Journal of Industrial and Systems Engineering

Journal of Industrial and Systems Engineering

Chance-constrained programming for Cryptocurrency portfolio optimization using Conditional Drawdown at Risk

Document Type : Research Paper

Authors
1 MSc Student in Industrial Engineering, Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
2 Iran University of Science and Technology
3 iran university of science and technology
4 Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
Abstract
Portfolio optimization is a widely studied problem in financial engineering literature. Its objective is to effectively distribute capital among different assets to maximize returns and minimize the risk of losing capital. Although portfolio optimization has been extensively investigated, there has been limited focus on optimizing portfolios consisting of cryptocurrencies, which are rapidly growing and emerging markets. The cryptocurrency market has demonstrated significant growth over the past two decades, offering potential profits but also presenting heightened risks compared to traditional financial markets. This situation creates challenges in constructing portfolios, necessitating the development of new and improved risk management models for cryptocurrency funds. This paper utilizes a new risk measurement approach called Conditional Drawdown at Risk (CDaR) in constructing portfolios within high-risk financial markets. Traditionally, portfolio optimization has been approached under certain conditions, considering risk and profit as decision criteria. However, recent approaches have addressed uncertainty in the decision-making process. To contribute to the advancement of scientific knowledge in this field, this paper proposes a new mathematical formulation of CDaR based on a chance-constrained programming (CCP) approach for portfolio optimization. To demonstrate the effectiveness of the proposed model, a practical empirical case study is conducted using real-world market data from 10 months focused on cryptocurrencies. The results obtained from this model can provide valuable guidance in making investment decisions in high-risk financial markets.
Keywords
Subjects

