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罗小胖 · 2023年10月01日

为什么,没懂

NO.PZ2023091701000096

问题如下:

A risk manager is estimating the 1-day 95% VaR on a domestic equity portfolio using a 100-day lookback period. The mean return, estimated from the historical data, is 0% with a standard deviation of 2%. The six most extreme negative returns over the lookback period, along with the time they occurred, are:


Over a period of 10 days after the risk manager computed the portfolio’s VaR, four new extreme declines occurred: -25%,-4.1%, -7.8% and -9.5%. On the other six days, the portfolio experienced positive returns. The risk manager must now update the previous VaR estimate to account for these changes. Assuming the portfolio has a current value of USD 100 million, what is the updated 1-day 95% VaR using the historical approach?

选项:

A.USD 3.28 million B.USD 4.70 million C.USD 10 million D.USD 25 million

解释:

为什么不是-10

1 个答案

李坏_品职助教 · 2023年10月01日

嗨,努力学习的PZer你好:


题目说的是要用historical approach计算更新后的(updated)1天的95%的VaR。

题目本来就有100个return数据,现在新加入了:-25%,-4.1%, -7.8% and -9.5%这几个数据,这样样本容量就超过100了。所以需要剔除一些距离现在最久远的数据,然后重新计算排在第5名的损失值(95%的置信度对应着5%的损失阈值,5%*100=5)。


加入几个新数据之后,损失值排名如下:-25%,-10%,-9.5%,-7.8%,-6.3%,-4.7%,注意这里面的-10%是95天之前的老数据,所以要剔除。那么剩下的数据里面,-4.7%正好排在第五名,所以VaR就是|-4.7%*100million| = 4.7million

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