Algorithmic Trading Methods: Applications Using Advanced Statistics, Optimization, and Machine Learning Techniques

Front Cover
Algorithmic Trading Methods
Algorithmic Trading Methods: Applications using Advanced Statistics,
Optimization, and Machine Learning Techniques
Copyright
Contents
Preface
Acknowledgments
1 - Introduction
	WHAT IS ELECTRONIC TRADING?
	WHAT IS ALGORITHMIC TRADING?
	TRADING ALGORITHM CLASSIFICATIONS
	TRADING ALGORITHM STYLES
	INVESTMENT CYCLE
	INVESTMENT OBJECTIVE
	INFORMATION CONTENT
	INVESTMENT STYLES
	INVESTMENT STRATEGIES
	RESEARCH DATA
	BROKER TRADING DESKS
	RESEARCH FUNCTION
	SALES FUNCTION
	IMPLEMENTATION TYPES
	ALGORITHMIC DECISION-MAKING PROCESS
2 - Algorithmic Trading
	ADVANTAGES
	DISADVANTAGES
	GROWTH IN ALGORITHMIC TRADING
	MARKET PARTICIPANTS
	CLASSIFICATIONS OF ALGORITHMS
	TYPES OF ALGORITHMS
	ALGORITHMIC TRADING TRENDS
	DAY OF WEEK EFFECT
	INTRADAY TRADING PROFILES
	TRADING VENUE CLASSIFICATION
		Displayed Market
		Dark Pool
		Dark Pool Controversies
	TYPES OF ORDERS
	REVENUE PRICING MODELS
		Order Priority
	EXECUTION OPTIONS
	ALGORITHMIC TRADING DECISIONS
		Macro Level Strategies
		Micro Level Decisions
		Limit Order Models
		Smart Order Routers
	ALGORITHMIC ANALYSIS TOOLS
		Pre-Trade Analysis
		Intraday Analysis
		Post-Trade Analysis
	HIGH FREQUENCY TRADING
		Auto Market Making
		Quantitative Trading/Statistical Arbitrage
		Rebate/Liquidity Trading
	DIRECT MARKET ACCESS
3 - Transaction Costs
	WHAT ARE TRANSACTION COSTS?
	WHAT IS BEST EXECUTION?
	WHAT IS THE GOAL OF IMPLEMENTATION?
	UNBUNDLED TRANSACTION COST COMPONENTS
		Commission
		Fees
		Taxes
		Rebates
		Spreads
		Delay Cost
		Price Appreciation
		Market Impact
		Timing Risk
		Opportunity Cost
	TRANSACTION COST CLASSIFICATION
	TRANSACTION COST CATEGORIZATION
	TRANSACTION COST ANALYSIS
		Measuring/Forecasting
		Cost vs. Profit and Loss
	IMPLEMENTATION SHORTFALL
		Complete Execution
		Opportunity Cost (Andre Perold)
		Expanded Implementation Shortfall (Wayne Wagner)
	IMPLEMENTATION SHORTFALL FORMULATION
		Trading Cost/Arrival Cost
	EVALUATING PERFORMANCE
		Trading Price Performance
		Benchmark Price Performance
		VWAP Benchmark
		Participation-Weighted Price Benchmark
		Relative Performance Measure
		Pretrade Benchmark
		Index-Adjusted Performance Metric
		Z-Score Evaluation Metric
		Market Cost-Adjusted Z-Score
		Adaptation Tactic
	COMPARING ALGORITHMS
		Nonparametric Tests
		Paired Samples
		Sign Test
		Wilcoxon Signed Rank Test
	INDEPENDENT SAMPLES
		Mann–Whitney U Test
	MEDIAN TEST
	DISTRIBUTION ANALYSIS
	CHI-SQUARE GOODNESS OF FIT
	KOLMOGOROV–SMIRNOV GOODNESS OF FIT
	EXPERIMENTAL DESIGN
		Proper Statistical Tests
		Small Sample Size
		Data Ties
		Proper Categorization
		Balanced Data Sets
	FINAL NOTE ON POSTTRADE ANALYSIS
4 - Market Impact Models
	INTRODUCTION
	DEFINITION
		Example 1: Temporary Market Impact
		Example 2: Permanent Market Impact
		Graphical Illustrations of Market Impact
		Illustration #1: Price Trajectory
		Illustration #2: Supply–Demand Equilibrium
			After Shares Transact, We Face Some Uncertainty—What Happens Next?
