Valuing pension annuities using an annuity certain payable for life expectancy

[Guest Navysalad]

I will be testifying this week (so prompt replies would be extremely appreciated!) regarding the value of a pension, currently in pay status as a joint & survivor annuity, in a divorce case. The expert (an accountant) on the opposing side calculated his present values for both the pension and even the survivor benefits by calculating the present value of an annuity certain payable for the life expectancy, based on 2001 CSO. Based on my suggestion, the attorney I'm working with plans to ask me what would happen if an actuary valued benefits for an annual IRS pension valuation by using the life expectancy approach. I'm trying to come up with the strongest fully supportable statement I can make denouncing this approach, recognizing that actuaries are generally allowed a fair amount of latitude in how they do their work.

I was initially planning to say something like "This approach would not comply with generally accepted actuarial standards of practice and the actuary would need to be prepared to justify his deviation from standard practice." -- however, there's got to be a stronger statement that I could make -- ideally that ties in with either IRS or Joint Board regs. Second best (since I don't think it would carry the same weight of law) would be something promulgated by the American Academy of Actuaries (AAA) or the Actuarial Standards Board (ASB). I've been trying to find something that _requires_ that the valuation be prepared in accordance with generally accepted actuarial principles and practices, but all the references to this that I've found are from the ASB or AAA and thus are internal requirements within the actuarial profession and not a legal requirement. Anyone have any suggestions?

Also under contention is the value of the survivor benefits. If the retiree outlives her beneficiary, then she gets a popup annuity. As I mentioned above, the accountant used the reasoning that, since the retiree has a slightly shorter life expectancy than her beneficiary, she is not "expected" to outlive him, therefore the value of her survivor benefits is zero. As much as I dislike seeing the life expectancy approach being used for a regular pension, at least it's a rough approximation. In the case of survivor benefits, however, this approach is (I believe) not even a rough approximation. Any other suggestions for nailing the accountant on this point?

Thanks!

[Guest Carol the Writer]

I have not done this in a very long time, but I think the State in which you will be testifying and its divorce laws make a difference as to the valuation of the annuity. Also - and more experienced people may consider this utterly irrelevant - there is the valuation of a so-called "private annuity" under a given State's tax and other codes that might help you. As I said, I have not done this in a long time, so don't waste too much time on these suggestions if they are not helpful. Good luck!

Carol Caruthers

[Blinky the 3-eyed Fish]

Using life expectancy to determine a present value is not valid because there is no interest rate assumption. Life expectancy by definition is just a mortality table with a 0% interest rate. That point alone should invalidate the use of that methodology unless the judge is an extreme pessimist concerning future returns and has his nestegg in his mattress.

[Guest Navysalad]

Using life expectancy to determine a present value is not valid because there is no interest rate assumption. Life expectancy by definition is just a mortality table with a 0% interest rate. That point alone should invalidate the use of that methodology unless the judge is an extreme pessimist concerning future returns and has his nestegg in his mattress.

Blinky -- I should have mentioned that he DID use an interest rate of 6%, so I don't think he's exposed on that issue.

[Blinky the 3-eyed Fish]

So then your beef is simply with the use of the 2001 CSO Table? If so, my discussion would be why that table versus AE or 94GAR. I don't have a "strong statement" for you though.

As for the survivor beef, there is not a 100% chance that the retiree will die beforehand and the probability of the retiree outliving the beneficiary is there. That probability has a value which should be captured. Is a quarter expected to come up heads twice if the coin is flipped twice - no. Can it easily happen - yes.

Play him a little game where you give him $1 for every time it doesn't come up heads twice and he gives you $5 every time it does. Then kick his family out of their house when you own it.

[SoCalActuary]

A valuation of a fixed annuity that expires at the "expected time" assumes that payments will be made sooner than a valuation of a lifetime annuity, in which the expected payments after the end of life expectancy are discounted for more years than the expected payments that are not paid upon death before the end.

Simple example:

1/3 die in 10 years, 1/3 in 20 years, and 1/3 in 30 years.

Using the avg life expectancy of 20 years, you have (1-v^20)/i as value.

Using proper actuarial mathematics, annuity is 1/3 x (1-v^10 + 1-v^20 + 1-v^30)/i

On the J&S benefit pop-up, there is a definite probability of utilization each year in the future, namely lx/ly * (1 - lz/lw) where x is an age in the future and y is the age of the annuitant, and z is the contingent beneficiary's age in the future based on current age w. This is measurable and has a clear method of being valued.

Having noted all these issues with the accountant's method of valuation, will your audience (the court) understand? I guess it depends on the quality of your explanation. Good luck.

[Guest Navysalad]

So then your beef is simply with the use of the 2001 CSO Table? If so, my discussion would be why that table versus AE or 94GAR. I don't have a "strong statement" for you though.

