题目
Which of the following statements comparing VaR with expected shortfall is true?
选项
A.Expected shortfall is sub-additive while VaR is not.
B.Both VaR and expected shortfall measure the amount of capital an investor can expect to lose over a given time period and are, therefore, interchangeable as risk measures.
C.Both VaR and expected shortfall depend on the assumption of a normal distribution of returns.
D.VaR can vary according to the confidence level selected, but expected shortfall will not.
答案
A
解析
VaR measures the expected amount of capital one can expect to lose within a given confidence level over a given period of time. One of the problems with VaR is that it does not provide information about the expected size of the loss beyond the VaR. VaR is often complemented by the expected shortfall, which measures the expected loss conditional on the loss exceeding the VaR. Note that since expected shortfall is based on VaR, changing the confidence level may change both measures. A key difference between the two measures is that VaR is not sub-additive, meaning that the risk of two funds separately may be lower than the risk of a portfolio where the two funds are combined. Violation of the sub-additive assumption is a problem with VaR that does not exist with expected shortfall.VaR衡量的是在给定的时间段内，在给定的置信度内，人们可以预期损失的资本的预期数量。 VaR的问题之一是，它没有提供有关超出VaR的预期损失规模的信息。 VaR通常由预期的缺口来补充，该预期的短缺以超过VaR的损失为条件来衡量预期的损失。 请注意，由于预期的缺口是基于VaR的，因此更改置信度级别可能会同时更改这两个指标。 两种方法之间的主要区别在于VaR不是次可加的，这意味着分别将两种基金的风险低于将两种基金合并在一起的投资组合的风险。 违反亚可加性假设是VaR的问题，在预期的短缺方面不存在。