Power systems are facing unprecedented complexity due to the increasing frequency and severity of High-Impact, Low-Frequency (HILF) events, such as widespread wildfires, prolonged droughts, polar vortexes, and cyber-physical attacks. These events challenge traditional reliability frameworks, especially as systems integrate more variable renewable energy sources. In response resilience has emerged as a vital complement to traditional reliability and risk analyses, enabling planners and operators not only to reinforce systems against a range of rare but foreseeable events, but also to guide them through the full spectrum of resilience stages, from anticipation and absorption to recovery and adaptation.

Among the wide range of metrics proposed to quantify resilience, risk-based are particularly relevant for HILF scenarios, as they incorporate the probabilistic nature of both event occurrence and potential impact. This paper focuses on the application of three risk-based metrics—Probability of Failure, Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR)—which quantify the likelihood and severity of adverse outcomes under uncertainty, and are well-established in financial risk analysis

A key contribution of this work is a unified framework that links risk metrics with cost functions, addressing a critical gap where these elements are often assessed in isolation. We argue that effective resilience planning must jointly consider failure likelihood, consequences, and the economic trade-offs of mitigation strategies.

We build on the interference model, which evaluates the risk of failure by analyzing the overlap between the probability distributions of catastrophic events and system failure. We then introduce a cost function comprising reconstruction and lost energy costs, and we demonstrate how these interact with system robustness and risk exposure.

By modeling both risk and cost as functions of the separation between the probability distributions of catastrophic events and equipment failure, we show that risk metrics alone are insufficient for guiding infrastructure investment decisions.

To support decision-making, we propose a unified analysis framework that maps risk measures against cost, incorporating key factors such as distribution shapes, confidence intervals, and mitigation cost structures. Results are communicated to stakeholders in visual format enabling them to assess trade-offs and make context-sensitive choices.

The methodology is validated using representative real-world data and illustrative figures. This work highlights the novel application of financial risk metrics in power systems and shows how they can be adapted to reflect system-specific characteristics, ultimately bridging the gap between probabilistic risk analysis and economic evaluation.