Research On The Validity Of Portfolio Fitting Under Two Kinds Of Lower Risk Measure

With the development of modern financial theory and financial regulation§Va R and CVa R method are proposed and employed in portfolio selection theory. But in fact§during the investment decision-making process §investors often inevitably add artificial, political and legal constraints on a subset of securities. Based on above problem§This article proposes a new concept of e?cient fitted portfolios§and explores its conditions and some test statistics by the LPM method with Va R and CVa R constraints. E?cient fitted portfolios are the e?cient problem of portfolio in whole stock set when some investment constraints are added into some stock subsets. Especially§When the limit become zero constraints the above mentioned problem becomes a problem of e?cient subset for portfolio selection.In this paper, the statistical inference technology will be utilized directly into the portfolio decision-making process, and in accordance with risk management and utilization §it will put forward the e?ciency problem of portfolio parameter estimation risk, which is di?erent from previous researches.Supposed that the hypothesis of yielding is normal distribution§This paper presents the formula of Va R and CVa R under a certain holding period and confidence level. The fitted e?cient portfolio of M-Va R model and M-CVa R model will be studied. What is more,in a given constraint of portfolio§it will deduce judging criteria§and the corresponding wald test statistics of e?cient fitted portfolio is to demonstrate. Thus from the perspective of statistical test, it will e?ectively resolve the problem how to determine and select e?ective securities subset added constraints.At the end of the article§combined with the Chinese stock market data§it will draw the e?cient frontiers of the M-Va R model and M-CVa R model§and compare the e?cient frontier with the monte carlo method and historical simulation method. The result is verified§with the premises are that the quantities of securities portfolio is enough§the return of portfolio of M- Va R model and M- CVa R model e?ective frontier almost overlap. Similarly,when investors consider investment constraints on a subset of securities, the fitted e?cientfrontiers of the two models have similar results. The results show that normal distribution hypothesis for the argument in this paper is reasonable. At the same time, empirical results show that the optimal portfolio may be ine?cient when adding some budget constraints§but it will be e?ciently fitted by choosing appropriate partition of stock set.