Expected mean return—standard deviation efficient frontier approximation with low‐cardinality portfolios in the presence of the risk‐free asset

Abstract

In the expected mean return, standard deviation portfolio selection problem, the first step is usually to derive the set of efficient portfolios, which in the space of objective function values is represented by the efficient frontier. With modern methods and software, it is an easy task even for thousands of assets provided that the problem is continuous. However, investors often introduce the requirement to limit the number of assets in portfolios (portfolio cardinality). The resulting mixed-integer quadratic formulations are computationally much more complex. In this work, we assume that besides risky assets, the risk-free asset is available to the investor, and short selling is not allowed. Since in this case the efficient frontier cannot be directly derived by a quadratic solver, we propose a naive but intuitive heuristic to approximate the efficient frontier in the presence of the risk-free asset. In contrast to the general-purpose evolutionary heuristics, we exploit the underlying mechanism of portfolio composition. We show by numerical experiments that in large-scale instances it works well, even compared to a state-of-the-art evolutionary multiobjective optimization algorithm. Moreover, the heuristic produces portfolios of remarkably limited cardinalities.

A low-cost alternating projection approach for a continuous formulation of convex and cardinality constrained optimization

“…The purpose of this simple example is to demonstrate properties of the problem and the proposed algorithm in an easy-to follow fashion. For the other data sets, involving real-world capital market indices, we consider some larger problems obtained from Beasley's OR Library (http://people.brunel.ac.uk/∼mastjjb/jeb/info.html), built from weakly price data from March 1992 to September 1997, and that we will denote as Port1 (Hang Seng index with n = 31), Port2 (DAX index with n = 85), Port3 (FTSE 100 index with n = 89), Port4 (S&P 100 index with n = 98), Port5 (Nikkei index with n = 225), and Port 6 (n = 600, former by assets from NY Stock Exchange, weekly prices from July 2001 to July 2018, [22]); see also [1,14].…”

Corporate Social Responsibility as an Alternative Approach to Financial Risk Management: Advantages for Sustainable Development

“…The central scientific category of this paper is financial risk. The existing literature sources (Bendall and Stent 2006;Chiang 2021;Juszczuk et al 2022;Werge 2021;Ling et al 2022;Sohibien et al 2022) note that one of the most popular and correct indicators of financial results (and through them-financial risks) is such proxy variable as return on assets (ROA). Thus, the measure of financial risk in this paper is the change of return on assets.…”

Model and efficient algorithm for the portfolio selection problem with real‐world constraints under value‐at‐risk measure

“…The well‐known mean‐variance model of Markowitz (1952) was one of the pioneering efforts in this field, and up to now, it has been extended from different aspects (Mencarelli and D'Ambrosio, 2018). One of the important extensions of the Markowitz model is the incorporation of real‐world constraints such as cardinality and position size constraints and transaction costs (Lwin et al., 2017; Cui et al., 2020; Juszczuk et al., 2023). As pointed out by Lwin et al.…”