Multi-period Optimization Analysis Of Mean-variance Of Stock Portfolio Under The Same Capital Structure

In order to maintain and increase the value of investment,investors generally pay much attention to the income and risk of financial products.In order to avoid risk,most investors generally use portfolio investment.Correspondingly,most financial products are also derived from the company's performance as a target product.Therefore,the relationship between asset portfolio and corporate performance and the factors affecting the two factors have always been the important areas of mainstream finance.On the basis of capital structure,a large number of documents discuss the pricing of capital assets under the condition of portfolio theory and method.The more representative theories include the MM theorem and the mean variance model.Among them,the MM theorem demonstrates the relationship between capital structure and company performance,which lays a good foundation for further research.But its basic assumptions are too harsh.For example,the risk-free interest rate of individuals or companies has nothing to do with capital structure,and different investors have fixed income for the same risk type company.These assumptions are contrary to the realities of the realities of the average return of stock returns and the risk of bankruptcy resulting in the correlation between the capital structure and the risk free interest rate.In addition,there is a situation that the cost of equity capital is lower than that of a non debt company with the same risk level.Therefore,the theory has obvious defects.The mean variance model although starting from the relationship between return and risk assets,discusses the uncertain optimal portfolio selection problem in economic system,is the cornerstone of the modern portfolio theory,but it is pointed out that the factors of system risk can not be dispersed and affect the existence of systemic risk,but no further analysis of whether there are micro factors,and is a single period static model.Based on the shortcomings of the above two theories,this paper assumes that different capital structure states have different influences on corporate performance.From this point of view,we need to study two questions:1)under what circumstances will the capital structure play a dominant role in the positive performance of the company's performance?Under what circumstances will it play a dominant role in the negative effect of the company's performance?2)whether the portfolio of risk assets is affected by the internal factors of the company,and whether these factors are not dispersible.Therefore,this paper uses the method of non arbitrage analysis and Lagrange multiplier method to deduce and verify the above conjectures.The main research contents are as follows:The first part is based on the characteristics of stock returns and mean reversion of returns.It is assumed that different investors have the same future income and risk expectations for the same scale and the same risk level,and the yield and yield of each period follow a stationary stochastic process.Then the external factor of bankruptcy risk is introduced,and the relationship between capital structure and risk free interest rate is described based on the principle of risk compensation.At the same time that individuals and companies like the existence of the risk of bankruptcy,through no arbitrage analysis method in capital structure is low,the positive effect of capital structure on corporate performance in a dominant position;the higher the capital structure,capital structure on corporate performance of the negative effects dominate,demonstrates the relationship between capital structure and company performance into inverted U type,more effectively describe the capital structure and corporate performance,and further extended to the relationship between capital structure and corporate performance of different production scale.The second part:Based on the first part,we conclude that capital structure has a great impact on company performance.Based on the model deduction,the capital structure is substituted into the mean variance model to find a more accurate portfolio.In order to calculate and analyze simple respectively to establish the same capital structure debt free multi period mean variance model and the same capital structure liabilities multi period mean variance model,analytic formula and obtains the expected return and variance of each issue,through the comparison of the two analysis found that the change of capital structure influence portfolio the benefits and risks,finally determine the effective boundary of portfolio assets into the envelope,at the same time that the system not only contains the risk of macro factors,micro factors still exist,the two factors influencing stock returns.The third part:through the study of the interests distribution of shareholders and creditors,the analysis of the second part of the model is verified.Generally speaking,agency problems are dominant among managers and shareholders under low growth opportunities,while agency problems between shareholders and creditors are dominant under high growth opportunities,so this paper selects gem data as validation data.In addition,the mean variance model is used to prove that the factors that affect the system risk are difficult to operate.Therefore,the index model is selected to solve the problem.In this paper,we choose a market index excluding capital structure and a market control index which do not consider capital structure to form a control group,and compare the impact of capital structure on company performance.The results show that:1)capital structure has a significant negative correlation with company performance,indicating that both macroeconomic factors and capital structure are all factors that affect systemic risk,and capital structure is in the right half of inverted U.2)compared with the traditional market index without considering the capital structure,the influence of market index which eliminated capital structure on corporate performance increased significantly,indicating that the negative effect of capital structure made the influence of macro factors on company performance lower.3)when the capital structure of all assets is higher,their portfolio returns are under the effective boundary of the multiphase mean variance model.In view of the above conclusions,this paper suggests that the means of controlling free cash flow and optimizing the financing platform are proposed.