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Transcript of Chapter 1 Discussion
7/29/2019 Chapter 1 Discussion
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Paper Overview
Major points
Minor points
An Empirical Analysis of the Limit Order Bookin the SGX Equities Market
Chapter 1: Order Aggressiveness
Author: Tze Hua Loh1
Discussant: Alex Nikolsko-Rzhevskyy2
1Department of FinanceUniversity of New South Wales
2Department of EconomicsUniversity of Memphis
September 20, 2011
Nikolsko-Rzhevskyy Order Aggressiveness
7/29/2019 Chapter 1 Discussion
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Paper Overview
Major points
Minor points
Summary
Main findings
Summary
The paper contributes to the literature by testing whether
placing of multiple simultaneous buy and sell orders is
used by traders
It utilized a new SGX-ST dataset, which is exceptionally
rich & allows answering many interesting questions
Dataset includes info on all executed and placed orders,
clients ID, clients types, etc., on a second-by-second basis
Due to confidentiality reasons, only 5 stocks over 5
different weeks are studied
Nikolsko-Rzhevskyy Order Aggressiveness
7/29/2019 Chapter 1 Discussion
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Paper Overview
Major points
Minor points
Summary
Main findings
Main findings
The results indicate that traders do seem to place multiple
orders at multiple prices
There is evidence that sometimes, trades are placed onboth sides of the LOB (limit order book)
Order sizes and aggressiveness vary by trader types
Some of the conclusions, however, appear somewhat
unjustified, and terminology – not fully developed
Now will discuss the potential problems with this paper in detail
starting with the major “conceptual” issues
Nikolsko-Rzhevskyy Order Aggressiveness
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 4/35
Paper Overview
Major points
Minor points
Summary
Main findings
Main findings
The results indicate that traders do seem to place multiple
orders at multiple prices
There is evidence that sometimes, trades are placed onboth sides of the LOB (limit order book)
Order sizes and aggressiveness vary by trader types
Some of the conclusions, however, appear somewhat
unjustified, and terminology – not fully developed
Now will discuss the potential problems with this paper in detail
starting with the major “conceptual” issues
Nikolsko-Rzhevskyy Order Aggressiveness
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 5/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Conceptual
Why only 1 stock is used when there is data on 4 more similar
stocks?
Yes, their samples (and hence market trends) are different,
but these findings are presented as general , so it shouldn’tmatter
Will help to remove time-specific and stock-specific effects
Many results (Proposition #4 in particular) are quite
different for different stocksSome results are currently statistically insignificant; maybe
increasing the sample in 5-fold will help
Nikolsko-Rzhevskyy Order Aggressiveness
P O i C l
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 6/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Conceptual
Why only 1 stock is used when there is data on 4 more similar
stocks?
Yes, their samples (and hence market trends) are different,
but these findings are presented as general , so it shouldn’tmatter
Will help to remove time-specific and stock-specific effects
Many results (Proposition #4 in particular) are quite
different for different stocksSome results are currently statistically insignificant; maybe
increasing the sample in 5-fold will help
Nikolsko-Rzhevskyy Order Aggressiveness
P O i C t l
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 7/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Conceptual
Why only 1 stock is used when there is data on 4 more similar
stocks?
Yes, their samples (and hence market trends) are different,
but these findings are presented as general , so it shouldn’tmatter
Will help to remove time-specific and stock-specific effects
Many results (Proposition #4 in particular) are quite
different for different stocksSome results are currently statistically insignificant; maybe
increasing the sample in 5-fold will help
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 8/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Conceptual
Why only 1 stock is used when there is data on 4 more similar
stocks?
Yes, their samples (and hence market trends) are different,
but these findings are presented as general , so it shouldn’tmatter
Will help to remove time-specific and stock-specific effects
Many results (Proposition #4 in particular) are quite
different for different stocksSome results are currently statistically insignificant; maybe
increasing the sample in 5-fold will help
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 9/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Conceptual
Why only 1 stock is used when there is data on 4 more similar
stocks?
