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Choose a common unit and horizon
The original model has losses −10, 0, 10 and 50 with probabilities 30%, 40%, 25% and 5%. A −10 loss means a 10-unit gain. All outcomes belong to one stated horizon and one loss unit; they are not four consecutive returns.
Sort from smallest loss to largest loss
| Loss units | Probability | Cumulative probability |
|---|---|---|
| −10 | 30% | 30% |
| 0 | 40% | 70% |
| 10 | 25% | 95% |
| 50 | 5% | 100% |
Convert profit or return consistently
If profit is P, define loss as L=−P. If a fixed initial value V has a simple return r, the corresponding value loss under this simplified setup is −Vr. For V=1,000,000 and r=−2%, the loss is +20,000. A +1% return produces −10,000 loss. This setup omits intervening cash flows.
Keep the output sign
A model containing only gains can have a negative VaR and negative expected shortfall under this loss convention. Replacing those numbers with zero changes the measure. Label the convention instead of assuming every risk output must be positive.