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anyewumian · 2021年03月31日

老师这道题呢详细解释一下吗

NO.PZ2020011901000037

问题如下:

Suppose that in a certain defined benefit plan the following simple situation exists. Employees work for 40 years with a salary that increases exactly in line with inflation. The pension is 60% of the final salary and increases exactly in line with inflation. Employees always live for 25 years after retirement. The funds in the pension plan are invested in bonds that earn the inflation rate. Which of the following is the best estimate of the percentage of the employee’s salary that must be contributed to the pension plan? (Hint: You should do all calculations in real rather than nominal terms so that salaries and pensions are constant and the interest earned is zero.)

选项:

A.

37.5%

B.

43.75%

C.

22.5%

D.

27.5%

解释:

A. The employee’s salary is constant in real (inflation-adjusted) terms. Suppose it is X. The pension is 0.6X. The real return earned is zero. The pension plan contributions therefore grow to 40XR where R is the (employer + employee) contribution rate as a percentage of the employee’s salary. The present value of the benefits is 25 * 0.6X = 15X. We therefore require 40XR = 15X so that R = 15/40 = 0.375. Contributions equal to 37.5% of salary are therefore necessary. This simple example illustrates the problems with defined benefit plans. Total contributions of employer and employee are, in practice, 15% or less, but much higher contributions are necessary to pay promised pensions with certainty.

老师这道题呢详细解释一下吗

1 个答案

小刘_品职助教 · 2021年03月31日

同学你好,

这道题题目提示了用real rate,可以简单把利率当成0来考虑简化问题。 DB的支出和收入应该是相等的。

支出方面, Employees work for 40 years with a salary that increases exactly in line with inflation. 因为不考虑通胀影响了,所以相当于员工现在的工资和40年之后是不变的,假设他是X,那DB plan的pension 就是0.6X,因为可以领取25年,再加上利率是0,所以pension的现值直接是25*0.6x=15x

收入方面,假设salary的比重是r,所以每年DB收到的收入就是r*x,收到40年,利率是0,总和是40*x*r

二者相等,求解出来比率是37.5%

这题假设的太多了,也不符合实际情况,重点是搞清楚DB是什么,有什么特征。

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