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zhenyu · 2024年08月03日

为什么乘以每只债券的价格？

  1. CFA III
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ202303270300007102

问题如下：

(2) 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 1.50 bps 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 1.50 bps yield volatility over 21 trading days equals 16 bps = (1.50 bps × 2.33 standard deviations × 211/2). 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)).

讲义里公式是change in bond position=-Duration*change in YTM*MktValue, 这里(–9.887 × .0016)就已经算出新加入portfolio的价格变动率了，直接乘以market value不行吗， 还是说change in bond position这个公式算的也是percentage change in bond price?

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zhenyu · 2024年08月03日

没事儿了，我看错了

1 个答案
已采纳答案

发亮_品职助教 · 2024年08月03日

104.0175是市场价格，但不是我们持有债券的总market value。

因为104.0175是每100面值的债券市场价格。我们持有的债券总面值是75million，所以持有债券的总market value是：

104.0175/100 × 75 million


其中104.0175/100是换算成每1元面值的市场价格，75million是持有的总面值par，于是持有的债券总market value是：

104.0175/100 × 75 million


需要基于以上market value来算VaR哈

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