -0.0424 -0.0264 -0.0419 -0.0442 -0.0301 -0.0144 -0.0361
-26
-25
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
0.0097 0.0095 0.0102 0.0083 0.0079 0.0095 0.0092 0.0101 0.0084
0.0098 0.0096 0.0101 0.0083 0.0079 0.0096 0.0094
0.01 0.0084
0.0098 0.0096 0.0102 0.0083 0.0078 0.0093 0.0093 0.0101 0.0084
0.0098 0.0097 0.0101 0.0083 0.0079 0.0093 0.0095 0.0101 0.0084
0.0097 0.0096 0.0101 0.0083 0.0079 0.0095 0.0095 0.0101 0.0084
0.0097
0.01 0.0102 0.0083 0.0079 0.0094 0.0093 0.0101 0.0084
0.0097 0.0099 0.0102 0.0083 0.0079 0.0093 0.0095 0.0102 0.0084
0.0097 0.0098 0.0103 0.0083 0.0078 0.0094 0.0095 0.0101 0.0084
0.0097 0.0097 0.0102 0.0082 0.0078 0.0095 0.0097 0.0101 0.0084
0.0099 0.0098 0.0101 0.0083 0.0079 0.0095 0.0094 0.0101 0.0084
0.01 0.0096 0.0102 0.0083 0.0079 0.0094 0.0094 0.0101 0.0084
0.0098 0.0095 0.0101 0.0082 0.0078 0.0095 0.0092
0.01 0.0084
0.01 0.0097 0.0102 0.0082 0.0078 0.0094 0.0096 0.0101 0.0085
0.0101 0.0097 0.0101 0.0082 0.0078 0.0093 0.0093 0.0102 0.0085
0.0098 0.0099 0.0102 0.0082 0.0079 0.0095 0.0095 0.0101 0.0085
0.0098 0.0097 0.0102 0.0082 0.0078 0.0094 0.0093 0.0102 0.0084
0.0098
0.01 0.0103 0.0082 0.0079 0.0095 0.0094 0.0102 0.0085
0.0097
0.01 0.0102 0.0082 0.0079 0.0095 0.0092 0.0102 0.0085
0.0097 0.0099 0.0102 0.0082 0.0079 0.0094 0.0094 0.0101 0.0085
0.0098
0.01 0.0101 0.0082 0.0079 0.0094 0.0093 0.0102 0.0085
0.0097 0.0097 0.0102 0.0082 0.0079 0.0093 0.0095 0.0101 0.0086
0.0099 0.0098 0.0103 0.0082 0.0079 0.0094 0.0096
0.01 0.0085
0.0097 0.0101 0.0102 0.0082 0.0078 0.0094 0.0098 0.0103 0.0085
0.0095 0.0098 0.0104 0.0082 0.0078 0.0096 0.0097 0.0102 0.0086
0.0097 0.0099 0.0104 0.0082 0.0078 0.0095 0.0095 0.0101 0.0086
0.0095 0.0098 0.0103 0.0082 0.0078 0.0095 0.0096 0.0102 0.0086
0.0096 0.0099 0.0103 0.0082 0.0078 0.0095 0.0096 0.0102 0.0087
0.0096 0.0098 0.0104 0.0082 0.0077 0.0096 0.0096 0.0102 0.0087
0.0096 0.0098 0.0103 0.0082 0.0078 0.0096 0.0097 0.0102 0.0087
0.0098 0.0097 0.0104 0.0083 0.0079 0.0097 0.0097 0.0103 0.0088
0.0097 0.0095 0.0104 0.0084
0.008 0.0097 0.0098 0.0102 0.0091
0.0098 0.0096 0.0103 0.0084
0.008 0.0096 0.0096 0.0104 0.0092
