This book is composed of six essays in the area of Portfolio Management. Its goal is to introduce a novice reader, but with a reasonable quantitative background (calculus, linear algebra, probability and statistics, at the undergraduate level) to some of the main topics in the area of Portfolio Management. As such the book is silent on institutional details and empirical issues. Readers who are interested in these issues will be (after reading this book) very comfortable in consulting one of the many textbooks in this area. This is also the reason the book does not refer to papers in the academic literature as these can also be obtained in one of the above books. The book is aimed at capitalizing on the quantitative background of the reader and the reader's familiarity (and comfort) with computers in order to achieve its goal. This is being accomplished by using the MAPLE software, however no prior knowledge of MAPLE is needed to read the book.  


No prior knowledge of Economics of Finance is assumed, and for this reason we have decided to start in an unorthodox way. In fact, the material covered in part of Chapter 1 starts with a review of time value of money and continues with a classical topic usually covered in an introduction to Microeconomics.  We have chosen to present this material at the start of the book for the following reasons. While being precise and mathematically oriented is a necessary condition for "Quantitative Finance", a solid understanding of the underlying Economics is essential for success in the innovation or engineering process. It helps in generating a deep understanding of the material and an intuition that leads us when we discover new grounds.  Intuition should always be consulted when facing such a task, but a necessary condition to obey by this rule is that the intuition does exist.  A deep understanding of the material and a strong intuition help us in developing new methods and dealing with new situations in the market.  


The e-book presents an interactive and dynamic friendly environment allowing readers to learn through hands-on experience. The book can only be read with the MAPLE software. We have chosen MAPLE because of its symbolic computation ability as well as its visualization capability and the structure of its files that allows embedding commands within the text.  This e-book is a series of MAPLE worksheets connected by hyperlinks and a table of contents which has links to each worksheet. It presents an Interactive Dynamic Environment for Advanced Learning (IDEAL) which is supported by a collection of procedures - a MAPLE package.  


A reader who follows the book on-screen, will find the commands are already typed in the appropriate files. The reader should merely re-execute the printed commands while reading. The technology allows readers to learn through immediate application of theory and concepts. Readers can use the prepared MAPLE files, follow the text on-screen, and explore different numerical examples with no prior programming knowledge. In fact, readers can keep generating their own examples, verifying and investigating different situations not addressed in the book. Learning is enhanced by altering the parameters of the commands, varying them at will, in order to experiment with applications of the concepts and different (reader-generated) examples, in addition to the ones already in the prepared file. It is this interaction and experimentation, making use of MAPLE together with the ability to bring to life on the screen the theoretical material of the chapter, which provides a unique, powerful, and entertaining way to learn about Portfolio Management. 


How to read the e-book 


If you are new to MAPLE it is suggested that you familiarize yourself with the basics of MAPLE before you continue to read the e-book. Click the 'Help' in the upper toolbar and choose `Take a Tour of Maple'. Or use the hyperlinks in the subgroup below. 

New user's tour 

The ten minute tour  

Numeric and Symbolic Computations  



This e-book is a series of MAPLE worksheets connected by hyperlinks and a table of contents which has links to each worksheet. It presents an Interactive Dynamic Environment for Advanced Learning (IDEAL) which is supported by a collection of procedures, and a small MAPLE package. This interactive technology creates a friendly environment and immediate application of theory and concepts allowing readers to learn through hands-on experience. 


When reading the e-book, if you happen to place the cursor elsewhere in a worksheet, place it back on the appropriate command line.  Please execute the commands in order as some computations require results from previous command lines. Learning is enhanced by altering the commands, varying them at will, in order to experiment with applications of the concepts and different (reader-generated) examples, in addition to the ones already in the prepared file.   


Suggested setting: 


The MAPLEPM package must be loaded before reading some of the files in the book, in order for the MAPLEPM commands in the book to work properly. The initialization is done by issuing the command ‘with(MAPLEPM):’  


> with (MAPLEPM):


Files that necessitate loading the package have a subgroup at the beginning of the file that contains this command in a subgroup named 'initialization', you just need to click the arrow below in order to open the subgroup and execute the command.  




