Use the original normal law
Unless changed by a question, mean loss is 0, dispersion 10 and confidence 95%. Positive loss means loss; negative loss means gain. The standard normal quantile is approximately 1.644854.
Identify the quantity being scaled
A standard quantile coefficient is dimensionless. Apply it to loss standard deviation, then add mean loss in the same unit. These are original teaching questions rather than official exam items.
Try the questions
What is the original 95% normal-model VaR?
- A.
16.448536 approximately
- B.
164.485363 approximately
- C.
20.627128 approximately
Answer and explanation
Answer: A
Use the quantile coefficient rather than the tail-mean coefficient.
- A
0+10×1.644854... applies the correct scale.
- B
This substitutes variance 100 for standard deviation 10.
- C
This is the selected-tail mean, not the threshold.
For fixed starting value 1,000,000 and mean return 1%, what is mean loss under L=−Vr?
- A.
+10,000
- B.
−10,000
- C.
−20,000
Answer and explanation
Answer: B
The mean transformation includes the negative sign.
- A
This reverses the stated positive-loss convention.
- B
Positive mean return produces negative mean loss.
- C
That would confuse the supplied 2% return dispersion with the mean.
The source reports loss variance 100 squared units. Which dispersion belongs in the normal tail formula?
- A.
100
- B.
10
- C.
−10
Answer and explanation
Answer: B
Use the positive square root before multiplying by a dimensionless coefficient.
- A
Variance uses squared units.
- B
The square root restores loss units.
- C
Standard deviation is nonnegative.