Canadian Annuitant Mortality Table

Canadian Annuitant Mortality Table

(CIP2005)

A Research Paper

R.C.W. (Bob) Howard, FCIA, FSA

2006 02 04

Table of Contents

1 Introduction 2

2 Source of Data 2

3 Limitations in Data 4

4 Main Graduation 6

4.1 Data to include 6

4.2 Graduation Method 9

5 Older Ages 9

6 Younger Ages 10

7 Final Table 11

8 Projection 12

9 Conclusion 14

10 Acknowledgements 14

11 Bibliography 15

Appendix 1. Whitaker-Henderson Graduation 16

Appendix 2. Joint and Survivor Tables 19

Appendix 3. Tax-Specific Tables 20

Appendix 4. Tables for Larger Amounts 21

Appendix 5. Select Table 22

Appendix 6. Contributing Companies 24

1  Introduction

No Canadian annuitant table has ever been published. The Canadian Institute of Actuaries recognized the need several years ago and began collecting data from a number of companies. There is now enough data to create a credible table.

This paper is presented as a case study in the construction of a mortality table. It is a pragmatic work. It includes some failed attempts as well as the finished product. I invite the readers to treat this as a travelogue which some may read to experience the journey vicariously and others to prepare for a similar journey of their own.

2  Source of Data

The data underlying the table comes from the Individual Annuitant Mortality Study (IAMS) of the Canadian Institute of Actuaries. This study has been gathering data on payout annuities from a number of Canadian companies since the early 1980’s. Studies are published by the Canadian Institute of Actuaries and can be obtained at http://www.actuaries.ca.

Table 1 shows the amount of data included in this work. The study includes the thirteen policy years, 1988-2001. Earlier data were rejected because there were too few contributing companies. All data were contributed on an annuitant basis. That is, there was one record for each single life policy, two for each joint and last survivor policy, while both were alive, and one for each joint and last survivor policy after one life had died. There was no attempt to combine records for an individual who may be an annuitant under more than one policy.

The record layout distinguishes the following features:

1. year of experience
2. gender of annuitant
3. whether a single life annuity, a joint with both alive, or the survivor of a joint annuity. (Some companies could not distinguish a single life annuitant from survivor annuitant.)
4. RRSP, RPP or non-registered
5. with or without a refund provision or period certain, regardless of whether the provision or period has expired
6. issue age (Most records use age nearest birthday, and records using age last birthday are converted to age nearest by splitting the exposure and deaths half to the calculated age, and half to the next higher age.)
7. duration from issue

In order to increase the amount of data used in constructing the table, I combined the fourth and fifth items above. The choice to combine refund and non-refund was easy because there is little non-refund business. Similarly there is too little RPP business captured to warrant showing it separately. Combining RRSP and non-registered is not really desirable, but I thought it better to make one good table rather than two less credible ones. However, it would seem reasonable to use a different percentage of the table when applying it to registered or non-registered business. Table 2 shows how much business is included for each tax type, and Table 3 shows the overall mortality ratios, to the 1983 IAM Basic table. (See 33 TSA 695.)

The RRSP and non-registered data are quite different, especially for single life. The average size of the RRSP business is much less, and so is the average age. There is proportionately more joint business than single for RRSP and RPP than non-registered.

Table 3 shows that RRSP and non-registered mortality are not very far apart. Generally RRSP ratios are lower. Age adjusted ratios would show a different pattern. The differences between RRSP and non-registered have been discussed in an earlier report by the committee. See http://www.actuaries.ca/members/publications/1996/9624e.htm. (See also Appendix 3.)

3  Limitations in Data

The data are considered to be quite accurate, particularly for single life annuitants. Each year’s submission must pass a consistency check with the prior year’s submission. The check matches by policy number, gender, and issue age. Accordingly the study’s death records can be considered as complete as those of the contributing companies. Of course some deaths are not reported until long after they occur. Late reporting is most common for the secondary annuitant under joint policies. A lag study on the data suggests that the amount of late reporting is not excessive. However, the main table is built only on single life data only, to minimize the effect of late reported deaths.

The characteristics of the data have been changing over the years. Table 4 shows a few of those characteristics. Note especially that the average annual income has been increasing, at more than 2% per year. This is significant because mortality rates tend to decrease when the amount of income increases. Also notice the increase in average age; this suggests that there are not enough new entrants to maintain a stationary population.

Table 5 shows similar data but for the policies newly issued in each year of experience. (For examples, the policies issued in 2000 appear as first year policies in the year of experience 2001.) The decrease in the proportion of RRSP business is very dramatic. The increase in average issue age may also be related to the decline in RRSP.

Part of the change is from changes in the companies that contributed data. Not all companies contributed data for all years. Each company has some unique characteristics in its data. In the 2001 submissions for example, the average attained age varied from a low of 75.3 to a high of 78.8. The proportion of data from RRSP policies varied from 45% to 84% (and one company cannot distinguish the tax status). The proportion of lives in single life policies varied from 38% to 66%. The average income varied from $2,100 to $6,800.

One strange feature of the data is that there is little observed improvement in mortality over the 13 years covered by the study. Mortality rates for the population show much more improvement. I suspect that the lack of improvement relates to the lack of homogeneity in the study over the 13 years. The committee's reports indicate that there has been a lot of thought on this issue, but there is still no satisfying explanation. I think it is still reasonable to use the data for constructing a mortality table, but it would be unwise to infer rates of improvement from the data.

