Heuristic Approaches to Portfolio Optimization by Abubakar Yahaya BSc (Statistics) Usmanu Danfodiyo University, Sokoto, Nigeria. MSc (Decision Modelling & Information Systems), Brunei University, UK. This thesis is submitted for the award of degree of Doctor of Philosophy in the Department of Management Science, Lancaster University Management School December 2010. ProQuest Number: 11003476 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 11003476 Published by ProQuest LLC(2018). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 LANCASTER 11 ' - Dedication To My lovely and caring wife: Amina My beautiful and lovely daughter: Fatima. My gorgeous sons: Muhammad, Ahmad and (my little Lancastrian) Al-Ameen. Page 2 of 277 LANCASTER Acknowledgement All praises and thanks are due to Almighty Allah (TWT), the LORD of all the seven heavens and earths alike. He is the LORD of whatever is contained therein. I praise Him, thank Him and ask for His forgiveness over all my sins and shortcomings. He is the provider of all provisions and sustenance to all living things. It is in the Name of such Allah (TWT), I begin to write this thesis. May the Peace, Blessings and Mercy of Allah (TWT) be with His most beloved slave, Prophet and Messenger, our Saviour and our Guide in person of Sayyidina Muhammad (SAW). May the same blessings be with the rest of Prophets and Messengers of Allah, pure (Ahl-Albayt) descendants of the Holy Prophet, his honourable companions and all those who follow the guidance of Islam until the Day of Resurrection. I would like to acknowledge the assistance and support I received from my supervisor, Professor Mike Wright, who upon all his numerous commitments sacrificed most of his precious time in supervising my research progress over the whole of my three-year research journey. I really say a big “thank you” for all your patience and support. I would also like to thank my viva voce examiners who managed to arrange a suitable Page 3 of 277 time for my viva , and most especially Professor Richard Eglese who has been part of my examiners right from my upgrade up to my final viva. Thank you, Richard. I would like to use this medium also to thank many, who positively touch my life in one way or the other. The first and foremost is my mum: Hajiya Khadeejatul Kubra whom I revere, love and admire more than any living mortal. She brought me up morally, guides me, prays for me, advices and put me on the right track. As for me, she really did her duty, and I’ll continue to appreciate her efforts, generosity and love towards me up to the end of my life. Thank you, Mum. My beloved, respectful, obedient, and caring wife: Amina Hassan Abubakar (Mrs) deserves all praises and thanks. Her advice, assistance, care, prayers and love helped a lot in shaping my life and our children’s. I appreciate (and will continue to do so) the sacrifices she made during my three-year academic journey and the role she plays as a wife and as a mother to our children. I Love you because you are really great. Remain blessed, Darling! I would like to thank a colleague and friend of mine: Dr. Amadou Gning (Department of Computing, Lancaster University, UK) whose invaluable criticisms and advices helped in shaping the composition of this thesis. He helped me a lot in my domestic and academic struggles. Amadou! May Allah (TWT) reward you immensely. My brothers, sisters, in-laws, friends and well-wishers deserve a word of commendation for their constant support and prayers in actualization of my academic dreams; thank you all and May Allah (TWT) continue to help and guide us all. Page 4 of 277 I would also like to acknowledge the support I received from my friends at Lancaster University Islamic Society (LUISOC). Similarly, I would like to acknowledge the support and assistance of Miss Gay Bentinck (PhD Coordinator, Department of Management Science, Lancaster University, Lancaster); Thank you all. Finally, I would like to express my heartfelt appreciation to the management of Petroleum Technology Development Fund (PTDF, Abuja) for funding my PhD programme. Page 5 of 277 LANCASTER J 1 U N I V L R S : : Declaration of Authorship I, Abubakar Yahaya, declare that this thesis entitled “Heuristic Approaches to Portfolio Optimization” is my own work and has not been submitted for the award of any similar or higher degree elsewhere. Page 6 of 277 LANCASTER List of Publications (i) Yahaya, A. and Wright, M. B. (2009). Effect of Initial Solution on Heuristics’ Performance: A Perspective from