The use of 2001 CSO _IS_ inappropriate in my opinion, but my beef as discussed here concerns valuing this annuity by calculating the present value of an annuity certain payable for the person's life expectancy (that old thing that was exposed as a fallacy over 50 years ago, at least in actuarial circles). What I'm hoping is to find something that says such benefits must be valued in accordance with "generally accepted actuarial principles and practices" and that this would NOT include the life expectancy method.

[Blinky the 3-eyed Fish]

You lost me with that. You say that the accountant is using the right table and I guess the interest rate is okay, but not the use of life expectancy? All mortality tables have life expectancy by defintion. What do you want to use? I must reiterate that I have no clue what your question is.

[Guest rubindj]

Your lawyer should point out is that CPA's are not qualified by the IRS to sign off on pension plan projections -- they must hire a certified actuary (cite code). I would then go on to state how his calculations were disproved 50 years ago (cite paper, textobook, or other authoritative source).

Finally, you say something like according to the methedology of ASA, here's how you would calculate the value of the pension.

[Guest Navysalad]

You lost me with that.  You say that the accountant is using the right table and I guess the interest rate is okay, but not the use of life expectancy?  All mortality tables have life expectancy by defintion.  What do you want to use?  I must reiterate that I have no clue what your question is.

My question's really that foggy? OK, let me recap: As I mentioned in my previous post, I feel using CSO mortality _is_ inappropriate (since it's designed for setting life insurance reserves, not for valuing annuities), but that issue was not the purpose of my post. My concern is that the accountant is using a method (ie calculating the PV of a life annuity by calculating the PV of an _annuity certain_ payable for the person's life expectancy) and that is not a "generally accepted actuarial standard of practice". [in blunt terms, I think the accountant is calculating his numbers the wrong way].

Yes, all actuarial tables inherently include life expectancy, however the issue is that I disagree with the practice of using those life expectancies, instead of a standard annuity factor, to calculate the value of a life annuity. If you're an actuary, then you've no doubt seen the proof that the present value of an annuity certain payable for a period equal to the life expectancy is never equal to the present value of a life annuity, at least if the interest is greater than zero.

I'm trying to come up with the strongest statement I can make regarding how the accountant's approach is inappropriate. So far, the strongest statement I feel I can make is merely that "this method would not comply with accepted actuarial standards of practice". Clearer now?

[Guest rubindj]

Ok....

How about" Anyone using this method to calculate the value of a pension annuity could cause their client to be heavily penalized by the IRS, and could face sanction on their right to practice in front of the same."

Going onward... Just as FASB sets the methods of accounting used by CPA's, the ASA sets the method of valuing pension annuites as recongized by Generally Acceptable Accounting Principles and by the IRS. The method used by Mr. CPA was abandoned over 50 years ago by the ASA because it created innaccurate and false numbers."

Hows that?

[Guest Navysalad]

Ok....

How about" Anyone using this method to calculate the value of a pension annuity could cause their client to be heavily penalized by the IRS, and could face sanction on their right to practice in front of the same."

Going onward... Just as FASB sets the methods of accounting used by CPA's, the ASA sets the method of valuing pension annuites as recongized by Generally Acceptable Accounting Principles and by the IRS. The method used by Mr. CPA was abandoned over 50 years ago by the ASA because it created innaccurate and false numbers."

Hows that?

Rubindj -- Yeah, that's the kind of statement I was looking for! But since everything I say in court has to be supportable, under what regulation or law would (a) the client be penalized, or (b) the practicioner be sanctioned? I've been poring over the Joint Board regs, the definitions of a reasonable funding method, etc. to find something outlawing this practice, but haven't found anything very concrete. I'm starting to think, however, that at minimum this practice wouldn't satisfy any of the six (I think) acceptable funding methods.

I do like the way you phrased the abandonment of Mr. CPA's method over 50 years ago. But again, do you have anything presentable in court that would support this statement?

Thanks

[david rigby]

To discuss, either positively or negatively, any mortality table, you must first know the development of that table: what data was used, what is the intended purpose of the table, etc. Find the document on the SOA website that does this. Read it carefully.

[Blinky the 3-eyed Fish]

Navy, okay that is clearer. You could break out the actuarial textbooks. But really you just need to explain why that methodology is wrong. The annuity is certainly not certain to be payable over his life expectancy. The annuitant could die sooner. Just compare the two methods for the court with an intelligent reasoned discussion of why one is correct and the other isn't. A thorough understanding of the mathematics behind the calculations should make this a snap.

[SoCalActuary]

At the risk of boring you, the two methods are intended to provide the same total expected payments, but the actuarial method, using probabilities at each age, is more sensitive to when the payments occur. The time value of money is the difference between an annuity certain for the period of the life expectancy vs. the lifetime annuity.

On the issue of the survivor pop-up benefit, the CPA is just wrong. The pop-up benefit does have a measurable value, and the CPA just ignores it.

I like your position that the mortality table matters. You should be prepared to explain why annuity values differ from life insurance values, and you should be prepared to explain its relevance to the attorney you work with. If he or she understands your issue, then their job is to explain it to the court.