0.0096 0.0098 0.0104 0.0082 0.0078 0.0097 0.0098 0.0103
0.009
0.0096 0.0096 0.0102 0.0082 0.0078 0.0097 0.0098 0.0103
0.009
0.0098 0.0096 0.0102 0.0082 0.0078 0.0096 0.0098 0.0103 0.0089
0.0097 0.0098 0.0103 0.0082 0.0077 0.0097 0.0096 0.0102 0.0089
0.0096 0.0098 0.0103 0.0081 0.0077 0.0097 0.0096 0.0103 0.0088
0.0097 0.0096 0.0101 0.0081 0.0076 0.0096 0.0096 0.0101 0.0088
0.0097 0.0099 0.0101
0.008 0.0076 0.0096 0.0097 0.0103 0.0089
0.0096 0.0096 0.0103 0.0081 0.0076 0.0096
0.01 0.0101 0.0089
0.0096 0.0096 0.0102 0.0081 0.0076 0.0094 0.0098 0.0102 0.0089
0.0096 0.0097 0.0101
0.008 0.0076 0.0096 0.0097 0.0102 0.0088
0.0096 0.0097 0.0101
0.008 0.0076 0.0095 0.0098 0.0102 0.0089
0.0097 0.0096 0.0102 0.0081 0.0077 0.0094 0.0098 0.0102 0.0089
0.0095 0.0097 0.0103 0.0081 0.0077 0.0095 0.0096 0.0102 0.0089
0.0096 0.0098 0.0103 0.0081 0.0077 0.0096 0.0098 0.0102 0.0088
0.0096
0.01 0.0102
0.008 0.0077 0.0094 0.0096 0.0102 0.0088
0.0096 0.0097 0.0101
0.008 0.0076 0.0095 0.0098 0.0102 0.0087
0.0095 0.0099 0.0102
0.008 0.0076 0.0096 0.0096 0.0102 0.0088
0.0097 0.0096 0.0102
0.008 0.0076 0.0096 0.0097 0.0102 0.0088
0.0095 0.0095 0.0102
0.008 0.0077 0.0096
0.01 0.0101 0.0089
0.0095 0.0097 0.0102
0.008 0.0076 0.0095 0.0096 0.0103 0.0089
0.0096 0.0097 0.0102
0.008 0.0076 0.0095 0.0094 0.0102 0.0088
-24
-23
-22
-0.131
-20
-0.1214
-0.1043
-0.0838
-16 -0.1079
-15
-14 -0.1284
-13 -0.1146
-12 -0.1678
-11
-10 -0.1445
-9 -0.1759
-8 -0.1498
-7 -0.0746
-6 -0.1284
-5 -0.1177
-4
-0.0612
-2 -0.1019
-0.0482
0
1 -0.0516
-0.0514
3
4
5 0.0328
6 0.0094
7 -0.0078
8 0.0028
9 -0.0274
-0.0051
11
-0.0309
0.002
14
15 0.0022
16
-0.0874
18 -0.0463
19 -0.0485
-0.0547
21 -0.0564
22 -0.0118
23
24 -0.0803
25
26 -0.0786
-0.047
-0.0371
-0.0294
0.0038
0.0142
-0.125
-0.1262
-0.1327
-0.0257
-0.0288
-0.0358
-0.0462
-0.0499
-0.0458
-0.066
-0.0384
-0.1284 -0.0637
-0.0766
-0.0971
-0.0448
-0.1119 -0.1103
-0.0806
-0.0705
-0.0567
-0.0718
-0.0373
0.0426
-0.0343 -0.0416
-0.0641
0.0205
-0.0408
-0.0129 -0.1174
0.0218
-0.088
0.0038
0.0472 0.0013
0.0526
0.034
0.0447 0.0168
0.0363
0.0423
-0.0457
0.0192
-0.0588
0.0505 -0.0255
0.0936
0.0309
0.0048
-0.0132
