GIUSEPPE PALEOLOGO is the Head of Risk Management at Hudson River Trading. He has also held senior positions at Millennium, Citadel, Axioma, and IBM Research. He was formerly a mathematical researcher at Stanford and an instructor in the master’s program in Financial Engineering at Cornell University.

• Chapter 1 For Whom? Why? And How? 11.1 What You Will Find Here 21.2 Asterisks; Or, How to Read This Book 31.3 Acknowledgments 3Chapter 2 The Problem: From Ideas to Profit 52.1 How to Invest in Your Edge, and Hedge the Rest 72.2 How to Size Your Positions 82.3 How to Learn from Your History 82.4 How to Trade Efficiently 92.5 How to Limit Factor Risk 92.6 How to Control Maximum Losses 102.7 How to Determine Your Leverage 102.8 How to Analyze New Sources of Data 10Chapter 3 A Tour of Risk and Performance 113.1 Introduction 123.2 Alpha and Beta 143.3 Where Does Alpha Come From? 153.4 Estimate Risk in Advance 183.4.1 What Is Risk? 183.4.2 Measuring Risk and Performance 203.5 First Steps in Risk Decomposition 253.6 Simple Hedging 263.7 Separation of Concerns 283.8 Takeaway Messages 29Chapter 4 An Introduction to Multi-Factor Models 304.1 From One Factor to Many 314.2 ★Frequently Asked Questions About Risk 354.3 ★The Machinery of Risk Models 404.4 Takeaway Messages 43Chapter 5 Understand Factors 445.1 The Economic Environment 475.1.1 Country 475.1.2 Industries 485.1.3 Beta 505.1.4 Volatility 545.2 The Trading Environment 565.2.1 Short Interest 565.2.2 Active Manager Holdings (AMH) 585.2.3 Momentum 605.3 The Company: Valuation Factors 665.3.1 Value 665.4 Takeaway Messages 71Chapter 6 Use Effective Heuristics for Alpha Sizing 726.1 Sharpe Ratio 746.2 Estimating Expected Returns 766.3 Risk-Based Sizing 796.4 ★Empirical Analysis of the Sizing Rules 816.5 From Ideas to Positions 886.6 Time-Series Risk-Based Portfolio Targeting 896.7 ★Frequently Asked Questions About Performance 956.8 Takeaway Messages 96Chapter 7 Manage Factor Risk 987.1 Tactical Factor Risk Management 997.1.1 Optimize If You Must 1047.2 Strategic Factor Risk Management 1077.2.1 Setting an Upper Limit on Factor Risk 1077.2.2 Setting a Limit on Market Exposure 1117.2.3 Setting an Upper Limit on Single-Stock Holdings 1137.2.4 Setting an Upper Limit on Single-Factor Exposures 1167.3 Systematic Hedging and Portfolio Management 1187.4 Takeaway Messages 121Chapter 8 Understand Your Performance 1238.1 Factor 1248.1.1 Performance Attribution 1248.2 Idiosyncratic 1278.2.1 Selection, Sizing, Timing 1288.2.2 The Relationship Between Performance and Diversification 1368.3 Trade Events Efficiently 1398.4 ★Use Alternative Data! 1428.5 ★Frequently Asked Questions About Performance 1468.6 Takeaway Messages 148Chapter 9 Manage Your Losses 1499.1 How Stop-Loss Works 1509.2 Why a Stop-Loss Policy? 1519.3 The Costs and Benefits of Stop-Loss 1549.4 Takeaway Messages 158Chapter 10 ★Set Your Leverage Ratio for a Sustainable Business 16010.1 A Framework for Leverage Decisions 16210.2 Takeaway Messages 166Chapter 11 ★★Appendix 16811.1 Essential Risk Model Formulas 16811.1.1 Factor Model 16811.1.2 Factor-Mimicking Portfolios 16911.1.3 Percentage Idio Variance 17011.1.4 Betas 17011.1.5 Marginal Contribution to Factor Risk 17011.2 Diversification 17111.3 Mean-Variance Formulations 17211.3.1 Mean-Variance Portfolios 17211.3.2 A Robust Mean-Variance Formulation 17311.4 Proportional-Rule Formulations 17411.5 Generating Custom Factors 17511.5.1 Interpretation and Use 17911.6 Optimization Formulations 17911.6.1 Equal-Sized Portfolio with Constraints on Participation Rate 17911.7 Tactical Portfolio Optimization 18011.7.1 Variants 18211.8 Hedging Formulations 18211.9 Optimal Event Trading 186References 191Index 197

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GIUSEPPE PALEOLOGO is the Head of Risk Management at Hudson River Trading. He has also held senior positions at Millennium, Citadel, Axioma, and IBM Research. He was formerly a mathematical researcher at Stanford and an instructor in the master’s program in Financial Engineering at Cornell University.

