Annuity Purchase Rates

[austin3515]

Where can I find annuity purchase rates for New Comp Xtesting for various mortality tables? I'm trying to build a model that will make it easier to find the best testing solution?

[Tom Poje]

the APR is a constant, so if you do not impute permitted disparity it doesn't make a difference which mortality table you use. Exceptions to the rule would be someone who has worked past normal retirement or late hires (e.g. age 62) and a plan with a retirement age of 65/5. but even with these exceptions, the differences in E-Bars are generally insignificant from one mortality table to another.

if you impute disparity, then usually 1983 IAF produces the best results. The APR for that table as compared to another table is the largest value, so as a general rule I think most people use that table without even considering other mortality tables.

[austin3515]

Thanks!!! Is there a web-site where I could get those tables?

I'd want to get the APR's for 7.5, 8.0 and 8.5 so I can mess around w/ pre and post retirement rates to find the best set of assumptions. I'm pretty sure the APR's for the same table differ depending on the insterest assumption, would that be a fair assumption?

[Tom Poje]

more than an assumption, that would be the truth.

In most cases, I'd go out on a limb and say the best you can do is to use 8.5% pre and 1983 IAF 7.5% for the mortality.

age definition nearest if the HCEs are born in the first half of the plan year.

Here is a comparison (sorry, it doesn't copy well) of 2 tables

UP 84 UP 84 UP 84 1983 IAF 1983 IAF 1983 IAF age

7.50% 8.00% 8.50% 7.50% 8.00% 8.50%

101.494 98.350 95.383 124.434 114.413 115.387 65

98.975 95.987 93.164 122.216 112.234 113.516 64

96.444 93.609 90.926 119.909 109.980 111.519 63

93.897 91.211 88.667 117.508 107.650 109.511 62

91.321 88.782 86.374 115.006 105.245 107.365 61

88.704 86.309 84.035 112.400 102.766 105.117 60

86.049 83.796 81.653 109.690 100.216 102.766 59

83.363 81.248 79.233 106.880 97.597 100.310 58

80.649 78.667 76.778 103.976 94.916 97.767 57

77.922 76.071 74.303 100.988 92.178 95.133 56

75.193 73.467 71.816 97.927 89.390 92.420 55

[david rigby]

the APR is a constant, so if you do not impute permitted disparity it doesn't make a difference which mortality table you use.

Well ... the APR is a constant after you have chosen the interest rate and mortality table.

[Tom Poje]

but it is a constant, nonetheless.

to determine an E-BAR you take the

contrib * (1.0I)^yrs to retirement

this gives you a lump sum at retirement.

you then divide by the APR to determine a monthly benefit at retirement age.

if everyone has the same retirement age then whether I divide by 95.383 (8.5% UP 84)

of divide by 115.387 (1983 IAF) everyone's e-bar is effected the same

[you then divide this monthly benefit by monthly comp to determine the E-BAR]

I will provide an example of when imputing disparity helps, but I still do some other work around the office.

ok, consider PYE 12/31/2009 - hce born 1/1/49, NHCE born 1/1/63

HCE 245,000 comp and 49,000 contribution

NHCE 20,000 comp and 1,100 contribution

E-BAR up 84 (8.5% pre and post interest)

HCE 3.783, NHCE 3.260 NOT in rate group, fails

with disparity

HCE 3.988, NHCE 3.910 NOT in rate group, fails

E BAR 1983 IAF (8.5%)

HCE 3.128, NHCE 2.695 NOT in rate group, FAILS

with disparity

HCE 3.332, NHCE 3.345 Now the NHCE is in the HCEs rate group.

[austin3515]

Tom -

I figured out a way to get the data out of relius (I created dummy employees, each with one age from 55 to 90), and I got a different APR than your 1983 IAF 8.0% - Relius came up with 119.76 for that one.

But thank you VERY VERY much - the suggestions you gave on assumptions are working AWESOME!!! We were using 84 usp, 8.5/8.5. Your's is much better!

[david rigby]

Difficult to read the table in Tom's post. However, I agree with Austin's value:

at age 65, IA83 table, 8.0%, female, the APR is 119.7554

[Tom Poje]

I had pulled my value from a spreadsheet someone sent me, so it could well be incorrect. I never use 8% so it doesn't effect anything I have done, but thanks for the note.

Austin:

the only time I have seen an interest rate other than 8.5% work is when there are a number of HCEs with different ages and in different groups (e.g. receiving different % of pay) along with some NHCEs with ages greater than some HCEs

In Relius, if you go to Data Entry/Tables/Actuarial/Annuities you can generate APRs for any mortality table on the system, for any age any interest rate.

(I also think on the table I had the ages reversed - they should have gone from age 65 up and not 65 down, but that is my own fault for copying and pasting stuff rather rapidly)