老师，请问什么时候用Key rate或者PVD呢？

NO.PZ2018120301000031 问题如下 ug,the newly hirechief ­financiofficer for the City of Raor asks theputy ­financimanager, Hui, to prepare analysis of the currentinvestment portfolio anthe city’s current anfuture obligations. The cityhmultiple liabilities of fferent amounts anmaturities relating to thepension fun infrastructure repairs, anvarious other obligations. Huiobserves ththe current ­fixeincome portfolio is structureto mattheration of ealiability. Previously, this structure causethe city toaccess a line of cret for temporary mismatches resulting from changes in theterm structure of interest rates. ugasks Hui for fferent strategies to manage the interest rate risk of thecity’s ­fixeincome investment portfolio against one-time shifts in the yielurve. Hui consirs two fferent strategies:Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity.Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. Whichration measure shoulmatchewhen implementing Strategy 2? A.Key rate B.Mo­fie C.Macaul CorreAnswer: is correct. investor having investment horizon equto the bons Macaulration is effectively protecte or immunize from the first change in interest rates, because priancoupon reinvestment effects offset for either higher or lower rates.本题考查Single liability ration matching的条件。这个条件只能使用Macaulration。因为只要当资产的Macaulration = 投资期时，债券的Pririsk和reinvestment risk才能相互抵消，债券才能实现利率风险免疫。我们认为实现利率风险免疫后的债券是安全的，投资是可靠的。所以用该债券去匹配负债是合适的，于是再让投资期等于负债的期限，即，让免疫后的债券投资匹配上了负债。如，单期负债的期限是5年，为了构建免疫，资产的投资期必须是5年，这样资产到期时可以偿还负债。为了让资产的投资对利率免疫，则找到macaulration = 投资期 = 5的债券，于是得到了Macaulration = 投资期 = 负债的期限，我们实现了利率免疫。 老师好，是不是strategy1和2都用Mac为single liability，如果是multiple liability，用mofie或money

NO.PZ2018120301000031问题如下 ug,the newly hirechief ­financiofficer for the City of Raor asks theputy ­financimanager, Hui, to prepare analysis of the currentinvestment portfolio anthe city’s current anfuture obligations. The cityhmultiple liabilities of fferent amounts anmaturities relating to thepension fun infrastructure repairs, anvarious other obligations. Huiobserves ththe current ­fixeincome portfolio is structureto mattheration of ealiability. Previously, this structure causethe city toaccess a line of cret for temporary mismatches resulting from changes in theterm structure of interest rates. ugasks Hui for fferent strategies to manage the interest rate risk of thecity’s ­fixeincome investment portfolio against one-time shifts in the yielurve. Hui consirs two fferent strategies:Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity.Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. Whichration measure shoulmatchewhen implementing Strategy 2? A.Key rateB.Mo­fie.Macaulay CorreAnswer: is correct. investor having investment horizon equto the bons Macaulration is effectively protecte or immunize from the first change in interest rates, because priancoupon reinvestment effects offset for either higher or lower rates. 麻烦问老师下如果是含权债券，是key rate ration match还是effective ration match？谢谢

NO.PZ2018120301000031 问题如下 ug,the newly hirechief ­financiofficer for the City of Raor asks theputy ­financimanager, Hui, to prepare analysis of the currentinvestment portfolio anthe city’s current anfuture obligations. The cityhmultiple liabilities of fferent amounts anmaturities relating to thepension fun infrastructure repairs, anvarious other obligations. Huiobserves ththe current ­fixeincome portfolio is structureto mattheration of ealiability. Previously, this structure causethe city toaccess a line of cret for temporary mismatches resulting from changes in theterm structure of interest rates. ugasks Hui for fferent strategies to manage the interest rate risk of thecity’s ­fixeincome investment portfolio against one-time shifts in the yielurve. Hui consirs two fferent strategies:Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity.Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. Whichration measure shoulmatchewhen implementing Strategy 2? A.Key rate B.Mo­fie C.Macaul CorreAnswer: is correct. investor having investment horizon equto the bons Macaulration is effectively protecte or immunize from the first change in interest rates, because priancoupon reinvestment effects offset for either higher or lower rates. 记得有道题与这道题背景差不多，关键点在于这个liability是MBS类型的，所以应该用e这道题也类似，有很多固定资产的债务，是不是也与mbs类似，要用effective ration？

NO.PZ2018120301000031问题如下 ug,the newly hirechief ­financiofficer for the City of Raor asks theputy ­financimanager, Hui, to prepare analysis of the currentinvestment portfolio anthe city’s current anfuture obligations. The cityhmultiple liabilities of fferent amounts anmaturities relating to thepension fun infrastructure repairs, anvarious other obligations. Huiobserves ththe current ­fixeincome portfolio is structureto mattheration of ealiability. Previously, this structure causethe city toaccess a line of cret for temporary mismatches resulting from changes in theterm structure of interest rates. ugasks Hui for fferent strategies to manage the interest rate risk of thecity’s ­fixeincome investment portfolio against one-time shifts in the yielurve. Hui consirs two fferent strategies:Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturity.Strategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration. Whichration measure shoulmatchewhen implementing Strategy 2? A.Key rateB.Mo­fie.Macaulay CorreAnswer: is correct. investor having investment horizon equto the bons Macaulration is effectively protecte or immunize from the first change in interest rates, because priancoupon reinvestment effects offset for either higher or lower rates. 为什么single liability用mration match，multiple liability用mofieration match