基于横截面回归和Fama-MacBeth估计的鲁棒投资组合优化问题研究

doi:10.15960/j.cnki.issn.1007-6093.2021.03.008

Abstract

Abstract: This paper considers a factor model different from Goldfarb and Iyengar (2003) and the uncertainty set for the mean profit vector and covariance matrix of the assets in the robust problems are constructed by the cross-sectional regression and Fama-MacBeth estimator. Based on the robust portfolio selection problems under the Markowitz mean-variance model and these uncertainty sets, we prosed multiple robust portfolio selection problems and prove that these problems can be re-written as Semidefinite programmings which are computationally tractable.

Key words: robust optimization, mean-variance model, cross-section regression, Semidefinite programming

CLC Number:

F224.3
O224

JIANG Bo, ZHU Xihua. Robust portfolio selection based on cross-sectional regression and Fama-Macbeth estimator[J]. Operations Research Transactions, 2021, 25(3): 133-146.

References

[1] Donald Goldfarb, Garud Iyengar. Robust portfolio selection problems[J]. Mathematics of Operations Research, 2003, 28(1):1-38.
[2] Harry M Markowitz. Protfolio selection[J]. The Journal of Finance, 1952, 7:77-91.
[3] Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski. Robust Optimization[M]. Princeton:Princeton university press, 2009.
[4] Aharon Ben-Tal, Arkadi Nemirovski. Robust convex optimization[J]. Mathematics of Operations Research, 1998, 23(4):769-805.
[5] Aharon Ben-Tal, Arkadi Nemirovski. Robust solutions of uncertain linear programs[J]. Operations Research Letters, 1999, 25(1):1-13.
[6] Aharon Ben-Tal, Arkadi Nemirovski. Robust solutions of linear programming problems contaminated with uncertain data[J]. Mathematical Programming, 2000, 88(3):411-424.
[7] Donald Goldfarb, Garud Iyengar. Robust convex quadratically constrained programs[J]. Mathematical Programming, 2003, 97(3):495-515.
[8] Allen L Soyster. Convex programming with set-inclusive constraints and applications to inexact linear programming[J]. Operations Research, 1973, 21(5):1154-1157.
[9] Dimitris Bertsimas, Melvyn Sim. The price of robustness[J]. Operations Research, 2004, 52(1):35-53.
[10] José Manuel Berutich, Francisco López, Francisco Luna, et al. Robust technical trading strategies using gp for algorithmic portfolio selection[J]. Expert Systems with Applications, 2016, 46:307-315.
[11] Giuseppe C Calafiore. Ambiguous risk measures and optimal robust portfolios[J]. SIAM Journal on Optimization, 2007, 18(3):853-877.
[12] Jörg Fliege, Ralf Werner. Robust multiobjective optimization & applications in portfolio optimization[J]. European Journal of Operational Research, 2014, 234(2):422-433.
[13] Paul Glasserman, Xingbo Xu. Robust portfolio control with stochastic factor dynamics[J]. Operations Research, 2013, 61(4):874-893.
[14] Takashi Hasuike, Mukesh Kumar Mehlawat. Investor-friendly and robust portfolio selection model integrating forecasts for financial tendency and risk-averse[J]. Annals of Operations Research, 2018, 269(1):205-221.
[15] Ai-fan Ling, Cheng-xian Xu. Robust portfolio selection involving options under a "marginal+ joint" ellipsoidal uncertainty set[J]. Journal of Computational and Applied Mathematics, 2012, 236(14):3373-3393.
[16] Somayyeh Lotfi, Stavros A Zenios. Robust var and cvar optimization under joint ambiguity in distributions, means, and covariances[J]. European Journal of Operational Research, 2018, 269(2):556-576.
[17] Zhaosong Lu. A computational study on robust portfolio selection based on a joint ellipsoidal uncertainty set[J]. Mathematical Programming, 2011, 126(1):193-201.
[18] Zhaosong Lu. Robust portfolio selection based on a joint ellipsoidal uncertainty set[J]. Optimization Methods & Software, 2011, 26(1):89-104.
[19] Karthik Natarajan, Dessislava Pachamanova, Melvyn Sim. Incorporating asymmetric distributional information in robust value-at-risk optimization[J]. Management Science, 2008, 54(3):573-585.
[20] Berc Rustem, Robin G Becker, Wolfgang Marty. Robust min-max portfolio strategies for rival forecast and risk scenarios[J]. Journal of Economic Dynamics and Control, 2000, 24(11-12):1591-1621.
[21] Napat Rujeerapaiboon, Daniel Kuhn, Wolfram Wiesemann. Robust growth-optimal portfolios[J]. Management Science, 2016, 62(7):2090-2109.
[22] Dedi Rosadi, Ezra Putranda Setiawan, Matthias Templ, et al. Robust covariance estimators for mean-variance portfolio optimization with transaction lots[J]. Operations Research Perspectives, 2020, 7:100154.
[23] Ruijun Shen, Shuzhong Zhang. Robust portfolio selection based on a multi-stage scenario tree[J]. European Journal of Operational Research, 2008, 191(3):864-887.
[24] Shushang Zhu, Masao Fukushima. Worst-case conditional value-at-risk with application to robust portfolio management[J]. Operations Research, 2009, 57(5):1155-1168.
[25] Dimitris Bertsimas, David B Brown, Constantine Caramanis. Theory and applications of robust optimization[J]. SIAM Review, 2011, 53(3):464-501.
[26] Li Chen, Simai He, Shuzhong Zhang. Tight bounds for some risk measures, with applications to robust portfolio selection[J]. Operations Research, 2011, 59(4):847-865.
[27] Victor DeMiguel, Francisco J Nogales. Portfolio selection with robust estimation[J]. Operations Research, 2009, 57(3):560-577.
[28] Erick Delage, Yinyu Ye. Distributionally robust optimization under moment uncertainty with application to data-driven problems[J]. Operations Research, 2010, 58(3):595-612.
[29] Adrian Gepp, Geoff Harris, Bruce Vanstone. Financial applications of semidefinite programming:a review and call for interdisciplinary research[J]. Accounting & Finance, 2020, 60(4):3527-3555.
[30] Mustafa Ç Pınar. On robust mean-variance portfolios[J]. Optimization, 2016, 65(5):1039-1048.
[31] Ioana Popescu. Robust mean-covariance solutions for stochastic optimization[J]. Operations Research, 2007, 55(1):98-112.
[32] Raghu Nandan Sengupta, Rakesh Kumar. Robust and reliable portfolio optimization formulation of a chance constrained problem[J]. Foundations of Computing and Decision Sciences, 2017, 42(1):83-117.
[33] Joong-Ho Won, Seung-Jean Kim. Robust trade-off portfolio selection[J]. Optimization and Engineering, 2020, 21(3):867-904.
[34] Eugene F Fama. Mandelbrot and the stable paretian hypothesis[J]. Journal of Business, 1963, 36(4):420-429.
[35] François M Longin. The asymptotic distribution of extreme stock market returns[J]. Journal of Business, 1996, 69(3):383-408.
[36] Shushang Zhu, Minjie Fan, Duan Li. Portfolio management with dual robustness in prediction and optimization:A mixture model based learning approach[J]. SSRN Electronic Journal, 2013, 117(1):1-7.
[37] Dimitris Bertsimas, Vishal Gupta, Nathan Kallus. Data-driven robust optimization[J]. Mathematical Programming, 2018, 167(2):235-292.
[38] Taozeng Zhu, Jingui Xie, Melvyn Sim. Joint estimation and robustness optimization[J/OL]. (2021-02-26)[2021-03-21]. Management Science, https://doi.org/10.1287/mnsc.2020.3898.
[39] Amit Goyal. Empirical cross-sectional asset pricing:a survey[J]. Financial Markets and Portfolio Management, 2012, 26(1):3-38.
[40] Eugene F Fama, James D MacBeth. Risk, return, and equilibrium:Empirical tests[J]. Journal of Political Economy, 1973, 81(3):607-636.
[41] Tze Leung Lai, Haipeng Xing. Statistical Models and Methods for Financial Markets[M]. New York:Springer, 2008.
[42] Vladimir A Yakubovich. S-procedure in nolinear control theory[J]. Vestnik Leninggradskogo Universiteta, Seriya Matematika, 1971, (1):62-77.

