Financial Signal Processing and Machine Learning

Chapter 2Sparse Markowitz Portfolios

Christine De Mol

Université Libre de Bruxelles, Belgium

2.1 Markowitz Portfolios

Modern portfolio theory originated from the work of Markowitz (1952), who insisted on the fact that returns should be balanced with risk and established the theoretical basis for portfolio optimization according to this principle. The portfolios are to be composed from a universe of securities with returns at time given by , , and assumed to be stationary. We denote by the vector of the expected returns of the different assets, and by the covariance matrix of the returns ( is the transpose of ).

A portfolio is characterized by a vector of weights , where is the amount ...