-0.0167
-0.0354
-0.025
0.0238
0.0928
0.0439
0.0602
0.0393
-0.0288
-0.0434
-0.0513
-0.0456
-0.0374
-0.0575
-0.0397
-0.0373
-0.0343
-0.0413
-0.0478
-0.0387
-0.0532
-0.0449
-0.0243
-0.0258
-0.0418
-0.0514
-0.0382
-0.0305
-0.0328
-0.0156
0.0402
0.0014
-0.018
-0.0325
-0.013
-0.0047
-0.0158
-0.0131
-0.0096
-0.0184
-0.0143
-0.0016
-0.0029
-0.0028
-0.0048
-0.0206
0.0056
-0.0327
-0.0224
-0.0632
-0.0672
-0.0525 -0.0233
-0.0161 -0.0363
-0.0236 -0.0198
-0.0391
0.0011
-0.0233 -0.0073
0.0241
-0.0081
-0.0394
-0.0613
-0.0089
0.0288
0.0276
-0.0399
-0.0158
-0.0258
-0.0276 -0.0535
-0.0117
-0.0461
-0.0649
-0.0376 -0.0977
-0.0415
-0.0924
-0.0463
0.0438
-0.1156
-0.038 -0.1267
-0.0237 -0.0994
-0.1193
-0.0632
-0.0823
-0.046
-0.0358 -0.0864
-0.031 -0.1103
-0.029
-0.034
-0.0208
-0.0198
-0.0554
0.0068
-0.0921
-0.0121
-0.1071
-0.0002
-0.0329
-0.1099
-0.0116 -0.1386
-0.1159
-0.1031
-0.0535
-0.0716
-0.0715
-0.1129
-0.0692
-0.0227
-0.0504
-0.0456
-0.0364
-0.0317
-0.0725
-0.0701
-0.0745
-0.0586
-0.0673
-0.0647
-0.0581 -0.0409
-0.0683
0.0904 -0.047
0.0978 -0.0446
-0.0433
-0.0172
0.0056
0.0159
-0.016
0.0743
-0.0337
0.0036
0.0021 0.0069
-0.0475 0.0188
-0.0661
-0.092 -0.0259
-0.1313
-0.0761
-0.0852
-0.0362
-0.0864 -0.0973
-0.0359
-0.0082 -0.0748
-0.0533
0.0183
-0.0272 -0.0813
-0.061
-0.0696 -0.0122
0.0119
-0.0603
-0.0255 -0.0415
-0.0225
0.013
-0.0424
0.0027
-0.031 -0.0299
-0.014
-0.0155
-0.0305
-0.0493
-0.0175
-0.0107
-0.0137
-0.0006
0.0128
0.0208
-0.0365
-0.025
0.0076
0.0019
-0.0068
-0.0136 0.0066
-0.0068 0.0187
-0.0242 -0.0021
-0.0257
0.021
-0.0197 0.0389
0.0457
0.0565
-0.0032 0.0171
-0.0022
0.017
-0.0059
0.0037 0.0032
0.0458
0.0314 0.0477
0.0412
0.0358
0.0683
0.0477 0.0673
0.0076
0.036
-0.0416
-0.0796 -0.0239
-0.0375
-0.0401
0.011
-0.0088
0.021
0.0025 0.0114
0.0094
0.0056
0.0065
0.0151 0.0234
0.0079 0.0034
0.011
-0.0169
-0.0154
0.0168
-0.0217
-0.018
-0.0212 0.0168
-0.001
0.0025 0.0334
-0.006
-0.0215
-24
-23
-22
-21
-20
-19
-18
-16
-12
-5
-4
-2
0
1
2
5
6
7
8
9
11
12
13
14
16
17
18
19
20
21
22
23
24
25
26
Figure 3: Cross-Sectional Means of Relative Spreads and Depth Imbalances
Around Buy and Sell Signals on Interval 0.
