State the joint assumption
Each of two components loses 100 with probability 4% and zero with probability 96%. Independence is explicitly supplied. The joint model has losses 0/100/200 with probabilities 92.16/7.68/0.16 percent.
Keep the inference narrow
A counterexample can disprove a universal property, but does not claim that every combination behaves the same way. No real portfolio selection or official exam question is supplied.
Try the questions
What is the probability of combined zero loss?
- A.
96%
- B.
92.16%
- C.
192%
Answer and explanation
Answer: B
Neither component must lose.
- A
This is one component’s zero-loss probability.
- B
0.96×0.96 uses the supplied independence.
- C
Probabilities of simultaneous events are not added this way.
Using the lower 95% quantile, which combined VaR follows?
- A.
0
- B.
100
- C.
200
Answer and explanation
Answer: B
The combined VaR exceeds the sum of individual VaRs zero.
- A
Only 92.16% probability is at zero, below confidence.
- B
Cumulative probability reaches 99.84% at 100.
- C
This is the maximum listed combined loss.
Which mass forms the combined worst 5%?
- A.
0.16% at 200 plus 4.84% at 100
- B.
All 7.68% at 100 and all 0.16% at 200
- C.
Only 0.16% at 200
Answer and explanation
Answer: A
The weighted sum 5.16 divided by 0.05 gives ES 103.2.
- A
These probabilities sum to exactly 5%.
- B
This selects too much probability.
- C
This selects too little probability.