发亮_品职助教 · 2021年04月16日
嗨，努力学习的PZer你好：
这道题是这样，Exhibit 2给了2个养老金的数据，然后问如果要给这两个养老金做匹配策略，三个选项里面，哪个最不合适。
注意看题干里面有个关键句子：
In both plans, participants receive a monthly benefit upon retirement based on average final pay and have no option for a lump sum distribution.
这两个养老金是按月支付现金流的。那显然用Cash flow matching肯定最不合适。
咱们学Cash flow matching这个方法时也知道，他是债券资产的Coupon现金流与本金现金流，正正好就发生在负债到期日，资产的现金流金额、发生日期会与负债的金额与日期严丝合缝的一致（或者可以容忍一定的偏差）。
对于普通负债，如果现金流非常有规律，那用Cash flow matching没有问题，但是在这道题里面，这个负债是每个月都有现金流流出，如果用Cash flow matching去匹配的话，难度非常大。
答案下面这段是在说，这两个养老金是按月收到现金流，用Cash flow matching去匹配的话，就需要用债券Coupon与本金现金流去匹配负债的现金流。
In both the Lawson and Wharton plans, participants are entitled to receive a monthly benefit. Cash flow matching entails building a dedicated portfolio of zero-coupon or fixed-income bonds to ensure there are sufficient cash inflows to pay the scheduled cash outflows.
下面这句说，（对于本题这种按月的负债流出，如果要用Cash flow matching来严丝合缝的匹配现金流金额与到期日）实际上是非常不现实的，（由于这种复杂的现金流流出，不可能正正好让资产的现金流匹配负债的现金流）可能会在负债到期日之前，资产已经会有现金流流入了，导致持有太多的Cash（造成资金浪费），并且还会存在Reinvestment risk。
However, such a strategy is impractical and can lead to large cash flow holdings between payment dates, resulting in reinvestment risk and forgone returns on cash holdings.
C选项的Contigent immunization可以用。题干有暗示：
For the Lawson and Wharton plans, we can consider one of three alternative strategies to manage the multiple liabilities associated with these plans. Whenever a plan’s surplus is less than 5%, we favor passive management strategies.
他说当养老金的Surlpus低于5%时，就是用Passive的匹配方式，那言下之意就是Surplus高于5%时，就可以使用Active的匹配方法，在Active的匹配方式下，可以让资产偏离负债，可以让资产寻找风险更大的投资、试图扩大资产的收益，进而扩大Surplus。
这个其实描述的就是Contigent immunization的策略。
答案这里解释了一下什么是Contigent immunization，并且结合了这道题的数据，发现这两个Portfolio目前都有Surplus>5%，因此当前都可以采用Active的匹配方法，如果一旦Surplus低于5%，就退回采用Passive匹配方式。
Contingent immunization allows for active bond portfolio management until a minimum threshold in the surplus is reached. The threshold of 5% (of assets greater than liabilities) is exceeded in both plans; the Lawson portfolio has a surplus of 7.7%, and the Wharton portfolio has a surplus of 11.8%.
关于A选的Duration-matching也可以用。因为这就是2个正常的养老金，用Duration-matching没有任何限制。同时题干里面也有暗示：
We could also use a derivatives strategy, and I prefer derivatives strategies that protect the portfolio against an increase in interest rates but will not produce large losses if rates decrease
他说使用衍生品的方法，在利率上升时保护Portfolio不受影响，在利率下降时，也不会让Portfolio受影响；这实际上就是Immunization状态了，对利率的变动免疫，即，达到了Duration-matching。那衍生品在这里的作用就是消除Duration-gap，让资产负债达到Duration-mathching。
答案这里说，这两个Portfolio也都可以用Duration-matching。但是由于两个组合目前都有Surplus，因此更好的方式其实是contigent Immunization，但是依然可以用Duration-matching的方法。
because duration management is also appropriate for both the Lawson and Wharton plans. In this case, however, because they enjoy a surplus of assets to liabilities, the contingent immunization strategy is most appropriate. Since the plans are in the process of being advised by Pavonia, Wharton would likely be advised to eliminate the duration gap in similar form to Lawson.
另外这道题在经典题何老师有讲，可以参考Reading 19，Liability-Driven Investing: Multiple liabilities知识点下的第6题。
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