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我们 · 2020年04月28日

问一道题：NO.PZ2016082406000085

  1. FRM II
  2. Credit Risk Measurement And Management

问题如下：

You are the credit risk manager for Bank Happy. Bank Happy holds Treasuries for USD 500 million: one large loan that has a positive probability of default for USD 400 million and another loan that has a positive probability of default for USD 100 million. The defaults are uncorrelated. The bank computes a credit VAR at 1% using CreditRisk+. Which of the following statements made about the VAR by the analyst who works for you is necessarily wrong?

选项：

A.

The VAR or WCL can be equal to zero.

B.

The expected loss on the portfolio exceeds the VAR.

C.

The expected loss on the portfolio is necessarily smaller than the VAR.

D.

None of the above statements is wrong.

解释：

ANSWER: C

The credit VAR could be zero. For instance, assume that the PD is 0.003. The joint probability of no default is then (1−0.003)(1−0.003)=99.4%{(1-0.003)}{(1-0.003)}=99.4\%. Because this is greater than the 99% confidence level, the worst loss is zero. The expected loss, however, would be 0.3% assuming zero recovery, which is greater than VAR.

没有看懂这个题目的解释，麻烦能再解释一下吗？


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2 个答案

品职答疑小助手雍 · 2020年04月28日

对啊，99%的var定义对应的是第一个累计概率超过99%的损失值，这题里第一个超过99%的累计概率是99.4%，对应的损失是0，那么wcl就是0.

品职答疑小助手雍 · 2020年04月28日

嗨，爱思考的PZer你好：


本题答案解析其实是举了一个极端的例子来说明各选项的。当违约概率非常低，比如解析中所给的0.3%时，两笔贷款d都不违约的概率是99.4%，而WCL的定义是 P(LOSS<= ?) = 99%.  所以根据定义，WCL就取0。所以A是可以成立的。

而 EL 就是总金额*违约概率*LGD，本题中，假设PD等于0.3%时，那就是0.003*500million 。此时EL就超过了CVAR了。B在这个极端的情况下也是成立的。


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我们 · 2020年04月28日

是因为两笔贷款都不违约的概率为99.4%，然后99.4%在99%左边（大于99%），所以WCL=0?

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