Yes, their samples (and hence market trends) are different,
but these findings are presented as general , so it shouldn’tmatter
Will help to remove time-specific and stock-specific effects
Many results (Proposition #4 in particular) are quite
different for different stocksSome results are currently statistically insignificant; maybe
increasing the sample in 5-fold will help
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 10/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Conceptual
More details on Handa and Schwartz (1996) theory would
benefit the paper
Placing multiple buy and sell orders should:1 reduce entry price searching costs ...2 ... but increase transaction costs
I personally am curious to see under which marketconditions this strategy is helpful. My guess would be:
1 Flat non-volatile market (I’ve checked STI – indeed flat)2 Placing multiple buy or sell orders: trending market
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 11/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Conceptual
More details on Handa and Schwartz (1996) theory would
benefit the paper
Placing multiple buy and sell orders should:1 reduce entry price searching costs ...2 ... but increase transaction costs
I personally am curious to see under which marketconditions this strategy is helpful. My guess would be:
1 Flat non-volatile market (I’ve checked STI – indeed flat)2 Placing multiple buy or sell orders: trending market
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 12/35
Paper Overview
Major points
Minor points
Conceptual
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Conceptual
More details on Handa and Schwartz (1996) theory would
benefit the paper
Placing multiple buy and sell orders should:1 reduce entry price searching costs ...2 ... but increase transaction costs
I personally am curious to see under which marketconditions this strategy is helpful. My guess would be:
1 Flat non-volatile market (I’ve checked STI – indeed flat)2 Placing multiple buy or sell orders: trending market
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 13/35
p
Major points
Minor points
p
Unjustified conclusions
Econometrics/Statistics
Major points3/3 Conceptual
Why are Aitken, Almeida, Harris, and McInish’s (2007 JFM)
results so different?
Author’s explanation:1 Their data is on institutional traders only2 The data consists of snapshots and thus doesn’t contain
info on market orders
But this shouldn’t matter for 2 reasons:1 Most traders (including Institutions) use Limit, not Market
(≈ 15% only), orders (Table 4.2)2 Placing multiple-price simultaneous buy and sell orders (the
focus of this paper) could only be done with limit orders
So in their data, we should expect to observe similar effects
(unless the market was trending – see my previous point)
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 14/35
p
Major points
Minor points
p
Unjustified conclusions
Econometrics/Statistics
Major points3/3 Conceptual
Why are Aitken, Almeida, Harris, and McInish’s (2007 JFM)
results so different?
Author’s explanation:1 Their data is on institutional traders only2 The data consists of snapshots and thus doesn’t contain
info on market orders
But this shouldn’t matter for 2 reasons:1 Most traders (including Institutions) use Limit, not Market
(≈ 15% only), orders (Table 4.2)2 Placing multiple-price simultaneous buy and sell orders (the
focus of this paper) could only be done with limit orders
So in their data, we should expect to observe similar effects
(unless the market was trending – see my previous point)
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 15/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points3/3 Conceptual
Why are Aitken, Almeida, Harris, and McInish’s (2007 JFM)
results so different?
Author’s explanation:1 Their data is on institutional traders only2 The data consists of snapshots and thus doesn’t contain
info on market orders
But this shouldn’t matter for 2 reasons:1 Most traders (including Institutions) use Limit, not Market
(≈ 15% only), orders (Table 4.2)2 Placing multiple-price simultaneous buy and sell orders (the
focus of this paper) could only be done with limit orders
So in their data, we should expect to observe similar effects
(unless the market was trending – see my previous point)
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview Conceptual
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 16/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points3/3 Conceptual
Why are Aitken, Almeida, Harris, and McInish’s (2007 JFM)
results so different?
Author’s explanation:1 Their data is on institutional traders only2 The data consists of snapshots and thus doesn’t contain
info on market orders
But this shouldn’t matter for 2 reasons:1 Most traders (including Institutions) use Limit, not Market
(≈ 15% only), orders (Table 4.2)2 Placing multiple-price simultaneous buy and sell orders (the
focus of this paper) could only be done with limit orders
So in their data, we should expect to observe similar effects
(unless the market was trending – see my previous point)
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview
M j i
Conceptual
U j ifi d l i
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 17/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Unjustified conclusions
Message on p.51: “Fact: Investors place multiple buy/sell
orders. Investors are smart, hence the strategy is profitable &
should be used” (one of the main results of the paper!)
Generally agree with the observation, but not with the
conclusion
This statement needs to be either made weaker or formally
tested
Testing should be very easy, as client ID is readily available
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview
M j i t
Conceptual
U j tifi d l i
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 18/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Unjustified conclusions
Message on p.51: “Fact: Investors place multiple buy/sell
orders. Investors are smart, hence the strategy is profitable &
should be used” (one of the main results of the paper!)
Generally agree with the observation, but not with the
conclusion
This statement needs to be either made weaker or formally
tested
Testing should be very easy, as client ID is readily available
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview
Major points
Conceptual
Unjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 19/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Unjustified conclusions
Message on p.51: “Fact: Investors place multiple buy/sell
orders. Investors are smart, hence the strategy is profitable &
should be used” (one of the main results of the paper!)
