À la Markowitz: A Tale of Simple Worlds

Paolo Sironi

A good portfolio is more than a long list of stocks and bonds. It is a balanced whole, providing the investor with protections and opportunities with respect to a wide range of contingencies.

Markowitz (1959)

We discuss Modern Portfolio Theory as a diversification framework, define the efficient frontier and the mean–variance objective function and introduce the tracking error and semi-variance approach, before going on to discuss expected shortfall.

INTRODUCTION

Investors act under uncertainty. This is a fundamental assumption of portfolio theory. If investors could gain advantage by not facing uncertainty, they would be indifferent about allocating available capital to any combination of securities giving the same maximum return. Instead, given the existence of uncertainty in future returns, rational investors must seek portfolio diversification and optimal asset allocations.

Modern Portfolio Theory assumes that investors (private or professional) know the probability distributions of future returns, whether these distributions are objective or subjective. Starting from the simplified belief that a probability distribution can be described by the first two