With recent outbreaks of multiple large-scale financial crises, amplified by interconnected risk sources, a new paradigm of fund management has emerged. This new paradigm leverages “embedded” quantitative processes and methods to provide more transparent, adaptive, reliable and easily implemented “risk assessment-based” practices.
This book surveys the most widely used factor models employed within the field of financial asset pricing. Through the concrete application of evaluating risks in the hedge fund industry, the authors demonstrate that signal processing techniques are an interesting alternative to the selection of factors (both fundamentals and statistical factors) and can provide more efficient estimation procedures, based on lq regularized Kalman filtering for instance.
With numerous illustrative examples from stock markets, this book meets the needs of both finance practitioners and graduate students in science, econometrics and finance.

Contents

Foreword, Rama Cont.
1. Factor Models and General Definition.
2. Factor Selection.
3. Least Squares Estimation (LSE) and Kalman Filtering (KF) for Factor Modeling: A Geometrical Perspective.
4. A Regularized Kalman Filter (rgKF) for Spiky Data.
Appendix: Some Probability Densities.

About the Authors

Serge Darolles is Professor of Finance at Paris-Dauphine University, Vice-President of QuantValley, co-founder of QAMLab SAS, and member of the Quantitative Management Initiative (QMI) scientific committee. His research interests include financial econometrics, liquidity and hedge fund analysis. He has written numerous articles, which have been published in academic journals.
Patrick Duvaut is currently the Research Director of Telecom ParisTech, France. He is co-founder of QAMLab SAS, and member of the Quantitative Management Initiative (QMI) scientific committee. His fields of expertise encompass statistical signal processing, digital communications, embedded systems and QUANT finance.
Emmanuelle Jay is co-founder and President of QAMLab SAS. She has worked at Aequam Capital as co-head of R&D since April 2011 and is member of the Quantitative Management Initiative (QMI) scientific committee. Her research interests include SP for finance, quantitative and statistical finance, and hedge fund analysis.

Serge Darolles is Professor of Finance at Paris-Dauphine University, Vice-President of QuantValley, co-founder of QAMLab SAS, and member of the Quantitative Management Initiative (QMI) scientific committee. His research interests include financial econometrics, liquidity and hedge fund analysis. He has written numerous articles, which have been published in academic journals.

Patrick Duvaut is currently the Research Director of Telecom ParisTech, France. He is co-founder of QAMLab SAS, and a member of the Quantitative Management Initiative (QMI) scientific committee. His fields of expertise encompass statistical signal processing, digital communications, embedded systems and QUANT finance.

Emmanuelle Jay is co-founder and President of QAMLab SAS. She has worked at Aequam Capital as co-head of R&D since April 2011 and is member of the Quantitative Management Initiative (QMI) scientific committee. Her research interests include SP for finance, quantitative and statistical finance, and hedge fund analysis.

Preface i

Introduction iii

Reading guide v

Notation vii

1 Factor Models and General Definition 1

1.1 Chapter 1 objectives 1

1.2 What are factor models? 1

1.2.1 Introduction 1

1.2.2 Description 2

1.3 Why factor models in finance? 3

1.3.1 Explanatory power 3

1.3.2 Dimension reduction 3

1.4 How to build factor models? 3

1.5 Historical perspective 3

1.5.1 CAPM and Sharpe’s market model  3

1.5.2 APT for Arbitrage Pricing Theory  5

1.5.3 Extensions 5

1.6 Chapter 1 practice 5

1.7 Chapter 1 highlights 5

1.8 Glossary . 7

2 Factor Selection 9

2.1 Chapter 2 objectives 9

2.2 Empirical ad-hoc selection 9

2.3 Eigenfactor selection 10

2.4 Model order choice 10

2.4.1 Information Criteria (AIC, BIC, MDL...) . 10

2.4.2 Large panel data criteria 11

2.4.3 Eigenvalue distribution test: RMT  11

2.4.4 Joint estimation 11

2.5 Chapter 2 practice 11

2.6 Chapter 2 highlights 11

3 Least Squares Estimation (LSE) and Kalman Filtering (KF) for factor modeling, a geometrical perspective 13

3.1 Why LSE and KF in factor modeling?  14

3.1.1 Factor model per return 14

3.1.2 Alphas and betas estimation per return 14

3.2 LSE setup 14

3.2.1 Current observation window and block processing 14

3.2.2 LSE regression 15

3.3 LSE objective & criterion 15

3.4 How LSE is working (for LSE users and programmers)? 15

3.5 Interpretation of LSE solution 18

3.5.1 Bias and variance 18

3.5.2 Geometrical interpretation of least squares estimate 18

3.6 LSE practice 18

3.7 Derivations of LSE solution 18

3.8 Why Kalman Filtering and which setup?  18

3.8.1 LSE method does not provide a recursive estimate 18

3.8.2 The state space model and its recursive component 18

3.8.3 Parsimony and orthogonality assumptions 18

3.9 Which are the main properties of the KF model? . 18

3.9.1 Self aggregation feature 18

3.9.2 Markovian property 18

3.9.3 Innovation property 18

3.10 What is the objective of KF? 18

3.11 How does the KF works (for users and programmers) ? 18

3.12 Interpretation of the KF updates 18

3.12.1 Prediction filtering, equation (??) 18

3.12.2 Prediction accuracy processing, equation (??) 18

3.12.3 Correction filtering, equation (??)-(??) 18

3.12.4 Correction accuracy processing, equation (??) 18

3.13 Geometrical derivation of KF updating equations . 18

3.13.1 Geometrical interpretation of MSE criterion and the MMSE solution 18

3.13.2 Derivation of the prediction filtering update . 18

3.13.3 Derivation of the prediction accuracy update 18

3.13.4 Derivation of the correction filtering update 18

3.13.5 Derivation of the correction accuracy update 18

3.14 Chapter 3 practice 18

3.15 Chapter 3 highlights 18

4 Regularized estimation methods 19

4.1 Chapter 4 objectives 19

4.2 Flexible Least Squares (FLS) 19

4.3 Robust Kalman filter 19

4.3.1 RKF description 19

4.3.2 Optimization of the regularization parameter 20

4.4 Regularized Kalman filter: the rgKF(NG,lq)  20

4.4.1 rgKF description 20

4.4.2 Comparing the l1 and the l2-regularization steps 20

4.4.3 rgKF performance 20

4.5 Chapter 4 practice 20

4.6 Chapter 4 highlights 20

5 Applications 21

5.1 Chapter 5 objectives 21

5.2 Return-based style analysis 21

5.2.1 Fung & Hsieh (F&H) risk factors  21

5.2.2 Hedge funds data 21

5.2.3 Eigenfactor selection 22

5.2.4 Estimation procedures 22

5.2.5 Results 22

5.2.6 RKF robustness 24

5.3 Portfolio construction 24

5.4 Illiquidity shocks detection 24

5.5 Chapter 5 highlights 26

Conclusion 27