Front Cover	1
	The Science of Algorithmic Trading and Portfolio Management	4
	Copyright Page	5
	Contents	8
	Preface	16
	Acknowledgments	18
	1 Algorithmic Trading	20
	Introduction	20
	Advantages	22
	Disadvantages	23
	Changing Trading Environment	24
	Recent Growth in Algorithmic Trading	30
	Investment Cycle	34
	Classifications of Algorithms	35
	Types of Algorithms	36
	Algorithmic Trading Trends	39
	Trading Venue Classification	40
	Displayed Market	40
	Dark Pool	40
	Grey Pool	40
	Dark Pool Controversies	41
	Types of Orders	42
	Execution Options	42
	The Trading Floor	44
	Research Function	45
	Sales Function	46
	Algorithmic Trading Decisions	48
	Macro-Level Strategies	48
	Step 1—Choose Implementation Benchmark	49
	Step 2—Select Optimal Execution Strategy	49
	Step 3—Specify Adaptation Tactic	51
	Micro-Level Decisions	52
	Limit Order Models	53
	Smart Order Routers	54
	Algorithmic Analysis Tools	56
	Pre-Trade Analysis	56
	Intraday Analysis	56
	Post-Trade Analysis	57
	Rule-Based Trading	57
	Quantitative Techniques	57
	High Frequency Trading	58
	Auto Market Making	58
	Quantitative Trading/Statistical Arbitrage	60
	Rebate/Liquidity Trading	60
	Direct Market Access	62
	Advantages	63
	Disadvantages	63
	2 Market Microstructure	66
	Introduction	66
	Market Microstructure Literature	68
	The New Market Structure	70
	Pricing Models	75
	Order Priority	76
	Equity Exchanges	76
	New NYSE Trading Model	76
	Designated Market Makers	77
	Supplemental Liquidity Providers	78
	Trading Floor Brokers	79
	NASDAQ Select Market Maker Program	79
	Empirical Evidence	80
	Trading Volumes	80
	Market Share	80
	Large and Small Cap Trading	81
	Do Stocks Trade Differently Across the Exchanges and Venues?	82
	Volume Distribution Statistics	82
	Day of Week Effect	84
	Intraday Trading Profiles	86
	Spreads	86
	Volumes	87
	Volatility	89
	Intraday Trading Stability—Coefficient of Variation	91
	Special Event Days	92
	Flash Crash	95
	Empirical Evidence from the Flash Crash	98
	What Should Regulators do to SafeGuard Investors from Potential Future Flash Crashes?	102
	Comparison with Previous Crashes	103
	Conclusion	104
	3 Algorithmic Transaction Cost Analysis	106
	Introduction	106
	What Are Transaction Costs?	107
	What Is Best Execution?	107
	What Is the Goal of Implementation?	108
	Unbundled Transaction Cost Components	108
	1. Commission	108
	2. Fees	108
	3. Taxes	108
	4. Rebates	109
	5. Spreads	109
	6. Delay Cost	110
	7. Price Appreciation	110
	8. Market Impact	110
	9. Timing Risk	111
	10. Opportunity Cost	111
	Transaction Cost Classification	111
	Transaction Cost Categorization	113
	Transaction Cost Analysis	113
	Measuring/Forecasting	115
	Cost versus Profit and Loss	116
	Implementation Shortfall	116
	Complete Execution	118
	Opportunity Cost (Andre Perold)	119
	Expanded Implementation Shortfall (Wayne Wagner)	120
	Implementation Shortfall Formulation	123
	Trading Cost/Arrival Cost	123
	Evaluating Performance	124
	Trading Price Performance	124
	Benchmark Price Performance	125
	VWAP Benchmark	125
	Participation Weighted Price (PWP) Benchmark	127
	Relative Performance Measure (RPM)	128
	Pre-Trade Benchmark	129
	Index Adjusted Performance Metric	130
	Z-Score Evaluation Metric	131
	Market Cost Adjusted Z-Score	132
	Adaptation Tactic	133
	Comparing Algorithms	134
	Non-Parametric Tests	135
	Paired Samples	136
	Sign Test	136
	Wilcoxon Signed Rank Test	137
	Independent Samples	139
	Mann-Whitney U Test	139
	Median Test	141
	Distribution Analysis	142
	Chi-Square Goodness of Fit	142
	Kolmogorov-Smirnov Goodness of Fit	143
	Experimental Design	144
	Proper Statistical Tests	145
	Small Sample Size	145
	Data Ties	145
	Proper Categorization	146
	Balanced Data Sets	146
	Final Note on Post-Trade Analysis	146
	4 Market Impact Models	148
	Introduction	148
	Definition	148
	Example 1: Temporary Market Impact	149
	Example 2: Permanent Market Impact	149
	Graphical Illustrations of Market Impact	150
	Illustration 1—Price Trajectory	150
	Illustration 2—Supply-Demand Equilibrium	151
	Illustration 3—Temporary Impact Decay Function	154
