NO.PZ2023032703000027
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.
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.
needs a higher cash flow yield.
has currently achieved zero replication.
解释：
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.
答案提示是，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.
但是框架图说，it is not the weighted average of duration，老师也说了应该把portfolio看成一个整体去计算，权重应该是用现金流加权，而不是组合的allocation 来加权吧？