Panel A: Relative Spreads
0.0098
0.0096
0.0094
0.0092
0.009
Buy
0.0088
Sell
24
26
24
26
22
20
18
16
14
12
8
10
6
4
2
0
-2
-4
-6
-8
0
2
-1
4
-1
6
-1
8
-1
0
-1
2
-2
4
-2
-2
-2
6
0.0086
Panel B: Depth Imbalances
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
Buy
-0.08
Sell
-0.1
22
20
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
0
-1
2
-1
4
-1
6
-1
8
-1
0
-2
2
-2
4
-2
-2
6
-0.12
Buy
Sell
rs
0.00912
0.0092
0.00914 0.00924
0.00914
0.0092
0.00916 0.00922
0.00912 0.00926
0.00922 0.00922
0.0092 0.00926
0.00918 0.00924
0.00912
0.0093
0.0092 0.00924
0.0092 0.00924
0.00908 0.00922
0.00918 0.00932
0.00918 0.00928
0.0092 0.00932
0.00914 0.00924
0.00924 0.00934
0.0092
0.0093
0.00918 0.00928
0.0092 0.00928
0.00914 0.00932
0.00922
0.0093
0.0092
0.0094
0.00914 0.00944
0.0092 0.00934
0.00912 0.00938
0.00916 0.00944
0.00914 0.00944
0.00914
0.0095
0.00922 0.00956
0.0092 0.00968
0.00922 0.00974
0.00916 0.00966
0.00908 0.00966
0.00912 0.00962
0.00914 0.00958
0.0091 0.00956
0.00902 0.00948
0.00906
0.0096
0.00904 0.00962
0.00902 0.00954
0.009 0.00952
0.009 0.00956
0.00906 0.00954
0.00906 0.00952
0.0091 0.00954
0.0091 0.00946
0.009 0.00948
0.00904
0.0095
0.00902 0.00952
0.00898
0.0096
0.009 0.00952
0.00902 0.00946
Buy
Sell
-0.04234 -0.02626
-0.04298 -0.03334
-0.05476
-0.05124
-0.05914
-0.0447
-0.04904
-0.06698
-0.07154
-0.07372
-0.08262
-0.07532
-0.05892
-0.0787
-0.08128
-0.10786
-0.09562
-0.10588
-0.08932
-0.07888
-0.06028
-0.03306
-0.03806
-0.0327
-0.05312
-0.02218
-0.05648
-0.03608
-0.0276
-0.03544
0.0282
0.0449
-0.01042
0.00478
-0.00238
-0.01672
-0.02084
-0.02994
-0.01694
-0.00374
0.00714
-0.01254
-0.02046
-0.03208
-0.02226
-0.02806
-0.01742
-0.0138
0.00872
-0.00774
-0.01624
-0.01436
-0.02634
-0.05232
-0.0513
-0.0336
-0.04216
-0.04166
-0.04736
-0.01804
-0.0185
-0.02192
-0.03026
-0.01568
-0.03816
-0.0384
-0.01738
-0.00372
0.02092
0.02712
-0.00092
0.01398
-0.00694
-0.00984
0.03178
0.00142
0.01138
-0.00494
0.01192
-0.00122
-0.01432
-0.06134
-0.09482
-0.07954
-0.0656
-0.03698
-0.05752
-0.03618
-0.02652
-0.03678
-0.03116
-0.02612
-0.02262
-0.0357
-0.00854
-0.026
-0.0327
-0.03346
-0.01824
-0.0303
-0.0345
-0.03282
-0.02106
-0.04688
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
mab1
-0.0001
-0.0004
-0.0003
-0.0003
-0.0002
-0.0002
-0.0001
-0.0003
-0.0002
-0.0003
-0.0001
0
0.0001
0.0001
-0.0003
0.0002
0
0
0.0003
0.001
0.0006
0.0008
0.001
0.0008
0.0011
0.0009
0.0011
0.0012
0.001
0.0015
0.0009
0.001
0.0002
