Shape memory alloy cables have emerged as an alternative to conventional steel cable restrainers for preventing the bridge spans from unseating during an extreme earthquake. Feasibility of high-cost NiTi shape memory alloy restrainers in retrofitting the bridges has been numerically investigated, and promising results have been published; however, considering the economic impacts, the effect of different types of shape memory alloy such as Cu-based and Fe-based shape memory alloy restrainers has not been discussed yet. The objective of this study is to address this problem in detail in order to propose the most cost-effective shape memory alloy restrainer suitable for bridge engineering applications. Seismic fragility and life-cycle loss (both direct and indirect) assessments are analytically performed on an isolated simply-supported highway bridge retrofitted by four types of shape memory alloy restrainers (i.e. NiTi, FeNiCoAlTaB, CuAlMn, and FeMnAlNi). Results showed that for all retrofitted bridges performed in the range of design displacement, the effect of type of shape memory alloy is significant on the damage probability and long-term seismic loss of the bridges. All the bridges retrofitted with shape memory alloy restrainers have a very low probability of collapse (less than 7%). It is also found that the bridge retrofitted with Fe-based shape memory alloy restrainers (SMA-II and SMA-IV) performed better as compared to the other cases. Compared to the bridge without restrainers and with NiTi shape memory alloy restrainers, Fe-based shape memory alloy restrainers can reduce the long-term loss by about 87% and 11%, respectively, at the design earthquake event specified in CHBDC-2014. The probabilistic risk analysis of highway bridges retrofitted with shape memory alloy restrainers can aid in paving the way toward widespread application of such smart materials in structural applications.