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moon · 2021年12月15日

6%的折现率问题

NO.PZ2019100901000014

问题如下:

Dianna Mark is the chief financial officer of Antiliaro, a relatively mature textile production company headquartered in Italy. All of its revenues come from Europe, but the company is losing sales to its Asian competitors. Earnings have been steady but not growing, and the balance sheet has taken on more debt in the past few years in order to maintain liquidity. Mark reviews the following facts concerning the company’s defined benefit (DB) pension plan:

●The DB plan currently has €1 billion in assets and is underfunded by €100 million in relation to the projected benefit obligation (PBO) because of investment losses.

●The company to date has made regular contributions.

●The average employee age is 50 years, and the company has many retirees owing to its longevity.

●The duration of the plan’s liabilities (which are all Europe based) is 10 years.

●The discount rate applied to these liabilities is 6%.

●There is a high correlation between the operating results of Antiliaro and pension asset returns.

Determine whether the risk tolerance of the DB plan is below average or above average. Justify your response with two reasons.

选项:

解释:

the DB plan is below average



之前老师关于这题回答过如何判断6%是不是过高的折现率,还是不太明白怎么判断的,以及为什么养老金风险承受能力下降,就要用更低的r,这样企业PV(liability)不是更大?



原回答:

因为这道题这个养老金,已经是Under-funded的状态了。第一点是本身在Under-funded的状态下,养老金的风险承受能力下降,应该使用的Discount rate更低才对;第二点是使用6%的Discount rate养老金依然是Under-funded状态,说明养老金本身的缺口比较大,6%的Discount并不合适。

绝对数字上没法判断是否Aggressive,咱们原版书有道例题,讲义67页,那里也是用了6%的折现率,但是完全OK。因为在那道题里养老金是Over-funded的状态。

所以要结合Discount rate与养老金状态来判断。一般是使用了这个Discount rate之后,这个养老金还是Under-funded,那说明这个Discount rate不合适,太高了。



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发亮_品职助教 · 2021年12月15日

嗨,努力学习的PZer你好:


之前老师关于这题回答过如何判断6%是不是过高的折现率,还是不太明白怎么判断的


负债的折现率基本上是和资产的收益率匹配的。如果资产的预期收益率越高的话(并且可实现的话),负债的折现率可以相对大一点,如果资产的预期收益率越低的话,那么负债的折现率需要小一点。

在决定负债的折现率时,除了会受到资产预期收益率的影响,还会有法律的要求,比如法律会要求使用高质量公司债的收益率等。

大体原则就是:资产的收益率越高,负债的折现率可以调高(但不能超过法律限制)。资产的收益率越低,负债的折现率可以低。


这道题就是因为题干说之前的投资收益低(有Investment losses),所以资产的收益为负,那实际上在这样的背景下,负债的折现率不能使用太大。因为不能和资产的收益差距过大。

第二点是因为:在资产收益为负,然后使用6%折现率的情况下(此时使用6%已经不合适了,因为折现率与资产的收益差距较大),我们算出来的Funded-status依然是underfunded,那就说明原本资产、负债的差距就比较明显,再进一步提升折现率的话,只会进一步拉大资产与负债间的收益率差。提升折现率只会暂时使得负债变小、暂时使得Funded-status变好看,但是随着资产、负债收益率差距的扩大,养老金的Funded-status后面会进一步恶化。

所以,提升折现率对养老金的Funded-status并不会带来实质提升。只有在资产的收益率会上升的情况下,提升负债的折现率才会对养老金的Funded-status有好的影响。


以及为什么养老金风险承受能力下降,就要用更低的r,这样企业PV(liability)不是更大?


是这样:

Underfunded的养老金 → 资产风险承受能力下降 → 投资低风险资产 → 资产预期收益下降 → 由于资产的收益下降,负债不能使用过高的折现率 → 负债的折现率下降。


所以基本上养老金有Underfunded的情况出现,提升负债的折现率是没有用的。只有资产的收益率提升的情况下,提升负债的折现率才会改善养老金的Funded-status。

但由于Underfunded时,一般养老金是倾向于降低风险偏好的,那此时,资产的风险承受能力受限,于是负债的折现率不能使用过高,需要调低负债折现率。所以,这种情况下,改善underfunded的方式就只有企业增加Contribution。


不过需注意有一种题型是:题目明确说企业也没钱缴纳Contribution,题目明确说明了要增加Risk tolerence,那此时就按照增加risk tolerance来。一般情况下,我们默认,Underfunded status是降低风险偏好。


以下是关于Discount rate与资产收益率的关系:

关于Discount rate是这样。雇主(企业)是倾向于用大的Discount rate的,因为Discount rate越大,折现出来的Liability就会越小。

那这样的话,雇主期初只需准备一点点资产(Contribution),就可以使得Pension fund达到Fully-funded的状态了。

负债使用的这个Discount rate,其实也是假设的负债增值率。因为从未来向现在进行折现,和从现在向未来进行复利,其实是一回事,只不过是一个相反的过程。所以给负债使用的这个Discount rate,其实也是我们假设的负债向未来复利增长的增长率。

于是,负债使用的Discount rate越大,其实是假设负债的增长率就越大。


那么问题就来了,如果资产的增值率无法达到负债的增值率的话,那Pension fund的Funded status迟早会变差,会从期初的Fully-funded状态变成Under-funded。给负债使用过大的折现率,其实最大的问题就是资产很有可能无法实现这样高的增长。使用高折现率,只会暂时让Funded-status变好看,但对养老金无实质影响。

所以对于养老金来讲,并不是使用的折现率越大越好,我们还要考虑这个折现率资产是否能够实现。也是由于这个原因,所以法律才会限制折现率的大小。


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