0.0002
0.0002
0.0002
0.0001
0.0001
0.0004
-0.0002
0.0003
0.0003
0.0002
0
0.0001
-0.0001
0.0001
0.0001
0.0001
-0.0002
0.0001
0.0001
0
mab2
-0.0001
-0.0002
0
-0.0003
-0.0001
0
-0.0003
-0.0005
0
0
-0.0003
0.0004
0.0003
-0.0001
0.0004
0.0005
0.0003
0.0006
0.0002
0.0013
0.0014
0.0015
0.0012
0.0015
0.0011
0.0014
0.0013
0.0015
0.0012
0.0013
0.0016
0.001
0.0001
0.0005
0.0004
-0.0001
0.0004
0
0.0005
0.0001
0.0003
-0.0003
0.0006
0.0002
0.0002
0
0
0.0001
0.0004
-0.0001
-0.0004
0
0
mab3
trbb1
trbb2
-0.0001 0.0004 0.0007
0.0001 0.0004 0.0006
-0.0001 0.0005 0.0006
0 0.0005 0.0006
0 0.0006 0.0008
-0.0002 0.0007
0.001
0.0002 0.0006 0.0007
-0.0002 0.0006 0.0008
-0.0002 0.0006 0.0008
0.0001 0.0006 0.0007
-0.0002 0.0006 0.0007
0 0.0006 0.0006
-0.0002 0.0006 0.0006
0 0.0007 0.0007
0.0001 0.0007 0.0008
-0.0002 0.0008 0.0009
0 0.0009 0.0009
-0.0001 0.0011 0.0011
0.0002 0.0012 0.0015
-0.0001 0.0011 0.0012
0.0001 0.0011 0.0012
0.0001 0.0012 0.0012
0.0001 0.0011 0.0012
0.0001 0.0011 0.0012
0 0.0011 0.0011
0.0001 0.0012 0.0013
0 0.0013 0.0013
0.0001 0.0015 0.0016
0.0001 0.0018
0.002
0 0.0025 0.0026
0.001 0.0038 0.0041
0.0025 0.0035 0.0036
0.0001 0.0005 0.0005
0.0001 0.0004 0.0004
0 0.0005 0.0004
0.0001 0.0003 0.0003
0 0.0003 0.0003
0 0.0004 0.0003
-0.0001 0.0003 0.0002
0.0001 0.0003 0.0002
-0.0001 0.0003 0.0002
0 0.0002 0.0002
0.0002 0.0003 0.0002
0.0002 0.0002 0.0002
0.0001 0.0001 0.0001
0
0
0
0 0.0001 0.0001
0.0001 0.0001 0.0001
-0.0001
0
0
0.0001
0
0
-0.0001
0
0
-0.0002
0
0
0
0 0.0001
mas1
0.0001
0.0003
0.0002
0.0002
0.0001
0
0.0004
0.0001
0.0003
0.0001
0.0001
0
0.0002
0
0
0.0002
0
0.0001
-0.0003
-0.001
-0.001
-0.0009
-0.0008
-0.0009
-0.0009
-0.0008
-0.0009
-0.001
-0.0013
-0.0012
-0.001
-0.0007
-0.0004
-0.0001
-0.0001
-0.0002
-0.0001
0
-0.0002
-0.0002
-0.0001
-0.0001
-0.0001
0
-0.0003
-0.0001
0
0.0001
-0.0002
0.0001
-0.0002
0.0001
-0.0001
mas2
-0.0003
0
-0.0001
-0.0002
-0.0002
-0.0003
-0.0003
0.0001
0
0.0001
0
-0.0002
0.0001
0.0001
0
0
0.0001
-0.0002
-0.0004
-0.0013
-0.0012
-0.0012
-0.0013
-0.0013
-0.0013
-0.001
-0.0011
-0.0008
-0.0011
-0.0014
-0.0015
-0.0017
-0.0001
0.0001
-0.0002
-0.0003
0
0
-0.0003
0.0001
-0.0004
-0.0001
-0.0002
0.0002
-0.0002
-0.0002
-0.0001
-0.0001
0
-0.0001
-0.0001
0.0001
-0.0002
mas3
-0.0001
0
0.0001
0
0
-0.0001
-0.0002
0
0.0001
-0.0002
0
-0.0002
0.0001
-0.0001
0
0.0001
0
0.0002
-0.0003
0
0
0
-0.0001
0.0001
0
-0.0001
0
-0.0001
-0.0001
0
-0.0011
-0.0024
-0.0001
0
0
-0.0001
0
-0.0002
-0.0001
-0.0001