Abdollahi Moghadam, M., Ebrahimi, S. B., & Rahmani, D. (2019). A two-stage robust model for portfolio selection by using goal programming. Journal of Industrial and Systems Engineering, 12(1), 1–17. https://www.jise.ir/article_76604.html
Ackooij, W. v., Zorgati, R., Henrion, R., & Möller, A. (2011). Chance-constrained programming and its applications to energy management, and stochastic optimization. Anonymous InTech.
Aljinović, Z., Marasović, B., & Šestanović, T. (2021). Cryptocurrency Portfolio Selection—A Multicriteria Approach. Mathematics 2021, Vol. 9, Page 1677, 9(14), 1677. https://doi.org/10.3390/MATH9141677
Bagheriyan, M., Ghanbari, H., & Tohidi, H. (2023). The Impact of gold and oil prices on the Nasdaq Composite. 7th International Conference on Researches in Science & Engineering & 4th International Congress on Civil, Architecture and Urbanism in Asia.
Bielstein, P. and J. J.-P. and W. P. (2023). A Novel way to Diversify Portfolio Weights. Wilmott, 2023(128). https://doi.org/10.54946/WILM.1115896
Chang, C.-T. (2005). A modified goal programming approach for the mean-absolute deviation portfolio optimization model. Applied Mathematics and Computation, 171(1), 567-572.
Charles, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6(1), 73-79.
Chekhlov, A., Uryasev, S., & Zabarankin, M. (2004). Portfolio optimization with drawdown constraints. In Supply chain and finance (pp. 209-228). World Scientific.
Chekhov, A., Uryasev, S., & Zabarankin, M. (2000). Portfolio Optimization with Drawdown Constraints. https://doi.org/10.2139/ssrn.223323
Chen, Z., Peng, S., & Lisser, A. (2020). A sparse chance constrained portfolio selection model with multiple constraints. Journal of Global Optimization, 77(4), 825–852. https://doi.org/10.1007/S10898-020-00901-3/METRICS
Crama, Y., & Schyns, M. (2003). Simulated annealing for complex portfolio selection problems. European Journal of Operational Research, 150(3), 546-571.
Dolat-Abadi, H.M. Optimizing decisions of fresh-product members in daily and bourse markets considering the quantity and quality deterioration: A waste-reduction approach. J. Clean. Prod. 2021, 283, 124647.
Eskorouchi, A., Ghanbari, H., & Mohammadi, E. (2023). A Scientometric Analysis of Robust Portfolio Optimization. Iranian Journal of Accounting, Auditing and Finance. https://doi.org/10.22067/IJAAF.2023.84137.1402
FONG, K., GALLAGHER, D. R., & NG, A. (2005). The Use of Derivatives by Investment Managers and Implications for Portfolio Performance and Risk * . International Review of Finance, 5(1–2), 1–29. https://doi.org/10.1111/J.1468-2443.2006.00049.X
Fooeik, A. M. L., Ghanbari, H., Bagheriyan, M., & Mohammadi, E. (2022). Analyzing the effects of global oil, gold and palladium markets: Evidence from the Nasdaq composite index. Journal of Future Sustainability, 2(3), 105–112. https://doi.org/10.5267/J.JFS.2022.9.010
Gaskin, S., Kalim, R., Wallace, K. J., Islip, D., Kwon, R. H., & Liew, J. K. S. (2023). Portfolio Optimization Techniques for Cryptocurrencies. Journal of Investing, 32(3), 50–65. https://doi.org/10.3905/JOI.2023.1.256
Geletu, A., & Ilmenau, T. (2012). Chance-constrained constrained optimization applications, properties, and numerical issues. Lilmenau Univ. Technol.
Ghanbari, H., Fooeik, A. M. L., Eskorouchi, A., & Mohammadi, E. (2022). Investigating the effect of US dollar, gold and oil prices on the stock market. Journal of Future Sustainability, 2(3), 97–104. https://doi.org/10.5267/J.JFS.2022.9.009
Ghanbari, H., Safari, M., Ghousi, R., Mohammadi, E., & Nakharutai, N. (2023a). Bibliometric analysis of risk measures for portfolio optimization. Accounting, 9(2), 95–108. https://doi.org/10.5267/J.AC.2022.12.003
Ghanbari, H., Shabani, M., & Mohammadi, E. (2023b). Portfolio Optimization with Conditional Drawdown at Risk for the Automotive Industry. Automotive Science and Engineering, 13(4), 4236–4242. https://doi.org/10.22068/ASE.2023.647
Ghazanfari, M., Mohammadi, H., Pishvaee, M.S., & Teimoury, E. (2019). Fresh-Product Trade Management Under Government-Backed Incentives: A Case Study of Fresh Flower Market. IEEE Transactions on Engineering Management, 66, 774-787.
Gotoh, J.-y., & Konno, H. (2000). Third-degree stochastic dominance and mean-risk analysis. Management Science, 46(2), 289-301.
Hauser, R., Krishnamurthy, V., & Tütüncü, R. (2018). Robust portfolio optimization based on minimax regret approach in Tehran stock exchange market. Journal of Industrial and Systems Engineering, 11(Special issue: 14th International Industrial Engineering Conference), 51–62. https://www.jise.ir/article_69383.html
Hrytsiuk, P., Babych, T., & Bachyshyna, L. (2019). Cryptocurrency portfolio optimization using Value-at-Risk measure. 385–389. https://doi.org/10.2991/SMTESM-19.2019.75
Jiang, R., & Guan, Y. (2016). Data-driven chance-constrained stochastic program. Mathematical Programming, 158(1-2), 291-327.
