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005 · 2023年07月01日

请问

NO.PZ2023061601000027

问题如下:

Berendsen explains to Adams, “I plan to continue saving for retirement, regularly adding funds to the portfolio until I retire, and I would like a low-risk solution to provide additional retirement income.”

Adams replies to Berendsen, “We focus on the ability of the portfolio to meet future cash flow needs and seek to immunize the liabilities as an objective in the management of the portfolio. If the fixed-income portfolio achieves an average annual investment return of at least 4% for the next four years, the proceeds of its liquidation will be enough to purchase an annuity sufficient to provide the funds needed to supplement your Social Security benefits.

Adams has summarized Berendsen’s (the client) fixed-income portfolio consisting of three government bonds in Exhibit 1. The yield curve has steepened since the bonds were purchased, which can be seen by comparing their respective yield to maturities (YTMs) of the purchase price yield to today’s yield.


Note 1: Interest earned on cash: 1.00%

Note 2: Portfolio cash flow yield: 4.15%

According to the information in Exhibit 1 and assuming Berendsen retires in four years, the fixed-income portfolio most likely: (2019 mock AM)

选项:

A.should have a shorter duration. B.needs a higher cash flow yield. C.has currently achieved zero replication.

解释:

Correct Answer: C

C is correct. The portfolio’s Macaulay duration of approximately 4.0 matches the time horizon of the liability and can be calculated as follows:

[(Portfolio weightBond 1×DurationBond 1) + (Portfolio weightBond 2×DurationBond 2) + (Portfolio weightBond 3 × DurationBond 3)] = 3.99.

When compared with the single liability due in four years, the portfolio has the same return and duration characteristics of a single zero-coupon bond maturing in four years. The interest rate risk has been immunized, which is known as zero replication.

A is incorrect because the portfolio’s current duration matches the duration of the liability, or retirement date.

B is incorrect because the cash flow yield matches the required investment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the required rate of return.

1.本题表中的YTM at time of purchase和YTM at current price怎么理解?通常解题中有什么作用 如何应用?

2.本题Note1的作用是?

麻烦老师详细解答下

1 个答案

pzqa31 · 2023年07月02日

嗨,从没放弃的小努力你好:


1.本题表中的YTM at time of purchase和YTM at current price怎么理解?通常解题中有什么作用 如何应用?

其实就是站在不同时间点算出来的YTM,可以看出收益率曲线是否发生变化了,这个题干中已经提示了: The yield curve has steepened since the bonds were purchased, which can be seen by comparing their respective yield to maturities (YTMs) of the purchase price yield to today’s yield.由于YTM随时间变化了,可以看出收益率曲线不是stable了。


2.本题Note1的作用是?

本题中用不到。


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ2023061601000027问题如下 Berenen explains to Ams, “I plto continue saving for retirement, regularly aing fun to the portfolio until I retire, anI woullike a low-risk solution to provi aitionretirement income.”Ams replies to Berenen, “We focus on the ability of the portfolio to meet future cash flow nee anseek to immunize the liabilities objective in the management of the portfolio. If the fixeincome portfolio achieves average annuinvestment return of least 4% for the next four years, the procee of its liquition will enough to purchase annuity sufficient to provi the fun neeto supplement your SociSecurity benefits.Ams hsummarizeBerenen’s (the client) fixeincome portfolio consisting of three government bon in Exhibit 1. The yielcurve hsteepenesinthe bon were purchase whicseen comparing their respective yielto maturities (YTMs) of the purchase priyielto toy’s yielNote 1: Interest earneon cash: 1.00%Note 2: Portfolio cash flow yiel 4.15%Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: (2019 moAM) A.shoulhave a shorter ration.B.nee a higher cash flow yielC.hcurrently achievezero replication.CorreAnswer: is correct. The portfolio’s Macaulration of approximately 4.0 matches the time horizon of the liability anccalculatefollows:[(Portfolio weightBon1×rationBon1) + (Portfolio weightBon2×rationBon2) + (Portfolio weightBon3 × rationBon3)] = 3.99.When comparewith the single liability e in four years, the portfolio hthe same return anration characteristiof a single zero-coupon bonmaturing in four years. The interest rate risk hbeen immunize whiis known zero replication.A is incorrebecause the portfolio’s current ration matches the ration of the liability, or retirement te.B is incorrebecause the cash flow yielmatches the requireinvestment return. Although not equivalent to investment return, it is likely the portfolio’s return will meet the requirerate of return.zero replication 是什么意思?

2023-07-12 23:40 1 · 回答