Generally agree with the observation, but not with the
conclusion
This statement needs to be either made weaker or formally
tested
Testing should be very easy, as client ID is readily available
Nikolsko-Rzhevskyy Order Aggressiveness
Paper Overview
Major points
Conceptual
Unjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 20/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points1/3 Unjustified conclusions
Message on p.51: “Fact: Investors place multiple buy/sell
orders. Investors are smart, hence the strategy is profitable &
should be used” (one of the main results of the paper!)
Generally agree with the observation, but not with the
conclusion
This statement needs to be either made weaker or formally
tested
Testing should be very easy, as client ID is readily available
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 21/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Unjustified conclusions
When testing Proposition #4, the author finds that “Institutions”
place relatively small orders. Hence she concludes that
Institutions “have sliced orders into small parcels to reduceprice impact”
To justify, need to look at the number of orders in addition
to volume
Table 4.4 shows that Institutions usually use only 1 price
level when placing orders
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 22/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Unjustified conclusions
When testing Proposition #4, the author finds that “Institutions”
place relatively small orders. Hence she concludes that
Institutions “have sliced orders into small parcels to reduceprice impact”
To justify, need to look at the number of orders in addition
to volume
Table 4.4 shows that Institutions usually use only 1 price
level when placing orders
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 23/35
Major points
Minor points
Unjustified conclusions
Econometrics/Statistics
Major points2/3 Unjustified conclusions
When testing Proposition #4, the author finds that “Institutions”
place relatively small orders. Hence she concludes that
Institutions “have sliced orders into small parcels to reduceprice impact”
To justify, need to look at the number of orders in addition
to volume
Table 4.4 shows that Institutions usually use only 1 price
level when placing orders
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 24/35
j p
Minor points
j
Econometrics/Statistics
Major points3/3 Unjustified conclusions
When testing Proposition #5, the author concludes that the
MKT/LMT order ratio is higher for “Trade Reps” than “Retail”
investors (difference significant at 5%)
However, this is 1 out of 30 cases ( 3%), and the rest 29
differences are insignificant.
Hence, this is just a statistical artifact and it doesn’t justify
the conclusion
We expect to see 1-2 out of 30 cases (which is 5%) appearsignificant at 5% even when the effect is not there
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 25/35
j p
Minor points
j
Econometrics/Statistics
Major points3/3 Unjustified conclusions
When testing Proposition #5, the author concludes that the
MKT/LMT order ratio is higher for “Trade Reps” than “Retail”
investors (difference significant at 5%)
However, this is 1 out of 30 cases ( 3%), and the rest 29
differences are insignificant.
Hence, this is just a statistical artifact and it doesn’t justify
the conclusion
We expect to see 1-2 out of 30 cases (which is 5%) appearsignificant at 5% even when the effect is not there
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 26/35
Minor points Econometrics/Statistics
Major points3/3 Unjustified conclusions
When testing Proposition #5, the author concludes that the
MKT/LMT order ratio is higher for “Trade Reps” than “Retail”
investors (difference significant at 5%)
However, this is 1 out of 30 cases ( 3%), and the rest 29
differences are insignificant.
Hence, this is just a statistical artifact and it doesn’t justify
the conclusion
We expect to see 1-2 out of 30 cases (which is 5%) appearsignificant at 5% even when the effect is not there
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
ConceptualUnjustified conclusions
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 27/35
Minor points Econometrics/Statistics
Major points3/3 Unjustified conclusions
When testing Proposition #5, the author concludes that the
MKT/LMT order ratio is higher for “Trade Reps” than “Retail”
investors (difference significant at 5%)
However, this is 1 out of 30 cases ( 3%), and the rest 29
differences are insignificant.
Hence, this is just a statistical artifact and it doesn’t justify
the conclusion
We expect to see 1-2 out of 30 cases (which is 5%) appearsignificant at 5% even when the effect is not there
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Mi i
ConceptualUnjustified conclusions
E i /S i i
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 28/35
Minor points Econometrics/Statistics
Major points1/1 Econometrics/Statistics
Investor Mean PIM Institution TrdRep Retail
Type (Aggressiveness) t -statistics
Proprietary 0.5667 -2.68* -7.12** -11.26**
Institution 0.9434 1.0 -8.34** -16.97**
TrdRep 1.6318 1.0 -6.32**
Retail 2.1992 1.0Notes: * 5%, ** 1% significance
Was autocorrelation taken into account?
PIM it = α+ β Institution i + it (1)
If PIM it correlates with PIM it −h or PIM depends on market
trend, it would be correlated; need NW adjustment
Why “-2.68” significant at 5, not 1 percent?