		Illustration #3: Temporary Impact Decay Function
		Example #3: Temporary Decay Formulation
		Illustration #4: Various Market Impact Price Trajectories
		Developing a Market Impact Model
		Essential Properties of a Market Impact Model
		The Shape of the Market Impact Function
		Example: Convex Shape
		Example: Linear Shape
		Example: Concave Shape
	DERIVATION OF MODELS
		Almgren and Chriss Market Impact Model
			Random Walk With Price Drift—Discrete Time Periods
			Random Walk With Market Impact (No Price Drift)
	I-STAR MARKET IMPACT MODEL
	MODEL FORMULATION
		I-Star: Instantaneous Impact Equation
		The Market Impact Equation
		Derivation of the Model
		Cost Allocation Method
		I∗ Formulation
		Comparison of Approaches
5 - Probability and Statistics
	INTRODUCTION
	RANDOM VARIABLES
	PROBABILITY DISTRIBUTIONS
		Example: Discrete Probability Distribution Function
		Example: Continuous Probability Distribution Function
		Descriptive Statistics
	PROBABILITY DISTRIBUTION FUNCTIONS
	CONTINUOUS DISTRIBUTION FUNCTIONS
		Normal Distribution
		Standard Normal Distribution
		Student\'s t-Distribution
		Log-Normal Distribution
		Uniform Distribution
		Exponential Distribution
		Chi-Square Distribution
		Logistic Distribution
		Triangular Distribution
	DISCRETE DISTRIBUTIONS
		Binomial Distribution
		Poisson Distribution
	END NOTES
6 - Linear Regression Models
	INTRODUCTION
		Linear Regression Requirements
		Regression Metrics
	LINEAR REGRESSION
		True Linear Regression Model
		Simple Linear Regression Model
		Solving the Simple Linear Regression Model
			Step 1: Estimate Model Parameters
			Step 2: Evaluate Model Performance Statistics
		Standard Error of the Regression Model
		R2 Goodness of Fit
			Step 3: Test for Statistical Significance of Factors
		T-test: Hypothesis Test:
		F-test: Hypothesis Test:
		Example: Simple Linear Regression
		Multiple Linear Regression Model
		Solving the Multiple Linear Regression Model
			Step 1: Estimate Model Parameters
			Step 2: Calculate Model Performance Statistics
		Standard Error of the Regression Model
		R2 Goodness of Fit
			Step 3: Test for Statistical Significance of Factors
		T-test: Hypothesis Test:
		F-test: Hypothesis Test:
		Example: Multiple Linear Regression
	MATRIX TECHNIQUES
		Estimate Parameters
		Compute Standard Errors of b
		R2 Statistic
		F-Statistic
	LOG REGRESSION MODEL
		Example: Log-Transformation
		Example: Log-Linear Transformation
	POLYNOMIAL REGRESSION MODEL
	FRACTIONAL REGRESSION MODEL
7 - Probability Models
	INTRODUCTION
	DEVELOPING A PROBABILITY MODEL
		Comparison of Linear Regression Model to Probability Model
		Power Function Model
		Logit Model
		Probit Model
			Comparison of Logit and Probit Models
		Outcome Data
			Model Formulation
			Mean
			Variance
		Grouping Data
		Solving Binary Output Models
		Step 1: Specify Probability Function
		Step 2: Set Up a Likelihood Function Based on Actual Outcome Results for all Observations. For Example, If We Have n Observ ...
