Date post: | 30-Mar-2015 |
Category: |
Documents |
Upload: | katrina-sherrill |
View: | 224 times |
Download: | 5 times |
© Nomura International plc© Nomura International plcSTRICTLY PRIVATE AND CONFIDENTIAL
Trade Scheduling in Equity Markets:Theory and Practice
Michael Simmonds
Liquid Markets Analytics
Contents
Nomura (Company and Analytics Teams)
Trade Scheduling Framework
Transaction Cost Estimation
Liquidity Prediction
Risk Estimation
Trade Scheduling Optimisation
Applications
Source:
Section Header (used to create Tab Pages and Table of Contents)
1
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
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
Approx 2,900 people
Japan
Acquired Japan franchise Approx 1,100 people
Asia (ex Japan)
Acquired Asia Pacific franchise Approx 1,500 people
Nomura moved quickly and decisively
Lehman Acquisition
2
Geography of Nomura
4
Europe & Middle East Asia-Pacific Americas
1,060 employees in 3 countries with presence in:
North America:
– New York
– San Francisco
– Toronto
South America:
– Sao Paolo
20,500 employees in 13 countries with presence in:
Asia ex-Japan:
– Bangkok
– Beijing
– Hanoi
– Hong Kong
– Jakarta
– Kuala Lumpur
– Manila
Japan:
– 171 branches countrywide
– Tokyo headquarters
– Melbourne
– Mumbai
– Seoul
– Shanghai
– Singapore
– Sydney
– Taipei
Note: (1) Subject to regulatory approval.All headcount figures are approximate.
4,500 employees in 18 countries with presence in:
Europe:
– Amsterdam
– Budapest
– Dublin
– Frankfurt
– Geneva
– London
– Luxembourg
– Madrid
Middle East:
– Bahrain
– Dubai
– Saudi Arabia
– Qatar(1)
– Milan
– Moscow
– Paris
– Rome
– Stockholm
– Vienna
– Warsaw
– Zurich
3
5
London Stock Exchange
80
70
60
50
40
30
20
10
Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
Rank 66 25 11 11 11 8 3 1
Market Share 0.11% 0.69% 2.71% 3.19% 3.15% 4.14% 6.24% 7.45%
Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09
200
150
100
50
Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09
0.00%
3.00%
6.00%
9.00%
Rank 182 61 6 6 4 3 3 1
Market Share 0.00% 0.15% 4.26% 4.92% 5.55% 6.35% 7.34% 10.66%
Dec-08 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09
Eurex Derivatives Exchange
Note: London Stock Exchange statistics are whole trading volumes, weighted by value tradedEurex statistics are for Listed Equity Index Volume whole traded volumes, weighted by value traded
4
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
Focus areas (in Equities) include algorithmic trading, market microstructure modelling, risk
estimation, structured product creation and volatility modelling
Section Header (used to create Tab Pages and Table of Contents)
UK
France
USA
Japan
Canada India
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
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
Measures shortfall due to the implementation process
Depends critically on the execution style and strategy (front-loaded, passive, back-loaded, etc)
Usually receives the least focus by Quant Portfolio Managers
Risk
Return
Cost
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
Trade Scheduling Algorithms are typically formulated as optimisation problems
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
Construction of Trade Scheduling Algorithms
Order parameters
Trade Schedule:
Number of shares to trade in each bin
Price evolution model
Market impact model
Performance criterion
Tra
de
Sch
ed
ulin
g A
lgo
rith
m
Current market conditions
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 Scheduling
Order Placement
Market Access
trade motivation order parameters liquidity profiles
limit order model short-term alpha signals
dynamic venue execution quality analysis
9
10
METRIC
Model Estimated TRade Impact Cost (METRIC)
Focused on Execution Costs
Cost models have limited constraints (other than
matching the data), but some no-arbitrage
constraints can be applied
Data set is large (~1M trades used in a calibration)
and noisy with ~40% of orders rejected using
reasonable criteria
Calibration methodology is critical, as is correct time
frame selection (matching sample size versus slow
timescale effects) to maintain stable parameters of
multiple data sets
execution costs
feestaxescommissions
fixed costs
trading costs
instantaneous impacttransient impactpermanent impact
opportunity costs
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
0.0
3.5
7.0
10.5
14.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2Time
Impact
Transient Impact Temporary Impact Permanent Impact
Total impact over the trade period
Trade PeriodPost-Trade
Period
2TvTvSMETRIC
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 QualityOut of Sample Performance Performance versus Trade Rate
Performance versus Period VolatilityPerformance versus Bid-Ask Spread
15
Risk Modeling Variance of cost model is closely correlated with period (time scaled) 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
0
10
20
30
40
0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2%
Period Volatility
Impact Standard Deviation (bps)
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:
Important to note that : mean reversion effect
t
p
iiti
p
iitit bYaY
11
0,0 11 ba
20
Liquidity Prediction: Model Quality
Define quality measure so that for time bin t on day j for stock i via:
So then P defines the improvement of our methodology versus the static predictions where
Similar results for volatility but
minimal improvement versus
historic for spread profiles
jti
D
d
djit
jit XD
X
1
,,
1
)var(
)var(1
i
iiP
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)):
Computed trade schedule is kept constant throughout trading interval (e.g., VWAP, TWAP) (i.e. pick appropriate discretisation)
TtttttMETRIC )(ˆ)()(ˆ))(;( X..σXX
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