答案A是不是不严谨

问题如下：

Which of the following statements comparing VaR with expected shortfall is true?

选项：

Expected shortfall is sub-additive while VaR is not.

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.

Both VaR and expected shortfall depend on the assumption of a normal distribution of returns.

VaR can vary according to the confidence level selected, but expected shortfall will not.

解释：

A is correct.

考点$：$Coherent Risk Measures

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.

我记得在正态分布的前提下 var是满足次可加性的？