A Generalized Risk Budgeting Approach to Portfolio Construction

28 Pages Posted: 5 Jul 2014 Last revised: 9 Jan 2016

See all articles by Martin Brendan Haugh

Martin Brendan Haugh

Imperial College Business School

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Irene Song

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: September 3, 2015

Abstract

Risk-based asset allocation models have received considerable attention in recent years. This increased popularity is due in part to the difficulty in estimating expected returns as well as the financial crisis of 2008 which has helped reinforce the key role of risk in asset allocation. In this study, we propose a generalized risk budgeting (GRB) approach to portfolio construction. In a GRB portfolio assets are grouped into possibly overlapping subsets and each subset is allocated a pre-specified risk budget. Minimum variance, risk parity and risk budgeting portfolios are all special instances of a GRB portfolio. The GRB portfolio optimization problem is to find a GRB portfolio with an optimal risk-return profile where risk is measured using any positively homogeneous risk measure. When the subsets form a partition, the assets all have the same expected return and we restrict ourselves to long-only portfolios, then the GRB problem can in fact be solved as a convex optimization problem. In general, however, the GRB problem is a constrained non-convex problem, for which we propose two solution approaches. The first approach uses a semidefinite programming (SDP) relaxation to obtain an (upper) bound on the optimal objective function value. In the second approach we develop a numerical algorithm that integrates augmented Lagrangian and Markov chain Monte Carlo (MCMC) methods in order to find a point in the vicinity of a very good local optimum. This point is then supplied to a standard non-linear optimization routine with the goal of finding this local optimum. It should be emphasized that the merit of this second approach is in its generic nature: in particular, it provides a starting-point strategy for any non-linear optimization algorithm.

Keywords: Risk Parity, Risk Budgeting, MCMC, Augmented Lagrangian, Portfolio Optimization, Semidefinite Programming

Suggested Citation

Haugh, Martin Brendan and Iyengar, Garud and Song, Irene, A Generalized Risk Budgeting Approach to Portfolio Construction (September 3, 2015). Available at SSRN: https://ssrn.com/abstract=2462145 or http://dx.doi.org/10.2139/ssrn.2462145

Martin Brendan Haugh (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States
+1 212-854-4594 (Phone)
+1 212-854-8103 (Fax)

Irene Song

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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