Value-at-risk method in the securities portfolio risk management
|School||University of Electronic Science and Technology|
|Course||Operational Research and Cybernetics|
|Keywords||Mean-VAR model minimum VAR portfolio Brownian motion long time horizon VAR|
The dawn of the theory of value at risk (VAR), many people pay attention to it. In the academic environment, many scholars have done a lot of work about VAR, and investigate some new models; they improve on methods in Risk Management theoretically. Among practitioners and regulators, VAR becomes more and more popular.In this paper, section 1 introduces the course of emergence of VAR, and then elaborates its history and development.Under the Mean-VAR model, Section 2 derives the sufficient and necessary condition of existing of minimum VAR portfolio. Then extend the results of Mean-variance model including a riskless security to the Mean-VAR model.The time horizon has influence on the VAR of asset and portfolio. In this paper, I utilize stochastic theory to solve the VAR of asset and portfolio on condition that the prices of assets follow a log-normal diffusion process. Furthermore, I analyze the sensitivity of the VAR to time horizon, at the same time, in order to attain minimum VAR I derive the right time horizon under different expected returns and volatility of assets.In section 4, using these VAR tools, I analyze the relation of every asset to portfolio VAR, and conclude the effect of long time horizon to portfolio VAR.In the end, I summarize the conclusion of the paper and give a prospect about VAR in the future.