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The Roles of Systematic Skewness and Systematic Kurtosis in Asset Pricing View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by RMIT Research Repository THE ROLES OF SYSTEMATIC SKEWNESS AND SYSTEMATIC KURTOSIS IN ASSET PRICING Minh Phuong Doan B Com (Hons) A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy (Economics and Finance) School of Economics, Finance and Marketing RMIT University March 2011 DECLARATION I, Minh Phuong Doan, declare that: a. except where due acknowledgement has been made, this work is that of myself alone; b. this work has not been submitted, in whole or part, to qualify for any other academic award; c. the content of the thesis is the result of work that has been carried out since the official commencement date of the approved research program; d. Ms Annie Ryan was paid for proofreading this work for grammar and clarity. Signed Date 10/03/2011 Minh Phuong Doan ii ACKNOWLEDGEMENTS This dissertation would not have been a real fulfilment without the backing and co- operation from various individuals through various means. First and foremost I offer my sincerest gratitude to my principal supervisor, Professor Heather Mitchell. She has inspired, guided and encouraged me throughout the difficult time of my PhD. Her exceptional intelligence and extraordinary experience have inspired and nourished my intellectual maturity, from which I will benefit for a long time to come. Heather has also given me her friendship, which is something much greater, in all the years I have known her. I have learnt so much from her and I am grateful to her in every possible way. I would also like to express my grateful thanks to my second supervisor, Professor Richard Heaney, for his valuable advice, generous supervision and continuous support. His encouragement for conference and journal submissions and his high regard for my work have made my study journey more meaningful and enjoyable. I wish him all the best for his new arrival at UWA and I hope to keep up our collaboration in the future. I would also like to express my sincere thanks to Dr Ashton De Silva, who has kindly accepted to take over the supervision from Richard since his departure from RMIT. Ashton‟s expertise in statistics has brought new light to my work and I thank him for the valuable advices he, as my colleague and supervisor, has given me in my PhD time. Further, I thank my professional supervisor, Professor Roslyn Russell, for giving me generous study leave to complete this study. She understood my frustration and has provided the iii best support I could have in my profession. She organised lunch and drink get-togethers to boost my spirits and celebrate some small achievement of my work in progress. I am also very grateful to my friends, Henry Bell and Nam Nguyen, for their help and support in completing this thesis. Henry has generously given his time to proofread my writing and has provided me valuable feedback. Nam helped me debug my code and provided generous assistance with computer-related problems. He also listened to my other problems and always trusted in my ability to achieve the best outcomes in my research. Finally and most importantly, words fail me to express my appreciation to my family for their love and support. I thank my parents for showing me the joy of intellectual pursuit and for doing the best they can to assist me with my learning journey. I thank my sister and brother for being supportive and caring siblings. iv TABLE OF CONTENTS LIST OF TABLES ..................................................................................................................... viii LIST OF FIGURES ...................................................................................................................... x ABSTRACT ................................................................................................................................... 1 CHAPTER 1. INTRODUCTION........................................................................................... 3 1.1 Understanding Skewness and Kurtosis .....................................................................................3 1.2 Causes of Skewness and Kurtosis in Asset Pricing ....................................................................5 1.3 Measures of Skewness and Kurtosis.........................................................................................6 1.4 Problems Investigated .............................................................................................................8 1.5 Motivation of the Study ..........................................................................................................9 1.6 Contribution of the Study ......................................................................................................10 1.7 Research Questions...............................................................................................................11 1.8 Methodology and Main Findings ...........................................................................................12 1.9 Structure of the Thesis ..........................................................................................................14 CHAPTER 2. LITERATURE REVIEW ............................................................................ 16 2.1 Introduction .........................................................................................................................16 2.2 Mean-Variance Efficiency Tests ............................................................................................17 2.2.1 Wald Test ......................................................................................................................18 2.2.2 Gibbons, Ross and Shanken (1989)Test of Mean-Variance Efficiency................................20 2.2.3 Using Bootstrap Method for Mean-Variance Efficiency Test in the Case of Multivariate Non-normal Errors......................................................................................23 2.3 The Relevance of Skewness and Kurtosis in Asset Pricing ......................................................25 2.3.1 Relationships between Beta Asymmetry and Higher Moments...........................................25 2.3.2 Asset Pricing Model in the Four-moment Framework .......................................................27 2.3.2.1 How Skewness Enters Asset Pricing ..........................................................................28 2.3.2.2 The Importance of Kurtosis in Asset Pricing...............................................................32 2.4 Applications of Skewness and Kurtosis ..................................................................................35 2.4.1 Performance Measures with Skewness and Kurtosis..........................................................35 2.4.2 Portfolio Optimisation with Skewness and Kurtosis ..........................................................37 2.5 Conclusions .........................................................................................................................38 CHAPTER 3. DATA AND SUMMARY STATISTICS..................................................... 40 3.1 Data.....................................................................................................................................40 3.2 Measures of Systematic Skewness and Systematic Kurtosis.....................................................41 v 3.3 Portfolio Construction...........................................................................................................42 3.4 Summary Statistics ...............................................................................................................44 3.5 Summary .............................................................................................................................49 CHAPTER 4. ARE ASSET RETURNS MEAN-VARIANCE EFFICIENT? ................. 50 4.1 Introduction .........................................................................................................................50 4.2 Methodology ........................................................................................................................52 4.2.1 Mean-Variance Efficiency Tests ......................................................................................52 4.2.2 Mean-Variance Efficiency with Multivariate Normal Errors .............................................54 4.2.2.1 The Wald Test ..........................................................................................................54 4.2.2.2 The Gibbon, Ross, Shanken (1989) Test of Zero Intercept ...........................................54 4.2.3 Bootstrap Tests with Multivariate Non-normal Errors .......................................................55 4.3 Empirical Results and Discussion ..........................................................................................57 4.3.1 Time-series Regression Analysis using the CAPM ............................................................57 4.3.2 Mean-Variance Efficiency Tests with Normal Errors ........................................................59 4.3.3 Bootstrap Test with Non-normal Errors ...........................................................................61 4.4 Conclusions .........................................................................................................................68 CHAPTER 5. ARE ASSET RETURNS MEAN-VARIANCE-SKEWNESS- KURTOSIS EFFICIENT? ........................................................................... 70 5.1 Introduction
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