Comparison of Portfolio Performance under Different Risk Measures

[[abstract]]Investors are seeking the portfolio which has higher return and lower risk in the portfolio selection problem; however, different researchers consider different risk measures. How to compare these portfolio selection rules under different risk measures to choose a proper portfolio selection rule for different investors? The purpose of this research is that we want to establish a criterion to compare the portfolio selection rules under different risk measures. This research is to compare the risk of nine portfolio selection rules under the cases that are economic downturn, economic flat and economic upturn, and use the optimal portfolio weights for every portfolio selection rule to calculate the risk under other risk measures. Then we compare the risk of nine portfolio selection rules under the same risk measure. According to our simulation results, it seems that the Sharpe ratio and Sortino portfolio selection rules have higher risk than other portfolio selection rules