Trade Scheduling in Equity Markets:
Theory and Practice
Michael Simmonds
Liquid Markets Analytics
STRICTLY PRIVATE AND CONFIDENTIAL
© Nomura International plc
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Contents

Nomura (Company and Analytics Teams)

Trade Scheduling Framework

Transaction Cost Estimation

Liquidity Prediction

Risk Estimation

Trade Scheduling Optimisation

Applications
Source:
1
Lehman Acquisition
Nomura moved quickly and decisively

14th Sept 2009:
Opened discussion with Lehman administrators

22nd Sept 2009:
Announced acquisition of Asia-Pacific, including Japan and Australia

23rd Sept 2009:
Announced acquisition of Europe and Middle Eastern equities and investment banking operations

7th Oct 2009:
Hired selected former Lehman Brothers fixed income staff

14th Oct 2009:
Completed acquisition of three Lehman companies in India
Europe & Middle East

Acquisition of equities and
investment banking operations

Approx 2,500 people

Hired ex-Lehman fixed income
staff: interest rate, credit and
currency linked operations

Approx 250 people
Japan

Acquired Japan franchise

Approx 1,100 people
India


Acquired three subsidiaries: LB
service India IT, Global Servicing;
LB Financial Services (India)
Research services; LB Structured
Finance Services Capital Markets
Support and Analytics
Asia (ex Japan)

Acquired Asia Pacific franchise

Approx 1,500 people
Approx 2,900 people
2
Geography of Nomura
Europe & Middle East

4,500 employees in 18 countries
with presence in:
Europe:
Asia-Pacific

20,500 employees in 13 countries
with presence in:
Asia ex-Japan:
Americas

1,060 employees in 3 countries with
presence in:
North America:
– Amsterdam
– Milan
– Bangkok
– Melbourne
– New York
– Budapest
– Moscow
– Beijing
– Mumbai
– San Francisco
– Dublin
– Paris
– Hanoi
– Seoul
– Toronto
– Frankfurt
– Rome
– Hong Kong
– Shanghai
– Geneva
– Stockholm
– Jakarta
– Singapore
– London
– Vienna
– Kuala Lumpur
– Sydney
– Luxembourg – Warsaw
– Madrid
– Zurich
– Manila
– Taipei
Middle East:
Japan:
South America:
– Bahrain
– 171 branches countrywide
– Sao Paolo
– Dubai
– Tokyo headquarters
– Saudi Arabia
– Qatar(1)
Note:
(1) Subject to regulatory approval.
All headcount figures are approximate.
3 4
London Stock Exchange
10
7.00%
20
6.00%
30
5.00%
40
4.00%
50
3.00%
60
2.00%
70
1.00%
80
Rank
Market Share
0.00%
Dec-08
Jan-09
Feb-09
Mar-09
Apr-09
May-09
Jun-09
Jul-09
Dec-08
Jan-09
Feb-09
Mar-09
Apr-09
May-09
Jun-09
Jul-09
66
25
11
11
11
8
3
1
0.11%
0.69%
2.71%
3.19%
3.15%
4.14%
6.24%
7.45%
50
9.00%
100
6.00%
150
3.00%
Eurex Derivatives Exchange
200
Rank
Market Share
Note:
London Stock Exchange statistics are whole trading volumes, weighted by value traded
Eurex statistics are for Listed Equity Index Volume whole traded volumes, weighted by value traded
0.00%
Dec-08
Jan-09
Feb-09
Mar-09
Apr-09
May-09
Jun-09
Jul-09
Dec-08
Jan-09
Feb-09
Mar-09
Apr-09
May-09
Jun-09
Jul-09
182
61
6
6
4
3
3
1
0.00%
0.15%
4.26%
4.92%
5.55%
6.35%
7.34%
10.66%
4 5
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Analytics Team

Based in London, New York, Tokyo, Hong Kong and Mumbai

London office quants are approximately 70% have PhDs

Highest degrees typically in Mathematics, Physics, Engineering, Computer Science
and Economics

Location of highest degree concentrated in UK/US/France
India
Canada
Japan
UK
USA

France
Focus areas (in Equities) include algorithmic trading, market microstructure modelling,
risk estimation, structured product creation and volatility modelling
5
The Troika of Quantitative Investment



Primary focus of the Quant community
Factor models to exploit behavioural biases in security valuation
Represent systematisation of the stock selection process
Return
Risk



Focus on loss preservation and efficient
capital allocation
Estimated using fundamental/statistical
factor models
Generally purview of third-party vendors but
recently an area of internal focus
Cost



Measures shortfall due to the
implementation process
Depends critically on the execution style
and strategy (front-loaded, passive, backloaded, etc)
Usually receives the least focus by Quant
Portfolio Managers
6
Trade Implementation as a Scientific Process
Market impact modeling (Transaction Cost Modeling)

