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小小悟空yu · 2021年05月11日

为什么这里的mr or不乘以12。5，直接相加

  1. FRM II
  2. Operational Risk and Resiliency

NO.PZ2016072602000032

问题如下：

Your bank calculates a one-day 95% VAR for market risk, a one-year 99% VAR for operational risk, and a one-year 99% VAR for credit risk. The measures are $100 million, $500 million, and $1 billion, respectively. Operational risk is defined to include all risks that are not market risks and credit risks, and these three categories are mutually uncorrelated. The market risk VAR assumes normally distributed returns, and the bank expects to be successful to keep its market risk VAR at that level for the whole year. Your boss wants your best estimate of a firmwide VAR at the 1% level. Among the following choices, your best estimate is:

选项：

A.

$1.7 billion

B.

$1.94 billion

C.

$2.50 billion

D.

It is impossible to aggregate risks with different distributions having only this information.

解释：

C is correct. First, we convert the daily VAR at the 95% level to the same parameters as the other. With the normality assumption, this is VARMKT = $100 x (2.326/ 1.645) 252\sqrt{252} = $2,245. We then combine the three VARs by taking the square root of the sum of squares, which gives VAR =$2,2452+$5002+$10002\sqrt{\$2,245^2+\$500^2+\$1000^2} = $2,458.

为什么这里的mr or不乘以12。5，直接相加
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1 个答案

小刘_品职助教 · 2021年05月11日

同学你好，

因为题目里说了mutually uncorrelated，意思就是三大风险每个风险的相关系数都为0。求总风险得先求出组合的总方差，然后开根号。因为相关系数为0，所以含ρ的项都为0。直接相加必须要相关系数都为1的。

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NO.PZ2016072602000032 问题如下 Your bank calculates a one-y 95% Vfor market risk, a one-ye99% Vfor operationrisk, ana one-ye99% Vfor cret risk. The measures are $100 million, $500 million, an$1 billion, respectively. Operationrisk is fineto inclu all risks thare not market risks ancret risks, anthese three categories are mutually uncorrelate The market risk Vassumes normally stributereturns, anthe bank expects to successful to keep its market risk Vthlevel for the whole year. Your boss wants your best estimate of a firmwi Vthe 1% level. Among the following choices, your best estimate is: $1.7 billion $1.94 billion $2.50 billion It is impossible to aggregate risks with fferent stributions having only this information. C is correct. First, we convert the ily Vthe 95% level to the same parameters the other. With the normality assumption, this is VARMKT = $100 x (2.326/ 1.645) 252\sqrt{252}252​ = $2,245. We then combine the three VARs taking the square root of the sum of squares, whigives V=$2,2452+$5002+$10002\sqrt{\$2,245^2+\$500^2+\$1000^2}$2,2452+$5002+$10002​ = $2,458. 如题

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