Research On Fuzzy Entropy-Based Portfolio Optimization Models

The fundamental goal of security investment is to earn profit. While revenue is always accompanied with risk, so it is vital for investors to measure security risk in a proper way. In the 1950s, Markowitz proposed the mean-variance model which opened the door to the quantitative method in portfolio selection research. However, variance measure involves many limitations such as "corner solution", "unstable parameter estimation" and "massive variables of covariance matrix" which severely affect the stability and persuasiveness in empirical research. Recently, due to the great feature in measuring the risk of financial asset and deducing the probability distribution of asset returns, the application of entropy was deeply researched in recent decades and a series of entropy indexes were put up, such as fuzzy entropy, residual entropy, hybrid entropy and sine entropy. Based on the above, we follow the step of Markowitz and take the security risk as the research object with collecting data during 2013 to 2015 in SSE and SZSE in this paper. We successively build up a series of portfolio selection model based on the fuzzy entropy and hybrid entropy, and we then add the Yager's entropy as well as liquidity constraints to optimize the model and estimate the efficiency through the example simulation and empirical analysis. The main work is as follows:(1) We systematically review and summarize the development history of theoretical research and applied application about security risk measure. On the basis of previous studies, we lay our emphasis on the fuzzy entropy-based portfolio selection model research;(2) Daily trading data of ten stocks were collected from both SSE and SZSE during 2013 to 2015 as sample, and we use the Markov method to obtain the fuzzy yields for the follow-up study;(3) According to the "credibility" method, we build up the Fuzzy Entropy-Yager's Entropy Model. Simulation results and empirical analysis demonstrate that the rationality of funds allocation can be greatly improved at the expense of a small decrease in yields after using Yager's entropy. We then add the turnover rate as the liquidity constraint, the empirical results show that the model with liquidity constraint can gain the extra yields with lower risk when the macro market performs well;(4) As the extension of fuzzy entropy research, we build up the Mean-Variance-Hybrid Entropy Model based on the combination of stochastic and fuzzy uncertain situation. Simulation results and empirical analysis indicate that the out-of-sample performance of the model we set is better than other single-index model. We further add the Yager's entropy to enhance the stability of model which can effectively avoid fluctuation risk;(5) Considering various market situation, we put up a series of advice to provide decision references for investors and regulators.