Mean-VaR And Dynamic Portfolio Models Analysis

Modern portfolio selection theory is concerned with the allocation of wealth among a basket of securities in an uncertain economy so as to achieve a reasonable balance between the return of the portfolio and the associated risk. The Mean-Variance model was first put forward by Markowitz in 1952, which established the foundation of modern portfolio selection theory. Since then, the framework of using expected return as a measure of return rate of a portfolio and using variance as a measure of risk is established in the contemporary financial theories.Modern portfolio theory has made great progresses during more than half scenturies. Besides traditional Mean-Variance model, many portfolio models can be found in literatures. For example, Mean-Absolute Deviation model, Mean-Semi Absolute Deviation model, Logarithm Utility model, Geometry Expected Earnings model, Safety-First model, and so on. Based on the prevail method of VaR in recent years and under the assumption that the rate of return of securities is normal distribution, a Mean-VaR portfolio selection model under constraint of investment chance is established in this paper. The efficient frontier of the Mean-VaR model with risk-free security under constraint of investment -chance is analysed. Finally, the dynamic portfolio-selection under constraints of investment chance and/or safety-criterion is studied. This paper differs from previous works in several aspects. Firstly, the Mean-VaR model is studied directly. Secondly, under constraint of investment chance, the efficient frontier of the Mean-VaR model with risk-free security is analysed. Thirdly, the dynamic portfolio selection model based on investment chance and/or safety criterion is discussed in this paper.On one hand, VaR characterizes the loss that may occur over a given period, at a given confidence level, due to exposure to market risk; On the other hand, VaR lets risk level between companies has a comparative criterion. Therefore, financial regulators view VaR as a very useful method of summary measure of risk. Since 1997, the Securites and Exchange Commissions in England and American have required banks to quantify and report their market risks exposure with VaR. Therefore, Mean-VaR model is of gereat importance for management of financial market risk. In addition, multiperiod (or continuous time) portfolio is more rational and practical in real financial markets. Therefore, the dynamic portfolio model based on investment chance and/or safety criterion can be conveniently applied to the practice of investment decisions and management.II...