Equally weighted cardinality constrained portfolio selection via factor models
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Equally weighted cardinality constrained portfolio selection via factor models Juan F. Monge1 Received: 13 March 2019 / Accepted: 12 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work a proposal and discussion of two different 0-1 optimization models is carried out in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios based on tracking the market index, among other objectives, and require to estimate smaller number of parameters than the classical Markowitz model. The addition of the cardinality constraints limits the number of securities in the portfolio. Restricting the number of securities in the portfolio allows to obtain a concentrated portfolio while also limiting transaction costs. To solve this problem a new quadratic combinatorial problem is presented to obtain an equally weighted cardinality constrained portfolio. For a single factor model, some theoretical results are presented. Computational results from the 0-1 models are compared with those using a state-of-the-art Quadratic MIP solver. Keywords Portfolio selection · Factor models · Minimum-variance portfolio · 0-1 quadratic optimization
1 Introduction The portfolio selection problem deals with selecting a collection of financial assets and in what proportion, according to the investor’s risk preference, with the aim of obtaining the maximum expected return. The selection of assets allocated to the portfolio can be managed using different approaches: minimum risk allocation, equal weighting, risk parity, Sharpe ratio, and many others. In the seminal work of Markowitz [26], return and risk are evaluated by means of the expected value and variance of the selected assets. Markowitz introduced the concept of an efficient frontier and showed that there is a set of optimal portfolios,
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Juan F. Monge [email protected] Department of Statistics, Mathematics and Computer Science, Center of Operations Research, Miguel Hernández University of Elche, Elche, Spain
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not only one. The classical Markowitz model can be formulated as a quadratic model, and the investor can find an optimal portfolio maximizing the expected return under a risk level, w ∗ = argw max{ w μ s.t. ww = σ ∗ , w 1 = 1}, or minimizing the risk under a return level, w∗ = argw min{ w w s.t. w μ = r ∗ , w 1 = 1}, where w denotes the vector of weights in the portfolio, μ the vector of expected returns, and the covariance matrix of expected returns. A significantly important portfolio is given when the constraint related to the return level is relaxed, obtaining the global minimum risk solution. This solution is important in the literature. For example, it is shown in [16] that the minimum variance portfolio is a more reliable and robust outsample than the traditional mean variance portfolios. The minimum-variance portfolio usually performs better out sample than any other mean-variance one. In [16] the authors present non-linear models to obtain a r
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