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思梦92 · 2022年01月03日

如何理解B选项

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000047

问题如下：

A portfolio manager is mapping a fixed-income portfolio into exposures on selected risk factors. The manager is analyzing the comparable mechanics and risk measurement outputs of principal mapping, duration mapping, and cash-flow mapping that correspond to the average portfolio maturity. Which of the following is correct?

选项：

A.

Principal mapping considers coupon and principal payments, and the portfolio VaR using principal mapping is greater than the portfolio VaR using cash-flow mapping.

B.

Duration mapping does not consider intermediate cash flows and the portfolio VaR using duration mapping is less than the portfolio VaR using principal mapping.

C.

Cash-flow mapping considers the timing of the redemption cash flow payments only, and the portfolio VaR using cash flow mapping is less than the portfolio VaR using duration mapping.

D.

Cash-flow mapping considers the present values of cash flows grouped into maturity buckets, and the undiversified portfolio VaR using cash-flow mapping is greater than the portfolio VaR using principal mapping.

解释：

B is correct.

考点 ： Mapping to Fixed Income Portfolios

解析 ： With duration mapping, a portfolio is replaced by a zero-coupon bond with maturity equal to the duration of the portfolio. The risk of the hypothetical zeros is less than the risk of a coupon bond of comparable maturity. Therefore, the portfolio VaR using duration mapping is less than the portfolio VaR using principal mapping.

With principal mapping, one risk factor is chosen that corresponds to the average portfolio maturity. With duration mapping, one risk factor is chosen that corresponds to the portfolio duration. With cash flow mapping, the portfolio cash flows are grouped into maturity buckets and the undiversified portfolio VaR using cash-flow mapping is less than the portfolio VaR using principal mapping since principal mapping ignores the intervening coupon payments, thus overstating the true risk of the portfolio.

我整体是理解B选项的,不过有个小问题,在计算Duration mapping时候用到了Mac D,计算MacD其实会用到映射债券的期间现金流,那怎么理解B中说不考虑期间现金流呢？谢谢

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2 个答案

李坏_品职助教 · 2023年01月25日

嗨，爱思考的PZer你好：


duration mapping并没有考虑每个现金流，他只是找了一个期限等同于债券组合久期的零息债，把这个零息债的risk作为组合的var。

参考讲义：

这里的实际上是用2年期限和3年期限的零息债，interpolate了出来一个虚构的2.73年的零息债。用这个虚构零息债的VaR来作为债券组合的VaR。

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李坏_品职助教 · 2022年01月04日

嗨，爱思考的PZer你好：


B选项：duration mapping相当于把bond组合看作是到期期限等于组合久期的零息债。


B项目的描述“does not consider cash flows”是针对这个零息债来说的，确实没有考虑零息债券的期间现金流。

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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！

Carmen · 2023年01月25日

感觉有点抠字眼了，站在整体现金流的角度来看，duration mapping是把每个现金流单独看成一个零息债券来考虑，对于整个组合来讲这都不算叫做consider cash flow吗？你选项也没说这是站在哪个角度来讲。

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