Financial Risk Modelling and Portfolio Optimization with R

5

Modern portfolio theory

5.1 Introduction

Sixty years have passed since Harry Markowitz’s path-breaking article ‘Portfolio Selection’ was published (see Markowitz 1952). Because the more recently advocated approaches to portfolio optimization are still based on this approach, Markowitz’s work on modern portfolio theory will be reviewed in this chapter. In the next section the approach itself will be discussed and subsequently the problems encountered in practice are highlighted. Within this last section the path is laid for the topics covered in Part III of the book, where portfolio optimization techniques designed to cope with the problems of modern portfolio theory and/or are tailor-made for certain investors’ demands will be covered.

Given the turbulence in the financial markets witnessed during the first decade of this century, the focus of academia and practitioners alike has again shifted to the Markowitz approach for selecting assets in a portfolio, in particular minimum variance portfolios. Thus, the concluding remark of Rubinstein’s article on the occasion of the fiftieth anniversary of Markowitz’s seminal paper remains true:

Near the end of his reign in 14 AD, the Roman emperor Augustus could boast that he had found Rome a city of brick and left it a city of marble. Markowitz can boast that he found the field of finance awash in the imprecision of English and left it with the scientific precision and insight made possible only by mathematics. (Rubinstein 2002)

5.2 Markowitz ...