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徐威廉 · 2024年10月27日

CASHFLOW MAPPING和 duration mapping 计算出的VaR谁大谁小?

NO.PZ2023100703000049

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:

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.

CASHFLOW MAPPING和 duration mapping 计算出的VaR谁大谁小?

2 个答案
已采纳答案

pzqa27 · 2024年10月29日

嗨,从没放弃的小努力你好:


使用 Duration Mapping 计算的 VaR 通常小于使用 Cashflow Mapping 计算的 VaR。这是因为 Cashflow Mapping 能捕捉不同期限现金流的波动风险,而 Duration Mapping 将所有现金流简化成一个久期,忽略了时间分布,导致低估了风险。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

徐威廉 · 2024年10月30日

那么这三个方法对应的VaR的大小关系就是, Principal mapping > Cashflow mapping> Duration mapping

pzqa27 · 2024年10月30日

嗨,努力学习的PZer你好:


是的,你的理解是正确的。根据三种方法的特点,VaR 的大小关系可以总结如下:

  1. Principal Mapping:通常会产生最大的 VaR,因为它考虑了整体投资组合的本金和利息支付,但可能会高估风险,因为它忽略了现金流的时间分布。
  2. Cash-flow Mapping:由于它考虑了每个现金流的时间和大小,因此通常产生的 VaR 会小于 Principal Mapping,但仍然大于 Duration Mapping,因为它能更全面地反映投资组合的风险。
  3. Duration Mapping:由于将投资组合简化为一个零息债券,只考虑了久期,且忽略了中间现金流,因此它通常产生最小的 VaR。

综上所述,VaR 的大小关系为: Principal Mapping > Cash-flow Mapping > Duration Mapping

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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