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lynn666 · 2023年05月16日

还是不明白为什么不能直接相加

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.

如题。三个var直接相加不行吗?一般巴塞尔协议不也是直接相加的吗,这还是巴塞尔的缺点之一,没有考虑diversification。题目中怎么看出来要平方后再开根号呢

1 个答案

DD仔_品职助教 · 2023年05月16日

嗨,从没放弃的小努力你好:


同学你好,

巴塞尔协议为了稳健,会要求VaR计算的能大一些多准备一些资本金会更好。

但是做题肯定有做题的方法,跟巴塞尔协议的要求没什么关系,这里计算VaR用的是三资产求sigma的公式,如下图,因为mutual unrelated,所以rho都为0,简化之后就是答案里的式子了:

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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