> with(MAPLEPM):



Execute the ‘with (MAPLEPM):’ command whenever you open a new worksheet with this subgroup at its top. 

Alternatively, you can set the MAPLE kernel to ‘Shared' which is done as follows: Choose the ‘Options’ item under ‘Tools’ and in the general tab make sure the circle next to "Always use these settings" is checked and select "share one engine for all documents" in the drop down menu below it. In the 'Display' tab make sure that the options: 'Replace existing output when re-executing groups', and 'Always insert new execution group after executing' (to avoid "text running"), are selected and that the 'show equations labels' is not selected. Under the Windows operating system you can read the book using the shortcut that is placed in 'C:\Program Files\Maple 11\toolbox\Essays in Portfolio Management', by copying it to the desktop. Reading the book using the shortcut ensures that the package is loaded. 


Possible use of the e-book in the classroom 


The book is a compilation of my lectures in the course "Portfolio Management". The course was taught in a computer teaching lab and most of the lectures were divided between the theoretical material and hands-on experience using Maple. The course was composed of about 12-13 lectures most of which had a lab project attached to it. The lab project was designed to enhance the understanding of concepts that were introduced during the theoretical part of the lecture. Some of the lab projects involved simulations to facilitate students experiencing a real life situation. Instructors that would like to use the book in this fashion will find below a suggestion for the course structure. This structure stipulates 13 sessions with the lab project that is attached to each session including suggestions for some homework. The lab projects are now listed as questions at the end of each chapter. The suggested outline for such a course is listed below. The setting I used for this course was of a weekly 3 hour lecture that was roughly divided into 1.5 hours of lecture followed by approximately 1.5 hours of lab time. Each student had the use of a workstation on which the MAPLE software and the e-book was installed. The instructor stayed in the lab during the lab time to alleviate some of the frustrations that may occur when new software is used or different packages of MAPLE were used for different topics. Many schools now require that students own a notebook and the setting of a computer lab may not be necessary. Maplesoft offers significant discounts to Maple for academic institutions and students. With these versions you get the full power of standard Maple at a very reasonable price. You can visit their Web site for more information. 


Throughout my ten years of teaching the portfolio management course in this fashion I found that it accelerated student's understanding of the theoretical material as well as prepared them to face the practical situations in real life. Below I stipulate the approximate structure of the course which was composed of 12 meetings for 3 hours each. The structure below stipulates 11 weeks or rather 11 topics, but in most cases it took 12-13 meetings to cover the material, where some topics (not always the same) required more than one meeting.   


Week 1 Introduction 

• Review time value of money  

• Modeling the consumer / investor decision process 

• Introduction to MAPLE 

• Reading :  Chapter 1, sections 1.1, 1.2   

• Lab 1:   Tour of Maple - Chapter 1, problem 0 

• Homework: Chapter 1, problems 1, 2 and 3 


Week 2   Utility and Saving vs. Investment  

• Introduction to Utility Analysis 

• Saving vs. Investment  

• Reading: Chapter 1, sections 1.3, 1.4 

• Lab 2:  Saving vs. investment a graphic solution -  Chapter 1, problem 10 

• Homework:  Chapter 1, problems 4, 5, 6 and 7 


Week 3   Rigorous formulation of the consumer optimization problem 

• Constrained Optimization and the Lagrange function. 

• Equilibrium: Illustration via a simple example  

• Reading: Chapter 1, sections 1.5, 1.6, and 1.7 

• Lab 3: Determining Equilibrium Interest Rates-  Chapter 1 problem 11 

• Homework:  Chapter 1, problems 8 and 9 and re-solve problem10 using the Lagrangian method.  