-0.0001
0.0001
-0.0002
-0.0003
0.0001
0
0.0001
0
0
0
0
-0.0001
0
trbs1
-0.0005
-0.0005
-0.0005
-0.0006
-0.0006
-0.0006
-0.0007
-0.0005
-0.0005
-0.0005
-0.0005
-0.0006
-0.0005
-0.0007
-0.0008
-0.0008
-0.0008
-0.001
-0.0012
-0.0009
-0.001
-0.001
-0.001
-0.001
-0.0011
-0.0012
-0.0013
-0.0015
-0.0018
-0.0024
-0.004
-0.0039
-0.0004
-0.0003
-0.0002
-0.0003
-0.0002
-0.0004
-0.0002
-0.0002
-0.0001
-0.0003
-0.0002
-0.0001
-0.0001
0
0
-0.0001
-0.0001
0
0.0001
0
-0.0001
trbs2
-0.0007
-0.0007
-0.0007
-0.0008
-0.0007
-0.0009
-0.0009
-0.0007
-0.0007
-0.0007
-0.0008
-0.0007
-0.0007
-0.0009
-0.001
-0.0009
-0.0008
-0.0014
-0.0016
-0.0014
-0.0013
-0.0012
-0.0012
-0.0011
-0.0013
-0.0014
-0.0016
-0.0017
-0.0019
-0.0028
-0.0048
-0.0046
-0.0005
-0.0002
-0.0003
-0.0004
-0.0004
-0.0003
-0.0003
-0.0003
-0.0001
-0.0005
-0.0003
-0.0001
-0.0001
-0.0002
0.0001
-0.0001
-0.0001
0
0.0001
0
0
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
-26
-25
mab1
mab2
mab3
trbb1
trbb2
mas1
mas2
mas3
trbs1
trbs2
0.0048 0.0042 0.0041 0.0044 0.0042 0.0039
0.004 0.0044 0.0049 0.0057
0.0049 0.0043 0.0043 0.0044 0.0043 0.0047 0.0037
0.004 0.0043 0.0045
-26
-25
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
0.0042
0.0044
0.0042
0.0045
0.004
0.0042
0.0043
0.0037
0.0042
0.0042
0.0046
0.0039
0.0044
0.0042
0.0043
0.0037
0.0037
0.004
0.0041
0.0042
0.0043
0.0044
0.0045
0.0042
0.0044
0.005
0.0045
0.0054
0.0045
0.005
0.0049
0.0043
0.0049
0.0044
0.0049
0.0065
0.0048
0.0045
0.0049
0.0046
0.0052
0.0047
0.0046
0.0048
0.0039
0.0053
0.0043
0.0059
0.0045
0.0045
0.0048
0.0039
0.0047
0.004
0.005
0.0042
0.0047
0.0049
0.0036
0.0045
0.0042
0.0046
0.0047
0.0042
0.0043
0.0041
0.0044
0.0042
0.005
0.0049
0.0047
0.0061
0.0056
0.0049
0.005
0.005
0.0055
0.0052
0.005
0.0061
0.0054
0.0045
0.0047
0.0045
0.005
0.0045
0.0043
0.0053
0.0045
0.0047
0.0046
0.0046
0.0049
0.0052
0.0039
0.0041
0.0043
0.0043
0.0049
0.0067
0.0042
0.0045
0.0044
0.0045
0.0043
0.0046
0.0043
0.0043
0.0041
0.0043
0.004
0.0041
0.004
0.004
0.0044
0.0044
0.0043
0.0044
0.0046
0.0044
0.0042
0.0043
0.0045
0.004
0.0042
0.0038
0.0039
0.0042
0.0041
0.0046
0.0045
0.006
0.0047
0.0045
0.0042
0.0046
0.0041
0.0043
0.0046
0.0045
0.0048
0.0043
0.0044
0.0045
0.0048
0.0053
0.0043
0.0053
0.0044
0.0041
0.0046
0.005
0.0043
0.0044
0.0047
0.0046
0.0049
0.0045
0.0041
0.0041
0.004
0.0042
0.0041
0.0042
0.0043
0.0043
0.0044
0.0046
0.0046
0.0051
0.0047
0.0045
0.0046
0.0043
0.0044
0.0046
0.0047
0.0047
0.0048
0.0052
0.0056