• Chapter 1 For Whom? Why? And How? 11.1 What You Will Find Here 21.2 Asterisks; Or, How to Read This Book 31.3 Acknowledgments 3Chapter 2 The Problem: From Ideas to Profit 52.1 How to Invest in Your Edge, and Hedge the Rest 72.2 How to Size Your Positions 82.3 How to Learn from Your History 82.4 How to Trade Efficiently 92.5 How to Limit Factor Risk 92.6 How to Control Maximum Losses 102.7 How to Determine Your Leverage 102.8 How to Analyze New Sources of Data 10Chapter 3 A Tour of Risk and Performance 113.1 Introduction 123.2 Alpha and Beta 143.3 Where Does Alpha Come From? 153.4 Estimate Risk in Advance 183.4.1 What Is Risk? 183.4.2 Measuring Risk and Performance 203.5 First Steps in Risk Decomposition 253.6 Simple Hedging 263.7 Separation of Concerns 283.8 Takeaway Messages 29Chapter 4 An Introduction to Multi-Factor Models 304.1 From One Factor to Many 314.2 ★Frequently Asked Questions About Risk 354.3 ★The Machinery of Risk Models 404.4 Takeaway Messages 43Chapter 5 Understand Factors 445.1 The Economic Environment 475.1.1 Country 475.1.2 Industries 485.1.3 Beta 505.1.4 Volatility 545.2 The Trading Environment 565.2.1 Short Interest 565.2.2 Active Manager Holdings (AMH) 585.2.3 Momentum 605.3 The Company: Valuation Factors 665.3.1 Value 665.4 Takeaway Messages 71Chapter 6 Use Effective Heuristics for Alpha Sizing 726.1 Sharpe Ratio 746.2 Estimating Expected Returns 766.3 Risk-Based Sizing 796.4 ★Empirical Analysis of the Sizing Rules 816.5 From Ideas to Positions 886.6 Time-Series Risk-Based Portfolio Targeting 896.7 ★Frequently Asked Questions About Performance 956.8 Takeaway Messages 96Chapter 7 Manage Factor Risk 987.1 Tactical Factor Risk Management 997.1.1 Optimize If You Must 1047.2 Strategic Factor Risk Management 1077.2.1 Setting an Upper Limit on Factor Risk 1077.2.2 Setting a Limit on Market Exposure 1117.2.3 Setting an Upper Limit on Single-Stock Holdings 1137.2.4 Setting an Upper Limit on Single-Factor Exposures 1167.3 Systematic Hedging and Portfolio Management 1187.4 Takeaway Messages 121Chapter 8 Understand Your Performance 1238.1 Factor 1248.1.1 Performance Attribution 1248.2 Idiosyncratic 1278.2.1 Selection, Sizing, Timing 1288.2.2 The Relationship Between Performance and Diversification 1368.3 Trade Events Efficiently 1398.4 ★Use Alternative Data! 1428.5 ★Frequently Asked Questions About Performance 1468.6 Takeaway Messages 148Chapter 9 Manage Your Losses 1499.1 How Stop-Loss Works 1509.2 Why a Stop-Loss Policy? 1519.3 The Costs and Benefits of Stop-Loss 1549.4 Takeaway Messages 158Chapter 10 ★Set Your Leverage Ratio for a Sustainable Business 16010.1 A Framework for Leverage Decisions 16210.2 Takeaway Messages 166Chapter 11 ★★Appendix 16811.1 Essential Risk Model Formulas 16811.1.1 Factor Model 16811.1.2 Factor-Mimicking Portfolios 16911.1.3 Percentage Idio Variance 17011.1.4 Betas 17011.1.5 Marginal Contribution to Factor Risk 17011.2 Diversification 17111.3 Mean-Variance Formulations 17211.3.1 Mean-Variance Portfolios 17211.3.2 A Robust Mean-Variance Formulation 17311.4 Proportional-Rule Formulations 17411.5 Generating Custom Factors 17511.5.1 Interpretation and Use 17911.6 Optimization Formulations 17911.6.1 Equal-Sized Portfolio with Constraints on Participation Rate 17911.7 Tactical Portfolio Optimization 18011.7.1 Variants 18211.8 Hedging Formulations 18211.9 Optimal Event Trading 186References 191Index 197

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GIUSEPPE PALEOLOGO is the Head of Risk Management at Hudson River Trading. He has also held senior positions at Millennium, Citadel, Axioma, and IBM Research. He was formerly a mathematical researcher at Stanford and an instructor in the master’s program in Financial Engineering at Cornell University.