Week 4  Portfolio Choice under Uncertainty: The Mean Variance Framework   

• Preliminaries 

• The Feasible Set in an Uncertain Environment: A First Look  

• Review: Variance, Covariance, VarCov Matrix, and Correlation Coefficient 

• Combinations of Two Risky Assets Revisited:  Short Sales Not Allowed 

• The Feasible Set with Two Assets. 

• Reading:  Chapter 2, sections 2.1-2.4 

• Lab 4:   From a parametric plot to a function - Chapter 2, problem 3 

• Homework: Chapter 2, problems 1 and 2 


Week 5 The Efficient Frontier General Formulation and Numerical Solutions 

• Short Sales Allowed with Riskless Lending and Borrowing 

• Short Sales Allowed: No Riskless Lending and Borrowing 

• Riskless Lending and Borrowing with Short Sales Not Allowed 

•             No Short Selling and No Riskless Lending and Borrowing 

• Reading: Chapter 2, section 2.5 

• Lab 5: Generating the efficient frontier -Chapter 2, problem 4 (part 2) 

• Homework : Chapter 2, problem 5 problem 4 (part 1 - you may want to make this solution available to the students before Lab 5) 


Week 6  Standard Capital Asset Pricing Model (CAPM) 

• The Assumptions Underlying the CAPM 

• The Capital Asset Pricing Model 

• Prices and the CAPM  

• Reading: Chapter 3 

• Lab 6: Graphical illustration & numerical solution of optimal portfolio given a utility function -  

              Chapter 3, problem 5  

• Homework: Chapter 3, problems 1-4 and 6 


Week 7   Single Index model  

• Single-Index Models (SIM):  An Overview 

• Characteristics of the Single-Index Model 

• Reading e-book/lecture notes:  Chapter 4, section 4.1    

• Lab 7:  SIM – a simulation - Chapter 4, problem 2 

• Homework:  Chapter 4, problem 1 


Week 8  Variations of the Single Index Model  

• The Market Model 

• SIM, Constant Correlation and the Efficient Frontier  

• Reading:  Chapter 4 sections 4.2 and 4.3 

• Lab 8: The SIM vs. the Market model – a simulation - Chapter 4, problem 3 

• Homework:  Chapter 4, problem 5 


Week 9  Multiple Index Model (MIM) & Introduction to Arbitrage Pricing Theory (APT)  

•             Multi-Index Models 

• Introduction to APT, The APT Model and Its Assumptions 

• Reading:  Chapter 4, section 4.4, Chapter 5, section 5.1 and 5.2 

• Lab 9: MIM a simulation - Chapter 4, problem 6 

• Homework:   Chapter 5, problem 1 


Week 10  Arbitrage Pricing Theory  

• The Intuition behind the APT 

•             Linear Programming and Arbitrage 

• Reading:  Chapter 5, sections 5.3-5.6 

• Lab 10: APT a simulation - Chapter 5, problem 3 

• Homework:  Chapter 5, problems 2 and 4 


Week 11  Safety First Models 

• Safety First 

• The Geometric Mean Return and the Stochastic Dominance Criteria 

• Reading:  Chapter 6 

• Lab 11: Chapter 6, problem 4 

• Homework:  Chapter 6, problem 1 



This book was compiled out of my lectures in the Portfolio Management course for students in the Financial Engineering collaborative program at the Schulich School of Business, York University, Toronto.  The comments, questions and suggestions of my students over the last few years are much appreciated. I would also like to thank Gillane Beard, the Financial Engineering Administrative Assistant who has spent numerous hours proof reading, compiling and linking the worksheets in the book.  


Last but not least, I would like to thank the benefactors of our school, Mr. Seymour Schulich for the  

chair I am holding which was established in the memory of his late friend, Nigel Martin. Without the chair, which provided for teaching time relapse and research support for an assistant, this work could have not been completed. 


I would appreciate any comments or error reporting from the readers which can be sent to I am of course responsible for any remaining errors in the e-book. 

Toronto 2007 


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