The data had a couple of anomalies. I spotted them when trying to understand a difficulty in graduation. The anomalies occurred only in the single life data. Charts 1 and 2 show the observed mortality rates for a few ages. The diamonds indicate the mortality rates. The lines above and below indicate two standard deviations (based on the 1983 IAM Basic table). There is one clear “outlier” for each of males and females. In the case of the males, the problem case could not be considered to fall on the trend line even at 3 standard deviations.

Any oddity has a reason. I found the problems listed in Table 6. My solution was to remove the problem by altering the offending cases. This decreases the amount of claims with no offsetting increase. However, the decrease represents only 0.3% of the single life deaths. The resulting data yields a much better table over these ages.

4  Main Graduation

4.1  Data to include

There are several choices to be made.

4.1.1  Sex Distinct or Unisex

In keeping with other published individual tables, I will keep male and female separate. The differences in the raw mortality rates between male and female are substantial. There is adequate data for both.

4.1.2  Select Period

Tables published in the USA since the a-49 table have been based on attained age data. (The a-49 table was an ultimate table with a 1-year select period.) This was seen as conservative because the attained age table would be lower than an ultimate table.

The IAMS data can be adjusted to any length of select period. To increase the data at each age, I decided to develop an attained age table. However, there seems some evidence for a select period of 3-5 years. There is some risk of bias because the payout annuity business has been declining slowly in recent years. Consequently there may be too much emphasis on the later durations. (I also developed a 5-year select table, which is discussed in Appendix 5.)

4.1.3  Plans included

As mentioned earlier, the main table is constructed from single life data only. I consider this the most reliable data. However, I also did some work on joint and survivor plans, which is presented later in this paper.

4.1.4  Ages Included

Ultimately we need a table with appropriate rates at all ages. However, since payout annuities are rarely sold under age 60, there is very little data at the younger ages. Because of attrition there will never be much data at the very high ages. Consequently the main data for constructing the table will have to be a shorter range than would be considered ideal. I found deciding which ages to include to be the most difficult part of the work. It is certainly key to the final table because the extrapolations at the younger and older ages are anchored to the ends of the main graduation.

My first thought was to look for ages for which the standard deviation in the mortality rate is acceptably low. In that case the data is likely to provide a fairly good estimate of the rate. I calculated the standard deviation in the expected mortality rate, on the 1983 IAM Basic table, and divided it by the observed mortality rate. (I didn’t use the standard deviation from the raw data because it would be influenced too much by fluctuations.) Table 7 shows these data by amount for single life policies only, for key ages. For brevity, I show only the males. The patterns are similar for females.

The problem with this measure is that the data looks more reliable when there are a lot of deaths, and less reliable when there are few. I then considered the ratios using the expected mortality rates rather than the actual. Table 8 shows the ratios for both actual and expected mortality. (Standard deviation is on the expected table in both cases.)

As expected the curve is much smoother when using the expected mortality rates. Notice that the ratios rise rapidly at either end of the table. I decided to choose as the main ages 64-95 for males. The ratio of standard deviation to mortality rate is under 15% throughout. For females, I chose ages 65-97.

I will pause here briefly to note that the standard deviation is calculated by the following.

If At, the annualized income for a policy, were the same for all n policies in the cell, which of course it is not, then the ratio of the standard deviation to the mortality rate would be simply,

Thus, the precision of the estimated mortality rate improves with the square root of the expected deaths.

There is one problem related to ages yet to be dealt with. Graduation often gives odd results at the end points. For example, heavy claims at the youngest age might cause the mortality curve to have a negative slope around that age. To avoid endpoint problems, I decided to include 10 extra ages below and 5 extra ages above the chosen ranges. As discussed below the extra ages below are used in grading to another table, and the extra ages above are ignored completely. Thus the graduation is performed on ages 54-100 for males and 55-102 for females.

4.2  Graduation Method

It was an easy choice to use Whitaker-Henderson Type B graduation. This method minimizes the sum of an expression involving fit between the graduated and actual data and an expression involving the smoothness of the graduated data. The choice of parameters to use is less obvious. Appendix 1 describes in detail the options available and the choices made.

The weights used for the measure of fit were the reciprocals of the variances of the mortality rates, adjusted to sum to the number of ages graduated. The smoothness was calculated as the squared fourth differences. The factor balancing between fit and smoothness was 300 for both males and females.

5  Older Ages

There is never enough data at the high ages to construct a credible table. (When asked what it was like to be her age, a woman of 104 replied, “There’s absolutely no peer pressure.”) The data that does exist is often suspect. In the case of insurance data, the company has no incentive to find that the death has already occurred. In the case of annuities, the amounts may be too small to bother with a “certificate of existence”; some cases remain “alive” because there is no valid address either for the payment or the certificate of existence. The rates at high ages are generally artificial. The concern is to keep the rates from being inconsistent with the data.

The traditional approach is to pick the last 3 ages that are considered sufficiently reliable and pass a cubic through them to reach 1.0 at a chosen high age. This method is simple to do and yields a nice smooth curve, but there are some problems.

1. Having mortality rates increase through these ages is conservative for insurance, but not for annuities.
2. Several studies have found the slope of the curve to decrease through these ages, perhaps even become flat.
3. Fitting a cubic to 1, does more that admitting there is not enough data; it ignores the data that do exist.

I tried fitting a cubic to 1, but I rejected that approach for the reasons given.