Multi-factor models and signal processing techniques : application to quantitative finance

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.

Author Notes

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 RD 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.

Rama Cont

Foreword	p. xi
Introduction	p. xv
Notations and Acronyms	p. xxi
Chapter 1 Factor Models and General Definition	p. 1
1.1 Introduction	p. 1
1.2 What are factor models?	p. 2
1.2.1 Notations	p. 2
1.2.2 Factor representation	p. 4
1.3 Why factor models in finance?	p. 7
1.3.1 Style analysis	p. 7
1.3.2 Optimal portfolio allocation	p. 10
1.4 How to build factor models?	p. 11
1.4.1 Factor selection	p. 11
1.4.2 Parameters estimation	p. 13
1.5 Historical perspective	p. 14
1.5.1 CAPM and Sharpe's market model	p. 14
1.5.2 APT for arbitrage pricing theory	p. 17
1.6 Glossary	p. 18
Chapter 2 Factor Selection	p. 23
2.1 Introduction	p. 23
2.2 Qualitative know-how	p. 24
2.2.1 Fama and French model	p. 25
2.2.2 The Chen et al. model	p. 26
2.2.3 The risk-based factor model of Fung and Hsieh	p. 27
2.3 Quantitative methods based on eigenfactors	p. 31
2.3.1 Notation	p. 32
2.3.2 Subspace methods: the Principal Component Analysis	p. 33
2.4 Model order choice	p. 36
2.4.1 Information criteria	p. 36
2.5 Appendix 1: Covariance matrix estimation	p. 38
2.5.1 Sample mean	p. 39
2.5.2 Sample covariance matrix	p. 40
2.5.3 Robust covariance matrix estimation: M-estimators	p. 43
2.6 Appendix 2: Similarity of the eigenfactor selection with the MUSIC algorithm	p. 46
2.7 Appendix 3: Large panel data	p. 48
2.7.1 Large panel data criteria	p. 49
2.8 Chapter 2 highlights	p. 56
Chapter 3 Least Squares Estimation (LSE) and Kalman Filtering (KF) for Factor Modeling: A Geometrical Perspective	p. 59
3.1 Introduction	p. 59
3.2 Why LSE and KF in factor modeling?	p. 60
3.2.1 Factor model per return	p. 60
3.2.2 Alpha and beta estimation per return	p. 61
3.3 LSE setup	p. 62
3.3.1 Current observation window and block processing	p. 62
3.3.2 LSE regression	p. 62
3.4 LSE objective and criterion	p. 63
3.5 How LSE is working (for LSE users and programmers)	p. 64
3.6 Interpretation of the LSE solution	p. 65
3.6.1 Bias and variance	p. 65
3.6.2 Geometrical interpretation of LSE	p. 66
3.7 Derivations of LSE solution	p. 70
3.8 Why KF and which setup?	p. 71
3.8.1 LSE method does not provide a recursive estimate	p. 71
3.8.2 The state space model and its recursive component	p. 72
3.8.3 Parsimony and orthogonality assumptions	p. 73
3.9 What are the main properties of the KF model?	p. 74
3.9.1 Self-aggregation feature	p. 74
3.9.2 Markovian property	p. 75
3.9.3 Innovation property	p. 75
3.10 What is the objective of KF?	p. 76
3.11 How does the KF work (for users and programmers)?	p. 77
3.11.1 Algorithm summary	p. 77
3.11.2 Initialization of the KF recursive equations	p. 80
3.12 Interpretation of the KF updates	p. 81
3.12.1 Prediction filtering, equation [3.34]	p. 81
3.12.2 Prediction accuracy processing, equation [3.35]	p. 82
3.12.3 Correction filtering equations [3.36]-[3.37]	p. 83
3.12.4 Correction accuracy processing, equation [3.38]	p. 84
3.13 Practice	p. 86
3.13.1 Comparison of the estimation methods on synthetic data	p. 86
3.13.2 Market risk hedging given a single-factor model	p. 92
3.13.3 Hedge fund style analysis using a multi-factor model	p. 97
3.14 Geometrical derivation of KF updating equations	p. 104
3.14.1 Geometrical interpretation of MSE criterion and the MMSE solution	p. 104
3.14.2 Derivation of the prediction filtering update	p. 106
3.14.3 Derivation of the prediction accuracy update	p. 106
3.14.4 Derivation of the correction filtering update	p. 107
3.14.5 Derivation of the correction accuracy update	p. 111
3.15 Highlights	p. 112
3.16 Appendix: Matrix inversion lemma	p. 116
Chapter 4 A Regularized Kalman Filter (rgKF) for Spiky Data	p. 117
4.1 Introduction	p. 117
4.2 Preamble: statistical evidence on the KF recursive equations	p. 119
4.3 Robust KF	p. 119
4.3.1 RKF description	p. 119
4.4 rgKF: the rgKF(NG,l q )	p. 121
4.4.1 rgKF description	p. 121
4.4.2 rgKF performance	p. 125
4.5 Application to detect irregularities in hedge fund returns	p. 128
4.6 Conclusion	p. 130
4.7 Chapter highlights	p. 130
Appendix: Some Probability Densities	p. 133
Conclusion	p. 141
Bibliography	p. 143
Index	p. 153

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Table of Contents