	SOLVING PROBABILITY OUTPUT MODELS
	EXAMPLES
		Example 7.1 Power Function
		Example 7.2 Logit Model
	COMPARISON OF POWER FUNCTION TO LOGIT MODEL
		Example 7.3 Logistic Regression
	CONCLUSIONS
8 - Nonlinear Regression Models
	INTRODUCTION
	REGRESSION MODELS
		Linear Regression Model
		Polynomial Regression Model
		Fractional Regression Model
		Log-linear Regression Model
		Logistic Regression Model
		Nonlinear Model
	NONLINEAR FORMULATION
	SOLVING NONLINEAR REGRESSION MODEL
	ESTIMATING PARAMETERS
		Maximum Likelihood Estimation (MLE)
			Step I: Define the Model
			Step II: Define the Likelihood Function
			Step III: Maximize the Log-Likelihood Function
	NONLINEAR LEAST SQUARES (NON-OLS)
		Step I: Define the Model
		Step II: Define the Error Term
		Step III: Define a Loss Function—Sum of Square Errors
		Step IV: Minimize the Sum of Square Error
	HYPOTHESIS TESTING
	EVALUATE MODEL PERFORMANCE
	SAMPLING TECHNIQUES
	RANDOM SAMPLING
	SAMPLING WITH REPLACEMENT
	SAMPLING WITHOUT REPLACEMENT
	MONTE CARLO SIMULATION
	BOOTSTRAPPING TECHNIQUES
	JACKKNIFE SAMPLING TECHNIQUES
		Important Notes on Sampling in Nonlinear Regression Models
9 - Machine Learning Techniques
	INTRODUCTION
	TYPES OF MACHINE LEARNING
	EXAMPLES
		Cluster Analysis
	CLASSIFICATION
	REGRESSION
	NEURAL NETWORKS
10 - Estimating I-Star Market Impact Model Parameters
	INTRODUCTION
	I-STAR MARKET IMPACT MODEL
	SCIENTIFIC METHOD
		Step 1: Ask a Question
		Step 2: Research the Problem
		Step 3: Construct a Hypothesis
		Step 4: Test the Hypothesis
		Step 6: Conclusions Communicate
			Solution Technique
				The Question
				Research the Problem
				Construct a Hypothesis
				Test the Hypothesis
		Underlying Data Set
		Data Definitions
		Imbalance/Order Size
		Average daily volume
		Actual market volume
		Stock volatility
		POV Rate
		Arrival Cost
			Imbalance Size Issues
		Model Verification
		Model Verification #1: Graphical Illustration
		Model Verification #2: Regression Analysis
		Model Verification #3: z-Score Analysis
		Model Verification #4: Error Analysis
		Stock Universe
		Analysis Period
		Time Period
		Number of Data Points
		Imbalance
		Side
		Volume
		Turnover
		VWAP
		First Price
		Average Daily Volume
		Annualized Volatility
		Size
		POV Rate
		Cost
		Estimating Model Parameters
		Sensitivity Analysis
		Cost Curves
		Statistical Analysis
			Error Analysis
		Stock-Specific Error Analysis
11 - Risk, Volatility, and Factor Models
	INTRODUCTION
	VOLATILITY MEASURES
		Log-Returns
		Average Return
		Variance
		Volatility
		Covariance
		Correlation
		Dispersion
		Value-at-Risk
	IMPLIED VOLATILITY
		Beta
		Range
	FORECASTING STOCK VOLATILITY
		Volatility Models
			Returns
			Historical Moving Average (HMA)
			Exponential Weighted Moving Average (EWMA)
			ARCH Volatility Model
			GARCH Volatility Model
			HMA-VIX Adjustment Model
		Determining Parameters via Maximum Likelihood Estimation
			Likelihood Function
			Measuring Model Performance
			Root Mean Square Error (RMSE)
			Root Mean Z-Score Squared Error (RMZSE)
			Outlier Analysis
	HISTORICAL DATA AND COVARIANCE
		False Relationships
			Example #1: False Negative Signal Calculations
			Example #2: False Positive Signal Calculation
		Degrees of Freedom
	FACTOR MODELS
		Matrix Notation
		Factor Model in Matrix Notation
	TYPES OF FACTOR MODELS
		Index Model
			Single-Index Model
			Multi-Index Models
		Macroeconomic Factor Models
			Cross Sectional Multi-Factor Model
		Statistical Factor Models
			How Many Factors Should be Selected?
