Application Research On The Capital Allocation Of Pairs Trading Using Multi-objective Evolutionary Algorithm

The MOEA was developed on the base of genetic algorithm.It aims to solve the multi objectives and get the so-called Pareto sets by using the evolutionary algorithm within some certain constraints.So far,the most two successful multi objective evolutionary algorithms are NSGA-? and MOEA/D.The pairs trading is a tool of statistical arbitrage.It just begun to attract Chinese investors' attention as the securities margin trading was allowed steadily.But it is still not common used in Chinese market as the limit of the institution and the strict supervision from the government.Pairs trading utilizes the historical data to get pairs of stocks.When trading,the positions of stocks are opened and closed decided by the statistical gap of price.When the price gap becomes bigger or smaller than the statistical data,the traders will start trading,and they will close the positions when the price gap regresses back to the mean value.It always gets both long and short positions in pairs trading.It is a hedge technic.Capital allocation is very important in the portfolio management.This essay focuses on researching the risk model of pairs trading,and using MOEA to optimize the capital allocation.The main content and innovations of this essay are showed as follows:1.The essay implements the test of pairs trading on the Chinese stock market,and 24 pairs of stocks are chosen to be experimental objectives which will be used in the MOEA.2.Based on the reference of mean-variance model,the essay designs a new risk model for pairs trading.The correlation coefficient is introduced into the risk model.3.Profit maximization and risk minimization are the two objectives we need to optimize,this paper suggests using NSGA-? and MOEA/D to get the Pareto set.As the experiments show,NSGA-? is better than MOEA/D on the diversity and convergence performance,though MOEA/D gets a bigger range of Pareto set.As showed that NSGA-?works better than MOEA/D on this specific topic,this paper then compares the results between real coded NSGA-? and binary coded NSGA-?.It proves that the real coded NSGA-? not only gets a better Pareto Front but also has a higher efficiency than the binary coded NSGA-?.This paper presents the whole solution of pairs trading,through the selection of stock pairs to the optimization of capital allocation.