Simchi-levi et al. (2014, 2015a) proposed a novel approach using the Time-To-Recover (TTR) parameters to analyze the Risk Exposure Index (REI) of supply chains under disruption. This approach is able to capture the cascading effects of disruptions in the supply chains, albeit in simplified environments – TTRs are deterministic, and at most one node in the supply chain can be disrupted. In this paper, we proposed a new method to integrate probabilistic assessment of disruption risks into the REI approach, and measure supply chain resiliency by analyzing the Worst-case CVaR (WCVaR) of total lost sales under disruptions. We show that the optimal strategic inventory positioning strategy in this model can be fully characterized by a conic program. We identify appropriate cuts that can be added to the formulation to ensure zero duality gap in the conic program. In this way, the optimal primal and dual solutions to the conic program can be used to shed light on comparative statics in the supply chain risk mitigation problem. This information can help supply chain risk managers focus their mitigation efforts on critical suppliers and/or installations that will have greater impact on the performance of the supply chain when disrupted.