12 - Volume Forecasting Techniques
	INTRODUCTION
	MARKET IMPACT MODEL
	AVERAGE DAILY VOLUME
		Methodology
		Definitions
		Monthly Volume Forecasting Model
		Analysis
		Regression Results
	OBSERVATIONS OVER THE 19-YEAR PERIOD: 2000–18
	OBSERVATIONS OVER THE MOST RECENT 3-YEAR PERIOD: 2016–18
		Volumes and Stock Price Correlation
	FORECASTING DAILY VOLUMES
		Our Daily Volume Forecasting Analysis is as Follows
			Definitions
				Daily Forecasting Analysis—Methodology
		Variable Notation
		ARMA Daily Forecasting Model
		Analysis Goal
		Step 1. Determine Which is More Appropriate: ADV or MDV and the Historical Look-Back Number of Days
		Conclusion #1
		Step 2. Estimate the DayOfWeek(t) Parameter
		Conclusion #2
		Step 3. Estimate the Autoregressive Parameter β^
		Forecast Improvements
		Daily Volume Forecasting Model
		Conclusion #3
		Forecasting Intraday Volumes Profiles
		Forecasting Intraday Volume Profiles
		Predicting Remaining Daily Volume
13 - Algorithmic Decision-Making Framework
	INTRODUCTION
	EQUATIONS
		Variables
		Important Equations
	ALGORITHMIC DECISION-MAKING FRAMEWORK
		Select Benchmark Price
			Arrival Price Benchmark
			Historical Price Benchmark
			Future Price Benchmark
	COMPARISON OF BENCHMARK PRICES
		Specify Trading Goal
			Further Insight
		Specify Adaptation Tactic
		Projected Cost
			Target Cost Tactic
			Aggressive in the Money
			Passive-in-the-Money
	COMPARISON ACROSS ADAPTATION TACTICS
	MODIFIED ADAPTATION TACTICS
		How Often Should we Reoptimization Our Tactic?
14 - Portfolio Algorithms and Trade Schedule Optimization
	INTRODUCTION
	TRADER\'S DILEMMA
		Variables
	TRANSACTION COST EQUATIONS
		Market Impact
		Price Appreciation
		Timing Risk
		One-Sided Optimization Problem
	OPTIMIZATION FORMULATION
		Constraint Description
			Objective Function Difficulty
			Optimization Objective Function Simplification
	PORTFOLIO OPTIMIZATION TECHNIQUES
		Quadratic Programming Approach
		Trade Schedule Exponential
		Residual Schedule Exponential
		Trading Rate Parameter
			Market Impact Expression
			Timing Risk Expression
		Comparison of Optimization Techniques
			How Long did it Take to Solve the Portfolio Objective Problem?
				How Accurate Was the Solution for Each Optimization Technique?
	PORTFOLIO ADAPTATION TACTICS
		Description of AIM and PIM for Portfolio Trading
		How Often Should we Reoptimize?
		Appendix
15 - Advanced Algorithmic Modeling Techniques
	INTRODUCTION
	TRADING COST EQUATIONS
		Model Inputs
	TRADING STRATEGY
		Percentage of Volume
		Trading Rate
		Trade Schedule
		Comparison of POV Rate to Trade Rate
	TRADING TIME
	TRADING RISK COMPONENTS
	TRADING COST MODELS—REFORMULATED
		Market Impact Expression
			I-Star
			Market Impact for a Single Stock Order
				Important note
			Market Impact for a Basket of Stock
	TIMING RISK EQUATION
		Derivation of the 1/3 Factor
		Timing Risk For a Basket of Stock
	COMPARISON OF MARKET IMPACT ESTIMATES
		Forecasting Covariance
		Efficient Trading Frontier
		Single Stock Trade Cost Objective Function
		Portfolio Trade Cost Objective Function
	MANAGING PORTFOLIO RISK
		Residual Risk Curve
		Minimum Trading Risk Quantity
		Maximum Trading Opportunity
		When to Use These Criteria?
		Program-Block Decomposition
16 - Decoding and Reverse Engineering Broker Models with Machine Learning Techniques
	INTRODUCTION
	PRE-TRADE OF PRE-TRADES
		I-Star Model Approach
		Neural Network Model Approach
	PORTFOLIO OPTIMIZATION
		What Should the Portfolio Manager Do?