	Example—Temporary Decay Formulation	156
	Illustration 4—Various Market Impact Price Trajectories	157
	Developing a Market Impact Model	158
	Essential Properties of a Market Impact Model	159
	Derivation of Models	161
	Almgren & Chriss—Market Impact Model	161
	Random Walk with Price Drift—Discrete Time Periods	162
	Random Walk with Market Impact (No price drift)	163
	I-Star Market Impact Model	165
	Model Formulation	166
	I-Star: Instantaneous Impact Equation	166
	Market Impact Equation	167
	Derivation of the Model	167
	Cost Allocation Method	168
	I* Formulation	170
	Comparison of Approaches	172
	Underlying Data Set	173
	Imbalance/Order Size	173
	Parameter Estimation Techniques	176
	Technique 1: Two-Step Process	176
	Step 1: Estimate Temporary Impact Parameter	176
	Step 2: Estimate ai Parameters	177
	Technique 2: Guesstimate Technique	179
	Technique 3: Non-Linear Optimization	179
	Model Verification	179
	Model Verification 1: Graphical Illustration	180
	Model Verification 2: Regression Analysis	180
	Model Verification 3: Z-Score Analysis	180
	Model Verification 4: Error Analysis	181
	5 Estimating I-Star Model Parameters	182
	Introduction	182
	Scientific Method	183
	Step 1: Ask a Question	183
	Step 2: Research the Problem	183
	Step 3: Construct the Hypothesis	183
	Step 4: Test the Hypothesis	183
	Step 5: Analyze the Data	184
	Step 6: Conclusion and Communication	184
	Solution Technique	185
	The Question	185
	Research the Problem	185
	Construct the Hypothesis	190
	Test the Hypothesis	192
	Data Definitions	194
	Universe of Stocks	195
	Analysis Period	195
	Time Period	195
	Number of Data Points	195
	Imbalance	195
	Side	196
	Volume	196
	Turnover	196
	VWAP	197
	First Price	197
	Average Daily Volume	197
	Annualized Volatility	197
	Size	198
	POV Rate	198
	Cost	198
	Estimating Model Parameters	198
	Sensitivity Analysis	200
	Cost Curves	205
	Statistical Analysis	206
	Error Analysis	206
	Stock Specific Error Analysis	208
	6 Price Volatility	212
	Introduction	212
	Definitions	213
	Price Returns/Price Change	213
	Average Return	213
	Volatility	215
	Covariance	215
	Correlation	216
	Dispersion	216
	Value-at-Risk	216
	Implied Volatility	217
	Beta	217
	Market Observations—Empirical Findings	218
	Forecasting Stock Volatility	221
	Volatility Models	221
	Price Returns	222
	Data Sample	222
	Historical Moving Average (HMA)	223
	Exponential Weighted Moving Average (EWMA)	224
	Arch Volatility Model	224
	GARCH Volatility Model	225
	HMA-VIX Adjustment Model	225
	Determining Parameters via Maximum Likelihood Estimation	227
	Likelihood Function	227
	Estimation Results	228
	Measuring Model Performance	228
	Root Mean Square Error (RMSE)	229
	Root Mean Z-Score Squared Error (RMZSE)	229
	Outlier Analysis	230
	Results	230
	Problems Resulting from Relying on Historical Market Data for Covariance Calculations	233
	False Relationships	233
	Degrees of Freedom	238
	Factor Models	240
	Matrix Notation	242
	Constructing Factor Independence	243
	Estimating Covariance Using a Factor Model	244
	Types of Factor Models	246
	Multi-Index Models	247
	Macroeconomic Factor Models	247
	Cross-Sectional Multi-Factor Models	248
	Index Model	246
	Single Index Model	246
	Statistical Factor Models	250
	7 Advanced Algorithmic Forecasting Techniques	254
	Introduction	254
	Trading Cost Equations	255
	Model Inputs	255
	Trading Strategy	256
	Percentage of Volume	256
	Trading Rate	257
	Trade Schedule	257
	Comparison of POV rate to Trade Rate	258
	Trading Time	258
	Trading Risk Components	259
	Trading Cost Models—Reformulated	260
	Market Impact Expression	260
	I-Star	260
	Market Impact for a Single Stock Order	260
	Market Impact for a Basket of Stock	262
	Timing Risk Equation	262
	Timing Risk for a Basket of Stock	267
	Comparison of Market Impact Estimates	267
	Volume Forecasting Techniques	270
	Daily Volumes	270
	Definitions	270
	Daily Forecasting Analysis—Methodology	271
	Variable Notation	271
	ARMA Daily Forecasting Model	271
	Analysis Goal	272
	Forecast Improvements	276
