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410140980 · 2023年07月01日

cash flow mapping一定是小于principal mapping?

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.

如题,老师是为撒啊?是因为现金流先回收了部分,所以到期时间缩短吗?

3 个答案

pzqa27 · 2023年07月06日

嗨,爱思考的PZer你好:


由于principal mapping不考虑中间的现金流,其duration会比考虑coupon的情况下要大,因此principal mapping 后计算的VaR要大一些,具体证明可以参考这图这个例题,把3种mapping都计算了一遍,结果也是比较直观的

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加油吧,让我们一起遇见更好的自己!

pzqa27 · 2023年07月05日

嗨,爱思考的PZer你好:


Cash-flow mapping: 组合的风险被分解到债券的每一笔单独的现金流。这种方法下的现金流是分散开的,计算出来的risk低于principal mapping,因为principal mapping不考虑债券组合到期前的coupon,所有风险集中于本金。


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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!

410140980 · 2023年07月05日

现金流分散的,计算的risk不就是等于相关性等于0。所以会比principal的risk低(现金流只有本金一笔相当于自己的自己的相关性为1),所以cash flow的risk低?

pzqa27 · 2023年07月03日

嗨,爱思考的PZer你好:


同学你好,cash flow mapping直接把每个期限现金流对应的风险相加,因为有期间的coupon拖后腿,所以比principle mapping小,而不是大。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

410140980 · 2023年07月04日

老师我更晕了,有coupon拖后腿了反而cash flow mapping小?

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