| STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES |
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| 作者姓名： | Wang Yi Chen Zhiping Zhang Kecun |
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| 作者单位： | Wang Yi Chen Zhiping Zhang Kecun Department of Scientific Computing and Applied Softwares，Faculty of Science，Xi'an Jiaotong University，Xi'an 710049，China. |
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| 基金项目： | Supported by the NNSF of China (10571141)
the Key Project of the NNSF of China (70531030). |
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| 摘 要： | In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.
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STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES |
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| Wang Yi Chen Zhiping Zhang Kecun.STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES[J].Applied Mathematics A Journal of Chinese Universities,2006(4). |
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| Authors: | Wang Yi Chen Zhiping Zhang Kecun |
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| Institution: | Wang Yi Chen Zhiping Zhang Kecun Department of Scientific Computing and Applied Softwares,Faculty of Science,Xi'an Jiaotong University,Xi'an 710049,China. |
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| Abstract: | In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision. |
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| Keywords: | mean-risk model portfolio optimization value at risk expected shortfall efficient frontier |
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