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July  2020, 16(4): 1861-1871. doi: 10.3934/jimo.2019032

CVaR-based robust models for portfolio selection

Yufei Sun 1, , Ee Ling Grace Aw 2, , Bin Li 3,, , Kok Lay Teo 2, and  Jie Sun 2,4,

1. 

School of Mathematical Sciences, Chongqing Normal University, No. 12 Tianchen Road, Shapingba, Chongqing 400047, China
2. 

Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845, Australia
3. 

College of Electrical Engineering and Information Technology, Sichuan University, No. 24 Yihuan Road, Chengdu, Sichuan 610065, China
4. 

School of Science, Hebei University of Technology, No. 5340 Xiping Road, Beichen, Tianjin 300130, China

* Corresponding author: Bin Li

The first and the third to fifth author were saddened by Grace's passing, and dedicate this joint paper to her memory

Received  April 2018 Revised  October 2018 Published  July 2020 Early access  May 2019

Fund Project: This work was partially supported by a grant from National Natural Science Foundation of China under number 61701124, a grant from Science and Technology on Space Intelligent Control Laboratory for National Defence, No. KGJZDSYS-2018-03, a grant from Sichuan Science and Technology Program under number 2019YJ0105, and a grant from Fundamental Research Funds for the Central Universities (China)

This study relaxes the distributional assumption of the return of the risky asset, to arrive at the optimal portfolio. Studies of portfolio selection models have typically assumed that stock returns conform to the normal distribution. The application of robust optimization techniques means that only the historical mean and variance of asset returns are required instead of distributional information. We show that the method results in an optimal portfolio that has comparable return and yet equivalent risk, to one that assumes normality of asset returns.

Keywords: Portfolio optimization, risk measure, CVaR, distributionally robust optimization, conic optimization.
Mathematics Subject Classification: Primary: 90C15.
Citation: Yufei Sun, Ee Ling Grace Aw, Bin Li, Kok Lay Teo, Jie Sun. CVaR-based robust models for portfolio selection. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1861-1871. doi: 10.3934/jimo.2019032
References:
[1]

X. Q. Cai, K. L. Teo, X. Q. Yang and X. Y.Zhou, Portfolio optimization under a minimax rule, Management Science, 46 (2000), 957-972.  doi: 10.1287/mnsc.46.7.957.12039.

[2]

W. Chen, M. Sim, J. Sun and C. Teo, From CVaR to uncertain set: Implications in joint chance-constrained optimization, Operations Research, 58 (2010), 470-485.  doi: 10.1287/opre.1090.0712.

[3]

M. C. Chiu, H. Y. Wong and D. Li, Roy's safety-first portfolio principle in financial risk management of disastrous events, Risk Analysis, 32 (2012), 1856-1872.  doi: 10.1111/j.1539-6924.2011.01751.x.

[4]

X. T. Deng, Z. F. Li and S. Y. Wang, A minimax portfolio selection strategy with equilibrium, European Journal of Operational Research, 166 (2005), 278-292.  doi: 10.1016/j.ejor.2004.01.040.

[5]

H. Konno, Piecewise linear risk function and portfolio optimization, Journal of the Operations Research Society of Japan, 33 (1990), 139-156.  doi: 10.15807/jorsj.33.139.

[6]

H. Konno and K. Suzuki, A mean-variance-skewness optimization model, Journal of the Operations Research Society of Japan, 38 (1995), 137-187.  doi: 10.15807/jorsj.38.173.

[7]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science, 37 (1991), 501-623.  doi: 10.1287/mnsc.37.5.519.

[8]

B. Li, J. Sun, K. L. Teo, C. J. Yu and M. Zhang, A distributionally robust approach to a class of three-stage stochastic linear programs, Pacific Journal of Optimization, to appear.

[9]

B. Li, J. Sun, H. L. Xu and M. Zhang, A class of two-stage distributionally robust stochastic games, Journal of Industrial and Management Optimization, 15 (2019), 387-400. 

[10]

B. Li, Q. Xun, J. Sun, K. L. Teo and C. J. Yu, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Applied Mathematical Modelling, 58 (2018), 86-97.  doi: 10.1016/j.apm.2017.11.039.

[11]

B. Li, Y. Rong, J. Sun and K. L. Teo., A distributionally robust minimum variance beamformer design, IEEE Signal Processing Letters, 25 (2018), 105-109.  doi: 10.1109/LSP.2017.2773601.

[12]

B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, IEEE Transactions on Wireless Communications, 16 (2017), 464-474.  doi: 10.1109/TWC.2016.2625246.

[13]

X. Li and Z. Y. Wu, Dynamic Downside Risk Measure and Optimal Asset Allocation, Presented at FMA, 2006.

[14]

H. Markowitz, Portfolio Selection, The Journal of Finance, 7 (1952), 77-91. 

[15]

H. Markowitz, Portfolio Selection: Efficient Diversification of Investment, New York: John Wiley & Sons, 1959.

[16]

A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.  doi: 10.1137/050622328.

