Lessons from Annuitant Studies

By Bob Howard, FCIA

The CIA sponsors two studies of annuitant mortality experience, one individual (“IAMS”) and one group (“GAMS”). (See CIA documents 217117 and 217047 for recent publications.) The individual study has been around since the 1980s, but the group study is fairly new, with data going back only to 2007. Both studies trap very similar information. All the annuities are insured by life companies. One might expect the experience to be fairly similar.

Comparing Experience

I measure experience by actual to expected (A/E) ratios. For the expected, I used CPM2014priv and MI-2017. (There are other good choices, but the comparisons would not show up much differently by any other choice.) I always measure A/E ratios weighted by annualized income rather than count in order to emphasize the financial impact. The amount of income for actual deaths is increased slightly to allow for incurred but not reported deaths; the adjustments are company specific.

In many cases, I show the standard deviation in the A/E ratio; the calculation is done on the expected and reflects the actual variation in amount for the annuities exposed. Differences in A/E ratio that are less than one standard deviation are unlikely to be significant, but differences of more than two are likely so.

I have restricted data to 2007–2014 because I have those years for both studies. I include only ages 60–95 because there is little exposure at younger ages, and the data are less reliable at older ages.

The overall experience is shown in table 1.

Table 1

It seems reasonable to conclude that the experience for the group study is significantly higher than for the individual study because the difference in the A/E ratios is more than twice the sum of the standard deviations. But that would be a false conclusion.


The group data can be divided into two segments, one coming from defined benefit (DB) pension plans and the other from defined contribution (DC) pension plans or group registered retirement saving plans (RRSPs) (“non-DB”).

The individual data can be divided into registered and non-registered annuities, and each of those divided again. The registered data is composed of RRSP data and registered pension plan (RPP) data. The non-registered annuities, less obviously, can be separated into refund and non-refund annuities. (“Refund” means that there are some guaranteed payments, usually a term certain; “non-refund” means that all payments are subject to survival of the annuitant(s).) The non-registered, refund segment is normally referred to simply as “refund”; the non-registered, non-refund segment as “non-refund” or “non-ref”.

Table 2 shows the average size, standard deviation, and skewness of each of the six segments. It is surprising to note how close non-DB is to RRSP and DB to RPP. The two non-registered are quite different from the other segments, especially in standard deviation and skewness.

Table 2

Now let’s look at the overall results by segment (see table 3):

Table 3

We see there is little difference between DB and non-DB, but there is a difference between RRSP and RPP which is moderately significant for males and more significant for females. The difference between non-DB and RRSP and between DB and RPP is not strongly significant.

It seems that the difference between group and individual that we noticed in table 1 is accounted for almost entirely by the difference between registered and non-registered.

Let’s look more closely at the registered segments of group and individual.

Figures 1–4 compare the experience by quinquennial age groups for two segments, one from the group study and one from the individual study. The tick marks represent one standard deviation above or below the mean shown by the line. The tick marks have the same shape and colour as the lines with which they are associated.  

Figures 1 and 2 compare non-DB and RRSP for males and for females. In both cases, the blue line (non-DB) is generally higher than the pink line (RRSP), but the two are close together, and for several age groups the ranges of +/- one standard deviation from the mean overlap with each other. It may be that when we have more data we will be able to conclude that experience for RRSP is lower than for non-DB, but for now we cannot make that statement with confidence.



Figures 3 and 4 compare DB and RPP for males and for females. The two lines are very similar for males. RPP is generally higher for females; there is considerable overlap at one standard deviation. There is no evidence to support a different mortality basis for these two segments.


In comparing all four figures, it seems clear that non-DB and DB are very close together, but there seems to be a persistent difference between RRSP and RPP for both males and females. The difference seems to be less at higher ages. It might be reasonable to conclude that there is more self-selection with RRSP than with the other segments.

Size Adjustments

There is another factor at play which seems even more important than segment.

Figures 5 and 6 show the A/E ratios for the registered segments by size band. The bands are in increments of $6,000 of annualized income; the tick marks on the lines are at the location of the lower limit of each band. The highest band is for $72,000+. It is remarkable how nearly parallel the four lines are until the band $42,000–$48,000. There are not much data in each of the higher bands.


It has been observed for decades that A/E ratios tend to be lower for higher amounts. The first instance that anyone sought to quantify the impact, that I am aware of, is the CPM study. That study published a set of size adjustment factors to go along with each of the mortality tables. There were many objections raised to the use of size adjustments, such as that an individual might have a small pension from one employer and a large one from another, but that individual would have the same mortality for both pensions. The objections all seem plausible, but nonetheless the factors were a strong feature of the data.

What would happen if the size adjustments for CPM2014priv were applied to the GAMS and IAMS data? Figures 7 and 8 show the result.


Personally, I find these graphs to be startling. There is a very strong horizontal trend at least to $36,000–$42,000, especially for males. That implies that size adjustment factors developed from uninsured DB pensions work well for insured pensions and for individual registered annuities. There would be very little overlap of data between GAMS and IAMS and the data underlying the CPM tables, but a very similar pattern by size emerges from all three.

Could size adjustments explain the large difference between registered and non-registered? Figures 9 and 10 show non-registered refund for males and females, both with size adjustments. The tick marks represent one standard deviation above and below the A/E ratio.


Clearly the trend is not horizontal. There is a distinct downward trend. That implies that the improvement in mortality by size is greater for refund than for the registered segments.

Figures 11 and 12 are comparable to figures 9 and 10 but for non-registered non-refund.


The downward trend is very strong for both males and females. The A/E ratios for the largest amount band are about half (and this is after size adjustment) of what we saw for registered, and the standard deviations are small enough that we can attach a high degree of significance to the lower A/E ratios. It is very likely that this segment includes a significant number of back-to-back annuities. (These are annuities sold in conjunction with large life insurance policies, typically guaranteed T100, that would have been medically underwritten. The annuities are intended to pay the premiums. There is no need for a refund provision because the focus in on the life insurance rather than on the annuity. Accordingly, the mortality experience will be much lower than normally anticipated for annuities.)

It is likely that we are seeing the impact of heterogeneity in the non-registered segments. Some annuities are purchased independently of any life insurance, with the focus on income and with limited self-selection. Other annuities are purchased in conjunction with life insurance, and have the advantage of insurance underwriting. The latter likely predominate for larger non-refund annuities, the former for smaller annuities. The latter are likely present in the refund segment with much lower prevalence than in non-refund.


Segment matters, particularly between registered and non-registered. There seems to be sufficient justification for a difference in the pricing tables between these two.

Size matters even more. It seems very clear that there is justification for using lower mortality for larger amounts. However, I know that it may be difficult to implement a higher price for large amounts because there would be an incentive to split the funds across three or four annuities, provided that the competition between insurers is tight enough. If some insurers made a distinction in price, the largest single premiums would go to those who hadn’t made a distinction. Would the first group be willing to give up some market share to get better profit margins? This could be a developing area for pricing strategy.

Bob Howard, FCIA, is a consulting actuary.

Canadian Institute of Actuaries/Institut canadien des actuaires