Actuarial Factors and Prudence

[ph97]

Hi,

The slides from Tutorial 1 stated:

"using prudent assumptions will usually increase the early retirement factor and therefore the early retirement pension, so not a prudent approach"

and

"using prudent assumptions will usually reduce the late retirement factor, and therefore the later retirement pension so is a prudent approach"


Can someone please explain the logic of this in layman terms:

a) how using prudent assumptions increases the early retirement factor
and
b) how it is not a prudent approach


Thanks

 

[a.begdai]

IMO, it should be interpreted as follows:

"using prudent assumptions will usually increase the early retirement factor and therefore the early retirement pension, so not a prudent approach"

With an increase in the early retirement factor and a subsequent increase in the early retirement pension, the total value of expected pension payment increases (as compared to the original expected pension payment). As a result, lower asset value is available to make payments for the remaining members. Because higher than expected pension will be paid to members opting for early retirement, it reduces the overall assets available for the remaining members of the scheme and hence the prudency (buffer reserve).

Similar argument but in the opposite direction for the second statement should hold true.

Let me know your thoughts and tutors can please advise on the interpretation.

 

[Gresham Arnold]

Hi

Just to add to a.begdai’s post (thank you for that!)

An early retirement pension can be calculated by multiplying the pension projected to NRA by an early retirement factor (ERF). So a prudent approach is to use a basis that leads to a low ERF, so the early retirement pension is low.

Equations of value for early and late retirement can be found on page 21 of Chapter 18 of the SP4 Course Notes. Rearranging the equation of value for early retirement, we can see that the ERF for a unit of pension payable at NRA, to be paid to a life retiring early at age x, can be calculated as:

\(ERF=\frac{{{l}_{NRA}}}{{{l}_{x}}}\frac{a_{NRA}^{{}}}{a_{x}^{{}}}{{v}^{(NRA-x)}}\)

So, for example, if we were to increase the prudence of the basis used to calculate the ERF by decreasing the pre-retirement discount rate, then \({{v}^{(NRA-x)}}\) would increase and so would the ERF. So increasing the prudence of the basis in this way would not be a prudent approach.

Similar arguments can be made for late retirement factors.

Best wishes

Gresham