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moon · 2022年05月08日

为什么不能直接用Var=u-z*standard deviation公式算99%可能性下最大损失

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202112010200002202

问题如下：

What is the approximate VaR for the bond position at a 99% confidence interval (equal to 2.33 standard deviations) for one month (with 21 trading days) if daily yield volatility is 0.015% and returns are normally distributed?

选项：

A.

$1,234,105

B.

$2,468,210

C.

$5,413,133

解释：

A is correct. The expected change in yield based on a 99% confidence interval for the bond and a 0.015% yield volatility over 21 trading days equals 16 bps = (0.015% × 2.33 standard deviations × √21).

We can quantify the bond’s market value change by multiplying the familiar (–ModDur × ∆Yield) expression by bond price to get $1,234,105 = ($75 million × 1.040175 ⨯ (–9.887 × .0016)).

为什么不能直接用Var=u-z*standard deviation公式算99%可能性下最大损失


要先求收益率的改变，而且为什么收益率改变=u-z*standard deviation，这个不是求Var的公式吗？

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2 个答案

pzqa015 · 2022年05月11日

嗨，爱思考的PZer你好：


本题让计算的是Bond Position的var，也就是一定概率下债券市值的最大损失。

根据△P=-P*md*△y，只有当△y取正且最大时，△P变动方向为负且最大，此时可以得到债券市值的最大损失。

所以，我们要先找到△y取正的最大值。

根据Var的公式，|μmonthly-2.33σmonthly|，这个公式得到是以μ为原点，向左、向右的最大值，向左得到的是最大亏损，向右得到的是最大收益。

如果已知y的μ和σ，-2.33σmonthly得到就是△y取负的最大值，2.33σmonthly得到的就是△y取正的最大值

所以，要用2.33*0.015%*21^(1/2)得到△y取正的最大值，进而根据△P=-P*md*△y来计算出bond position的最大损失。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

pzqa015 · 2022年05月11日

嗨，努力学习的PZer你好：


不好意思同学，这里写错了，应该是0.015%，不是0.08%。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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