在備考FRM二級考試中，常常有考生因?yàn)榇笠舛鲥e(cuò)題目。今天，小編就為大家分享一篇易錯(cuò)題，送給備考的你！

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

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.

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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.

Akey 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.

翻譯如下：

以下哪項(xiàng)將VaR與預(yù)期短缺進(jìn)行比較的陳述是正確的？

A）預(yù)期缺口是次加性的，而VaR不是。

B）VaR和預(yù)期缺口衡量的是投資者在給定時(shí)間段內(nèi)預(yù)期損失的資本量，因此，作為風(fēng)險(xiǎn)衡量指標(biāo)是可互換的。

C）VaR和預(yù)期缺口都依賴于收益正態(tài)分布的假設(shè)。

D）VaR可以根據(jù)所選的置信水平而變化，但預(yù)期短缺不會變化。

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解析：VaR衡量的是一個(gè)人在給定的信心水平下，在給定的時(shí)間段內(nèi)，預(yù)期損失的資本額。VaR的一個(gè)問題是，它沒有提供關(guān)于VaR之外的預(yù)期損失大小的信息。

VaR通常由預(yù)期虧損來補(bǔ)充，預(yù)期虧損以虧損超過VaR為條件來衡量預(yù)期虧損。請注意，由于預(yù)期虧損是基于VaR的，因此改變信心水平可能會改變這兩種衡量標(biāo)準(zhǔn)。

這兩個(gè)指標(biāo)的最大區(qū)別在于VaR不是次加性的，這意味著兩個(gè)基金單獨(dú)投資的風(fēng)險(xiǎn)可能低于兩個(gè)基金組合投資的風(fēng)險(xiǎn)。違反次加性假設(shè)是一個(gè)風(fēng)險(xiǎn)值的問題，不存在預(yù)期短缺。

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