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FRM一级考前复习题<2>

来源：高顿网校 2015-03-27

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　　2. EVT中那个字母说明尾部形状，大于1肥尾，小于0细尾，而数量分析习题课第52题第二个说法，说这个字母为负的时候说明尾部比正态分布尾部消失的快，尾部细不就是消失得快吗？

　　Which of the following statements about Extreme Value Theory (EVT) and its application to value at risk are true?

　　I. EVT extends the Central Limit Theorem to the distribution of the tails of independent, identically distributed random variables drawn from an unknown distribution.

　　II. For empirical stock market data, the shape parameter in EVT is negative implying tails that disappear more rapidly than a normal distribution.

　　III. EVT can help avoid a shortcoming of the historical simulation method which may have difficulty calculating VaR reliably due to a lack of data in the tails.

　　IV. For empirical stock market data, standard value at risk estimates at the 95% confidence level are exceeded more often than 5% of the time and would therefore benefit from the use of extreme value theory.

　　A. I and III

　　B. II and IV

　　C. I, III and IV

　　D. III and IV

　　Answer: A

　　I. correct. Whereas the Central Limit Theorem concerns the distribution of the average of independent, identically distributed variables drawn from an unknown distribution, EVT deals with the distribution of the tails.

　　II. incorrect. The shape parameter in EVT for empirical stock market data is typically between 0.2 and 0.4, implying that the tails disappear more slowly than a normal distribution.

　　III. correct. Due to its reliance on historical data which may lack sufficient tail data (i.e., extreme events), reliably calculating VaR with the historical simulation method can be difficult; EVT can help avoid this shortcoming.

　　IV． incorrect. For empirical stock market data, standard value at risk estimates at the 95% confidence level tend to be fairly accurate, and generally only becomes inaccurate at the 99.5% confidence level and beyond.

　　答疑：Shape parameter determines the speed at which the tail disappears. The normal distribution corresponds to shape parameter equals zero while typical financial data have a positive shape parameter which implies fat tails. (Handbook P364)。这道题的问题出在for empirical stock market data, 应该是肥尾的现象，对应正的shape parameter。而后半句没有问题。

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