0.0065
0.0071
0.006
0.0053
0.0051
0.0049
0.0048
0.0051
0.0049
0.0051
0.0051
0.0052
0.0051
0.0052
0.0054
0.005
0.0048
0.0046
0.0044
0.0044
0.0044
0.0044
0.0046
0.0042
0.0046
0.0045
0.005
0.0046
0.0041
0.0041
0.0041
0.0041
0.0039
0.0042
0.0044
0.0043
0.0043
0.0045
0.0047
0.0052
0.0048
0.0048
0.0046
0.0044
0.0045
0.0045
0.0048
0.0048
0.005
0.0055
0.0058
0.0069
0.0073
0.006
0.0054
0.005
0.0047
0.0048
0.0048
0.0047
0.0052
0.0052
0.0052
0.0053
0.0052
0.0057
0.005
0.0048
0.0045
0.0043
0.0045
0.0045
0.0045
0.0045
0.0043
0.0043
0.0047
0.0042
0.0043
0.0041
0.0041
0.0042
0.004
0.0039
0.0039
0.0039
0.0038
0.0039
0.0042
0.004
0.0037
0.0043
0.0042
0.004
0.0038
0.0042
0.0044
0.0042
0.0045
0.0054
0.0061
0.0063
0.0059
0.0042
0.0049
0.0047
0.0044
0.0042
0.0043
0.0044
0.0043
0.0043
0.0046
0.0045
0.0053
0.0044
0.0046
0.0048
0.0042
0.0052
0.0052
0.0043
0.0044
0.0042
0.0043
0.0038
0.0038
0.0044
0.0043
0.0048
0.0033
0.0044
0.0039
0.0035
0.0039
0.0043
0.0041
0.0037
0.0041
0.0041
0.0039
0.0047
0.0047
0.0057
0.0051
0.0056
0.0089
0.0044
0.0056
0.0049
0.0047
0.0045
0.005
0.0054
0.0075
0.0045
0.0044
0.0044
0.0046
0.0051
0.0043
0.0045
0.0058
0.0046
0.0039
0.005
0.0045
0.005
0.0053
0.0049
0.0047
0.0044
0.0056
0.0046
0.0039
0.0046
0.0043
0.0043
0.0042
0.0046
0.0046
0.0042
0.004
0.0042
0.0042
0.0039
0.0042
0.0041
0.0038
0.0038
0.0044
0.0043
0.0046
0.0046
0.0043
0.0041
0.0043
0.0041
0.004
0.004
0.0037
0.0041
0.0042
0.0042
0.0048
0.0069
0.0051
0.0043
0.0041
0.0042
0.0043
0.0048
0.0048
0.0047
0.0041
0.0047
0.0044
0.0048
0.0047
0.0046
0.0044
0.0043
0.0052
0.0047
0.0042
0.0048
0.0043
0.0048
0.0046
0.0049
0.0049
0.0046
0.0043
0.0051
0.0049
0.005
0.0051
0.0043
0.0045
0.0054
0.005
0.0052
0.0061
0.0062
0.006
0.0059
0.0052
0.0049
0.0045
0.005
0.0051
0.0057
0.0059
0.0057
0.0062
0.0082
0.0091
0.0068
0.0059
0.0062
0.0056
0.0057
0.0057
0.0056
0.006
0.0056
0.0054
0.0061
0.0061
0.0063
0.0051
0.0049
0.005
0.0048
0.0053
0.0054
0.0053
0.0056
0.0057
0.005
0.0053
0.005
0.0046
0.0047
0.0061
0.0062
0.0062
0.0063
0.0048
0.0049
0.0068
0.0053
0.0055
0.0074
0.0075
0.0076
0.0074
0.0062
0.0056
0.0048
0.006
0.0057
0.0065
0.0068
0.0064
0.0072
0.0101
0.0106
0.0082
0.0069
0.0075
0.0066
0.0066
0.0066
0.0066
0.0071
0.0065
0.0062
0.0071
0.0072
0.0074
0.0057
0.0056
0.0055
0.0053
0.0066
0.0066
0.0065
0.0055
-24
-23
-22
-21
-20
-19
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Figure 2-3: Mean and Standard Deviation of Quote Revisions Around Buy & Sell Signals.