Model estimation principles similar to multi-factor modeling in alpha research

Markets have memory so static impact models are not adequate

Example: Nomura METRIC model
Liquidity, volume profile and volatility prediction

PCA decomposition of volume into systematic and idiosyncratic components

Estimating volatility using non-stationary and non-synchronous tick data

Example: Nomura Volume Prediction and Volatility Prediction Models
Optimal trade scheduling

Non-linear optimisation techniques similar to multi-period portfolio construction

Example: Nomura PortfolioIS Algorithm
7
Construction of Trade Scheduling Algorithms
Price evolution
model
Order
parameters
Performance
criterion
Current market
conditions
Market impact
model
Trade Scheduling Algorithm
Trade Scheduling Algorithms are typically formulated as optimisation problems
Trade Schedule:
Number of shares to trade in
each bin

Price evolution model: Random walk, Short-term momentum, Mean-reversion

Market impact model: Instantaneous, with Memory

Performance criteria – deviation from a target benchmark

Trade as quickly as possible to reduce opportunity cost without causing market impact
8
Execution Algorithms Systematise Implementation
Execution algorithms implement a systematic trade implementation process

process vast amount of real-time market data

make simultaneous trading decisions at different time scales
Execution algorithms can be decomposed into three modules

Trade scheduling algorithm slices the original institutional size order into
a sequence of smaller trades (minutely horizon decisions)

Order placement algorithm decides type and timing of trades to send to
the market (secondly horizon decisions)

Market access algorithm decides which destination to route each order
(millisecond horizon decisions)
trade motivation
order parameters
liquidity profiles
Trade
Scheduling
limit order model
short-term alpha
signals
Order
Placement
dynamic venue
execution quality
analysis
Market
Access
9
10
METRIC

Model Estimated TRade Impact Cost (METRIC)

Focused on Execution Costs

Cost models have limited constraints (other than
fixed costs
matching the data), but some no-arbitrage
constraints can be applied

Data set is large (~1M trades used in a calibration)
trading
costs
execution
costs
and noisy with ~40% of orders rejected using
fees
taxes
commissio
ns
instantaneous
impact
transient impact
permanent impact
reasonable criteria

Calibration methodology is critical, as is correct time
opportunity
costs
frame selection (matching sample size versus slow
timescale effects) to maintain stable parameters of
multiple data sets
11
METRIC: Observations

The dependence of execution cost on many descriptive variables is quite intuitive and is easily
verified:
 Large orders are relatively expensive to trade.
 Stocks with high volume tend to be cheaper to trade
 Stocks with higher bid-ask spreads tend to be more expensive to trade
 Volatile stocks tend to be more expensive to trade than stocks that stay in tight trading ranges
 Similar stocks in different countries and on different exchanges within a country may be more
or less expensive, depending on exchange structure and data reporting conventions.
12
METRIC: Structure

Decompose cost into three parts:
 Instantaneous impact: A measure of our micro execution skills which only affects child
orders individually and then dissipates immediately.
 Transient impact: Caused by temporary imbalances between supply and demand caused by
our trades which lead to temporary price movement from equilibrium. Transient impact
induced price will reverse after our trade and decay to 0 at the end.
 Permanent impact: Impact due to changes in the equilibrium price caused by our trading,
which accumulates and remains for the life of the trade. Permanent impact induced price will
not mean reverse and stay at the end price level after trading. Therefore, we can capture
permanent impact if and only if we wait long enough.
13
METRIC
Impact
14.0
Post-Trade Period
Trade Period
10.5
7.0
3.5
0.0
0.0
0.1
0.2
0.3
Transient Impact
0.4
0.5
0.6
0.7
Time
0.8
Temporary Impact
0.9
1.0
1.1
1.2
Permanent Impact
Total impact over the trade period


METRIC    S    v   T
    v   T 

2
Where S is the average bid-ask spread,  is the volatility, v is the trade rate and T is the trade
duration
14
METRIC: Model Quality
Out of Sample Performance
Performance versus Trade Rate
Performance versus Bid-Ask Spread
Performance versus Period Volatility
15
Risk Modeling

Variance of cost model is closely correlated with period (time scaled) volatility
Impact Standard Deviation (bps)
40
30
20
10
0
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
Period Volatility

Stock price moves are heavily correlated, though stock-wise correlation is not found in transaction cost
estimates

Principles are fundamentally based on a linear mappings (given a return vector R with expected return µ one
assumes that for a set of factors with returns F then there exist L such that R - µ = L.F +  where E( ) = 0 and
the matrix L is the factor loading matrix. If E( F ) = 0 and cov( L. ) =0 then
cov( R - µ ) = cov(L.F +  ) = L.cov( F ).LT + cov( ) = L.cov( F ).LT +  where  = cov( )