Mean-Variance Portfolio Optimization Problem. Presented at the 1st Student Conference in Operational Research (SCOR2009) held at Lancaster University, Lancaster, UK [March 27th - 29th, 2009]. (ii) Yahaya, A. and Wright, M. (2009). On Portfolio Selection Using Metaheuristics. Presented at the 10th Annual Meeting of the EUropean chapter on MEtaheuristics (EU/MEeting 2009) held at the Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal [April 29th - 30th, 2009]. (http://www.dcc.fc.up.pt/eume2009/pdf/proceedings.pdf). (iii) Yahaya, A. and Wright, M. (2009). Solving a Constrained Portfolio Selection Problem Using Particle Swarm Optimization. Presented at the 3rd Annual Graduate Conference on Social Sciences and Management held at Norcroft Centre, University of Bradford, Bradford, UK [October 8th - 9th, 2009]. (http ://www.bradford. ac. uk/1 ss/gradschool/conference/abstracts .pdf). (iv) Yahaya, A. (2010). Portfolio Selection Using Genetic Algorithms. Presented at the 2nd Annual Postgraduate Research ‘Creativity and Change’ Conference held at Lancaster University, Lancaster, UK on 20th March, 2010. (http://createandchange.org.uk/) (v) Yahaya, A. and Wright, M. (2010). SW AN-A hybridized approach for solving Portfolio Selection Problems (PSP). Presented at the 2nd Student Conference on Operational Research (SCOR2010) held at Sir Clive Granger Building, University Park campus, University of Nottingham, Nottingham, UK [April 9th - 11th, 2010]. (http://www.scor2010.co.uk/downloads/scor proceedings.pdf). Page 7 of 277 LANCASTER 11 U N I V L S J. \ Abstract One of the most frequently studied areas in finance is the classical mean-variance portfolio selection model pioneered by Harry Markowitz; which is also, undoubtedly recognized as the foundation of modern portfolio theory. The model in its basic form deals with the selection of portfolio of assets such that a reasonable trade-off is achieved between the conflicting objectives of maximum possible return at a minimum risk, given that the right choice of constituent assets is made and proper weights are allocated. However, despite its enormous contribution to this branch of knowledge, the model is not immune from criticisms ranging from those associated with its in ability to capture the realism of an investment setting - such as transaction costs, cardinality constraints, floor and ceiling constraints, etc. In this research we extended the classical model by incorporating into it the cardinality as well as the floor & ceiling constraints after which we implemented six different metaheuristic algorithms to solve this advanced model. We then designed and implemented some neighbourhood transition strategies to enable our designed algorithms solve the problem in an efficient and intelligent way. Furthermore, we proposed a new portfolio selection model with target-semivariance (as defined in a previous research) as the objective, and constrained by additional real life (cardinality and floor & ceiling) constraints. Page 8 of 277 List of Tables Table 1: Showing values of the mEd and average execution time ..............................................158 Table 2: Showing the C-metric values for all algorithms against each other for the Hang Seng dataset .................................................................................................................................................. 164 Table 3: Showing the C-metric values for all algorithms against each other for the FTSE100 166 Table 4: Showing the values of uniformity metric for all algorithms from the two datasets usedl68 Table 5: Showing the mEds and the average time (in secs) for the Hang Seng dataset ........ 201 Table 6: Showing the mEds and the average time (in secs) for the FTSE100 dataset .......... 202 Table 7: Comparison of the results for the unconstrained optimization problems ................ 218 Table 8: Comparison of the results for the G11 constrained problem ..................................... 220 Table 9: Comparison of the results for the PVD problem ......................................................... 221 Table 10: Possible decisions in a test of statistical hypothesis (TSH) .................................... 224 Table 11: A TSH analysis between SWAN and FSA ............................................................... 227 Table 12: Summary of different settings on cooling schedules ............................................... 265 Table 13: Summary of objective values and time taken by different cooling schedules ..... 266