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上小学 · 2023年07月29日

请问此题目在说什么？谢谢

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000042

问题如下：

An analyst is using the delta-normal method to determine the VaR of a fixed income portfolio. The portfolio contains a long position in 1-year bonds with a $1 million face value and a 6% coupon that is paid semi-annually. The interest rates on six-month and twelve-month maturity zero-coupon bonds are, respectively, 2% and 2.5%. Mapping the long position to standard positions in the six-month and twelve-month zeros, respectively, provides which of the following mapped positions?

选项：

A.

$30,000 and 1,030,000

B.

$29,500 and 975,610

C.

$29,703 and 1,004,878

D.

$30,300 and 1,035,000

解释：

C is correct.

考点 ： Mapping to Fixed Income Portfolios

解析 ： The long position is mapped into a combination of market values of the zero-coupon bonds that provide the same cash flows:

Xsix=300001+0.02/2=29703X_{six}=\frac{30000}{1+0.02/2}=29703

Xtwelve=10300001+0.025=1004878X_{twelve}=\frac{1030000}{1+0.025}=1004878

看不懂题目在说什么，要求是什么？什么是多头转换为标准？

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1 个答案
已采纳答案

pzqa27 · 2023年07月30日

嗨，爱思考的PZer你好：


这道题目是关于使用Delta-Normal方法来计算一个固定收益组合的价值风险（VaR）。该投资组合包含一份价值100万美元的1年期债券，其票面利率为6%，半年付息一次。6个月期和12个月期零息债券的利率分别为2%和2.5%。现在需要将这个长头寸的投资组合映射成6个月期和12个月期零息债券的标准头寸，问哪个选项是正确的？

正确答案是选项 C。

在Delta-Normal方法中，VaR的计算需要将投资组合的头寸映射成基础风险因素的标准头寸。在这个问题中，基础风险因素就是6个月期和12个月期零息债券的利率。

为了将这份1年期债券映射成6个月期和12个月期零息债券的标准头寸，我们需要计算这些零息债券的市场价值，使得它们能够提供与1年期债券相同的现金流。

具体计算步骤如下：

  1. 对于6个月期零息债券：
  2. 6个月期零息债券的市场价值 = 3万 / (1 + 0.02/2) ≈ 29703
  3. 对于12个月期零息债券：
  4. 12个月期零息债券的市场价值 = 1030000 / (1 + 0.025) ≈ 1004878

因此，正确的映射头寸为：

选项 C：6个月期零息债券标准头寸为29,703美元，12个月期零息债券标准头寸为1,004,878美元。

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