Study Of Investment Strategy On High-dimensional Pairs Trading

Traditional pairs trading method mainly has two kinds:one kind is based on data mining and statistical research methods,the most common is cointegration test method,because of the limitations of the method,the optimal strategy can only obtain the optimal execution time of opening and closing stock positions,but can not give the optimal quantity of opening and closing stock positions.The size of the quantity is usually decided through the experience of fund managers,which has a certain risk and instability.The other kind of research method is under the theoretical framework of stochastic control.The investment strategy given by this method is a dynamic strategy,which changes over time and provides the investment plan at each moment.This kind of method is constrained by the solution of HJB equation,and generally only considers the problem that only a pair of paired assets are included in the portfolio.The main content of this paper is the extension of the second type of stochastic control method,and the main object of the study is the investment strategy of high-dimensional paired assets.By considering the portfolio consists of a pair of matching assets expand to include multiple paired risky assets and risk-free asset,through the price difference of matching assets are assumed to be Ornstein-Uhlenbeck process,maximize the value of investment target due to wealth,on the basis of stochastic control theory,the model of high dimensional pairs trading strategy has been set up,for each pair of assets in pairs trading portfolio investment weights,and related parameters is given.Finally,a portfolio of four-dimensional paired stocks is taken as an example to analyze the relevant conclusions.By 461 stocks in the ShenZhen A shares selection,matching of 106030 pairs of stock right,1186 to the empirical analysis of matching stock,on December 25,2017 to August 15,2019 daily closing price as the parameter estimation of time sequence,to August 16,the empirical simulation analysis was conducted from August 16,2019 to December 23,2020,and the following conclusions were drawn:First,the price spread between pairs of stocks has an inverse relationship with the investment strategy;Secondly,the annualized return rate of the portfolio is 11.85%,and the maximum pullback rate is 11.33%,which has a high return rate.Thirdly,the strategy choice of investors with different risk preferences is given.When the risk aversion coefficient of investors increases,the annual return rate of the portfolio will decrease gradually.Finally,through the analysis of the portfolio containing different pairs of paired stocks,it is found that when the portfolio contains a large number of paired stocks,its return rate will also be higher,and the winning rate will be closer to 100%.This paper constructs a high-dimensional investment strategy model of paired assets based on the stochastic control,which is reflected in the fact that the portfolio contains multiple pairs of paired assets and a class of risk-free assets,which is a new attempt.Through the empirical simulation,the model has a high rate of return,low investment risk,and has a certain effectiveness and operability in China's stock market.