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Robust portfolio optimization with fuzzy TODIM, genetic algorithm and multi-criteria constraints

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Abstract

This paper adopts the multi-criterion decision-making model of fuzzy-TODIM and genetic algorithm (GA) for optimal portfolio allocation. We applied Markowitz’s portfolio parameters as inputs for the fuzzy TODIM model to rank stocks that are constituents of each index from three different markets. Portfolios are then generated dynamically using three weighting techniques and subject to multi-objective criteria and additional constraints. The results indicate a significant variation in performance metrics between the model-generated portfolios and the market indices. Replication of the procedure produces a similar outcome. Moreover, the out-of-sample tests conducted over 3 years validate the results’ robustness, indicating that fuzzy TODIM, combined with GA, can achieve superior performance in dynamic portfolio allocation.

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Notes

  1. MCDM models include a wide variety like tabu search, genetic algorithm, and simulated annealing (Chang et al., 2000; Ehrgott et al., 2004; Liu & Zhang, 2015); multi-objective evolutionary algorithm (Branke et al., 2009); particle swarm optimization (Deng et al., 2012; Kaucic, 2019), artificial bee colony (Chen, 2015), and fireworks algorithm (Zhang & Liu, 2017) which have been widely adapted to address multiple objectives as well as constraints in portfolio optimization.

  2. For details, see Xiao et al. (2012)

  3. Throughout this paper, we have reported the results only for the Indian market for the sake of brevity. The findings regarding the United States and United Kingdom markets (S&P 500 and FTSE 100) can be found in the Appendix.

  4. We have experimented with various combinations of lower and upper limits for all three indexes.

  5. The results of S&P 500 and FTSE 100 emulate that of Nifty 50 index.

  6. We have not reported the Sharpe’s results for the sake of brevity and be sourced from the authors on request. We have also used alternative techniques for validation.

References

  • Alali, F., & Tolga, A. C. (2019). Portfolio allocation with the TODIM method. Expert Systems with Applications, 124, 341–348.

    Article  Google Scholar 

  • Alexeev, V., & Dungey, M. (2015). Equity portfolio diversification with high frequency data. Quantitative Finance, 15(7), 1205–1215.

    Article  Google Scholar 

  • Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285–1297.

    Article  Google Scholar 

  • Ballestero, E., Günther, M., Pla-Santamaria, D., & Stummer, C. (2007). Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges. European Journal of Operational Research, 181(3), 1476–1487.

    Article  Google Scholar 

  • Banerjee, A. K. (2021). Futures market and the contagion effect of COVID-19 syndrome. Finance Research Letters, 43, 102018.

    Article  Google Scholar 

  • Banerjee, A. K. (2022). You sneeze, and the markets are paranoid: The fear, uncertainty and distress sentiments impact of the COVID-19 pandemic on the stock–bond correlation. The Journal of Risk Finance, 23(5), 652–668.

    Article  Google Scholar 

  • Banerjee, A. K., Akhtaruzzaman, M., Dionisio, A., Almeida, D., & Sensoy, A. (2022). Nonlinear nexus between cryptocurrency returns and COVID–19 COVID-19 news sentiment. Journal of Behavioral and Experimental Finance, 36, 100747.

    Article  Google Scholar 

  • Biglova, A., Ortobelli, S., Rachev, S. T., & Stoyanov, S. (2004). Different approaches to risk estimation in portfolio theory. The Journal of Portfolio Management, 31(1), 103–112.

    Article  Google Scholar 

  • Bjerring, T. T., Ross, O., & Weissensteiner, A. (2017). Feature selection for portfolio optimization. Annals of Operations Research, 256, 21–40.

    Article  Google Scholar 

  • Borkovec, M., Domowitz, I., Kiernan, B., & Serbin, V. (2010). Portfolio optimization and the cost of trading. The Journal of Investing, 19(2), 63–76.

    Article  Google Scholar 

  • Brandes, Y., Domowitz, I., & Serbin, V. (2012). Transaction costs and equity portfolio capacity analysis. In B. Scherer & K. Winston (Eds.), The Oxford Handbook of Quantitative Asset Management. Oxford University Press.

    Google Scholar 

  • Brandtner, M. (2013). Conditional Value-at-Risk, spectral risk measures and (non-) diversification in portfolio selection problems–A comparison with mean–variance analysis. Journal of Banking & Finance, 37(12), 5526–5537.

    Article  Google Scholar 

  • Branke, J., Scheckenbach, B., Stein, M., Deb, K., & Schmeck, H. (2009). Portfolio optimization with an envelope-based multi-objective evolutionary algorithm. European Journal of Operational Research, 199(3), 684–693.

    Article  Google Scholar 

  • Brown, D. B., & Smith, J. E. (2011). Dynamic portfolio optimization with transaction costs: Heuristics and dual bounds. Management Science, 57(10), 1752–1770.

    Article  Google Scholar 

  • Cavaglia, S., Fan, J. H., & Wang, Z. (2022). Portable beta and total portfolio management. Financial Analysts Journal, 78(3), 49–69.

