Sparse and Stable Markowitz Portfolios

23 Pages Posted: 30 Oct 2008

See all articles by Joshua Brodie

Joshua Brodie

Princeton University

Ingrid Daubechies

Princeton University - Department of Mathematics

Christine De Mol

Free University of Brussels (VUB/ULB) - European Center for Advanced Research in Economics and Statistics (ECARES)

Domenico Giannone

Federal Reserve Banks - Federal Reserve Bank of New York; Centre for Economic Policy Research (CEPR)

Ignace Loris

Vrije Universiteit Brussel (VUB)

Multiple version iconThere are 2 versions of this paper

Date Written: September 30, 2008

Abstract

We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the sum of the absolute values of the portfolio weights. This penalty regularizes (stabilizes) the optimization problem, encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs. Our approach recovers as special cases the no-short-positions portfolios, but does allow for short positions in limited number. We implement this methodology on two benchmark data sets constructed by Fama and French. Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the naive evenly-weighted portfolio which constitutes, as shown in recent literature, a very tough benchmark.

Keywords: Portfolio Choice, Sparse Portfolio, Penalized Regression

JEL Classification: G11, C00

Suggested Citation

Brodie, Joshua and Daubechies, Ingrid and De Mol, Christine and Giannone, Domenico and Loris, Ignace, Sparse and Stable Markowitz Portfolios (September 30, 2008). ECB Working Paper No. 936. Available at SSRN: https://ssrn.com/abstract=1258442

Joshua Brodie (Contact Author)

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Ingrid Daubechies

Princeton University - Department of Mathematics ( email )

Princeton, NJ 08544-1021
United States

Christine De Mol

Free University of Brussels (VUB/ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium

Domenico Giannone

Federal Reserve Banks - Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Ignace Loris

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

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