• Chapter 1 For Whom? Why? And How? 11.1 What You Will Find Here 21.2 Asterisks; Or, How to Read This Book 31.3 Acknowledgments 3Chapter 2 The Problem: From Ideas to Profit 52.1 How to Invest in Your Edge, and Hedge the Rest 72.2 How to Size Your Positions 82.3 How to Learn from Your History 82.4 How to Trade Efficiently 92.5 How to Limit Factor Risk 92.6 How to Control Maximum Losses 102.7 How to Determine Your Leverage 102.8 How to Analyze New Sources of Data 10Chapter 3 A Tour of Risk and Performance 113.1 Introduction 123.2 Alpha and Beta 143.3 Where Does Alpha Come From? 153.4 Estimate Risk in Advance 183.4.1 What Is Risk? 183.4.2 Measuring Risk and Performance 203.5 First Steps in Risk Decomposition 253.6 Simple Hedging 263.7 Separation of Concerns 283.8 Takeaway Messages 29Chapter 4 An Introduction to Multi-Factor Models 304.1 From One Factor to Many 314.2 ★Frequently Asked Questions About Risk 354.3 ★The Machinery of Risk Models 404.4 Takeaway Messages 43Chapter 5 Understand Factors 445.1 The Economic Environment 475.1.1 Country 475.1.2 Industries 485.1.3 Beta 505.1.4 Volatility 545.2 The Trading Environment 565.2.1 Short Interest 565.2.2 Active Manager Holdings (AMH) 585.2.3 Momentum 605.3 The Company: Valuation Factors 665.3.1 Value 665.4 Takeaway Messages 71Chapter 6 Use Effective Heuristics for Alpha Sizing 726.1 Sharpe Ratio 746.2 Estimating Expected Returns 766.3 Risk-Based Sizing 796.4 ★Empirical Analysis of the Sizing Rules 816.5 From Ideas to Positions 886.6 Time-Series Risk-Based Portfolio Targeting 896.7 ★Frequently Asked Questions About Performance 956.8 Takeaway Messages 96Chapter 7 Manage Factor Risk 987.1 Tactical Factor Risk Management 997.1.1 Optimize If You Must 1047.2 Strategic Factor Risk Management 1077.2.1 Setting an Upper Limit on Factor Risk 1077.2.2 Setting a Limit on Market Exposure 1117.2.3 Setting an Upper Limit on Single-Stock Holdings 1137.2.4 Setting an Upper Limit on Single-Factor Exposures 1167.3 Systematic Hedging and Portfolio Management 1187.4 Takeaway Messages 121Chapter 8 Understand Your Performance 1238.1 Factor 1248.1.1 Performance Attribution 1248.2 Idiosyncratic 1278.2.1 Selection, Sizing, Timing 1288.2.2 The Relationship Between Performance and Diversification 1368.3 Trade Events Efficiently 1398.4 ★Use Alternative Data! 1428.5 ★Frequently Asked Questions About Performance 1468.6 Takeaway Messages 148Chapter 9 Manage Your Losses 1499.1 How Stop-Loss Works 1509.2 Why a Stop-Loss Policy? 1519.3 The Costs and Benefits of Stop-Loss 1549.4 Takeaway Messages 158Chapter 10 ★Set Your Leverage Ratio for a Sustainable Business 16010.1 A Framework for Leverage Decisions 16210.2 Takeaway Messages 166Chapter 11 ★★Appendix 16811.1 Essential Risk Model Formulas 16811.1.1 Factor Model 16811.1.2 Factor-Mimicking Portfolios 16911.1.3 Percentage Idio Variance 17011.1.4 Betas 17011.1.5 Marginal Contribution to Factor Risk 17011.2 Diversification 17111.3 Mean-Variance Formulations 17211.3.1 Mean-Variance Portfolios 17211.3.2 A Robust Mean-Variance Formulation 17311.4 Proportional-Rule Formulations 17411.5 Generating Custom Factors 17511.5.1 Interpretation and Use 17911.6 Optimization Formulations 17911.6.1 Equal-Sized Portfolio with Constraints on Participation Rate 17911.7 Tactical Portfolio Optimization 18011.7.1 Variants 18211.8 Hedging Formulations 18211.9 Optimal Event Trading 186References 191Index 197

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