“1”s at the main diagonal are confusing
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Mi i t
ConceptualUnjustified conclusions
E t i /St ti ti
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 29/35
Minor points Econometrics/Statistics
Major points1/1 Econometrics/Statistics
Investor Mean PIM Institution TrdRep Retail
Type (Aggressiveness) t -statistics
Proprietary 0.5667 -2.68* -7.12** -11.26**
Institution 0.9434 1.0 -8.34** -16.97**
TrdRep 1.6318 1.0 -6.32**
Retail 2.1992 1.0Notes: * 5%, ** 1% significance
Was autocorrelation taken into account?
PIM it = α+ β Institution i + it (1)
If PIM it correlates with PIM it −h or PIM depends on market
trend, it would be correlated; need NW adjustment
Why “-2.68” significant at 5, not 1 percent?
“1”s at the main diagonal are confusing
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
ConceptualUnjustified conclusions
Econometrics/Statistics
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 30/35
Minor points Econometrics/Statistics
Major points1/1 Econometrics/Statistics
Investor Mean PIM Institution TrdRep Retail
Type (Aggressiveness) t -statistics
Proprietary 0.5667 -2.68* -7.12** -11.26**
Institution 0.9434 1.0 -8.34** -16.97**
TrdRep 1.6318 1.0 -6.32**
Retail 2.1992 1.0Notes: * 5%, ** 1% significance
Was autocorrelation taken into account?
PIM it = α+ β Institution i + it (1)
If PIM it correlates with PIM it −h or PIM depends on market
trend, it would be correlated; need NW adjustment
Why “-2.68” significant at 5, not 1 percent?
“1”s at the main diagonal are confusing
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
ConceptualUnjustified conclusions
Econometrics/Statistics
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 31/35
Minor points Econometrics/Statistics
Major points1/1 Econometrics/Statistics
Investor Mean PIM Institution TrdRep Retail
Type (Aggressiveness) t -statistics
Proprietary 0.5667 -2.68* -7.12** -11.26**
Institution 0.9434 1.0 -8.34** -16.97**
TrdRep 1.6318 1.0 -6.32**
Retail 2.1992 1.0Notes: * 5%, ** 1% significance
Was autocorrelation taken into account?
PIM it = α+ β Institution i + it (1)
If PIM it correlates with PIM it −h or PIM depends on market
trend, it would be correlated; need NW adjustment
Why “-2.68” significant at 5, not 1 percent?
“1”s at the main diagonal are confusing
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
Terminology
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 32/35
Minor points
Minor points1/1 Terminology
When calculating the “MKT/LMT ratios,” the author actually
computes the share of MKT orders in total orders
I would recommend either changing the name or changing
the formula
In Table 4.9: One of the columns is called “Ranking of limit
order placement sizes, most (1) to least (4)”
“most” and “least” sound confusing as in that table,
(1)(“most”) corresponds to the smallest, and (4)(“least”) – highest rank
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
Terminology
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 33/35
Minor points
Minor points1/1 Terminology
When calculating the “MKT/LMT ratios,” the author actually
computes the share of MKT orders in total orders
I would recommend either changing the name or changing
the formula
In Table 4.9: One of the columns is called “Ranking of limit
order placement sizes, most (1) to least (4)”
“most” and “least” sound confusing as in that table,
(1)(“most”) corresponds to the smallest, and (4)(“least”) – highest rank
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
Terminology
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 34/35
Minor points
Minor points1/1 Terminology
When calculating the “MKT/LMT ratios,” the author actually
computes the share of MKT orders in total orders
I would recommend either changing the name or changing
the formula
In Table 4.9: One of the columns is called “Ranking of limit
order placement sizes, most (1) to least (4)”
“most” and “least” sound confusing as in that table,
(1)(“most”) corresponds to the smallest, and (4)(“least”) – highest rank
Nikolsko-Rzhevskyy Order Aggressiveness
Paper OverviewMajor points
Minor points
Terminology
7/29/2019 Chapter 1 Discussion
http://slidepdf.com/reader/full/chapter-1-discussion 35/35
p
Minor points1/1 Terminology
When calculating the “MKT/LMT ratios,” the author actually
computes the share of MKT orders in total orders
I would recommend either changing the name or changing
the formula
In Table 4.9: One of the columns is called “Ranking of limit
order placement sizes, most (1) to least (4)”
“most” and “least” sound confusing as in that table,
(1)(“most”) corresponds to the smallest, and (4)(“least”) – highest rank
Nikolsko-Rzhevskyy Order Aggressiveness