Therefore the risk matrix, , is defined by  = L.cov( F ).LT +  and is constant for rotations of factors (i.e. if a
new family of factors F’=Q.F and one defines L’=L.QT such that Q.QT = I then ’ =  )
Weighting schema, time scale and factor selection are critical to producing good quality risk estimates
16
Liquidity Prediction

The METRIC and Nomura algorithms are very sensitive to the intra-day liquidity profiles used

Major project to improve liquidity prediction versus using historic profiles
17
Liquidity Prediction

Focus on volume, but same methodology is applied to volatility and spread

Profile shows a characteristic and persistent U shape

Suggest:
Stock Profile = “Market Profile” + Stock Specific Deviation

Given a list of stocks i=1, …., N and intraday time bins t=1, … , 35 can define a matrix of profiles
for any given day Xi,t and hence a correlation matrix can be defined
18
Liquidity Prediction

First examine the eigenvalues: first mode is largest and explains more than 40% of the
variance, magnitude of first three eigenvalues are much larger than the others
Eigenvalues of the correlation matrix of X
First eigenmode
19
Liquidity Prediction: Stock Specific

The following is observed for the profile after discounting the market profile for each
stock:
 Null hypothesis of stochastic non-stationarity is rejected using Augmented Dickey
Fuller Test (ADF)
 Box-Jenkins (noting ACF and partial ACFs decay exponentially) suggests that
ARMA(1,1) is optimal; describing next bin in terms of the current one and the
deviation of the previous bin:
p
p
i 1
i 1
Yt   aiYt i  bi t i  t
 Important to note that a1  0, b1  0 : mean reversion effect
20
Liquidity Prediction: Model Quality

Define quality measure so that for time bin t on day j for stock i via:
X

j
t ,i
1 D j d
  X t ,i  tij
D d 1
So then P defines the improvement of our methodology versus the static predictions
where
var(  )
Pi  1 

Similar results for volatility but
minimal improvement versus
historic for spread profiles
i
var(  i )
Universe
Min
1st Qu.
Median
Mean
2nd Qu.
Max
FTSE 100
-0.23
0.20
0.27
0.27
0.33
0.58
FTSE MidCap
-0.20
0.14
0.18
0.18
0.24
0.50
FTSE Small Cap
-2.81
0.06
0.13
0.08
0.18
0.45
DAX 30
-0.44
0.22
0.26
0.25
0.33
0.46
Cac 40
-0.76
0.21
0.27
0.22
0.31
0.44
Tokyo (300 stocks)
0.01
0.15
0.24
0.25
0.35
0.56
Korea (200 stocks)
0.07
0.24
0.30
0.29
0.34
0.48
Hong Kong
-0.06
0.25
0.31
0.31
0.41
0.58
NYSE
-0.14
0.24
0.34
0.34
0.45
0.78
Nasdaq
-0.10
0.17
0.29
0.29
0.39
0.78
21
Liquidity Prediction: Enhancements

The model predicts the next bin, but can be extended to produce an expected profile
for the remainder of the day at any point through the day

However can improve upon this by adjusting according to the volume traded so far
22
Trade Scheduling

Can combine risk, liquidity prediction and cost models to run mean-variance
minimisation of the objective function (for a given set of positions X(t)):
ˆ (t ).σ(t ).X
ˆ (t )T
METRIC (t ; X(t ))  X

Computed trade schedule is kept constant throughout trading interval (e.g.,
VWAP, TWAP) (i.e. pick appropriate discretisation)
23
Trade Scheduling

Static Trade Scheduling Algorithms
 optimisation to compute trade schedule is performed initially
 computed trade schedule is kept constant throughout trading interval (e.g., VWAP, TWAP)

Dynamic Trade Scheduling Algorithms
 trade schedule is re-optimized at the beginning of each bin
 optimisation criterion is fixed but depends on market conditions (e.g., Participation, Dynamic
VWAP)

Adaptive Trade Scheduling Algorithms
 trade schedule is re-optimized at the beginning of each bin
 optimisation criterion changes in response to market condition (e.g., Aggressive/Passive In The
Money)
24
Conclusions

Cash markets require a variety of different modeling techniques to trade
effectively

Calibration methodology is critical to maintain stable and explanatory models

Trade data and intraday data are both critical to effective trade scheduling

Most clients of top-tier brokers have insufficient data (and possibly quantitative
resources) to manage this process themselves

Second tier brokers will struggle to keep pace with developments and may be
forced to “white label” algorithms
25
References

Almgren, Chriss, “Optimal Execution of Portfolio Transactions” (2001)

Almgren, Lorenz, “Adaptive Arrival Price” (2006)

Bialkowski, Darolles and Le Fol, “Decomposing Volume for VWAP Strategies”
(2005)
26