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张昕洋 · 2020年03月02日

问一道题:NO.PZ2019100901000014 [ CFA III ]

问题如下图:请问老师,为什么有缺口就说明discount rate高了呀?折现率高,liability现值就小呀,不是有利于弥补缺口吗

1 个答案

发亮_品职助教 · 2020年03月02日

嗨,爱思考的PZer你好:


“为什么有缺口就说明discount rate高了呀?折现率高,liability现值就小呀,不是有利于弥补缺口吗”


注意,提高折现率并不能弥补缺口,用提高折现率这种方法,不一定能改善Funded status的。

使用这么高的折现率,意味着资产必须要实现这么高的收益才行,否则仅仅提高折现率是无法改善Funded status的。


假设我们用8%这个数,把将来的Liability折现到当期,得到当期的PBO,这就意味着从现在这个时间点来看,PBO会以8%的折现率复利到未来;也就是我们给负债用多大的折现率,也对应着负债往未来复利的增长率是多少。

这样的话,资产一定需要至少实现与负债一样的增长率,才能保证现在现值Cover,终值也Cover。或者才能保证现在的Funded status是多少,将来的缺口才不会进一步变差。

所以如果8%这个折现率,资产的收益率实现不了的话,那说明负债增值比资产快,将来养老金还是有缺口的,并且资产能实现的收益率与8%差的越远,资产负债的缺口的会拉的越大。

所以一般在养老金这里的折现率,我们会使用比较稳健的折现率,例如国债的收益率,那就代表只要资产实现一个国债的收益率,就能保证资产与负债同步增长,养老金缺口不会被进一步拉大,所以这个收益对资产的要求很低,比较容易满足。

或者一般给负债使用的折现率是资产的预期收益率,这就能保证资产与负债实现同步复利,当期是Fully-funded,同步增长之后未来仍然能Fully-funded。

如果给负债的折现率过大,资产无法实现,那就是“人为”降低负债现值,实际上对改善Funded status没有什么用。因为过大的折现率意味着负债以很大的增长率复利,而资产实际无法实现这么高的增值率,所以期初“人为”改善Funded status,将来迟早会变差。



总结下,负债的折现率并不是越高越好,越高的话资产的收益率达不到这个值,资产负债的缺口迟早会暴露,并且越来越大。一般负债的折现率是资产预期能够实现的收益率,代表着资产与负债能实现同步增长、或者如果期初是Underfunded的话,缺口至少不会进一步被拉大。



这道题是这样,首先综合一系列信息,可以判断出Pension是Below average的risk tolerance,所以我们不能采取风险较高的投资,对应资产无法实现较高的预期收益率,也就对应不能给负债使用较高的折现率;

现在我们已经给负债使用了6%的折现率,发现资产负债仍然是Underfunded,并且除了已有的deficit,当前资产的实际投资收益是负数(Investment losses),那就说明已实现的资产收益率更低,负债的折现率更不能使用6%的折现率了,相比资产负收益,这个折现率还是过高。

应该的做法是:资产能实现的收益很低(甚至已实现的为负),那负债的折现率不能使用6%,应该进一步降低折现率。

法律要求Funded ratio要保持在一个线上,进一步降低折现率,充分暴露当前Underfunded状态,就会进一步促使公司补足Contribution达到法律要求线(这个要求我们原版书考纲没涉及,只是为了解释)。

假设继续使用6%的折现率,那Funded status看起来还OK,不需要公司进一步补足Contribution,但是资产实际能实现的收益还为负,那实际上会进一步扩大Under-funded状况,所以继续使用6%的折现率不合适。


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