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SUN · 2020年11月28日

问一道题:NO.PZ2019103001000031 [ CFA III ]

问题如下:

Doug Kepler, the newly hired chief financial officer for the City of Radford, asks the deputy financial manager, Hui Ng, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Ng observes that the current fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates

Kepler asks Ng for different strategies to manage the interest rate risk of the city’s fixed-income investment portfolio against one-time shifts in the yield curve. Ng considers two different strategies:

Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity

Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

Which duration measure should be matched when implementing Strategy 2?

选项:

A.

Key rate

B.

Modified

C.

Macaulay

解释:

C is correct.

An investor having an investment horizon equal to the bond’s Macaulay duration is effectively protected, or immunized, from the first change in interest rates, because price and coupon reinvestment effects offset for either higher or lower rates.

我看发亮老师一直说这个是单期债券,但是题干说了他是包括养老金,基础建设等等很多债券,如果这里面含权,是不是只能用effective duration了? 拿在什么时候用modified duration呢
SUN · 2020年11月28日

虽然mac d和modified d有关系。但是多负债的时候用的条件是bpv,那是不是可以理解为多负债本质上都用的modified duration?

1 个答案

发亮_品职助教 · 2020年11月30日

嗨,从没放弃的小努力你好:


他是这样,Multiple liabilities 利用我们三级学到的匹配方法,实际上是至少可以用两种匹配方法:

第一种,就是对Multiple liabilities整体进行匹配,其实就是我们学的多期负债匹配,Match的时候看资产、负债的BPV,满足多期负债匹配条件即可。

第二种,就是Multiple liabilities里面,有可能可拆分成多个单期负债,如果我们对里面的单期负债进行逐个匹配,那最终站在Multiple liabilities的角度,这个多期负债也是匹配成功的。


这道题里面,Strategy 1和2,就是利用了逐个匹配的方法,他题干说:

Ng observes that the current fixed-income portfolio is structured to match the duration of each liability.

他是Match each liability,也就是逐个匹配单期负债,但是利率改变时,就会造成Mismatch,现在让NG同学推荐一个新的策略,NG同学就说了:

Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

注意,这里依然是对Single liabilities进行逐个匹配。但是用了continuously matching duration,所以避免了Mismatch的问题。


单期负债匹配只用看Macaulay duration。

多期负债匹配只用看Money duration(BPV/PVBP),现在的匹配条件里面无需看Effective duration、Modified duration。

如果出现含权债券,其实也不用Effective duration。

负债是含权债券,我们可以用含权债券资产匹配。或者可以像我们讲义那道例题一样,使用衍生品Remove掉负债的Call option,然后使用一个普通债券进行匹配,如果有遗忘的话可以参考一下讲义原题。


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


发亮_品职助教 · 2020年11月30日

对的,如果题目没给BPV的时候,需要求BPV的话就用Modified duration或者Effective duration算一下。 不过匹配这里的题目,一般BPV是已知条件。

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NO.PZ2019103001000031问题如下ug Kepler, the newly hirechief financiofficer for the City of Raor asks the puty financimanager, Hui Ng, to prepare analysis of the current investment portfolio anthe city’s current anfuture obligations. The city hmultiple liabilities of fferent amounts anmaturities relating to the pension fun infrastructure repairs, anvarious other obligations.Ng observes ththe current fixeincome portfolio is structureto matthe ration of ealiability. Previously, this structure causethe city to access a line of cret for temporary mismatches resulting from changes in the term structure of interest ratesKepler asks Ng for fferent strategies to manage the interest rate risk of the city’s fixeincome investment portfolio against one-time shifts in the yielcurve. Ng consirs two fferent strategies:Strategy 1: Immunization of the single liabilities using zero-coupon bon helto maturityStrategy 2: Immunization of the single liabilities using coupon-bearing bon while continuously matching ration.Whiration measure shoulmatchewhen implementing Strategy 2?A.Key rateB.Mofie.MacaulayC 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.是因为single liab吗?那如果Multiple liab呢?

2022-03-24 20:01 1 · 回答

NO.PZ2019103001000031 能否下KEY RATE RATION不选的原因,谢谢!

2021-12-30 12:01 1 · 回答

NO.PZ2019103001000031 MofieMacaul C 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. immunization的2个条件,PVa=PVL,=,是为了hee pririsk和ri risk带来的价格变动的影响,所以不是应该用的mify ration吗?mofy ration一样,这也利率变动,asset和liab的price变动一样,这也也能继续match了。为什么是mration,平均还款期呢?

2021-12-11 14:46 2 · 回答

NO.PZ2019103001000031 这道题我懂了,但是这两策略有什么区别呀

2021-09-16 06:15 2 · 回答

NO.PZ2019103001000031 MofieMacaul C 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. 如果前者匹配,后者不也一样匹配吗?毕竟就差个1/(1+y)

2021-04-20 18:51 18 · 回答