Quote Revision
0.03
0.02
0.01
24
26
24
26
22
20
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-1
0
-1
2
-1
4
-1
6
-1
8
-2
0
-2
2
-2
4
-2
6
0
-0.01
Buy
Sell
Buy-CR
-0.02
Sell-CR
-0.03
Quote Revision Volatility
0.009
0.008
0.007
0.006
0.005
0.004
0.003
Buy
0.002
Sell
0.001
22
20
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-1
0
-1
2
-1
4
-1
6
-1
8
-2
0
-2
2
-2
4
-2
6
0
Buy
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0
0
0
0
-0
-0
-0
0
Buy
0
0
Sell
Buy-CR
Sell-CR
-0.0003 0.00016
-0.0003
-0.00018 0.00026 -0.00048
-0.0002
0.0004 -0.00068
-0.00028
0.0005 -0.00096
-0.00028 0.00072 -0.00124
-0.00038 0.00098 -0.00162
-0.00034
0.0012 -0.00196
-0.0002 0.00128 -0.00216
-0.00016 0.00148 -0.00232
-0.00024
0.0017 -0.00256
-0.00024 0.00184
-0.0028
-0.00034 0.00216 -0.00314
-0.00016 0.00244
-0.0033
-0.00032 0.00272 -0.00362
-0.00036 0.00306 -0.00398
-0.00028
0.0035 -0.00426
-0.0003 0.00392 -0.00456
-0.00046 0.00446 -0.00502
-0.00076 0.00514 -0.00578
-0.00092 0.00604
-0.0067
-0.0009 0.00692
-0.0076
-0.00086 0.00788 -0.00846
-0.00088
0.0088 -0.00934
-0.00084 0.00974 -0.01018
-0.00092 0.01062
-0.0111
-0.0009
0.0116
-0.012
-0.00098
0.0126 -0.01298
-0.00102 0.01378
-0.014
-0.00124
0.015 -0.01524
-0.00156 0.01658
-0.0168
-0.00248 0.01886 -0.01928
-0.00266 0.02118 -0.02194
-0.0003 0.02146 -0.02224
-0.0001 0.02178 -0.02234
-0.00016 0.02208
-0.0225
-0.00026 0.02224 -0.02276
-0.00014 0.02246
-0.0229
-0.00018 0.02262 -0.02308
-0.00022 0.02288
-0.0233
-0.00014 0.02298 -0.02344
-0.00016 0.02318
-0.0236
-0.00018 0.02326 -0.02378
-0.0002 0.02356 -0.02398
-0.00006 0.02372 -0.02404
-0.00012 0.02384 -0.02416
-0.0001 0.02382 -0.02426
0.00002 0.02388 -0.02424
-0.00004 0.02398 -0.02428
-0.00008 0.02406 -0.02436
0 0.02402 -0.02436
-0.00002 0.02394 -0.02438
0.00002 0.02392 -0.02436
-0.00008 0.02394 -0.02444
Sell
0.00458
0.00424
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.01
0.01
0.01
0.01
0
0
0
0
0.01
0
0
0
0
0
0
0.01
0
0
0
0
0
0
0
0
0.00458
0.0044
0.0047
0.0046
0.00458
0.00412
0.00474
0.00468
0.00458
0.00462
0.0043
0.0043
0.0047
0.00442
0.00468
0.00514
0.00534
0.00544
0.0055
0.00492
0.00484
0.0053
0.00476
0.00492
0.00506
0.00538
0.00538
0.00578
0.00688
0.00766
0.0059
0.00524
0.00532
0.00504
0.0052
0.00516
0.00516
0.00558
0.00508
0.00494
0.00558
0.0054
0.0056
0.0051
0.0048
0.00494
0.00498
0.0053
0.00504
0.00494
0.00486