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State the quantile rule
This reference uses q(c)=inf{l:F(l)≥c} on the loss distribution. Other sample interpolation conventions can produce different finite-data answers. Keep the rule with the result rather than calling one unqualified percentile universal.
Build the cumulative record
| Loss units | Probability | Cumulative probability |
|---|---|---|
| −10 | 30% | 30% |
| 0 | 40% | 70% |
| 10 | 25% | 95% |
| 50 | 5% | 100% |
Locate the first crossing
At 90% confidence, cumulative probability first reaches the level at loss 10, so VaR is 10 loss units. At exactly 95%, the same lower-quantile rule still gives 10 because F(10)=95%. At 97.5%, the crossing is at 50.
Explain what the threshold does not say
The threshold is not the maximum model loss and does not describe the average severity beyond it. The supplied probabilities are assumptions, not established frequencies of future events. A horizon or confidence change needs a separate model record.