Multi-moment Asset Allocation and Pricing Models

by Jurczenko, Emmanuel; Maillet, Bertrand; Rubinstein, Mark

• ISBN13: 9780470034156
• ISBN10: 0470034157
• Format: Hardcover
• Copyright: 2006-10-27
• Publisher: WILEY

Summary

While mainstream financial theories and applications assume that asset returns are normally distributed and individual preferences are quadratic, the overwhelming empirical evidence shows otherwise. Indeed, most of the asset returns exhibit "fat-tails" distributions and investors exhibit asymmetric preferences. These empirical findings lead to the development of a new area of research dedicated to the introduction of higher order moments in portfolio theory and asset pricing models.This book presents the state-of-the art in multi-moment asset allocation and pricing models and provides many new developments in a single volume, collecting in a unified framework theoretical results and applications previously scattered throughout the financial literature. The topics covered in this comprehensive volume include: four-moment individual risk preferences, mathematics of the multi-moment efficient frontier, coherent asymmetric risks measures, hedge funds asset allocation under higher moments, time-varying specifications of (co)moments and multi-moment asset pricing models with homogeneous and heterogeneous agents.Written by leading academics, Multi-moment Asset Allocation and Pricing Modelsoffers a unique opportunity to explore the latest findings in this new field of research.

Author Biography

EMMANUEL F. JURCZENKO is an Associate Professor in Finance at the ESCP-EAP and a Head of Quantitative Analysts within AAAdvisors-QCG (ABN Amro Group) and Variances. He is graduated in Economics and in Finance, and holds a PhD in Economics (Multi-moment Asset Pricing Models) from the University of Paris-1 (Panthéon-Sorbonne). He gained market experience for several years as a Quantitative Analyst within a subsidiary of ABN Amro dedicated to funds of funds. He is appointed as an Associate Professor of Finance at the ESCP-EAP European School of Management since 2000 where he teaches Portfolio Management, Financial Mathematics, Options and Other Derivatives, and Corporate Finance. His centre of interests mainly concerns Portfolio Management, Asset pricing and Applications of Statistics in Finance. He is also associate researcher at CES/CNRS (Center for National Research) at the University of Paris-1.

BERTRAND B. MAILLET is CEO and Head of Research within AAAdvisors-QCG (ABN Amro Group) and Variances, and Lecturer in Economics at the University of Paris-1. He is graduated in Economics, in Finance and in Statistics, and holds a PhD in Economics (Market Efficiency and Performance Measurements) from the University of Paris-1 (Panthéon-Sorbonne). After being qualified as a Lecturer in Economics in the same university in 1997 (lectures in Financial Econometrics, International Finance and Microeconomics), and appointed as Professor of Finance at the ESCP-EAP European School of Management (lectures in Risk and Portfolio Management), he developed consulting activities in various financial institutions, before joining the ABN Amro Group as a Head of Research in a multi-fund activity. His domain of expertise covers risk management, performance measurement, portfolio management and asset pricing. He has published several articles in academic journals such as Quantitative Finance, Review of International Economics and The European Journal of Finance, chapters in books edited by John Wiley, Springer and Kluwer Academics, and serves as a referee in several international leading journals. He is also currently associate researcher at CES/CNRS (Center for National Research) at the University of Paris-1 and at the Financial Markets Group of the London School of Economics.

