PPA J&S 75 Solution

[Young Curmudgeon]

My plan already offers a 50% & 100% J&S option for which we have printed tables. J&S 50 is the normal form. My problem is that the records are so old, nobody seems to know where the tables originated. They don't match any standard tables so it seems long ago an in-house actuary developed them. Rather than spend a pile of money to have someone recreate, can I just amend the normal form to J&S 100 and leave things as they are?

[Andy the Actuary]

Assumption is that the standard form is a life annuity so it is assumed that by normal form you mean an actuarial equivalent J&S. In such case, your approach seems reasonable. Any bias in the tables would come out in the relative values. In any event, you could only get rid of the tables on a wear-away basis so they'd still be around.

[Blinky the 3-eyed Fish]

How will changing the normal form to J&100%S help you since the QOSA has to be actuarially equivalent to the SLA?

[Young Curmudgeon]

My understanding is that if the QJSA options are the actuarial equivalent of the SLA and the 100% form is the normal form of benefit, if you already offer the 50% option, you don't need to add anything. Is the incorrect?

[Blinky the 3-eyed Fish]

That is correct. I think I understand your issue now. You were going to be unable to produce an actuarially equivalent J&75% option because you had no table to make the conversion but you can produce it for the J&50% option.

Do you not have stated actuarial equivalent interest and mortality in the plan document but rather some set of conversion tables?

[Young Curmudgeon]

Only the paper tables, which appear to be more favorable than SLA equivalent.

[ak2ary]

The formula to convert a J&50%S reduction factor to a J&75%S reduction factor is:

S = 2 x F / (3 - F)

Where S is the Joint and 75% Survivor reduction factor and

F is the J&50%S reduction factor.

This will allow you to convert a tabular factor from J&50 to j&75 without having the underlying tables...so you can reconstruct a J&75 table

Check it out where you know the factors...

[Blinky the 3-eyed Fish]

Nifty formula. They didn't teach me that one at actuary school.

[ak2ary]

I am sure it came from some actuary skool...but not the one I went to either.

When discussing precisely this issue earlier this year and how to deal with it, one of my partners said, "why dont we just use the two times F formula?" The rest of the room looked at him like he had three heads, but he wrote the formula on a white board (without referencing any books) and we tested it against about 20 combinations of interest rates and mortality tables and it worked.

Since then another actuary in my office has proven it works by deriving it from commutation functions