An Evolutionary Optimization Approach to Risk Parity Portfolio Selection

In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the optimization problem becomes non-trivial in the long-short case. To solve this problem, we propose a genetic algorithm as well as a local search heuristic. This algorithmic framework is able to compute solutions successfully. Numerical results using real-world data substantiate the practicability of the approach presented in this paper

Equity portfolio management with cardinality constraints and risk parity control using multi-objective particle swarm optimization

The financial crisis and the market uncertainty of the last years have pointed out the shortcomings of traditional portfolio theory to adequately manage the different sources of risk of the investment process. This paper addresses the issue by developing an alternative portfolio design, that integrates risk parity into the cardinality constrained portfolio optimization model. The resulting mixed integer programming problem is handled by an improved multi-objective particle swarm optimization algorithm. Three hybrid approaches, based on a repair mechanism and different versions of the constrained-domination principle, are proposed to handle constraints. The efficiency of the algorithm and the effectiveness of the solution approaches are assessed through a set of numerical examples. Moreover, the benefits of adopting the proposed strategy instead of the cardinality constrained mean-variance approach are validated in an out-of-sample experiment

Probabilistic Portfolio Modeling in Python

Master's thesis in Petroleum engineeringThe portfolio selection problem has been known for centuries. However, Markowitz (1952) was the first to introduce a robust framework for optimized portfolios on financial markets. Later this approach was applied in the petroleum industry to increase the corporate performance of oil and gas companies and to manage associated risks (Hightower et al. (1991)). Nevertheless, despite the lack of uncertainty optimization, simple portfolio selection techniques such as the Rank and Cut method remains popular in the industry (Wood (2016)). In this thesis, the advantages and disadvantages of this approach were briefly mentioned. Besides Markowitz Portfolio Theory and the Rank and Cut Method, a number of new portfolio selection methods were developed that not only improve the performance and minimize the risks but also can be used as processes and tools to deliver shareholder value or to achieve strategic corporate goals. One such approach is the use of multi-objective time series portfolio optimization, where the corporate goals are defined as constraints, the level of constraint accomplishment is quantified in terms of probability of exceeding the constraint and net present value is set as the main objective. This method was used to select an optimal portfolio from the pool of petroleum projects. One of the main contributions of this work is to provide a tool and process that can be used by management teams to evaluate different portfolios quickly using multiple time-dependent corporate constraints. The tool can be used to evaluate the impact on the portfolio of changing constraints or weighting the constraints differently. The ability to do this interactively is essential as it allows the management team to evaluate and address the key elements of their portfolio decision problem. A crucial part of the portfolio optimization problem is the choice of optimization algorithms. Several algorithms that facilitate the petroleum industry’s needs of portfolio optimization were studied, and a brief overview of them was presented. We also included a discussion of the choice of programming language for portfolio models. Although we built the project model in R, we ended up using Python as it provided significant computational speed improvements over R. We also argued why Excel, although very popular, is far from an optimal tool for portfolio modeling

Portfolio Optimization: A Comparative Study

Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks. This chapter presents a comparative study of three portfolio design approaches, the mean-variance portfolio (MVP), hierarchical risk parity (HRP)-based portfolio, and autoencoder-based portfolio. These three approaches to portfolio design are applied to the historical prices of stocks chosen from ten thematic sectors listed on the National Stock Exchange (NSE) of India. The portfolios are designed using the stock price data from January 1, 2018, to December 31, 2021, and their performances are tested on the out-of-sample data from January 1, 2022, to December 31, 2022. Extensive results are analyzed on the performance of the portfolios. It is observed that the performance of the MVP portfolio is the best on the out-of-sample data for the risk-adjusted returns. However, the autoencoder portfolios outperformed their counterparts on annual returns.Comment: This is the preprint of the book chapter accepted for publication in the book titled "Deep Learning - Recent Finding and Researches" edited by Manuel Dom\'inguez-Morales. The book is scheduled to be be published by IntechOpen, London, UK in January 2024. This is not the final version of the chapte

Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach

[EN] Sustainable finance, which integrates environmental, social and governance criteria on financial decisions rests on the fact that money should be used for good purposes. Thus, the financial sector is also expected to play a more important role to decarbonise the global economy. To align financial flows with a pathway towards a low-carbon economy, investors should be able to integrate into their financial decisions additional criteria beyond return and risk to manage climate risk. We propose a tri-criterion portfolio selection model to extend the classical Markowitz's mean-variance approach to include investor's preferences on the portfolio carbon risk exposure as an additional criterion. To approximate the 3D Pareto front we apply an efficient multi-objective genetic algorithm called ev-MOGA which is based on the concept of epsilon-dominance. Furthermore, we introduce a-posteriori approach to incorporate the investor's preferences into the solution process regarding their climate-change related preferences measured by the carbon risk exposure and their loss-adverse attitude. We test the performance of the proposed algorithm in a cross-section of European socially responsible investments open-end funds to assess the extent to which climate-related risk could be embedded in the portfolio according to the investor's preferences.Hilario Caballero, A.; Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Vercher, M. (2020). Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach. International Journal of Environmental research and Public Health. 17(17):1-15. https://doi.org/10.3390/ijerph17176324S1151717Morningstar Low Carbon Designationhttps://bit.ly/2SfAFUAKrueger, P., Sautner, Z., & Starks, L. T. (2020). The Importance of Climate Risks for Institutional Investors. The Review of Financial Studies, 33(3), 1067-1111. doi:10.1093/rfs/hhz137Syam, S. S. (1998). A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals. European Journal of Operational Research, 108(1), 196-207. doi:10.1016/s0377-2217(97)00048-9Li, D., Sun, X., & Wang, J. (2006). OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN-VARIANCE FORMULATION FOR PORTFOLIO SELECTION. Mathematical Finance, 16(1), 83-101. doi:10.1111/j.1467-9965.2006.00262.xBertsimas, D., & Shioda, R. (2007). Algorithm for cardinality-constrained quadratic optimization. Computational Optimization and Applications, 43(1), 1-22. doi:10.1007/s10589-007-9126-9Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121. doi:10.1016/0304-405x(75)90025-2Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Mansini, R. (2003). LP solvable models for portfolio optimization: a classification and computational comparison. IMA Journal of Management Mathematics, 14(3), 187-220. doi:10.1093/imaman/14.3.187Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302. doi:10.1016/s0305-0548(99)00074-xMaringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25(4), 481-495. doi:10.1007/s00291-003-0139-1Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23(3), 411-420. doi:10.1080/10556780701722542Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063. doi:10.1016/j.eswa.2008.06.007Anagnostopoulos, K. P., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications. doi:10.1016/j.eswa.2011.04.233Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37, 104-125. doi:10.1016/j.swevo.2017.06.005Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 267(1-2), 281-319. doi:10.1007/s10479-016-2377-zMetaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Liagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Babaei, S., Sepehri, M. M., & Babaei, E. (2015). Multi-objective portfolio optimization considering the dependence structure of asset returns. European Journal of Operational Research, 244(2), 525-539. doi:10.1016/j.ejor.2015.01.025Ruiz, A. B., Saborido, R., Bermúdez, J. D., Luque, M., & Vercher, E. (2019). Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences. Journal of Global Optimization, 76(2), 295-315. doi:10.1007/s10898-019-00782-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hu, Y., Chen, H., He, M., Sun, L., Liu, R., & Shen, H. (2019). Multi-Swarm Multi-Objective Optimizer Based on p-Optimality Criteria for Multi-Objective Portfolio Management. Mathematical Problems in Engineering, 2019, 1-22. doi:10.1155/2019/8418369Rangel-González, J. A., Fraire, H., Solís, J. F., Cruz-Reyes, L., Gomez-Santillan, C., Rangel-Valdez, N., & Carpio-Valadez, J. M. (2020). Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem. International Journal of Fuzzy Systems, 22(8), 2760-2768. doi:10.1007/s40815-020-00928-4Garcia-Bernabeu, A., Salcedo, J. V., Hilario, A., Pla-Santamaria, D., & Herrero, J. M. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity, 2019, 1-12. doi:10.1155/2019/6095712Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Matlab Central: ev-MOGA Multiobjective Evolutionary Algorithmhttps://bit.ly/3f2BYQMBlasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

A Multi-Criteria Portfolio Analysis of Hedge Fund Strategies

This paper features a tri-criteria analysis of Eurekahedge fund data strategy index data. We use nine Eurekahedge equally weighted main strategy indices for the portfolio analysis. The tri-criteria analysis features three objectives: return, risk and dispersion of risk objectives in a Multi-Criteria Optimisation (MCO) portfolio analysis. We vary the MCO return and risk targets and contrast the results with four more standard portfolio optimisation criteria, namely the tangency portfolio (MSR), the most diversi_ed portfolio (MDP), the global minimum variance portfolio (GMW), and portfolios based on minimising expected shortfall (ERC). Backtests of the chosen portfolios for this hedge fund data set indicate that the use of MCO is accompanied by uncertainty about the a priori choice of optimal parameter settings for the decision criteria. The empirical results do not appear to outperform more standard bi-criteria portfolio analyses in the backtests undertaken on our hedge fund index data