    Article  Google Scholar 

  • Chang, K. H., & Young, M. N. (2019). Behavioral stock portfolio optimization considering holding periods of B-stocks with short-selling. Computers & Operations Research, 112, 104773.

    Article  Google Scholar 

  • Chang, K. H., Young, M. N., Liu, C. C., & Chung, H. P. (2018). Behavioral stock portfolio optimization through short-selling. International Journal of Modeling and Optimization, 8(2), 125–130.

    Article  Google Scholar 

  • Chang, T. J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimization. Computers & Operations Research, 27(13), 1271–1302.

    Article  Google Scholar 

  • Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica a: Statistical Mechanics and Its Applications, 429, 125–139.

    Article  Google Scholar 

  • DeMiguel, V., Garlappi, L., & Uppal, R. (2009). How inefficient are simple asset allocation strategies? Review of Financial Studies, 22(5), 1915–1953.

    Article  Google Scholar 

  • Deng, G. F., Lin, W. T., & Lo, C. C. (2012). Markowitz-based portfolio selection with cardinality constraints using improved particle swarm optimization. Expert Systems with Applications, 39(4), 4558–4566.

    Article  Google Scholar 

  • Diaz-Balteiro, L., González-Pachón, J., & Romero, C. (2017). Measuring systems sustainability with multi-criteria methods: A critical review. European Journal of Operational Research, 258, 607–616.

    Article  Google Scholar 

  • Edelen, R., Evans, R., & Kadlec, G. (2013). Shedding light on “invisible” costs: Trading costs and mutual fund performance. Financial Analysts Journal, 69(1), 33–44.

    Article  Google Scholar 

  • Ehrgott, M., Klamroth, K., & Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3), 752–770.

    Article  Google Scholar 

  • Fabozzi, F. J., Huang, D., & Zhou, G. (2010). Robust portfolios: Contributions from operations research and finance. Annals of Operations Research, 176, 191–220.

    Article  Google Scholar 

  • Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007). Robust portfolio optimization. The Journal of Portfolio Management, 33(3), 40–48.

    Article  Google Scholar 

  • Galagedera, D. U., Fukuyama, H., Watson, J., & Tan, E. K. (2020). Do mutual fund managers earn their fees? New measures for performance appraisal. European Journal of Operational Research, 287(2), 653–667.

    Article  Google Scholar 

  • Gomes, L. F. A. M., & Lima, M. M. P. P. (1992). TODIM: Basics and application to multi-criteria ranking of projects with environmental impacts. Foundations of Computing and Decision Sciences, 16, 113–127.

    Google Scholar 

  • Hafner, C. M., & Wang, L. (2022). Dynamic portfolio selection with sector-specific regularization. Econometrics and Statistics. https://doi.org/10.1016/j.ecosta.2022.01.001

    Article  Google Scholar 

  • Hatami-Marbini, A., & Kangi, F. (2017). An extension of fuzzy TOPSIS for a group decision making with an application to Tehran stock exchange. Applied Soft Computing, 52, 1084–1097.

    Article  Google Scholar 

  • Hoberg, G., Kumar, N., & Prabhala, N. (2017). Mutual fund competition, managerial skill, and alpha persistence. The Review of Financial Studies, 31(5), 1896–1929.

    Article  Google Scholar 

  • Jacobs, B. I., Levy, K. N., & Markowitz, H. M. (2005). Portfolio optimization with factors, scenarios, and realistic short positions. Operations Research, 53(4), 586–599.

    Article  Google Scholar 

  • Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263–291.

    Article  Google Scholar 

  • Kaucic, M. (2019). Equity portfolio management with cardinality constraints and risk parity control using multi-objective particle swarm optimization. Computers & Operations Research, 109, 300–316.

    Article  Google Scholar 

  • Kellner, F., Lienland, B., & Utz, S. (2019). An a posteriori decision support methodology for solving the multi-criteria supplier selection problem. European Journal of Operational Research, 272(2), 505–522.

    Article  Google Scholar 

  • Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2018). Recent advancements in robust optimization for investment management. Annals of Operations Research, 266, 183–198.

    Article  Google Scholar 

  • Kobayashi, K., Takano, Y., & Nakata, K. (2023). Cardinality-constrained distributionally robust portfolio optimization. European Journal of Operational Research., 309(3), 1173–1182.

    Article  Google Scholar 

  • Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371.

    Article  Google Scholar 

  • Krohling, R. A., & de Souza, T. T. (2012). Combining prospect theory and fuzzy numbers to multi-criteria decision making. Expert Systems with Applications, 39, 11487–11493.

    Article  Google Scholar 

  • Li, J., & Xu, J. (2013). Multi-objective portfolio selection model with fuzzy random returns and a compromise approach-based genetic algorithm. Information Sciences, 220, 507–521.

    Article  Google Scholar 

  • Lin, C. C., & Liu, Y. T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research, 185(1), 393–404.

    Article  Google Scholar 

  • Liu, Y. J., & Zhang, W. G. (2015). A multi-period fuzzy portfolio optimization model with minimum transaction lots. European Journal of Operational Research, 242(3), 933–941.

