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lea · 2024年01月24日

为什么barbell的convexity最high?

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NO.PZ202209060200004006

问题如下:

Of the differences between a laddered strategy for fixed-income portfolios and bullet and barbell strategies described by Honanie, which is least likely correct?

选项:

A.Difference 3 B.Difference 2 C.Difference 1

解释:

Solution

C is correct. Given the same value and duration, of the three types, the bullet portfolio would have the lowest convexity and the barbell portfolio would have the highest. The laddered portfolio would have a convexity in between the two.

A is incorrect because the laddered portfolio would regularly buy new long-term securities to replace maturing securities on the short end. To the extent interest rates are volatile, the laddered portfolio would eventually contain a mixture (diversity) of high- and low-yielding securities.

B is incorrect because the laddered portfolio would always have some securities with little time remaining before maturity. These would be good collateral for a repo or loan or would shortly turn into cash (upon maturity), thus providing high liquidity.

为什么barbell的convexity最high? bullet convexity lowest?

1 个答案
已采纳答案

pzqa31 · 2024年01月25日

嗨,努力学习的PZer你好:


duration相同或相近,barbell、laddered、bullet三个portfolio convexity大小是:bullet<laddered<barbell。


债券的Convexity可以用下面这个公式来计算。

当Barbell/Bullet/Laddered这3个组合放到一起比较时,这3个Portfolio的性质是一模一样的,如Macaulay duration大小一致,Cash flow yield大小一致,投资期一致等等。总之,3个Portfolio唯一的差异就是现金流的分布不同

那这样的话,当3个Portfolio的Macaulay duration一致时,现金流的分布其实影响的是Portfolio现金流的离散程度Disperion。

根据下面公式,当现金流分布越分散的时候,现金流离散程度Dispersion越大,则Portfolio的Convexity越大;

当现金流分布越集中的时候,现金流离散程度Dispersion越小,则Portfolio的Convexity越小。

这3个Portfolio里面,Barbell的现金流分布最分散,因为有很大一部分现金流权重在短期、有很大一部分现金流权重在长期。

而Laddered的现金流分散程度居中,因为Laddered现金流分布较为均匀,短期、中期、长期都有现金流分布,但各自的权重又都很少,于是算出来的现金流离散程度数据相对更小一些;

而Bullet的现金流最集中,因为他的现金流就集中在Macaulay duration附近,所以算出来的Dispersion数据在3个Portfolio最小。

那这样的话,3个Portfolio里面,Barbell的现金流最分散,Laddered居中,Bullet最集中;

对应到Convexity就是,Barbell的Convexity最大,Laddered居中,Bullet最小。



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NO.PZ202209060200004006 问题如下 Of the fferences between a laerestrategy for fixeincome portfolios anbullet anbarbell strategies scribeHonanie, whiis least likely correct? A.fferen3 B.fferen2 C.fferen1 SolutionC is correct. Given the same value anration, of the three types, the bullet portfolio woulhave the lowest convexity anthe barbell portfolio woulhave the highest. The laereportfolio woulhave a convexity in between the two.A is incorrebecause the laereportfolio woulregularly buy new long-term securities to replamaturing securities on the short en To the extent interest rates are volatile, the laereportfolio wouleventually contain a mixture (versity) of high- anlow-yielng securities.B is incorrebecause the laereportfolio woulalways have some securities with little time remaining before maturity. These woulgoocollaterfor a repo or loor woulshortly turn into cash (upon maturity), thus proving high liquity. No.PZ202209060200004006来源: HanookOf the fferences between a laerestrategy for fixeincome portfolios anbullet anbarbell strategies scribeHonanie, whiis least likely correct?您的回答正确答案是: CAfferen3Bfferen2C正确fferen1数据统计(全部)做对次数: 154做错次数: 12正确率: 92.77%数据统计(个人)做对次数: 1做错次数: 0正确率: 100.00%解析SolutionC is correct. Given the same value anration, of the three types, the bullet portfolio woulhave the lowest convexity anthe barbell portfolio woulhave the highest. The laereportfolio woulhave a convexity in between the two.A is incorrebecause the laereportfolio woulregularly buy new long-term securities to replamaturing securities on the short en To the extent interest rates are volatile, the laereportfolio wouleventually contain a mixture (versity) of high- anlow-yielng securities.B is incorrebecause the laereportfolio woulalways have some securities with little time remaining before maturity. These woulgoocollaterfor a repo or loor woulshortly turn into cash (upon maturity), thus proving high liquity.请问下fference3 这个versification这个怎么理解?laer的verfication更好吗?

2023-08-13 13:15 1 · 回答