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Jwang · 2024年07月19日

如题

  1. CFA III
  2. Fixed Income

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.

B.

needs a higher cash flow yield.

C.

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.

老师好，yield curve has steepened这个条件在这道题里有用吗？不用考虑yield curve动态变化吗？

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发亮_品职助教 · 2024年07月21日

老师好，yield curve has steepened这个条件在这道题里有用吗？不用考虑yield curve动态变化吗？


没用，这是一个干扰信息。Yield curve has steepened since the bonds were purchased，表明利率的改变已经发生过了，不是在将来发生。


接着后面一段话说，这种利率的改变可以通过对比YTM at the time of purchase与YTM at current price来发现，即可以对比表格里面的，买债券时刻的YTM，和当前的YTM：

which can be seen by comparing their respective yield to maturities (YTMs) of the purchase price yield to today’s yield.


所以发生steepeng是以前的事，已经对组合的数据产生过影响了，这个表格给的又是债券当前的数据并非历史数据，基于当前的Macaulay/convexity数据发现组合还是符合duration-matching要求的。


如果说是已经构建好了组合，然后利率steepening是发生在未来，那可能需要考虑一下免疫的效果。

Jwang · 2024年07月21日

明白了，看题还是要更仔细一点，谢谢老师！

发亮_品职助教 · 2024年07月21日

不用客气！

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