Khalili-Fard, A., Tavakkoli-Moghaddam, R., Abdali, N., Alipour-Vaezi, M., & Bozorgi-Amiri, A. (2024). A roommate problem and room allocation in dormitories using mathematical modeling and multi-attribute decision-making techniques. Journal of Modelling in Management, ahead-of-print(ahead-of-print). https://doi.org/10.1108/JM2-09-2023-0214/FULL/XML
Konno, H., & Wijayanayake, A. (2001). Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming, 89, 233-250.
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to the Tokyo stock market. Management Science, 37(5), 519-531.
Koumou, G. B. (2020). Diversification and portfolio theory: a review. Financial Markets and Portfolio Management, 34(3), 267–312. https://doi.org/10.1007/S11408-020-00352-6/METRICS
Krokhmal, P., Uryasev, S., & Zrazhevsky, G. (2005). Numerical comparison of conditional value-at-risk and conditional drawdown-at-risk approaches: application to hedge funds. In Applications of stochastic programming (pp. 609-631). SIAM.
Kurosaki, T., & Kim, Y. S. (2022). Cryptocurrency portfolio optimization with multivariate normal tempered stable processes and Foster-Hart risk. Finance Research Letters, 45, 102143. https://doi.org/10.1016/J.FRL.2021.102143
Larni-Fooeik, A. M., Ghanbari, H., Shabani, M., & Mohammadi, E. (2024). Bi-Objective Portfolio Optimization with Mean-CVaR Model: An Ideal and Anti-Ideal Compromise Programming Approach. Studies in Systems, Decision and Control, 518, 69–79. https://doi.org/10.1007/978-3-031-51719-8_5
Larni-Fooeik, A. M., Sadjadi, S. J., & Mohammadi, E. (2024). Stochastic portfolio optimization: A regret-based approach on volatility risk measures: An empirical evidence from The New York stock market. PLOS ONE, 19(4), e0299699. https://doi.org/10.1371/JOURNAL.PONE.0299699
Li, X., Qin, Z., & Yang, L. (2010). A chance-constrained portfolio selection model with risk constraints. Applied Mathematics and Computation, 217(2), 949–951. https://doi.org/10.1016/J.AMC.2010.06.035
Ma, Y., Ahmad, F., Liu, M., & Wang, Z. (2020). Portfolio optimization in the era of digital financialization using cryptocurrencies. Technological Forecasting and Social Change, 161, 120265. https://doi.org/10.1016/J.TECHFORE.2020.120265
Markovitz, H. M. (1959). Portfolio selection: Efficient diversification of investments. John Wiley.
Markowitz, H. (1952). The Utility of Wealth. Https://Doi.Org/10.1086/257177, 43–50. https://doi.org/10.1086/257177
Markowitz, H. M. (1991). Foundations of portfolio theory. The journal of finance, 46(2), 469-477.
Mohammadi, E. (2018). Portfolio Optimization Using Chance Constrained Compromise Programming. Financial Engineering and Portfolio Management, 2(35), 221.
Mohammadi, H., Ghazanfari, M., Teimouri, E., Pishvaee, M. S. (2018). Optimization of Transactions in the Plant and Flower Organized Market Considering Third-Party Logistics Company under Uncertainty. Modern Research in Decision Making, 2018; 2(4): 179-205.
Mousavi Loleti, S. A., Ghanbari, H., & Mohammadi, E. (2024). Portfolio optimization using the semi-variance model with a focus on positive potential (Case study: Tehran Stock Exchange). Budget and Finance Strategic Research, 5(1), 57–78. https://fbarj.ihu.ac.ir/article_208951_en.html
Nouri, M., Pishvaee, M. S., & Mohammadi, E. (2023). A Novel Multi-Stage Stochastic Portfolio Optimization Model Under Transaction Costs. Decision Making: Theory and Practice.
Nozari, H., Ghahremani-Nahr, J., Fallah, M., & Szmelter-Jarosz, A. (2022). Assessment of cyber risks in an IoT-based supply chain using a fuzzy decision-making method. International Journal of Innovation in Management, Economics and Social Sciences, 2(1).
Ogryczak, W. (2000). Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97(1-4), 143-162.
Peykani, P., Mohammadi, E., & Emrouznejad, A. (2021). An adjustable fuzzy chance-constrained network DEA approach with application to ranking investment firms. Expert systems with applications, 166, 113938.
Rahmaty, M., & Nozari, H. (2023). Optimization of the hierarchical supply chain in the pharmaceutical industry. Edelweiss Applied Science and Technology, 7(2), 104-123.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21-42.
Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities. Computers & chemical engineering, 28(6-7), 971-983.
Shing, C., & Nagasawa, H. (1999). Interactive decision system in stochastic multiobjective portfolio selection. International Journal of Production Economics, 60, 187-193.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The review of economic studies, 25(2), 65-86.
Zarezade, R, Ghousi, R, & Mohammadi, E. (2023). Spillover effects of volatility between the Chinese stock market and selected emerging economies in the Middle East: A conditional correlation analysis with portfolio optimization perspective Accounting, 10.5267/j.ac.2023.11.001.
Volume 16, Issue 2 - Serial Number 2
Spring 2024
Pages 130-153

  • Receive Date 24 January 2024
  • Revise Date 16 March 2024
  • Accept Date 30 March 2024