	Daily Volume Forecasting Model	276
	Forecasting Monthly Volumes	277
	Forecasting Covariance	282
	Efficient Trading Frontier	284
	Single Stock Trade Cost Objective Function	286
	Portfolio Trade Cost Objective Function	286
	8 Algorithmic Decision Making Framework	288
	Introduction	288
	Equations	289
	Algorithmic Decision Making Framework	291
	1) Select Benchmark Price	291
	Arrival Price Benchmark	291
	Historical Price Benchmark	292
	Future Price Benchmark	294
	Comparison of Benchmark Prices	295
	2) Specify Trading Goal	295
	1. Minimize Cost	296
	2. Minimize Cost with Risk Constraint	298
	3. Minimize Risk with Cost Constraint	299
	4. Balance Trade-off between Cost and Risk	299
	5. Price Improvement	300
	Further Insight	302
	3) Specify Adaptation Tactic	303
	Projected Cost	304
	Target Cost Tactic	307
	Aggressive-in-the-Money	308
	Passive-in-the-Money	310
	Comparison across Adaptation Tactics	312
	Modified Adaptation Tactics	313
	How Often Should We Re-Optimize Our Tactics?	313
	9 Portfolio Algorithms	316
	Introduction	316
	Trader’s Dilemma	317
	Variables	318
	Transaction Cost Equations	319
	Market Impact	320
	Price Appreciation	320
	Timing Risk	321
	One-Sided Optimization Problem	321
	Optimization Formulation	321
	Constraint Description	322
	Objective Function Difficulty	324
	Optimization Objective Function Simplification	324
	Portfolio Optimization Techniques	325
	Quadratic Programming Approach	325
	Trade Schedule Exponential	327
	Residual Schedule Exponential	328
	Trading Rate Parameter	329
	Market Impact Expression	329
	Timing Risk Expression	330
	Comparison of Optimization Techniques	331
	Portfolio Adaptation Tactics	335
	Description of AIM and PIM for Portfolio Trading	336
	How Often Should We Re-Optimize?	338
	Managing Portfolio Risk	339
	Residual Risk Curve	339
	Minimum Trading Risk Quantity	341
	Maximum Trading Opportunity	342
	When to Use These Values?	343
	Program-Block Decomposition	344
	Appendix	347
	10 Portfolio Construction	350
	Introduction	350
	Portfolio Optimization and Constraints	351
	Transaction Costs in Portfolio Optimization	354
	Portfolio Management Process	358
	Example: Efficient Trading Frontier w/ and w/o Short Positions	359
	Example: Maximizing Investor Utility	359
	Trading Decision Process	360
	Unifying the Investment and Trading Theories	362
	Cost-Adjusted Frontier	367
	Determining the Appropriate Level of Risk Aversion	369
	Best Execution Frontier	370
	Portfolio Construction with Transaction Costs	371
	Quest for best execution frontier	373
	Return	374
	Risk	374
	Conclusion	378
	11 Quantitative Portfolio Management Techniques	380
	Introduction	380
	Are the Existing Models Useful Enough for Portfolio Construction?	382
	Current State of Vendor Market Impact Models	383
	Pre-Trade of Pre-Trades	386
	Estimation Process	387
	Applications	391
	Example 1	391
	Example 2	392
	Example 3	392
	Example 4	392
	How Expensive Is It to Trade?	393
	Acquisition and Liquidation Costs	396
	Portfolio Management—Screening Techniques	399
	MI Factor Scores	403
	Derivation of the MI Factor Score for Shares	403
	Current State of MI Factor Scores	405
	MI Factor Score Analysis	405
	Alpha Capture Program	407
	Example 5	408
	Example 6	409
	Alpha Capture Curves	412
	12 Cost Index & Multi-Asset Trading Costs	414
	Introduction	414
	Cost Index	415
	Cost Basis	416
	Cost Strategy	417
	Normalization Process	419
	Customized Indexes	421
	Real-Time Cost Index	422
	Back-Testing	427
	Market Impact Simulation	429
	Simulation Scenario	431
	Multi-Asset Class Investing	434
	Investing in Beta Exposure and Other Factors	434
	Beta Investment Allocation	438
	Multi-Asset Trading Costs	439
	Global Equity Markets	440
	Multi-Asset Classes	441
	13 High Frequency Trading and Black Box Models	448
	Introduction	448
	Data and Research	450
	Strategies	451
	Statistical Arbitrage	451
	Triangular Arbitrage	455
	Liquidity Trading	458
	Market-Neutral Arbitrage	459
	Index and Exchange Traded Fund Arbitrage	461
	Merger Arbitrage	462
	Evaluation	465
	Summary	469
	References	472
	Index	484