Spectral Measures Of Risk And Its Efficient Frontier

Financial risks management is a hot topic in financial instituations, academia, and financial supervisors for recent years. Risks measurement is the core of effective risks management. Therefore, it is significantly important to study risks measurement in the background of financial globalization. Reasonable risks measurment is fundamental for China's risk management study, as well as China's finance development and finalcial markets construction.In this paper, we discuss Spectral measures of risk, It grows from Expected Shortfall and generalizes it. Synchronously, Spectral measures of risk sums up a new approach of coherent risk measures. As a modern risks measurement, Spectral measures of risk sets its base on statistics, mathematical algorithms, combined with engineering science and computer science. In this paper, we will use quantitative analysis more than qualitative analysisTo begin with, based on the Spectral Measures of Risk (M)—a new approach of coherent risk measures introduced by Acerbi (2002), this paper discusses some properties of Spectral Measures of Risk and one especial cases of this kind of risk. Then discusses the existence and some important function properties and curve characters of the Mean—Spectral Measures of Risk(M) efficient frontier of portfolio under the assumption of general loss distributions, which are generally valid for convex measures of risk, then the economic implications are examined. At the same time, this paper estimates the special case of Mean—M efficient frontier of portfolio of Shanghai and Shenzhen stock markets. Then this paper principally studies the Mean—M efficient frontier of portfolio, examines the economic implications under the assumption of normality of risk securities and gets idiographic analytical equation and figures. Moreover, the comparison between the Mean—M efficient frontier,the Mean—Variance efficient frontier and the Mean—ES efficient frontier is provided. Some interesting and practical results are obtained. Fourthly this paper establishes optimal investment strategy of the portfolio including n risky assets and one risk-free asset. First and Foremost, We first strictly solve optimal problems and get the optimal portfolios and the Mean—Spectral Measures of Risk efficient frontier using optimization method in theory, besides, discusses optimal investment strategy of the portfolio involving n risky assets and one risk-free asset from mathematics and economics. Last but not least, The generalized Two-Fund Separation principle under the Spectral Measures of Risk is proposed. Furthermore, This paper uses GARCH model and General error distribution to fit time series of yield and its distribution, Genetic algorithm is put forward to improve the estimating accurary of the parameters of GARCH model, and the results are applied to set up the VaR model and Spectral Measures of Risk estimation model . Moreover we give a back testing to validate the use of the model. Finally, we mentioned the directions of the further research.