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Funding Methods - chapter 15

S

shelly

Member
Hi all,

I've been finding a couple of concepts in Chapter 15 a little tricky and was wondering if anyone could help.

For the CU and PU standard contribution rates, which salary should we use -that at beginning/mid way through/end of control period? It makes sense to me to use salaries projected forward by six months for a 1 year contol period, but that doesn't seem to be approach followed.

For the CU rate, why do we project salaries forward by one year in the nominator but then use current salaries in the denominator? I would have expected these to be consistent values.

Finally, I don't quite understand how AA funding method creates a surplus, when for a stable scheme, AA=PU and PU approach doesn't create any surplus. Does this depend on whether or not AA is calculated more than just once?

Any thoughts on these would be appreciated.

Thanks,

S
 
First point is correct.

In the algebra section introducing PUM (pg 14 in 2007 notes) the denominator a1 is annuity...(allowing for the timing of contributions and salary increases)

So yes, if salary increases are random and on average in half a year you allow for it by (1+e)^0.5.

Note that if you use a net discount rate for a1, eg i-e or (1+i)/(1+e)-1 then it already implicitly includes allowance for increases in salary that year.

Not sure what you're looking at to suggest that this is not the approach. Possibly, that example assumes salary increases are on annual basis (with the last round just applied) or this "extra complication" was ignored.

Various approaches are acceptable. You can also use half years contributions at first earnings rate plus second half at higher rate. It depends on the situation and how accurate/approximate you need to be.



The CU rate is similar. If annual salary increase has just been applied, the it is correct to use
1 year of salary increase in the numerator (since at the end of the year the liabilities will be based on the higher salary)
no salary increase in the denominator (since the contributions for this year are based on current salary)


Cant say that AA=PU (they are different)
AAAL = PUAL ie the past service liability is equal BUT
AASCR> PUSCR ie the future service cost is more.

If you pay more each year but want the same fund (past service) set aside at the end of the year, you are building up a surplus.

You can think of the AASCR as an average of PUSCR for each age from now to retirement.
If you calculate the AASCR once, and pay that rate from now to retirement, you would not get a surplus (of course once all experience is as assumed)
It's the average rate for future ages. At some point the (recalculated) PUSCR will exceed the rate you're paying and you make up for the excess you already paid.

If you keep recalculating the AASCR, then you will always have an average for higher ages (between time of calc and retirement).
Higher ages usually mean higher figures, so you're always "paying too much" and result in a surplus.
 
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