UNIVERSITY OF THE AEGEAN DEPARTMENT OF FINANCIAL & MANAGEMENT ENGINEERING THESIS “An integrated optimization model for immunizing and matching pension funds bond portfolios” GEORGIOS BOUZIANIS Supervisor: Dr. P. Xidonas Athens, June 2016 UNIVERSITY OF THE AEGEAN DEPARTMENT OF FINANCIAL & MANAGEMENT ENGINEERING THESIS “An integrated optimization model for immunizing and matching pension funds bond portfolios” GEORGIOS BOUZIANIS Supervisor: Dr. Panos Xidonas Approved by the 3-member committee in June 2016. .................................... ................................. .............................. Dr. Panos Xidonas Dr. Vasilis Koutras Dr. Evangelos Vassiliou Adjunct Lecturer Lecturer Adjunct Lecturer Athens, June 2016 GEORGIOS BOUZIANIS Copyright© Georgios Bouzianis, 2016 All rights reserved. Copying, storage and distribution of this paper for commercial purposes is forbidden. Reproduction, storage and distribution of this paper for research purposes, is allowed as long as the source is mentioned. The views and conclusions drawn in this document express only authors’ opinions and do not represent official views of the Department of Financial & Management Engineering. ABSTRACT The primary purpose of this thesis is to develop two innovative bond portfolio optimization models, based on the portfolio dedication and immunization strategies. The first mathematical program minimizes the initial capital required for the creation of a bond portfolio, and is best suited to a defined liability-driven investment strategy. The second mathematical program operates under the uncertainty of term structure alterations, approached with Hull-White recombining trinomial lattice. In both cases, the exposure of transaction costs as well as the diversification and investment policy constraints regarding the portfolio structure, are strongly taken into account. In this sense, two mixed-integer linear programs are formulated. The validity of the proposed approach for the first model is verified through duration and convexity empirical testing. For the second model, it is verified through scenario evaluation in a well- diversified investment universe of bonds, including: US corporate bonds, European corporate bonds and sovereign bonds. Keywords: Bond portfolio optimization; Stochastic dynamic integrative asset and liability management strategy; Matching, immunization mathematical programming PROLOGUE I would like to express my profound gratitude to my supervisor, Dr. Panos Xidonas, for the assignment of this particular thesis and huge inspiration he provided me with. His excellent guidance, teaching ability and overall assistance were critical success factors for the completion of this work. I would also like to thank Professor Dimosthenis Drivaliaris, since he was the one who gave robust and mature shape in the mathematical skills and thinking potential of mine. His contribution to my progress was very important. My interaction with these two men changed the way I approach both science and life. I would also like to express my sincere thanks to the members of my thesis committee, Dr. Vasilis Koutras and Dr. Evangelos Vassiliou, for their useful comments and their overall contribution. Moreover, I would also like to thank all the people who contributed in their own unique way in supporting me during the time of my thesis elaboration. Finally, I dedicate this endeavor to my father Stavros, whose presence and input have been invaluable. Georgios Bouzianis Athens, 2016 TABLE OF CONTENTS CHAPTER 1 - INTRODUCTION ............................................................. 11 1.1 The problem ......................................................................................... 11 1.2 The Subject and the Aim of the Thesis .......................................... 19 1.3 The Contribution of the Thesis ........................................................ 20 1.4 The Structure of the Thesis .............................................................. 21 CHAPTER 2 - PROPOSED METHODOLOGY FOR SMALL AND PARALLEL SHIFTS IN THE TERM STRUCTURE ............................ 24 2.1 Objective function .............................................................................. 25 2.2 Cashflow matching constraint ........................................................ 26 2.3 Immunization constraints ................................................................ 27 2.4 Investment policy adjustment ......................................................... 32 CHAPTER 3 - STOCHASTIC SHORT RATE MODELS ...................... 36 3.1 Vasicek Model ...................................................................................... 37 3.2 Hull-White Model ................................................................................ 39 3.3 Dothan Model ...................................................................................... 43 3.4 Black-Derman-Toy Model ................................................................. 44 3.5 Cox Ingersoll Ross Model .................................................................. 46 CHAPTER 4 - PROPOSED METHODOLOGY WITH EMBEDDED HULL - WHITE STOCHASTIC SHORT RATE MODEL ..................... 50 4.1 Hull-White scenario structures ....................................................... 51 4.2 General Methodological approach.................................................. 55 CHAPTER 5 - EMPIRICAL TESTING ................................................... 59 5.1 Data and field of application............................................................ 59 5.2 Results and discussion for the proposed methodology for small and parallel shifts in the term structure ............................................. 60 5.3 Results and discussion for the proposed methodology with embedded Hull-White stochastic short rate model ........................... 65 CHAPTER 6 - CONCLUSIONS - PERSPECTIVES ............................. 72 6.1 Conclusions .......................................................................................... 72 6.2 Perspectives ......................................................................................... 73 APPENDIXES A Programming code for the proposed methodology for small and parallel shifts in the term structure ..................................................... 76 B Programming code for the proposed methodology with embedded Hull-White stochastic short rate model ........................... 82 REFERENCES .......................................................................................... 91 LIST OF FIGURES CHAPTER 1 Figure 1.1.1 Depiction of a normal yield curve. ................................. 15 Figure 1.1.2 Depiction of a flat yield curve. ........................................ 15 Figure 1.1.3 Depiction of an inverted yield curve. ............................ 16 Figure 1.1.4 The u.s. bond market size is (in billions) according to the securities industry and financial markets association (SIFMA) as of Q4 2013 ............................................................................................... 17 Figure 1.1.5 Outstanding u.s. bond market debt (in billions) from 1980 to 2014, according to sifma. ........................................................... 17 Figure 1.1.6 Components of an alm system and basic procedure…………………………………………………………………………19 CHAPTER 2 Figure 2.2.1 A liability (lt) and the total inflows from mismatched portfolios (A and B), and from a perfectly matched portfolio (C)..27 Figure 2.3.1 The price-yield curve with approximations of duration and convexity. .......................................................................... 32 CHAPTER 4 Figure 4.1.1 Recombining trinomial Hull-White lattice, with five trading dates. ............................................................................................. 51 Figure 4.1.2 A scenario structure derived from the trinomial lattice in figure 4.1.1. ................................................................................ 53 Figure 4.1.3 A scenario structure with common states up to t=3, derived from the trinomial lattice in figure 4.1.1. ............................. 54 CHAPTER 5 Figure 5.2.1 Investment to the i-th bond of the portfolio and expected earnings. .................................................................................... 64 Figure 5.2.2 Bond portfolio incomes, necessary overflows and liabilities. .................................................................................................... 64 Figure 5.3.1 Shifts in the term structure in the form of trinomial lattice, with Hull-White model. .............................................................. 69 LIST OF TABLES Table 5.2.1 Individual characteristics of the 70 bonds in the optimized portfolio ................................................................................... 61 Table 5.2.2 Monetary synthesis of the portfolio and evaluation of the earnings (in USD) from every incorporated bond...................... 61 Table 5.2.3 Required overflows and overall inflows at any period t and corresponding liabilities (in USD). ............................................... 62 Table 5.3.1 Individual characteristics of the 170 bonds in the optimized portfolio. .................................................................................. 66 Table 5.3.2 Monetary synthesis of the portfolio and evaluation of the earnings (in USD) from every incorporated bond...................... 66 Table 5.3.3 Required overflows and overall inflows at any period t and state stv(t), and corresponding liabilities