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JK_MMMM · 2022年03月15日

为什么算exposure是两个的相减?不应该是相加么?

NO.PZ2020011303000237

问题如下:

Suppose a portfolio has an exposure of +50 to a one basis-point increase in the five-year Treasury rate in Table 13.1, an exposure of -100 to a one-basis-point increase in the ten-year Treasury rate in Table 13.1, and no other exposures.

Using Table 13.2, calculate the standard deviation of the daily change in the portfolio above based on its exposure to the first two factors.


选项:

解释:

The exposure to one unit of the first factor is 50×(0.410)100×(0.414)=20.950\times(-0.410)-100\times (-0.414)=20.9

The exposure to one unit of the second factor is 50×0.203100×(0.193)=29.4550\times0.203-100\times(-0.193)=29.45

Using Table 13.2, the standard deviation is

14.152×20.92+4.912×29.452=329.19\sqrt{14.15^2\times20.9^2+4.91^2\times29.45^2}=329.19

如题

1 个答案

DD仔_品职助教 · 2022年03月15日

嗨,努力学习的PZer你好:


同学你好,

因为这道题是用了前面的一题的条件,前面的题目给出的条件如下图:

给出来的exposure一个正数一个负数,exposure就是两个数相加,题目简写了,就直接写成了相减。

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NO.PZ2020011303000237问题如下 Suppose a portfolio hexposure of +50 to a one basis-point increase in the five-yeTreasury rate in Table 13.1, exposure of -100 to a one-basis-point increase in the ten-yeTreasury rate in Table 13.1, anno other exposures. Using Table 13.2, calculate the stanrviation of the ily change in the portfolio above baseon its exposure to the first two factors. The exposure to one unit of the first factor is 50×(−0.410)−100×(−0.414)=20.950\times(-0.410)-100\times (-0.414)=20.950×(−0.410)−100×(−0.414)=20.9The exposure to one unit of the seconfactor is 50×0.203−100×(−0.193)=29.4550\times0.203-100\times(-0.193)=29.4550×0.203−100×(−0.193)=29.45Using Table 13.2, the stanrviation is14.152×20.92+4.912×29.452=329.19\sqrt{14.15^2\times20.9^2+4.91^2\times29.45^2}=329.1914.152×20.92+4.912×29.452​=329.19题目问假设有一个组合,当5年的treasury利率上升1bp时,exposure变成+50;10年的treasury利率上升1bp时,exposure变成-100。没有其他的exposure。根据图表与前两个factors,计算一天的组合标准差。先根据下图前两个factor,求组合的exposure。factor 150 × (−0.410) − 100 × (−0.414) = 20.9factor 250 × 0.203 − 100 × (−0.193) = 29.45组合标准差=14.152×20.92+4.912×29.452=329.19\sqrt{14.15^2\times20.9^2+4.91^2\times29.45^2}=329.1914.152×20.92+4.912×29.452​=329.19 对于计算组合方差疑问,应该用组合的权重乘以各自因素的方差,不应该是绝对值。谢谢

2023-03-23 17:53 4 · 回答

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2020-07-28 00:47 1 · 回答

(14.152 × 20. 92 + 4.912 × 29.452 )1/2= 329.19 不明白为什么算标准差 把第一问的exposure给放进来???

2020-06-17 22:02 2 · 回答

请教答案中20.9和29.45是怎么来的,谢谢

2020-04-01 22:53 1 · 回答