		Deriving Portfolio Optimization Market Impact Models
		Example: Share Quantity Regression Model
		Example: Trade Value Regression Model
17 - Portfolio Construction with Transaction Cost Analysis
	INTRODUCTION
	PORTFOLIO OPTIMIZATION AND CONSTRAINTS
	TRANSACTION COSTS IN PORTFOLIO OPTIMIZATION
	PORTFOLIO MANAGEMENT PROCESS
		Example: Efficient Trading Frontier With and Without Short Positions
		Example: Maximizing Investor Utility
	TRADING DECISION PROCESS
		What is the Appropriate Optimal Strategy to Use?
	UNIFYING THE INVESTMENT AND TRADING THEORIES
		Which Execution Strategy Should the Trader Use?
	COST-ADJUSTED FRONTIER
	DETERMINING THE APPROPRIATE LEVEL OF RISK AVERSION
	BEST EXECUTION FRONTIER
	PORTFOLIO CONSTRUCTION WITH TRANSACTION COSTS
		Quest for Best Execution Frontier
			Return
			Risk
	EXAMPLE
		Important Findings
	CONCLUSION
18 - Quantitative Analysis with TCA
	INTRODUCTION
		Quantitative Overlays
		Market Impact Factor Scores
		Cost Curves
		Alpha Capture
		Investment Capacity
		Portfolio Optimization
		Backtesting
		Liquidation Cost
		Sensitivity Analysis
	ARE THE EXISTING MODELS USEFUL ENOUGH FOR PORTFOLIO CONSTRUCTION?
		Current State of Vendor Market Impact Models
	PRETRADE OF PRETRADES
		Applications
		Example #1
		Example #2
		Example #3
		Example #4
	HOW EXPENSIVE IS IT TO TRADE?
		Acquisition and Liquidation Costs
		Portfolio Management—Screening Techniques
	BACKTESTING STRATEGIES
	MARKET IMPACT SIMULATION
		Simulation Scenario
	MULTI-ASSET CLASS INVESTING
		Investing in Beta Exposure and Other Factors
		Example #5
			Equities
			Exchange-Traded Funds
			Futures
				Beta Investment Allocation
	MULTI-ASSET TRADING COSTS
		Global Equity Markets
		Multi-Asset Classes
			Why do Trading Costs Vary Across Asset Classes?
			Definitions
			Observations
			Equities
			Exchange Traded Funds
			Futures
			Bonds
			Commodities
			Currency
			Room for Improvement
	MARKET IMPACT FACTOR SCORES
		Current State of Market Impact Factor Scores
	MARKET IMPACT FACTOR SCORE ANALYSIS
	ALPHA CAPTURE PROGRAM
		Example #6
		Example #7
		Alpha Capture Curves
			Important Note
19 - Machine Learning and Trade Schedule Optimization
	INTRODUCTION
	MULTIPERIOD TRADE SCHEDULE OPTIMIZATION PROBLEM
		Setting up the Problem
		Trader\'s Dilemma Objective Function
	NONLINEAR OPTIMIZATION CONVERGENCE
		Newton\'s Method
		Example #1
		Example #2
	MACHINE LEARNING
		Neural Networks
		Neural Network Errors
	MACHINE LEARNING TRAINING EXPERIMENT
		Step I: Generating Simulated Trade Baskets
		Step II: Compile Stock and Basket Data Statistics
			X-Input Variables
			Y-Output Variable
		Step III: Solve the Multiperiod Trade Schedule Optimization Problem
		Step IV: Train the NNET
		Step V. Calculate the Initial Parameter Values for the NNET
		Principal Component Analysis
		Stepwise Regression Analysis
		Neural Network Structure
		Neural Network Error
	PERFORMANCE RESULTS
	CONCLUSIONS
20 - TCA Analysis Using MATLAB, Excel, and Python
	INTRODUCTION
	TRANSACTION COST ANALYSIS FUNCTIONS
	TRANSACTION COST MODEL
	MATLAB FUNCTIONS
	EXCEL AND PYTHON FUNCTIONS
	TCA REPORT EXAMPLES
	CONCLUSION
21 - Transaction Cost Analysis (TCA) Library
	INTRODUCTION
		TCA Library
	TRANSACTION COST ANALYSIS USING THE TCA LIBRARY
		List of TCA Functions
			Pretrade Analysis
			Posttrade Analysis
			Portfolio Management
			Optimization
			Calculations
			Conversions
REFERENCES
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	Y
	Z
Back Cover