Use the supplied original loss table
| Loss units | Probability | Cumulative probability |
|---|---|---|
| −10 | 30% | 30% |
| 0 | 40% | 70% |
| 10 | 25% | 95% |
| 50 | 5% | 100% |
Retain the defined percentile convention
Use the smallest loss with cumulative probability at least the stated confidence. All listed losses have one common horizon and unit. Read the loss sign rather than treating the scenarios as a time sequence.
Try the questions
Using the lower cumulative rule, what is the original model’s 95% VaR?
- A.
10 loss units
- B.
50 loss units
- C.
2 loss units
Answer and explanation
Answer: A
The first loss reaching 95% is 10.
- A
F(10)=95%, which satisfies the ≥ crossing rule.
- B
This skips the exact cumulative boundary.
- C
This is the mean of the full model.
Under a positive-loss convention, what does loss −10 describe?
- A.
A loss of 10
- B.
A gain of 10
- C.
A 10% probability
Answer and explanation
Answer: B
Use the stated economic sign before ordering outcomes.
- A
This reverses the sign convention.
- B
Negative loss is positive gain under the stated convention.
- C
The loss value and probability have different units.
Twenty equally weighted ordered losses 1 through 20 use the lower empirical 95% quantile. Which rank is selected?
- A.
19
- B.
20
- C.
19.5
Answer and explanation
Answer: A
Other sample estimators require a different stated convention.
- A
ceil(20×0.95)=19, counting from one.
- B
This is the largest observation, not the first crossing.
- C
This interpolates instead of using the declared rank rule.