A NOTE ON SEMIVARIANCE |
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| Authors: | Hanqing Jin Harry Markowitz Xun Yu Zhou |
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| Institution: | Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong; Harry Markowitz Company, San Diego, CA, USA; Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong |
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| Abstract: | In a recent paper ( Jin, Yan, and Zhou 2005 ), it is proved that efficient strategies of the continuous-time mean–semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean–semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below-target semivariance model the attainability is established under the arbitrage-free condition. Finally, we extend the results to problems with general downside risk measures. |
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| Keywords: | single period semivariance below-mean below-target downside risk coercivity |
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