Algorithmic Trading Methods

 

CHAPTER 1 Introduction ...................................................................................1

What is Electronic Trading? ......................................................................... 2

What is Algorithmic Trading? ...................................................................... 3

Trading Algorithm Classifications ................................................................ 3

Trading Algorithm Styles ............................................................................. 4

Investment Cycle .......................................................................................... 5

Investment Objective .................................................................................... 5

Information Content...................................................................................... 6

Investment Styles .......................................................................................... 7

Investment Strategies .................................................................................... 9

Research Data ............................................................................................. 15

Broker Trading Desks................................................................................. 16

Research Function....................................................................................... 17

Sales Function............................................................................................. 18

Implementation Types................................................................................. 19

Algorithmic Decision-Making Process ....................................................... 20

CHAPTER 2 Algorithmic Trading ....................................................................... 23

Advantages.................................................................................................. 25

Disadvantages ............................................................................................. 26

Growth in Algorithmic Trading.................................................................. 27

Market Participants ..................................................................................... 28

Classifications of Algorithms...................................................................... 31

Types of Algorithms ................................................................................... 31

Algorithmic Trading Trends ....................................................................... 35

Day of Week Effect .................................................................................... 37

Intraday Trading Profiles ............................................................................ 39

Trading Venue Classification...................................................................... 42

Displayed Market ................................................................................... 42

Dark Pool ............................................................................................... 42

Dark Pool Controversies ........................................................................ 43

Types of Orders .......................................................................................... 44

Revenue Pricing Models............................................................................. 45

Order Priority ......................................................................................... 46

Execution Options....................................................................................... 46

Algorithmic Trading Decisions................................................................... 47

Macro Level Strategies .......................................................................... 47

Micro Level Decisions ........................................................................... 48

Limit Order Models ............................................................................... 48

Smart Order Routers .............................................................................. 48

Algorithmic Analysis Tools........................................................................ 49

Pre-Trade Analysis ................................................................................. 49

Intraday Analysis ................................................................................... 49

Post-Trade Analysis ............................................................................... 49

High Frequency Trading............................................................................. 50

Auto Market Making.............................................................................. 50

Quantitative Trading/Statistical Arbitrage.............................................. 52

Rebate/Liquidity Trading ....................................................................... 52

Direct Market Access.................................................................................. 54

CHAPTER 3 Transaction Costs .......................................................................... 57

What are Transaction Costs? ...................................................................... 57

What is Best Execution?............................................................................. 58

What is the Goal of Implementation?......................................................... 58

Unbundled Transaction Cost Components ................................................. 59

Commission............................................................................................ 59

Fees ........................................................................................................ 59

Taxes ...................................................................................................... 59

Rebates ................................................................................................... 60

Spreads ................................................................................................... 60

Delay Cost.............................................................................................. 60

Price Appreciation.................................................................................. 61

Market Impact ........................................................................................ 61

Timing Risk............................................................................................ 62

Opportunity Cost.................................................................................... 62

Transaction Cost Classification................................................................... 62

Transaction Cost Categorization................................................................. 65

Transaction Cost Analysis .......................................................................... 65

Measuring/Forecasting ........................................................................... 66

Cost vs. Profit and Loss ......................................................................... 67

Implementation Shortfall ............................................................................ 67

Complete Execution ............................................................................... 69

Opportunity Cost (Andre Perold)........................................................... 70

Expanded Implementation Shortfall (Wayne Wagner).......................... 71

Implementation Shortfall Formulation........................................................ 74

Trading Cost/Arrival Cost...................................................................... 74

Evaluating Performance .............................................................................. 75

Trading Price Performance..................................................................... 75

Benchmark Price Performance............................................................... 75

VWAP Benchmark................................................................................. 76

Participation-Weighted Price Benchmark .............................................. 77

Relative Performance Measure .............................................................. 78

Pretrade Benchmark ............................................................................... 80

Index-Adjusted Performance Metric ...................................................... 80

Z-Score Evaluation Metric ..................................................................... 81

Market Cost-Adjusted Z-Score .............................................................. 83

Adaptation Tactic ................................................................................... 83

Comparing Algorithms ............................................................................... 84

Nonparametric Tests .............................................................................. 85

Paired Samples ....................................................................................... 86

Sign Test ................................................................................................ 86

Wilcoxon Signed Rank Test .................................................................. 87

Independent Samples .................................................................................. 89

ManneWhitney U Test.......................................................................... 89

Median Test ................................................................................................ 91

Distribution Analysis .................................................................................. 92

Chi-Square Goodness of Fit ....................................................................... 93

KolmogoroveSmirnov Goodness of Fit..................................................... 94

