This paper compared the composition and performance of portfolios constructed by employing different risk measures utilizing the Malaysian share market data in three diverse economic scenarios. The risk measures considered were the mean-variance (MV) and their alternatives; the semi-variance (SV), mean absolute deviation (MAD) and conditional value at risk (CVAR). The data were divided into three sub-periods representing the growth period in the economy, financial crisis and the recovery period. The results of this study showed different optimal portfolios’ performances and compositions for the three economic periods. Nevertheless, among the risk models tested, CVAR(0.99) model gave the highest portfolio skewness. High skewness means that the probability of getting large negative returns is decreased. As a conclusion, for the Malaysian stock market, the CVAR(0.99) model is the most appropriate portfolio optimization model for downside risk aversion investors in all three economic scenarios.