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徐威廉 · 2022年08月17日

追问VaR

  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)).

“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。 ”


这段话什么意思？什么取负最大值，取正最大值，到底本题的VaR算出来是+0.0016还是-0.0016？

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pzqa015 · 2022年08月18日

嗨，从没放弃的小努力你好：


本题计算的var是债券value的最大损失

根据△P/P=-MD*△y，要计算P的最大损失，就要用到△y取最大值的最大收益。

根据y的均值和方差，μmonthly+2.33σmonthly就是△y的最大值，是+16bp。

这道题的条件给错了，σ应该是0.015%而不是1.5%。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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