[17]

Y. Sun, G. Aw, K. L. Teo and G. Zhou, Portfolio optimization using a new probabilistic risk measure, Journal of Industrial and Management Optimization, 11 (2015), 1275-1283.  doi: 10.3934/jimo.2015.11.1275.

[18]

Y. Sun, G. Aw, K. L. Teo, Y. Zhu and X. Wang, Multi-period portfolio optimization under probabilistic risk measure, Finance Research Letter, 44 (2016), 801-807.  doi: 10.1016/j.orl.2016.10.006.

[19]

K. L. Teo and X. Q. Yang, Portfolio selection problem with minimax type risk function, Annals of Operations Research, 101 (2001), 333-349.  doi: 10.1023/A:1010909632198.

[20]

S. Zymler, D. Kuhn and B. Rustem, Distributionally robust jonit chance constraints with second-order moment information, Math. Program. Ser. A, 137 (2013), 167-198.  doi: 10.1007/s10107-011-0494-7.

show all references

References:
[1]

X. Q. Cai, K. L. Teo, X. Q. Yang and X. Y.Zhou, Portfolio optimization under a minimax rule, Management Science, 46 (2000), 957-972.  doi: 10.1287/mnsc.46.7.957.12039.

[2]

W. Chen, M. Sim, J. Sun and C. Teo, From CVaR to uncertain set: Implications in joint chance-constrained optimization, Operations Research, 58 (2010), 470-485.  doi: 10.1287/opre.1090.0712.

[3]

M. C. Chiu, H. Y. Wong and D. Li, Roy's safety-first portfolio principle in financial risk management of disastrous events, Risk Analysis, 32 (2012), 1856-1872.  doi: 10.1111/j.1539-6924.2011.01751.x.

[4]

X. T. Deng, Z. F. Li and S. Y. Wang, A minimax portfolio selection strategy with equilibrium, European Journal of Operational Research, 166 (2005), 278-292.  doi: 10.1016/j.ejor.2004.01.040.

[5]

H. Konno, Piecewise linear risk function and portfolio optimization, Journal of the Operations Research Society of Japan, 33 (1990), 139-156.  doi: 10.15807/jorsj.33.139.

[6]

H. Konno and K. Suzuki, A mean-variance-skewness optimization model, Journal of the Operations Research Society of Japan, 38 (1995), 137-187.  doi: 10.15807/jorsj.38.173.

[7]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science, 37 (1991), 501-623.  doi: 10.1287/mnsc.37.5.519.

[8]

B. Li, J. Sun, K. L. Teo, C. J. Yu and M. Zhang, A distributionally robust approach to a class of three-stage stochastic linear programs, Pacific Journal of Optimization, to appear.

[9]

B. Li, J. Sun, H. L. Xu and M. Zhang, A class of two-stage distributionally robust stochastic games, Journal of Industrial and Management Optimization, 15 (2019), 387-400. 

[10]

B. Li, Q. Xun, J. Sun, K. L. Teo and C. J. Yu, A model of distributionally robust two-stage stochastic convex programming with linear recourse, Applied Mathematical Modelling, 58 (2018), 86-97.  doi: 10.1016/j.apm.2017.11.039.

[11]

B. Li, Y. Rong, J. Sun and K. L. Teo., A distributionally robust minimum variance beamformer design, IEEE Signal Processing Letters, 25 (2018), 105-109.  doi: 10.1109/LSP.2017.2773601.

[12]

B. Li, Y. Rong, J. Sun and K. L. Teo, A distributionally robust linear receiver design for multi-access space-time block coded MIMO systems, IEEE Transactions on Wireless Communications, 16 (2017), 464-474.  doi: 10.1109/TWC.2016.2625246.

[13]

X. Li and Z. Y. Wu, Dynamic Downside Risk Measure and Optimal Asset Allocation, Presented at FMA, 2006.

[14]

H. Markowitz, Portfolio Selection, The Journal of Finance, 7 (1952), 77-91. 

[15]

H. Markowitz, Portfolio Selection: Efficient Diversification of Investment, New York: John Wiley & Sons, 1959.

[16]

A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2006), 969-996.  doi: 10.1137/050622328.

[17]

Y. Sun, G. Aw, K. L. Teo and G. Zhou, Portfolio optimization using a new probabilistic risk measure, Journal of Industrial and Management Optimization, 11 (2015), 1275-1283.  doi: 10.3934/jimo.2015.11.1275.

[18]

Y. Sun, G. Aw, K. L. Teo, Y. Zhu and X. Wang, Multi-period portfolio optimization under probabilistic risk measure, Finance Research Letter, 44 (2016), 801-807.  doi: 10.1016/j.orl.2016.10.006.

[19]

K. L. Teo and X. Q. Yang, Portfolio selection problem with minimax type risk function, Annals of Operations Research, 101 (2001), 333-349.  doi: 10.1023/A:1010909632198.

[20]

S. Zymler, D. Kuhn and B. Rustem, Distributionally robust jonit chance constraints with second-order moment information, Math. Program. Ser. A, 137 (2013), 167-198.  doi: 10.1007/s10107-011-0494-7.

Figure 1.  Efficient Frontier Comparison
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