Robust portfolio selection based on cross-sectional regression and Fama-Macbeth estimator

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 14

Recommended Articles

Metrics

Comments

[1]	ZHONG Weiya, SHI Yimei. Robust optimization of rehearsal scheduling under uncertain duration [J]. Operations Research Transactions, 2020, 24(3): 77-86.
[2]	GENG Xiaolu, TONG Xiaojiao. A review on distributionally robust chance constrained optimization problems [J]. Operations Research Transactions, 2020, 24(1): 115-130.
[3]	LI Jianling, ZHANG Hui, YANG Zhenping, JIAN Jinbao. A globally convergent SSDP algorithm without a penalty function or a filter for nonlinear semidefinite programming [J]. Operations Research Transactions, 2018, 22(4): 1-16.
[4]	WANG Feng, LIU Sanyang. Pareto efficiency in robust optimization [J]. Operations Research Transactions, 2018, 22(4): 141-147.
[5]	WANG Yishui, XU Dachuan, WU Chenchen. A semidefinite programming rounding algorithm for correlation clustering problem [J]. Operations Research Transactions, 2018, 22(1): 67-76.
[6]	CHEN Zhongwen, ZHAO Qi, BIAN Kai. A successive linearization method with flexible penalty for nonlinear semidefinite programming [J]. Operations Research Transactions, 2017, 21(2): 84-100.
[7]	YUAN Chunhong. The epsilon-weak proper efficiency of multiobjective semidefinite programming with set-valued maps [J]. Operations Research Transactions, 2017, 21(1): 23-32.
[8]	LI Yongling, YANG Yang, LUO Honglin. The optimality conditions and duality theory for multiobjective semidefinite programming [J]. Operations Research Transactions, 2016, 20(3): 68-78.
[9]	SUN Ting, LI Gaidi, XU Wenqing. Approximation algorithms for max cut and max bisection problems using semi-definite programming relaxations [J]. Operations Research Transactions, 2016, 20(3): 21-32.
[10]	LI Jianling, YANG Zhenping, JIAN Jinbao. Introduction of some algorithms for nonlinear semidefinite programming [J]. Operations Research Transactions, 2016, 20(2): 1-22.
[11]	YANG Yang, LUO Honglin, LUO Huilin. A note on a wide neighborhood infeasible interior-point algorithm for semidefinite programming [J]. Operations Research Transactions, 2016, 20(2): 79-87.
[12]	FENG Zengzhe, ZHANG Xixue, LIU Jianbo$, FANG Liang. A new wide neighborhood infeasible interior-point algorithm for semidefinite programming [J]. Operations Research Transactions, 2014, 18(2): 49-58.
[13]	LIANG Xikun, XU Chengxian, ZHENG Dong. The research progress of robust portfolio optimization [J]. Operations Research Transactions, 2014, 18(2): 87-95.
[14]	HAN Yingwei, XIA Yong. A dual method for the pose estimation problem [J]. Operations Research Transactions, 2013, 17(3): 86-92.