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MODERN PORTFOLIO THEORY TOOLS A METHODOLOGICAL DESIGN AND APPLICATION Siu Han Wang A research report submitted to the Faculty of Engineering and the Built Environment, of the University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2008 i DECLARATION I declare that this research report is my own, unaided work. It is submitted in partial fulfilment of the requirements for the degree of Master of Science in Engineering in the University of Witwatersrand, Johannesburg. It has not been submitted before for any degree of examination in any other University. ___________________ Siu Han Wang _____________ day of _____________ (year) _____________ ii ABSTRACT A passive investment management model was developed via a critical literature review of portfolio methodologies. This model was developed based on the fundamental models originated by both Markowitz and Sharpe. The passive model was automated via the development of a computer programme that can be used to generate the required outputs as suggested by Markowitz and Sharpe. For this computer programme MATLAB is chosen and the model’s logic is designed and validated. The demonstration of the designed programme using securities traded is performed on Johannesburg Securities Exchange. The selected portfolio has been sub-categorised into six components with a total of twenty- seven shares. The shares were grouped into different components due to the investors’ preferences and investment time horizon. The results demonstrate that a test portfolio outperforms a risk- free money market instrument (the government R194 bond), but not the All Share Index for the period under consideration. This design concludes the reason for this is due in part to the use of the error term from Sharpe’s single index model. An investor following the framework proposed by this design may use this to determine the risk- return relationship for selected portfolios, and hopefully, a real return. iii To my family, for their support iv ACKNOWLEDGEMENTS I would like to thank the following people whom have helped me during various stages of this report. My first supervisor, Dr. Harold Campbell, for his invaluable guidance, insights and time. To Prof. Snaddon, for his consistent support and his willingness to take over the supervision of this project after Dr. Campbell left University of the Witwatersrand. To Ms. Bernadette Sunjka, for her consistent guidance, insights and her enthusiasm when she was appointed to take over the supervision of this design. To my friend, Randall Paton, for his patience and assistance in writing the MATLAB codes. To Joanne Hobbs, for the detailed foundation she laid in her honours project. To Thomas Tengen, for his insights in the further improvements of the mathematical models. To Michael Boer, Megan Chatterton, Peter Langeveldt, Michael Mill, Martin Perold and Po-Hsiang Wang for all the proof reading they have done and their support. v TABLE OF CONTENTS DECLARATION ............................................................................................................ii ABSTRACT...................................................................................................................iii ACKNOWLEDGEMENTS.............................................................................................v TABLE OF CONTENTS ...............................................................................................vi LIST OF FIGURES........................................................................................................ix LIST OF TABLES .........................................................................................................xi LIST OF SYMBOLS.....................................................................................................xii NOMENCLATURE…………………………………………………………………….xiv Chapter 1 Introduction ................................................................................................1 1.1 Background......................................................................................................1 1.2 Motivation .......................................................................................................2 1.3 Scope of Design...............................................................................................3 1.4 Limitations of Design.......................................................................................4 1.5 Statement of Task ............................................................................................4 1.6 Methodology....................................................................................................6 Chapter 2 Development of a Passive Management Model Via a Critical Literature Review of Portfolio Methodologies .................................................................................8 2.1 Introduction .....................................................................................................8 2.2 Modern Portfolio Theory .................................................................................9 2.3 Financial Engineering ....................................................................................11 2.4 Active and Passive Management ....................................................................12 2.4.1 Active Management ...............................................................................12 2.4.2 Passive Management ..............................................................................13 2.5 Portfolio Construction....................................................................................14 2.5.1 Security Valuation..................................................................................15 2.5.2 Asset Allocation.....................................................................................19 2.5.3 Portfolio Optimisation............................................................................21 2.5.4 Performance Measurement .....................................................................21 vi 2.6 Development of The Model ...........................................................................21 2.6.1 Markowitz’s Mean-Variance Framework ...............................................22 2.6.2 Sharpe’s Single Index Model..................................................................25 2.6.3 Efficient Market Hypothesis...................................................................34 2.7 Next Steps......................................................................................................38 Chapter 3 Development of Computer Programme .....................................................39 3.1 Design Requirement Specifications................................................................39 3.1.1 The Objectives .......................................................................................39 3.1.2 Needs Analysis.......................................................................................39 3.1.2.1 Design Overview....................................................................................39 3.1.2.2 Design Requirement Specification..........................................................40 3.2 Software Selection .........................................................................................41 3.2.1 Introduction............................................................................................41 3.2.2 Types of Statistical Packages..................................................................41 3.2.3 Decision Process ....................................................................................45 3.3 Code Written for Computer Programme.........................................................46 3.3.1 Introduction............................................................................................46 3.3.2 Detailed Computer Programme Logic ....................................................46 3.3.3 Final Computer Programme ...................................................................50 3.3.4 Testing of Computer Programme............................................................54 Chapter 4 Selection of Test Portfolio.........................................................................57 4.1 Choice of Constituents in Test Portfolio.........................................................57 4.1.1 Portfolio Selection..................................................................................57 4.2 Choice of Index..............................................................................................66 Chapter 5 Design Outcomes ......................................................................................67 5.1 Introduction ...................................................................................................67 5.2 The Data ........................................................................................................67 5.3 Results with Discussion .................................................................................67 5.3.1 Results of Components...........................................................................69 5.3.2 Results of Overall Test Portfolio ............................................................96 5.4 Summary .....................................................................................................105 vii Chapter 6 Conclusions & Further Work...................................................................107
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