    Article  Google Scholar 

  • Loistl, O. (2015). Does mean-variance portfolio management deserve expected utility’s approximative affirmation? European Journal of Operational Research, 247(2), 676–680.

    Article  Google Scholar 

  • Lourenzutti, R., & Krohling, R. A. (2013). A study of TODIM in an intuitionistic fuzzy and random environment. Expert Systems with Applications, 40(16), 6459–6468.

    Article  Google Scholar 

  • Lwin, K. T., Qu, R., & MacCarthy, B. L. (2017). Mean-VaR portfolio optimization: A nonparametric approach. European Journal of Operational Research, 260(2), 751–766.

    Article  Google Scholar 

  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7, 77–91.

    Google Scholar 

  • Markowitz, H. (2014). Mean-variance approximations to expected utility. European Journal of Operational Research, 234(2), 346–355.

    Article  Google Scholar 

  • Marttunen, M., Lienert, J., & Belton, V. (2017). Structuring problems for multi-criteria decision analysis in practice: A literature review of method combinations. European Journal of Operational Research, 263, 1–17.

    Article  Google Scholar 

  • Petajisto, A. (2013). Active share and mutual fund performance. Financial Analysts Journal, 69(4), 73–93.

    Article  Google Scholar 

  • Petchrompo, S., Wannakrairot, A., & Parlikad, A. K. (2022). Pruning Pareto optimal solutions for multi-objective portfolio asset management. European Journal of Operational Research, 297(1), 203–220.

    Article  Google Scholar 

  • Qi, R., & Yen, G. G. (2017). Hybrid bi-objective portfolio optimization with pre-selection strategy. Information Sciences, 417, 401–419.

    Article  Google Scholar 

  • Statman, M. (1987). How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis, 22(3), 353–363.

    Article  Google Scholar 

  • Tang, G. Y. (2004). How efficient is naive portfolio diversification? An Educational Note. Omega, 32(2), 155–160.

    Google Scholar 

  • Vetschera, R., & De Almeida, A. T. (2012). A PROMETHEE-based approach to portfolio selection problems. Computers & Operations Research, 39(5), 1010–1020.

    Article  Google Scholar 

  • Woodside-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.

    Article  Google Scholar 

  • Wu, Q., Liu, X., Qin, J., Zhou, L., Mardani, A., & Deveci, M. (2022). An integrated multi-criteria decision-making and multi-objective optimization model for socially responsible portfolio selection. Technological Forecasting and Social Change, 184, 121977.

    Article  Google Scholar 

  • Xiao, Z., Xia, S., Gong, K., & Li, D. (2012). The trapezoidal fuzzy soft set and its application in MCDM. Applied Mathematical Modelling, 36(12), 5844–5855.

    Article  Google Scholar 

  • Xidonas, P., Mavrotas, G., Zopounidis, C., & Psarras, J. (2011). IPSSIS: An integrated multi-criteria decision support system for equity portfolio construction and selection. European Journal of Operational Research, 210(2), 398–409.

    Article  Google Scholar 

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  Google Scholar 

  • Zhang, T., & Liu, Z. (2017). Fireworks algorithm for mean-VaR/CVaR models. Physica a: Statistical Mechanics and Its Applications, 483, 1–8.

    Article  Google Scholar 

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Authors and Affiliations

  1. XLRI -Xavier School of Management, Jamshedpur, Jharkhand, India

    Ameet Kumar Banerjee & H. K. Pradhan

  2. Faculty of Business Administration, Bilkent University, Ankara, Turkey

    Ahmet Sensoy

  3. Adnan Kassar School of Business, Lebanese American University, Beirut, Lebanon

    Ahmet Sensoy

  4. Carey Business School, Johns Hopkins University, Baltimore, USA

    Frank Fabozzi

  5. XIM, XIM University, Bhubaneswar, India

    Biplab Mahapatra

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  1. Ameet Kumar Banerjee
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  2. H. K. Pradhan
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  3. Ahmet Sensoy
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  4. Frank Fabozzi
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  5. Biplab Mahapatra
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Correspondence to Frank Fabozzi.

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Appendix

Appendix

See Table 

Table 4 Alternative rankings of stocks for the case of TODIM and F-TODIM method
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4 and

Table 5 Number of portfolios that beat the S&P 500 and FTSE 100 index with cardinality, round-lot constraint, and transaction cost
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5, Figs.

Fig. 8
figure 8

Unconstrained portfolio with 100 stocks. A indicates the efficient frontier of an unconstrained portfolio with n = 100 securities. B–F represents the holding period returns of the portfolio against the S&P 500 US Stock Index

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8 and

Fig. 9
figure 9

Unconstrained portfolio with 100 stocks. A indicates the efficient frontier of an unconstrained portfolio with n = 100 securities. B–F represents the holding period returns of the portfolio against the FTSE 100 UK Stock Index

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9.

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Banerjee, A.K., Pradhan, H.K., Sensoy, A. et al. Robust portfolio optimization with fuzzy TODIM, genetic algorithm and multi-criteria constraints. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05865-1

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