Use the original 95% model
Mean loss is zero and dispersion ten. Standard normal z is approximately 1.644854, density at z approximately 0.1031356404 and upper-tail probability 0.05.
Keep the three objects distinct
The density equality follows from the normal first-moment integral. A density height is not itself a point probability or an already normalised tail mean.
Try the questions
What is the 95% standard-normal tail-mean multiplier?
- A.
0.1031356404 approximately
- B.
2.0627128075 approximately
- C.
1.644853627 approximately
Answer and explanation
Answer: B
The selected tail probability supplies the denominator.
- A
This is the unnormalised first moment.
- B
Divide the first moment by 0.05.
- C
This is the quantile threshold.
What is probability at exactly zero under a positive-dispersion continuous normal law?
- A.
0
- B.
0.398942 approximately
- C.
50%
Answer and explanation
Answer: A
Interval area, not curve height, gives probability.
- A
A single point has zero probability under this continuous law.
- B
That is the standard density height at zero.
- C
That confuses a point with a half-line event.
With mean loss 7 and dispersion zero, how should the tool treat the record?
- A.
Constant loss, VaR and ES both 7, no density figure
- B.
Divide the density by zero
- C.
Set both summaries to zero
Answer and explanation
Answer: A
The constant loss amount need not be zero.
- A
This is the degenerate constant limit.
- B
The positive-scale expression is undefined.
- C
That discards the entered constant loss.