Two Portfolio Models And Its Optimization Algorithm

Financial markets are unpredictable,and risk is uncertain.At present,how to control expected returns and risks in a relatively reasonable state is an important issue to be solved.In 1952,Harry Markowitz proposed the mean-variance portfolio model.In this paper,the capital asset pricing model(CAPM)and the mean-absolute deviation model studied are based on the improvement and extension of this model.As the mathematical portfolio model of the solution and optimization algorithm is inseparable,the paper combines the optimization algorithms and portfolio model,and also makes an empirical research.For the CAPM,this paper introduces the portfolio of riskless assets and non-riskless assets.The model shows that the relationship between the expected return and the risk of the securities is linear.And the value of Beta can measure the systematic risk of the securities investment,and then the study of the model derived by the multiplier method.According to many researchers on the SSE securities research,the paper analyzes the CAPM and its extended model Fama-French three-factor model and Fama-French five-factor model in the GEM market.For the modified mean-absolute deviation model,this paper introduces the risk measure under the original mean-absolute deviation model.As the rate of return on securities is different,the risk measure should also be different.The weight coefficient is used to modify the model,and then the generalized projection conjugate gradient algorithm is used to solve the model,and combined with the Shenzhen A-shares for numerical experiments.