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:
- portfolio’s current yield and the return inception to date.
- average employee tenure and the portfolio’s effective duration.
- 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？
