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Nomura International plc STRICTLY PRIVATE AND CONFIDENTIAL Trade Scheduling in Equity Markets: Theory and Practice Michael Simmonds Liquid Markets Analytics Slide 2 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 Slide 3 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 Slide 4 Geography of Nomura 4 Europe & Middle EastAsia-PacificAmericas 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 Slide 5 5 London Stock Exchange Eurex Derivatives Exchange 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 4 Slide 6 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) 5 Slide 7 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 Slide 8 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 Slide 9 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 Trade Scheduling Algorithm Current market conditions 8 Slide 10 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 Slide 11 10 Slide 12 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 fees taxes commissio ns fixed costs trading costs instantaneous impact transient impact permanent impact opportunity costs 11 Slide 13 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 Slide 14 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 Slide 15 METRIC Total impact over the trade period Trade Period Post-Trade Period Where S is the average bid-ask spread, is the volatility, v is the trade rate and T is the trade duration 14 Slide 16 METRIC: Model Quality Out of Sample PerformancePerformance versus Trade Rate Performance versus Period VolatilityPerformance versus Bid-Ask Spread 15 Slide 17 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 one assumes that for a set of factors with returns F then there exist L such that R - = 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 - ) = cov(L.F + ) = L.cov( F ).L T + cov( ) = L.cov( F ).L T + where = cov( ) Therefore the risk matrix,, is defined by = L.cov( F ).L T + and is constant for rotations of factors (i.e. if a new family of factors F=Q.F and one defines L=L.Q T such that Q.Q T = I then = ) Weighting schema, time scale and factor selection are critical to producing good quality risk estimates 16 Slide 18 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 Slide 19 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 X i,t and hence a correlation matrix can be defined 18 Slide 20 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 XFirst eigenmode 19 Slide 21 Liquidity Prediction: Stock Specific The following is observed for the profile after discounting the market profile for each stock: Null hypoth