Generalization And Application Of The Optimal Portfolio Dual Problem

By defining return and risk as the mathematical expectation and variance of price return rate,Markowitz obtained the optimal portfolio for a given level of return to minimize the risk and got the efficient frontier.Original model’s dual problem is to seek the optimal portfolio for a given level of risk to maximize the return rate and got the efficient frontier.This paper makes theoretical generalization and empirical analysis on this basis.Introduce the risk preference coefficient α,0 ≤α≤1.The Markowitz risk(price risk)is generalized to the weighted sum of price risk and volume risk(the sum of weight coefficient is 1).We consider two cases,the portfolio is composed of all risky assets,and the portfolio is composed of risk-free security and risky assets.It solves the optimal portfolio of securities with the highest expected return rate and its effective frontier under the given risk level.We do the further research and reveal the relationship of the optimal portfolio between Markowitz model and the dual model.We use Eviews and MATLAB software to program to analyze the daily and monthly data of six groups of stocks in Shanghai and Shenzhen stock markets.From the perspective of empirical analysis,the generalized results are more in line with the actual situation.