Title Mean squared variance portfolio: A mixed-integer linear programming formulation
External publication No
Means Mathematics
Scope Article
Nature Científica
JCR Quartile 1
SJR Quartile 3
Area International
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85099932392&doi=10.3390%2fmath9030223&partnerID=40&md5=218e205cef54840ba0ac2e4809faa92f
Publication date 01/01/2021
ISI 000615387500001
Scopus Id 2-s2.0-85099932392
DOI 10.3390/math9030223
Abstract The mean-variance (MV) portfolio is typically formulated as a quadratic programming (QP) problem that linearly combines the conflicting objectives of minimizing the risk and maximizing the expected return through a risk aversion profile parameter. In this formulation, the two objectives are expressed in different units, an issue that could definitely hamper obtaining a more competitive set of portfolio weights. For example, a modification in the scale in which returns are expressed (by one or percent) in the MV portfolio, implies a modification in the solution of the problem. Motivated by this issue, a novel mean squared variance (MSV) portfolio is proposed in this paper. The associated optimization problem of the proposed strategy is very similar to the Markowitz optimization, with the exception of the portfolio mean, which is presented in squared form in our formulation. The resulting portfolio model is a non-convex QP problem, which has been reformulated as a mixedinteger linear programming (MILP) problem. The reformulation of the initial non-convex QP problem into an MILP allows for future researchers and practitioners to obtain the global solution of the problem via the use of current state-of-the-art MILP solvers. Additionally, a novel purely data-driven method for determining the optimal value of the hyper-parameter that is associated with the MV and MSV approaches is also proposed in this paper. The MSV portfolio has been empirically tested on eight portfolio time series problems with three different estimation windows (composing a total of 24 datasets), showing very competitive performance in most of the problems. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords Mean-variance portfolio; Mixed-integer linear programming; Non-convex quadratic programming; Portfolio diversification
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