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Financial Signal Processing and Machine Learning by Dmitry M. Malioutov, Sanjeev R. Kulkarni, Ali N. Akansu

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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 c02-math-0001 securities with returns at time c02-math-0002 given by c02-math-0003, c02-math-0004, and assumed to be stationary. We denote by c02-math-0005 the c02-math-0006 vector of the expected returns of the different assets, and by c02-math-0007 the covariance matrix of the returns (c02-math-0008 is the transpose of ).

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

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