AoS - Conts vs. Accrual - use of actual salaries? (X6 Q1)

[Revelation]

Hi all,

I have a question on AoS methodology in the notes:

In Chapter 24, p.18 it tells us that when carrying out the comparison between conts paid in and benefits accrued over the intervaln period, we should use actual salaries rather than expected.

This approach is then used in numerous ActEd solutions to AoS questions, even where the component for the effect of salary increases is analysed first. A good example of this is the solution to X6 Q1(iii).

However, this seems inconsistent with the general principle that once an item is analysed, later parts of the analysis should be based on the expected rather than actual position.

If you think about the situation where the effect of salary increases vs. expected is analysed based off the new liability figure (rather than rolled forward from the old liability position) then this analysis will include the impact of salary increases on accrual over the period as the new liability figure will cover the liabilities accrued over the intervaln period.

We should allow for changes in the membership over the period but I can't see how allowing for actual salary increases is anything other than double-counting.


I've tested this idea out with algebra, which I will reproduce below:

Let A1, A2, L1, L2 be the assets and liabilities at the start and end of the period.
We will use a period of 1 year with interest rate i, expected sal incs e, actual sal incs f, initial payroll S,
contributions C paid at the end of the period for simplicity

So we move from a surplus of (A1 - L1) to (A2 -L2)

Where A2 = A1 (1+i) + C
L2 = L1 (1+i) (1+f)/(1+e) + PUSCR * S (1+f)

So the movement in surplus is:
i (A1 - L1) + L1 (1+i) (e-f)/(1+e) + C - PUSCR * S (1+f) (*)

The normal analysis we do for effect of salary increases is:
L2 (e-f)/(1+f)
which equals (from the expression above)::
L1 (1+i) (e-f)/(1+e) + PUSCR * S (e-f)

This represents a good chunk of expression (*) above, leaving only this item left in our analysis:
C - PUSCR * S (1+e)
This is the difference between the conts paid and the benefits accrued based on expected salary increases, not actual.

 

[GoSlow]

Hi Revelation

You should use actual contributions and compare this with cost of accrual.

This is to negate membership movements, which can be big with members joining and leaving. The effect of membership movements will be much bigger than the salary increase error.

Preferably calculate cost of accrual using the actual contributions if the actual contributions are a percentage of salary so that you are comparing closer to like for like.

As you point out this will not be perfect due to any salary increase differences but the answer will be accurate enough for AoS purposes.

In your example you said the movement in surplus is:
i (A1 - L1) + L1 (1+i) (e-f)/(1+e) + C - PUSCR * S (1+f)

• i (A1 - L1) is the interest on surplus
• L1 (1+i) (e-f)/(1+e) is the difference due to salaries
• C - PUSCR * S (1+f) is the difference due to contributions – and, similar to what I said before, preferably calculate the salary from the actual contributions if the actual contributions are a percentage of salary and that way you can drop the (1=+f) too.

Hope that helps and good luck
GoSlow