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Chinese Journal of Management Science ›› 2005, Vol. ›› Issue (5): 6-11.

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The Mean-Spectral Measures of Risk Efficient Frontier of Portfolio and Its Empirical Test

LI Xiao-ping, LIU Xiao-mao   

  1. Mathematics Department, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2004-12-13 Revised:2005-08-22 Online:2005-10-28 Published:2012-03-07

Abstract: 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,principally studies the Mean-M efficient frontier of portfolio and examines the economic implications under the assumption of normality of risk securities.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.At the same time,as a generic case,the result of ES accords with that of M corresponsively.Finally,this paper gives the Mean-M efficient frontier of portfolio selected from Shanghai and Shenzhen stock markets using foregoing conclusion.

Key words: coherent risk measures, spectral measures of risk, risk spectrum, efficient frontier

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