Solving Nonfactor Return And Sharpe Ratio By Using ADMM

As for an passive index or index fund,minimizing its nonfactor return is used to find its efficient portfolio;as for an investment portfolio,maximizing its sharpe ratio is used to find its optimal risk investment portfolio.This thesis is aimed at using the Alternating Direction Method of Multipliers(ADMM)to minimize the nonfactor return and maximize the sharpe ratio of an investment portfolio.The detail is as follows:As for nonfactor return,the objective function of which is convex,the definition domain can be proved convex;as for sharpe ratio,this paper proves that sharpe ratio as an nonconvex objective function can be turned into convex function and the definition domain is also a convex set.Then use ADMM to solve the two problems.In order to find the suitable lagrange multiplier,an improved ADMM is designed,which increases an circulation of lagrange multipliers.Under certain conditions,problem can be solved in limited steps,and the improved ADMM can converge to the optimum solution.Finally,analyse the two problems in empirical research by using ADMM.The relaxation parameter which can accelerate the convergence rate of ADMM on quadratic programs of this problem has been found.By comparing ADMM with other methods which are similarly used to solve convex programs,the performance of ADMM is found to be more superior,the convergence rate of ADMM is also relatively fast.