Robust Stock Portfolio Models And Its Empirical Studies Under Uncertain Environments

The stock portfolio problem is always a research emphasis in the financial field,because it involves the lots of uncertainties under the uncertain environment.Some of the uncertainties are from the input parameters of the portfolio model,some are from the movement characteristics of stock market,of course,some are from the extreme events and so on.Their perturbations deeply influence on the choice of the optimal portfolio strategies,and resulting in them inefficient and unreliable as well as the portfolio performances very poor.Markowitz’s meanvariance(MV)portfolio model which is one of the most excellent model has been the analytical framework to study the portfolio problems.However,MV model does not consider the uncertainties of the uncertain environment,so a large number of scholars employ series of methods to reduce the adverse impacts of uncertainties on the optimal portfolios and their performances.Recently,robust optimization based portfolio approach is extensively favored by the academic and practitioners.Considering uncertainties of the input parameters,it introduces robust optimization to MV model,and focuses on the worse possible realization of the uncertain input parameters in the uncertain set so as to build the portfolio model under the uncertain environment(RMP-minmax).Due to ensure the optimal portfolio feasible and reliable,studies and application of RMP-minmax model are quickly obtained so that this approach is called robust portfolio.But there is a defect in robust portfolio that the optimal robust portfolios are very conservative,resulting in the portfolio performance considerable inferior.Furthermore,the scholars are united on the stock markets,especially,the emerging stock markets,have the unidirectional motion characteristics,that is,the movement statuses and statuses periods not only exist but also seriously influence the portfolio performances.However,it is very interesting that the movement statuses and statuses periods are few considered in the portfolio studies and applications.Based on MV model,this paper employ set-value theory,the uncertain optimization theory and robust optimization as well as the decision criteria under the uncertain environment,study how to build the stock portfolio model and select the optimal portfolio strategies under the uncertain environment combined with the movement statuses and statuses periods of the stock markets,providing the more feasible,specific and reliable portfolio strategies to the stock market under the different movement statuses.Firstly,this paper transfers the MV model to the uncertain multi-objective optimization problem from the portfolio choice viewpoint under the uncertain environment,and analyzes the upper set relationship between the objective function values of RMP-minmax robust portfolio optimization model and the strong robustness of the optimal solutions the upper set relationship and its optimal solutions properties together with the risk aversion characteristics using in the pessimism decision standards of the uncertain environment as well as the upper set ordered relationship and its optimal solutions properties,explaining the portfolio conservative and performances inferiority of the optimal robust portfolios concentrating on the worst possible realizations of the uncertain input parameters in the uncertain set.To enhance the overall performances of the portfolios,relax the robust feasibility and reduce the robust conservative,the present paper borrows the optimistic decision criteria of the uncertain environment as well as the lower set ordered relationship and its optimal solutions’ properties in the set-value theory,build the new robust multi-objective portfolio model(RMP-minmin)considering the best possible realizations of the uncertain input parameters in the uncertain set,and hence to analyze the weak robustness of the optimal robust solutions and its risk preference characteristics in RMP-minmin model.Additionally,based on the alternaitve ordered relationship and its optimal solutions’ properties as well as Hurwicz criteria,discusses the alternative ordered optimal solutions that are the optimal portfolios reflecting risk neutral.But they are always empty in the real application,and can be substituted with MV if they do not exist,considering the fact that the optimal portfolios of MV which can balance the radical(risk preference)and the conservative(Risk aversion)have the risk neutral.Here,the methodology of RMP-minmax robust multi-objective portfolio model has been analyzed,and RMP-minmin robust multi-objective portfolio model is also constructed,proposing three kinds of the different optimal portfolios with risk preference,which reflects the theoretical innovation.The present studies few investigate the best possible realizations together with the intersection case of the worst possible realizations and the best possible realizations of the uncertain input parameters in uncertain set.Thus,RMP-minmin model in this paper can enrich the portfolio theoretical research and cover the shortage of RMP-minmax model.Then,this paper explores the more targeted optimal portfolio strategies under the different movement statuses as well as the more reliable optimal portfolio strategies under the different statuses periods in order to study the strange phenomenon about the influences of the movement statuses and statuses periods of stock market on the portfolio performances.The stock daily return data of three industries including finance,energy and real estate which are selected from June 1,2014 to May 31,2019 in China,involve such extreme events as the collapse of China’s stock market in 2015 and the market meltdown in 2016 as the study period(i.e.,No,2 of status period).Moreover,the study period is divided into the bull,bear and steady of movement statues,and the whole period without the division is called the mixed movement status.After the optimal portfolio performances of MV,RMP-minmax and RMP-minmin(robust)portfolio models are testified through the data from each of movement status the observations are that the whole portfolio performances of the optimal portfolio strategies of RMPminmin are the most competitive,and MV’s is more suitable for the steady movement status,inversely,RMP-minmax’s is still conservatively inferior on any movement status of the stock market.It is one empirical exploration and innovation,which can provide the new viewpoint for seeking the well-directed optimal portfolio strategy to study the stock market at the different movement statues.Further,comparison between the bull,the bear and the steady of movement status and the mixed movement status observes that it is very meaningful to divide the movement status of stock market and provide the optimal portfolio strategies for each movement status,which can be improve the portfolio performances.It needs to be pointed out that our purpose is to study the influences of the different movement status on the optimal portfolio rather than precisely divide the movement status of stock market so as to verify the followed conclusions:(1)it is very necessary to consider the movement status of stock market for the portfolio problems under the uncertain environment.(2)the more targeted optimal portfolio strategy is provided to the different movement status of stock market,which can enhance the portfolio performances.(3)the optimal portfolio strategies at various of movement statuses have not the significant difference with the variation of the industry sectors of stock market.Thirdly,we employ the same method with the above to investigate the reliability of the optimal portfolio strategies of MV,RMP-minmax and RMPminmin models under the different statuses periods of stock market,that is,the data of the daily returns from the industry sectors of finance,energy and real estate are selected from January 1,2006 to May 31,2014 in China.They contain such extreme events as 2008 global financial crisis,2008 Wenchuan earthquake,taken as the comparison period(i.e.,No.1 of status period).Similarly,the movement statuses in the comparison period can be divided into the bull,the bear and the steady.Moreover,the data from different status period is used to test the optimal portfolio strategies so as to investigate the reliability of the optimal portfolio strategies under the same movement status of the different status period.This is the other empirical exploration and innovation,which can provide a new viewpoint of studying the reliability of the optimal portfolio strategy.Observations are obtained that the portfolio performances of RMP-minmin are considerable outstanding at the bull and the bear of the different status period;meanwhile,MV’s is extraordinary at the steady.However,the portfolio performances of RMP-minmax are still extremely poor at any movement status of two status periods,such result is identical with the above.In addition,comparison results indicate that it is difficult to ensure the reliability of the optimal portfolio strategies of MVand RMP-minmax under the different status periods if only comparison between them is conducted,which verifies that construction of RMP-minmin robust multi-objective portfolio model in this paper has the applied value,and the proposed optimal portfolio strategies under the uncertain environment have the good feasibility,pertinence and reliability.Lastly,studies and observations of robust stock portfolio problem under the uncertain environment are concluded in this paper,at same time,suggestions are provided to the theoretical study and its application in the portfolio field.Also,the future tendencies of robust stock portfolio problems considering the movement features(i.e.,movement status,status period)of stock market are proposed.