Table of Contents

About the Contributors	xiii
Foreword	xvii
Preface	xxi
Theoretical Foundations of Asset Allocation and Pricing Models with Higher-order Moments	1	(36)
Emmanuel Jurczenko
Bertrand Maillet
Introduction	1	(2)
Expected utility and higher-order moments	3	(7)
Expected utility as an exact function of the first four moments	10	(6)
Expected utility as an approximating function of the first four moments	16	(6)
Conclusion	22	(15)
Appendix A	23	(1)
Appendix B	24	(1)
Appendix C	25	(2)
Appendix D	27	(1)
Appendix E	28	(2)
Appendix F	30	(1)
Acknowledgements	31	(1)
References	32	(5)
On Certain Geometric Aspects of Portfolio Optimisation with Higher Moments	37	(14)
Gustavo M. de Athayde
Renato G. Flores Jr
Introduction	37	(1)
Minimal variances and kurtoses subject to the first two odd moments	38	(6)
Homothetic properties of the minimum variance set	39	(2)
The minimum kurtosis case	41	(3)
Generalising for higher even moments	44	(2)
Further properties and extensions	46	(2)
Concluding remarks	48	(3)
Appendix: The matrix notation for the higher-moments arrays	48	(2)
Acknowledgements	50	(1)
References	50	(1)
Hedge Fund Portfolio Selection with Higher-order Moments: A Nonparametric Mean--Variance--Skewness--Kurtosis Efficient Frontier	51	(16)
Emmanuel Jurczenko
Bertrand Maillet
Paul Merlin
Introduction	51	(2)
Portfolio selection with higher-order moments	53	(2)
The shortage function and the mean--variance-skewness-kurtosis efficient frontier	55	(3)
Data and empirical results	58	(5)
Conclusion	63	(4)
Appendix	64	(1)
Acknowledgements	65	(1)
References	65	(2)
Higher-order Moments and Beyond	67	(12)
Luisa Tibiletti
Introduction	67	(1)
Higher-order moments and simple algebra	68	(3)
Higher moments: Noncoherent risk measures	71	(1)
One-sided higher moments	72	(3)
Portfolio left-sided moment bounds	73	(1)
Properties of the upper bound Up(S_)	74	(1)
Preservation of marginal ordering under portfolios	75	(1)
Drawbacks in using higher moments	75	(1)
Advantages in using left-sided higher moments	75	(1)
Conclusion	76	(3)
Appendix	77	(1)
References	77	(2)
Gram--Charlier Expansions and Portfolio Selection in Non-Gaussian Universes	79	(34)
Francois Desmoulins-Lebeault
Introduction	79	(1)
Attempts to extend the CAPM	80	(5)
Extensions based on preferences	80	(3)
Extensions based on return distributions	83	(2)
An example of portfolio optimisation	85	(4)
Portfolio description	86	(1)
The various ``optimal'' portfolios	86	(3)
Extension to any form of distribution	89	(9)
Obstacles to distribution-based works	89	(1)
Generalised Gram-Charlier expansions	90	(5)
Convergence of the fourth-order Gram-Charlier expansion	95	(3)
The Distribution of Portfolio Returns	98	(7)
Feasible approaches	98	(1)
The moments of the portfolio returns' distribution	98	(2)
Possible portfolio selection methods	100	(5)
Conclusion	105	(8)
Appendix A: Additional statistics for the example portfolio	105	(1)
Moments and co-moments	105	(2)
Statistical tests of normality	107	(1)
Appendix B: Proofs	108	(1)
Positivity conditions theorem	108	(1)
Approximation of the optimal portfolio density	109	(1)
Acknowledgements	110	(1)
References	110	(3)
The Four-moment Capital Asset Pricing Model: Between Asset Pricing and Asset Allocation	113	(52)
Emmanuel Jurczenko
Bertrand Maillet
Introduction	113	(3)
The four-moment capital asset pricing model	116	(14)
Notations and hypotheses	116	(4)
Aggregation of the individual asset demands and a two-fund monetary separation theorem	120	(5)
The four-moment CAPM fundamental relation and the security market hyperplane	125	(5)
An N risky asset four-moment CAPM extension	130	(7)
General properties of the mean--variance--skewness-kurtosis efficient set	131	(3)
A zero-beta zero-gamma zero-delta four-moment CAPM	134	(3)
The four-moment CAPM, the cubic market model and the arbitrage asset pricing model	137	(5)
The cubic market model and the four-moment CAPM	137	(2)
The arbitrage pricing model and the four-moment CAPM	139	(3)
Conclusion	142	(23)
Appendix A	143	(2)
Appendix B	145	(1)
Appendix C	146	(1)
Appendix D	147	(3)
Appendix E	150	(1)
Appendix F	151	(1)
Appendix G	152	(2)
Appendix H	154	(1)
Appendix I	155	(1)
Appendix J	156	(1)
Acknowledgements	157	(1)
References	157	(8)
Multi-moment Method for Portfolio Management: Generalised Capital Asset Pricing Model in Homogeneous and Heterogeneous Markets	165	(30)
Yannick Malevergne
Didier Sornette
Introduction	165	(2)
Measuring large risks of a portfolio	167	(5)
Why do higher moments allow us to assess larger risks?	168	(1)
Quantifying the fluctuations of an asset	168	(2)
Examples	170	(2)
The generalised efficient frontier and some of its properties	172	(6)
Efficient frontier without a risk-free asset	173	(2)
Efficient frontier with a risk-free asset	175	(1)
Two-fund separation theorem	176	(1)
Influence of the risk-free interest rate	176	(2)
Classification of the assets and of portfolios	178	(3)
The risk-adjustment approach	179	(2)
Marginal risk of an asset within a portfolio	181	(1)
A new equilibrium model for asset prices	181	(3)
Equilibrium in a homogeneous market	182	(1)
Equilibrium in a heterogeneous market	183	(1)
Conclusion	184	(11)
Appendix A: Description of the dataset	184	(1)
Appendix B: Generalised efficient frontier and two-fund separation theorem	185	(1)
Case of independent assets when the risk is measured by the cumulants	185	(2)
General case	187	(1)
Appendix C: Composition of the market portfolio	188	(1)
Homogeneous case	188	(1)
Heterogeneous case	189	(1)
Appendix D: Generalised Capital Asset Pricing Model	190	(1)
Acknowledgements	191	(1)
References	191	(4)
Modelling the Dynamics of Conditional Dependency Between Financial Series	195	(28)
Eric Jondeau
Michael Rockinger
Introduction	195	(2)
A model for the marginal distributions	197	(3)
Hansen's skewed student-t distribution	197	(2)
The cdf of the skewed student-t distribution	199	(1)
A GARCH model with time-varying skewness and kurtosis	199	(1)
Copula distribution functions	200	(5)
Generalities	200	(1)
Construction of the estimated copula functions	201	(4)
Modelling dependency and estimation of the model	205	(2)
Conditional dependency	205	(1)
Estimation in a copula framework	206	(1)
Empirical Results	207	(8)
The data	207	(2)
Estimation of the marginal model	209	(2)
Estimation of the multivariate model	211	(4)
Further research topics	215	(8)
Acknowledgements	218	(1)
References	219	(4)
A Test of the Homogeneity of Asset pricing Models	223	(8)
Giovanni Barone-Adesi
Patrick Gagliardini
Giovanni Urga
Introduction	223	(1)
The Quadratic Market Model	224	(1)
Empirical Results	225	(4)
Data description	225	(1)
Results	226	(3)
Conclusion	229	(2)
Acknowledgements	229	(1)
References	229	(2)
Index	231