working out pension annuity factors

"sylvian stone" wrote

Well, not quite. The mortailty rate would be written as 'qx'. 'Dx' is the standard actuarial commutation factor used to signify 'lx . v^x'...

"sylvian stone" wrote

I'd instead assume that 'n' is the length of any guaranteed period...

"sylvian stone" wrote

Are you sure that there isn't the "top and right sides of a square" surrounding the 'n' in the formula? If so - and I'm guessing that there is, for several reasons - then 'n' is the term of any guarantee, rather than the age of the life involved.

Hi,

The formula above is exactly as given in the document where I read it:

There are no 'top and right sides' in the formula, and I'm struggling to figure it out.

This is section 6.6.80 - 81 of the FSA's conduct of business manual, which can be found at :

Thanks SS.

"sylvian stone" wrote

So it is! Very bad production on their part; but it is obvious from the wording in section 6.6.80 -- "...the annuity will be payable monthly in advance for a ** term certain of n years ** ..." -- that they did, indeed, mean a guaranteed term rather than a life's age ('term certain' is another way of saying a guarantee period).

Do you have a copy of the PMA92 & PFA92 tables? Don't forget that you'll need the appropriate "Year of Birth" projections of those tables... (see 6.6.84).

Hi,

I got the tables from the Institute of Actauries website.

What they show is:

Age![x]q{x} Age!x+0 Years ( expectancy)

So, it should be no problem to work this out on current age, rather than year of birth (I guess it is one and the same).

I'm still not sure how to apply the formula J =(1 +I)/(1 +R)-1 to the factors above.

Saying that, I'm still a bit confused in general.

Assuming n = 5 (guaranteed term) and Dx is the mortality factor, what figure is plugged into ä ?

Is that the value of the pension fund that is to be annuitised ?

I think I need to read a decent book on actuarial notation and calculations. Can anybody recommend anything ?

Thanks again. SS

"sylvian stone" wrote

Good - did you find just the 'Base' tables, or a 'Year of Birth' projection? [Or some other projection?]

"sylvian stone" wrote

Hmmm. Are all the rates really shown as the same, ie 0.000112 for that age range (20-25) ?

If *any* are shown as 0.000112, then you must have found a projection - the base tables exceed that figure even at the lowest ages, even for female mortality.

"sylvian stone" wrote

You need to work it out at current age, but *also* on the appropriate "Year of Birth" projection - not on eg any "Calendar Year of Use" projection...

"sylvian stone" wrote

When you calculate the 'a' factor - from age, mortality, interest, guarantee, frequency etc - you need an interest rate. You need to use the value of J above as this interest rate in 'a'.

"sylvian stone" wrote

Yes - you don't seem to quite appreciate the complexity of the calculation of 'a'. For instance, you can't simply add or multiply a few numbers and get it that easily!

"sylvian stone" wrote

As I said before, Dx is *not* the mortality factor. It is actually more like a "discounted survival factor, based on an arbitrary radix".

"sylvian stone" wrote

Many, many figures are. You need to look at mortality rates (or alternatively, survival factors) for each and every age from "current" to the end of the table (age 120). [Which is why actuaries invented the 'Nx' commutation factor!!]

"sylvian stone" wrote

'a' is the quotient obtained from dividing the value of the fund, by the yearly amount of the annuity. [But, obviously, you don't work it out that way - instead, you use the fund and 'a' to compute " annuity = fund / 'a' "...]

"sylvian stone" wrote

W.F.Scott, the author of a number of actuarial books, recently (earlier this year) offered to send anyone a PDF copy of one-or-two of his books - if they just asked by email. He may still be agreeable - you could try emailing "w DOT f DOT scott AT maths DOT abdn DOT ac DOT uk" (amend the capitalised bits appropriately).

Happy reading!