题目
The measurement error in VaR due to sampling variation should be greater with:
选项
A.More observations and a high confidence level (e.g. 99%)
B.Fewer observations and a high confidence level(e.g. 99%)
C.More observations and a low confidence level (e.g. 95%)
D.Fewer observations and a low confidence level (e.g. 95%)
答案
B
解析
Sampling variability (or imprecision) increases with: (i) fewer observations and (ii) higher confidence levels. To show (i), we can refer to the formula for the precision of the sample mean, which varies inversely with the square root of the number of data points. A similar reasoning applies to (ii). A higher confidence level involves fewer observations in the left tails, from which VaR is computed.抽样变异性（或不精确性）随着以下因素的增加而增加：（i）观测值减少和（ii）高置信度。 为了显示（i），我们可以参考公式来计算样本均值的精度，该精度与数据点数的平方根成反比。 类似的推理适用于（ii）。 置信度越高，在左尾部观察到的值越少，从而可以计算VaR。