Experimental Design................................................................................... 95

Proper Statistical Tests ........................................................................... 95

Small Sample Size ................................................................................. 95

Data Ties ................................................................................................ 96

Proper Categorization............................................................................. 96

Balanced Data Sets................................................................................. 96

Final Note on Posttrade Analysis ............................................................... 97

CHAPTER 4 Market Impact Models ................................................................... 99

Introduction ................................................................................................. 99

Definition .................................................................................................... 99

Example 1: Temporary Market Impact................................................ 100

Example 2: Permanent Market Impact ................................................ 100

Graphical Illustrations of Market Impact............................................. 101

Illustration #1: Price Trajectory ........................................................... 101

Illustration #2: SupplyeDemand Equilibrium..................................... 102

Illustration #3: Temporary Impact Decay Function............................. 105

Example #3: Temporary Decay Formulation ...................................... 108

Illustration #4: Various Market Impact Price Trajectories .................. 108

Developing a Market Impact Model.................................................... 109

Essential Properties of a Market Impact Model .................................. 110

The Shape of the Market Impact Function .......................................... 112

Example: Convex Shape ...................................................................... 114

Example: Linear Shape ........................................................................ 114

Example: Concave Shape..................................................................... 114

Derivation of Models ................................................................................ 115

Almgren and Chriss Market Impact Model ......................................... 115

I-Star Market Impact Model ..................................................................... 120

Model Formulation ................................................................................... 120

I-Star: Instantaneous Impact Equation ................................................. 121

The Market Impact Equation ............................................................... 122

Derivation of the Model....................................................................... 122

Cost Allocation Method....................................................................... 123

I* Formulation...................................................................................... 126

Comparison of Approaches.................................................................. 128

CHAPTER 5 Probability and Statistics .............................................................. 129

Introduction ............................................................................................... 129

Random Variables..................................................................................... 129

Probability Distributions ........................................................................... 130

Example: Discrete Probability Distribution Function.......................... 131

Example: Continuous Probability Distribution Function..................... 132

Descriptive Statistics ............................................................................ 135

Probability Distribution Functions............................................................ 136

Continuous Distribution Functions ........................................................... 137

Normal Distribution ............................................................................. 137

Standard Normal Distribution .............................................................. 138

Student’s t-Distribution ........................................................................ 139

Log-Normal Distribution...................................................................... 141

Uniform Distribution............................................................................ 142

Exponential Distribution ...................................................................... 143

Chi-Square Distribution ....................................................................... 145

Logistic Distribution ............................................................................ 146

Triangular Distribution......................................................................... 148

Discrete Distributions................................................................................ 149

Binomial Distribution........................................................................... 149

Poisson Distribution ............................................................................. 150

End Notes.................................................................................................. 150

CHAPTER 6 Linear Regression Models ............................................................. 151

Introduction ............................................................................................... 151

Linear Regression Requirements ......................................................... 154

Regression Metrics............................................................................... 154

Linear Regression ..................................................................................... 156

True Linear Regression Model ............................................................ 156

Simple Linear Regression Model......................................................... 156

Solving the Simple Linear Regression Model ..................................... 157

Standard Error of the Regression Model ............................................. 159

R2 Goodness of Fit............................................................................... 159

T-test: Hypothesis Test......................................................................... 159

F-test: Hypothesis Test ........................................................................ 159

Example: Simple Linear Regression.................................................... 159

Multiple Linear Regression Model ...................................................... 161

Solving the Multiple Linear Regression Model................................... 162

Standard Error of the Regression Model ............................................. 164

R2 Goodness of Fit............................................................................... 164

T-test: Hypothesis Test......................................................................... 164

F-test: Hypothesis Test ........................................................................ 165

Example: Multiple Linear Regression ................................................. 165

Matrix Techniques .................................................................................... 167

Estimate Parameters ............................................................................. 167

Compute Standard Errors of b ............................................................. 168

R2 Statistic ............................................................................................ 169

F-Statistic ............................................................................................. 169

Log Regression Model.............................................................................. 169

Example: Log-Transformation ............................................................. 169

Example: Log-Linear Transformation.................................................. 171

Polynomial Regression Model.................................................................. 171

Fractional Regression Model .................................................................... 172

CHAPTER 7 Probability Models....................................................................... 175

Introduction ............................................................................................... 175

Developing a Probability Model............................................................... 175

Comparison of Linear Regression Model to Probability Model ......... 177

Power Function Model......................................................................... 177

Logit Model.......................................................................................... 178

Probit Model ........................................................................................ 179

Outcome Data....................................................................................... 180

Grouping Data...................................................................................... 182

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