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Dongying · 2023年11月15日

Portfolio effective duration impact

Li continues, “The plan’s benefit is defined as a percentage of each year’s compensation subject to a fixed 4% annual interest rate credit accumulating each year to a total lump sum. Pure, which has sufficient cash flow, has a policy of contributing an amount sufficient to cover accumulated vested plan benefits annually into a corporate trust. The plan’s trust portfolio is entirely composed of fixed-income securities. The employee gradually accrues rights to the full amount of the benefit from the beginning of Employment Years 3 through 6. Upon separation from employment, the employee may receive distribution of the entire vested benefit or leave it in the plan to accumulate further. Those who do not remain employed long enough to become fully vested forfeit some or all of the benefit. Pure uses these forfeited funds to reduce its future contributions to the plan’s trust. A majority of the participating technical employees remain at least five years, and we lose only about 20% of our staff within the first four years. The average tenure of our technical staff is 5.5 years. Exhibit 2 shows some of the characteristics of the portfolio backing the benefit.”

Exhibit 2

Portfolio Characteristics

Market value of plan assets (in USD)

5,820,300

Current value of vested benefits (in USD)

5,675,000

Portfolio effective duration

4.95

Portfolio current yield

2.95%

Annualized portfolio return inception to date

4.00%

Question

Based on Li’s description of the deferred compensation plan and the data in Exhibit 2, the funding status of the plan is most likely explained by the difference between the:

  1. portfolio’s current yield and the return inception to date.
  2. average employee tenure and the portfolio’s effective duration.
  3. amount of the contributions and the growth rate of the vested benefits.

Solution

C is correct. The portfolio’s assets exceed the present value of the deferred compensation plan’s vested benefits, so the plan currently has a surplus. Contributions are made for the 20% of employees who leave before their benefits have vested, providing a source of excess funding for the plan as the benefits are forfeited.

A is incorrect. The portfolio’s current yield is less than the interest credit, while the portfolio return is only equal to the required rate of return. These would not lead to a surplus in funding.

B is incorrect. The shorter duration of the portfolio compared with the average employee tenure would not contribute to a surplus, especially in a time when short-term rates are lower than long-term rates.


请问为什么portfolio duration < employee tenure不可以有surplus呢? duration衡量的不是对interest rate 变动的敏感程度吗?

1 个答案
已采纳答案

lynn_品职助教 · 2023年11月17日

嗨,努力学习的PZer你好:


请问为什么portfolio duration < employee tenure不可以有surplus呢? duration衡量的不是对interest rate 变动的敏感程度吗?


这个Case就是官网practice exam中的题目,其实题目的考点不是很清晰,完全是要根据它题干里的信息来做题,看题目,截图里的一大段描述,其实是在说这个Deffered compensation plan是如何运作的。


解这道题,需要用到其中的一些信息,以及Exhibit 2。现在题目问我们,这个Plan的Funded status是可以用ABC 3个选项哪个来解释,其实是问我们这个Pension plan有Surplus,那这个Surplus是ABC 3个因素里,哪一个引起的?


B选项说,员工的工作年限Tenure小于Portfolio effective duration,这个因素会引起Surplus。


这两个因素其实不可比,他俩的大小关系也不能说明什么问题。员工的工作年限Tenure,这是一个时间概念,他决定的是Pension liability是否生效,如这题题干的下面这句,他说员工工作从第3年至第6年,才会逐渐有权利拿到Pension benefit,也就是说,员工至少要干满3年,才会有资格拿Pension,此时他们对应的Pension liability才会生效。

The employee gradually accrues rights to the full amount of the benefit from the beginning of Employment Years 3 through 6.


下面这句说,如果有员工工作年限不达标,那他们就会放弃掉一部分养老金。

Those who do not remain employed long enough to become fully vested forfeit some or all of the benefit.


所以,Tenure员工的在职年限,影响的是员工是否有资格拿Pension,他影响的是Pension liability amount,如果有员工早早离职,那他们对应的Pension liability就会失效,但是,他们已经缴纳的Contribution,依然会在Pension asset里面。所以相当于他们已经缴纳的养老金依然在Pension asset里,继续累积给还在职的员工。


但是,Asset duration = 4.95,这是一个利率敏感度的概念,他只能说明资产的利率的敏感度是这个数。

员工在职年限Tenure,小于Asset duration(资产的利率敏感度),这说明不了任何问题,也不会造成Surplus;因为这是两个不同维度的概念。


如果B选项改一下,改成,员工的Tenure下降。那此时在职年限下降、离职率上升,有更多的Pension liability会作废,同时他们已经缴纳的Contribution依然在Pension asset里面供继续在职的员工,此时Pension Liability下降,而Pension asset不变,因此Surplus上升。因此,B选项改动之后,Tenure下降(离职率上升),会造成这个Surplus。

但本题的B选项:Tenure小于Asset duration说明不了问题哈。

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