Mortality Study Trend Analysis - Part II
March  2007

When examined closely, mortality studies can reveal more than just aggregate mortality experience. Actuaries can analyze the experience by grouping the data into meaningful segments with the hopes of revealing interesting trends. We will now use a practical example to illustrate this approach. Our sample case study has the following parameters:

  • Policies issued from calendar years 1992 to 2001
  • Claims observed during calendar years 1996 to 2001
  • Expected mortality is based upon the Society of Actuaries 1975-80 Select and Ultimate Tables 
  • Fully underwritten term insurance only
  • Based upon face amount of insurance, before excess retention reinsurance

An initial high-level look at the data shows a large claim count which indicates a highly credible study but otherwise gives us very little insight into the experience itself: 

Bottom-line Results

  Exposure Claim Actual Amt Expected Amt A/E Ratio
($millions) Count ($thousands) ($thousands)  
Grand Total 478 ,374 5,478 344 ,042 834 ,430 41.2 %

 Table 1 - Aggregated Mortality Experience


The large claim count permits data to be segmented across various dimensions while maintaining acceptable credibility. Let’s first review experience by issue year:

What Happened in 1995?

Policy Issue
Year
Exposure
($millions)
Claim  Count Actual Amt
($thousands)
Expected Amt
($thousands)
A/E Ratio
1992   14,478 218 20,147 48,527 41.5 %
1993   23,035 351 28,149 65,382 43.1 %
1994   27,379 336 30,311 66,323 45.7 %
1995   30,861 294 44,485 62,838 70.8 %
1996   50,327 442 26,859 79,997 33.6 %
1997   87,884 962 61,221 150 ,360 40.7 %
1998   98,314 1,418 68,749 157 ,965 43.5 %
1999   122 ,571 1,181 54,423 176 ,139 30.9 %
2000   16,376 203 6,913 19,089 36.2 %
2001   7,149 73 2,786 7,811 35.7 %
Grand Total 478 ,374 5,478 344 ,042 834 ,430 41.2 %

Table 2 - Experience by Issue Year

Clearly something interesting occurred with the policy cohort issued in 1995. It is possible that either the entire block was poorly underwritten or that a few large claims have skewed the results. A second view of the data by calendar year of claim reveals additional information (see Table 3).

Abnormal A/E Ratio in 1997

Calendar           Exposure   Claim Count     Actual Amt
Year of Claim   ($millions)                           ($thousands)
Expected Amt
($thousands)
A/E Ratio
1996   29,491 251 18,865 47,695 39.6 %
1997   41,564 324 35,365 66,350 53.3 %
1998   63,745 601 40,933 101 ,253 40.4 %
1999   93,137 971 56,570 152 ,133 37.2 %
2000   123 ,840 1,473 85,866 213 ,089 40.3 %
2001   126 ,596 1,858 106 ,444 253 ,910 41.9 %
Grand Total 478 ,374 5,478 344 ,042 834 ,430 41.2 %

Table 3 - Experience by Calendar Year

Claims that occurred in 1997 appear to be an anomaly. A review of the claims listing for 1997 showed a few large claims that were covered by the company's excess retention reinsurance. Limiting those claims to the company's retention limit brings the suspect 1995 issue year actual-to-expected (A/E) Ratio of 70.8 percent to a more reasonable 46.3 percent and the 1997 claim year A/E ratio to 44.5 percent.

Now that we have resolved some obvious anomalies in the data, it would be a good time to graph our issue year A/E ratios and plot a simple linear regression line (shown in red):

Result: Mortality Trending Downward
Mortality Trending Downward
Table 4 - A-to-E Ratio by Issue Year

While the data shows variability around the regression line, it is the downward slope of the line that reveals a possible trend worth investigating – a trend which may not have been obvious from the data points alone.

One explanation for a downward trend in mortality by issue year could be a tightening of underwriting standards during the period in question. However, analysis of the company’s historical underwriting has revealed fairly stable business practices.

Upon further review, it was discovered that the company introduced several new preferred underwriting classes during the 1990s. As market forces placed more and more business into these new preferred classes, the effect was to reduce overall expected mortality. This effect has manifested itself in the experience as a downward trend in overall actual mortality – which shouldn’t come as a surprise.

By now, one can begin to see that trend analysis involves slicing-and-dicing experience and interpreting the patterns that emerge. Sometimes the patterns are relatively easy to interpret; other times a little extra effort is recommended. In Part III of this series, we will continue to carve up our sample case study and investigate trends by policy year and underwriting class.