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一灰两灰三四灰 · 2022年12月23日

daily yield volatility不是应该再乘一个ytm吗？

  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)).

例题中不是应该再乘一个ytm才能继续计算吗？

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2 个答案

pzqa015 · 2022年12月25日

嗨，爱思考的PZer你好：


σmonthly=21^1/2*σdaily，所以0.0016不是monthly volatility。用不上现在的ytm

我们要找出ytm的最大取值。

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。

回到本题

2.33*0.015%*21^(1/2)得到△y取正的最大值，也就是0.0016

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pzqa015 · 2022年12月24日

嗨，努力学习的PZer你好：


1,234,105 = ($75 million × 1.040175 ⨯ (–9.887 × .0016)).

0.0016就是Ytm

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努力的时光都是限量版，加油！

一灰两灰三四灰 · 2022年12月24日

0.0016是month yield volatility吧？例题讲解中是把0.015先乘了现在的ytm（本题是2.85%)再去月化再乘2.33的

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