## 2 Methodology
### Risk Evaluation
#### 2.4.1 Financial Risk Evaluation Using VaR and CVaR  
To assess financial risk, the model incorporates two key indicators: Value at Risk (VaR) and Conditional Value at Risk (CVaR). These risk metrics quantify the probability and severity of unfavorable economic conditions, particularly in scenarios where Net Present Value (NPV) could become negative.  
Value at Risk (VaR) serves as an industry standard tool for assessing risk. It provides a statistical evaluation of value with a specified probability. This concept is grounded in [PERSON]'s optimal portfolio theory [47], which posits that variance is a key measure of risk.  
VaR is calculated through 4 steps [48]:  
1. Determine the time period during which the organization wants to assess the potential loss. This can be for one day, a month, a year, or for the entire life of the mine in our case.
2. Choose the confidence level used in VaR estimation, which typically ranges from 90% to 99%, and can occasionally exceed that. The 99% confidence level is used primarily due to regulatory requirements, as stakeholders are concerned with potential losses from catastrophic scenarios.
3. Establish the probability distributions of outcomes for the portfolio or assets we are considering. Several methods can be used for this, and the distribution will be represented as a curve that often resembles a normal distribution curve, illustrating the likelihood of a loss occurring.
4. Calculate VaR by examining the amount of losses associated with the area below the critical confidence level on the distribution, as illustrated in Figure 2.  
However, this risk assessment measure has its drawbacks, as noted in the study by [PERSON] et al. [49], which points out that VaR does not specify the maximum size of potential losses, nor does it account for the size of less likely losses. Due to these shortcomings, [PERSON] and [PERSON] [50] proposed an improved risk assessment measure known as Conditional Value at Risk (CVaR). CVaR roughly (or exactly, under certain conditions) equals the average of the worst-case loss scenarios for a certain percentage [51].  
The risk evaluation framework in this study follows three structured steps:  
1. Generating probability distributions of net present value (NPV) and other key economic indicators through 100 stochastic pit optimizations.
2. Calculating VaR and CVaR at the 90%, 95%, and 97% confidence levels to establish financial risk thresholds.
3. Interpreting risk thresholds to determine financial stability and assess the necessity of implementing risk mitigation strategies.  
The selection of confidence levels follows both industry best practices and project-specific analysis:  
* The 90% confidence level (VaR 90%) represents a benchmark threshold, providing a probabilistic estimate of financial loss in 10% of scenarios.
* The 95% confidence level (VaR 95%) identifies more extreme financial risks, indicating potential losses that occur in only 5% of cases.  
Figure 2: The VaR and CVaR for a 95% confidence level.  
* The 97% confidence level (VaR 97%) was determined based on 100 pit optimizations, showing that at this threshold, the probability of financial loss is only 3%, defining the project's financial stability limit.