duration计算

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC 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 = 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. 老师好，大案里这个[(Portfolio weightBon1 × rationBon1) + (Portfolio weightBon2 × rationBon2) + (Portfolio weightBon3 × rationBon3)] ÷ 3 = 3.99.具体是怎么算出来的啊？我用allocation那三个百分比配合macauly ration算，算得应该是4.0143，是我哪里用的有问题吗

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC 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 = 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. 解析说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.但zero replication (immulization)条件有三种，目前只有mration 4满足，其他条件如PV, convexity我没有在原文中找到啊，况且解析说的same return 也不算三个免疫条件中的一种啊

NO.PZ202209060200004602问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely:A.shoulhave a shorter ration.B.nee a higher cash flow yielC.hcurrently achievezero replication.SolutionC 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 = 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 什么意思？就是免疫成功的意思么？

NO.PZ202209060200004602 问题如下 Accorng to the information in Exhibit 1 anassuming Berenen retires in four years, the fixeincome portfolio most likely: A.shoulhave a shorter ration. B.nee a higher cash flow yiel C.hcurrently achievezero replication. SolutionC 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 = 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. 请问这个portfolio的cash flow yiel是加权平均算吗？