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The investment risk is measured by the variance in traditional mean-variance (MV) portfolio theory. Both overperformance and underperformance are considered as risk under the variance. However most investors worry about underperformance rather than overperformance. Hence, Bawa and Lindenberg (1977) employed the lower partial moment (LPM) to evaluate the downside risk. Rockafellar and Uryasev (2000) used the conditional value-at-risk (CVaR) to find efficient portfolios. Recently. Estrada (2008) introduced a heuristic approach for the mean semivariance (MSV) optimization. Furthermore, the complexity of covariance matrix results in the difficulty of implementation of MV model. Konno and Yamazaki (1991) proposed the mean-mean absolute deviation (MMAD) model and claimed that MMAD model retains all the advantages of the MV model. It results form that the covariance matrix is not used in their model. This research intends to compare efficient portfolios generated from different risk measures, such as variance, LPM, SV , CVaR. and MAD. The result shows that whether the dataset is multinormally distributed or not, if the investor is risk lover and tend to concern about underperformance, this study recommends that the investor may refer to MCVaR model provided the optimal decision-making. And if they are both concern about underperformance and overperformance, this study recommends that the investor may refer to MMAD model provided the optimal decision-making. Relatively, if the investor is risk averser and both concern about underperformance and overperformance. When the dataset is not multinormally distributed, this study recommends that the investor may refer to MV model provided the optimal decision-making. When the dataset is multinormally distributed and the investors tend to concern about underperformance, this study recommends that the investor may refer to MSV model provided the optimal decision-making. In addition, our study demonstrates in any kind of portfolio model. the more investment instruments that investors have, the higher portfolio performance could be produce, no matter what kind of portfolio model.
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