<p>In recent years, adopting the portfolio optimization (PO) model integrating expectile value at risk (EVaR) has gained significant attention. Its coherence, elicitable characteristics, and ease of solving the associated linear programming model are the main driving forces. We introduce the PO model within the safety framework, considering the trade-off between return and risk. Risk is evaluated using EVaR and Deviation EVaR (DEVaR). All proposed models are LP problems, making them computationally viable. We evaluate the out-of-sample statistics of the PO model using EVaR and compare them with the statistics generated by PO models utilizing conditional value at risk (CVaR). The PO model with EVaR does better than the PO model with CVaR in most financial datasets concerning various performance metrics like mean returns, standard deviation, value at risk (VaR), CVaR, and different reward-to-risk ratios. Additionally, our empirical results show that the DEVaR model does better than the EVaR model in yielding higher returns, better reward-risk ratios, and lower risk metric values. Similarly, the Deviation CVaR (DCVaR) model outperforms the CVaR model within a similar setting. The analysis highlights the significance of deviation risk measures. We also present robust PO models that consider uncertainty in probability distributions. These models use EVaR and DEVaR as risk metrics within a box uncertainty set. However, it is noted that these robust models do not outperform their traditional, non-robust counterparts in terms of financial outcomes.</p>