A Risk-Free Protection Index Model for Multi-Objective Uncertain Portfolio Selection with Entropy and Variance Constraints

doi:10.23940/ijpe.18.12.p22.31293139

Abstract

Abstract:

This paper discusses a multi-objective portfolio in the case where the distributions of security returns are subject to reputable experts' evaluations instead of historical data. Based on the assumption that the security returns of risk assets are uncertain variables, we put forward a new risk-free protection index (RFPI) model for multi-objective uncertain portfolio selections with entropy and variance constraints by using expected value as a measurement of portfolio return and take both variance and RFPI as measurements of a portfolio's risk measurements. To determine a suitable confidence level and criticality value of FRPI, we regard FRPI maximization as the second goal under the premise of maximum expected return rather than relying on the investors' risk preference and tolerance. To avoid excessive dispersion or concentration of investment, the proportion entropy and variance constraints are added to the FRPI model. The Delphi method is used to solve our model, and its algorithm is also shown. In the ending example, a comparative analysis is illustrated to show our multi-objective uncertain portfolio model with FRPI maximization added as the second objective function performs better than the traditional mean-variance model (MVM) and the risk-free protection index-entropy model (RFPIEM).

Key words: multi-objective portfolio selection, risk-free protection index, entropy constraint, uncertain variable

Jianwei Gao and Huicheng Liu. A Risk-Free Protection Index Model for Multi-Objective Uncertain Portfolio Selection with Entropy and Variance Constraints [J]. Int J Performability Eng, 2018, 14(12): 3129-3139.

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Figures/Tables 9

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References 10

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Assets	Stock 1	Stock 2	Stock 3	Stock 4	Bonds	Risk-free asset
Weight	0.0508	0.0655	0.0522	0.1127	0.1971	0.5217
RFPI	Variance	Expected return rate	VaRU(0.9)
0.10	0.01	0.0796	0.0856

Assets	Stock 1	Stock 2	Stock 3	Stock 4	Bonds	Risk-free asset
Weight	0.0804	0.0865	0.0370	0.1973	0.0878	0.5110
RFPI	Variance	Expected return rate	VaRU(0.9)
0.20	0.01	0.1002	0.1105

RFPI	Stock 1	Stock 2	Stock 3	Stock 4	Bonds	Risk-free asset	Expected return rate	Variance	VaRU
10%	0.0873	0.1277	0.0324	0.2151	0.0375	0.5000	0.1052	0.0100	0.1296
20%	0.0804	0.0865	0.0370	0.1973	0.0878	0.5110	0.1002	0.0100	0.1105
30%	0.0000	0.0000	0.0000	0.2257	0.0943	0.6800	0.0921	0.0100	0.0987
40%	0.0000	0.0000	0.0000	0.1752	0.1000	0.7248	0.0788	0.0059	0.0802
50%	0.0000	0.0000	0.0000	0.1268	0.1000	0.7732	0.0643	0.0032	0.0701
60%	0.0000	0.0000	0.0000	0.0861	0.1000	0.8139	0.0612	0.0012	0.0617
70%	0.0000	0.0000	0.0000	0.0550	0.1000	0.8450	0.0550	0.0005	0.0545
80%	0.0000	0.0000	0.0000	0.0301	0.1000	0.8699	0.5000	0.0002	0.0487
90%	0.0000	0.0000	0.0000	0.0010	0.1000	0.8890	0.0460	0.0001	0.0440

Stock 1	Stock 2	Stock 3	Stock 4	Bonds	Risk-free asset	Expected return rate	RFPI	Variance	VaRU
0.0893	0.1380	0.1380	0.2281	0.0000	0.5000	0.1053	0.1020	0.0100	0.1328
0.0854	0.1092	0.1077	0.1455	0.0522	0.5000	0.0921	0.1913	0.0050	0.1098
0.0462	0.0500	0.0818	0.0515	0.1000	0.6705	0.0678	0.1913	0.0010	0.0784