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JustJuve · 2021年03月13日

麦考利久期和修正久期的区别在哪?

NO.PZ2019103001000031

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.

我印象中这两个的定义没有本质区别啊?

JustJuve · 2021年03月13日

本章基础班讲义第45页解释E(Change in price based on investor's views of yields and yield spreads)的时候,明确说MD is the modified duration of a bond

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发亮_品职助教 · 2021年03月14日

麦考利久期和修正久期的区别在哪?我印象中这两个的定义没有本质区别啊?


有区别的。

Macaulay duration是时间概念,他是有单位的,单位是:Year;例如,债券的Macaulay duration = 9 years;

Macaulay duration衡量的是:投资债券,我们拿到债券所有现金流的平均时间。

例如,9年期的零息债券,唯一一笔现金流发生在第9年年末,因此,我们投资该债券,拿到所有现金流的平均时间Macaulay duration = 9 years;

而9年期、Coupon rate = 10%的债券,由于有Coupon发生在9年之前,因此,我们投资该债券,拿到所有现金流的平均时间<9,例如,他的Macaulay duration = 6 years。也就是投资该债券,拿回所有现金流,平均来看需要6年。


而Modified duration,是利率敏感度的概念,这是一个弹性系数,没有单位。他衡量:利率变动1单位时,债券的价格变动多少幅度。

我们平时经常会研究利率变动时,债券的价格变动多少,因此平时经常用的就是Modified duration。一般情况下,Duration默认的也是Modified duration。


由于很多情况下,Modified duration与Macaulay duration基本上差异不是很大,所以经常看到有地方将Macaulay duration也当成是利率敏感度,也会出现混用的情况。这种用法只是近似,但不规范,有误差。我们考试就考查的是定义、概念的区别,因此咱们用的时候要区别对待、要用规范。


和Modified duration有一个近似的概念,就是effective duration。

区别就是适用范围不同:Modified duration只适用于普通债券;而Effective duration适用于普通债券、含权债券、浮动利率债券。


Modified duration(Effective duration)只能衡量债券的价格变动率,也就是只能衡量债券的价格变动幅度。如果要看债券具体变动多少金额,我们就引入了以下几个概念:

Money duration、BPV、PVBP,这几个是近亲。

Money duration = modified duration × Market value

BPV(PVBP)= modified duration × Market value × 0.0001

他们都衡量,利率变动1单位时,债券具体变动多少金额。


本章基础班讲义第45页解释E(Change in price based on investor's views of yields and yield spreads)的时候,明确说MD is the modified duration of a bond

是的。这里是计算利率变动时,债券的价格变动幅度(Change in price),因此我们只能用利率敏感度,Modifed duration or effective duration。不能使用Macaulay duration。

而提问里的这道题目,是做单期负债匹配,在单期负债匹配这里,只能用Macaulay duration。

玛卡巴卡 · 2022年01月27日

所以是single liability match的时候用Mac D , multiple liability match的时候BPV里面用modified D吗?

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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