In analyzing client mortality studies over the years, I noticed that companies with very similar underwriting practices, guidelines, preferred criteria, and marketing strategies often have very different experience. Even after normalizing for age, gender, mortality class, exposure period and other identifiable characteristics, credible actual-to-expected (A/E) ratios for these supposedly similar companies can differ significantly.
I call this phenomenon “the funnel effect,” i.e., a company’s mortality experience is partially determined by the population funneled to it (via distribution channels and market forces). Even though a company’s underwriting process selects and segments this applicant pool, if a company’s funnel draws from a population having worse/better than average mortality, such mortality deviations will permeate the company’s segmented experience due to unspecified but relevant population characteristics.
Recently, I considered applying some science around my observed funnel effect hypothesis in order to “substitute facts for appearances.”1 This article discusses the results of such an experiment.
Defining the Experiment
The funnel effect implies that a company’s early duration mortality experience does not converge at some point to an industry average as measured by, for example, a Society of Actuaries Inter-company study or a reinsurer’s combined experience table. Thus, the concept behind my experiment was to see if a company’s mortality remained stable over durational time. In other words, did a company with high early duration mortality also have high mortality in later durations? Likewise, did a company with low early duration mortality have low mortality in later durations?
An ideal experiment would look at current early duration A/E ratios for a wide variety of companies and then follow these closed blocks of business for the next 30+ years to see if the initial A/E ratios hold steady into the future (all else being equal). This would provide solid evidence that individual company experience does not converge to a common level.
Unfortunately, I did not have the luxury of waiting this long for results. Instead, using information from a large industry mortality study, I compared today’s recent experience among companies for policies issued during 1980-84, 1985-89, 1990-94, 1995-99 and 2000-04. This allowed me to view A/E ratio trends by company for durations 1-5, 6-10, 11-15, 16-20 and 21-25, using the SOA 2008 VBT as the expected basis.
This form of the experiment is far from perfect due to marketplace evolution over the issue periods surveyed. Elements such as target market, product characteristics, distribution channels, underwriting philosophy, company reputation and mergers/acquisitions could have affected historical mortality experience. However, I filtered the data as much as possible to compensate for these items.
I obtained data from 20 companies’ experience (labeled A through T). The first analysis entailed ranking the company A/E ratios from lowest (1) to highest (20) for each of the five issue era periods.
Figure 1 shows the results for the seven companies that appeared to have very stable rankings from period to period. An additional nine companies had rankings that were reasonably stable (one anomalous period). The final four companies had rankings that varied from period to period.
These preliminary results were promising since they showed that many companies have maintained their relative mortality position in the marketplace over the past 25 to 30 years. However, the question still persisted as to whether the A/E ratios used to rank the companies remained reasonably stable over that time period.
From a research perspective, the heart of the problem I was trying to solve was: “Is a company’s early duration mortality experience predictive of later duration mortality?” That is, can our pricing actuaries be confident that overall A/E ratios derived from a client’s experience study covering, say, the first 8-10 durations predict later duration A/E ratios?
To provide an answer to this question, I used the A/E ratio data from the 20 companies and averaged the ratios for durations 1-10 (issue years 1995-2004) and for durations 11-25 (issue years 1980-1994). Figure 2 shows these average ratios by company.
Figure 2 – Average Ratios by Company|
Average A/E Ratios (%)|
While one can identify some deviation among certain
companies, late duration A/E ratios in general tend
to follow early duration A/Es. This would seem to
suggest that companies' early duration A/Es are
are somewhat predictive of later duration A/Es.
Next, I plotted each company’s set of ratios as shown in Figure 3. In statistics, the Pearson product-moment correlation coefficient is a measure of the linear dependence between two variables. Its value can range between +100 percent and −100 percent, where 100 percent is total positive correlation, 0 percent is no correlation, and −100 percent is total negative correlation2.
If our predictions of duration 11-25 A/E ratios based upon duration 1-10 A/E ratios were absolutely perfect, all of the data points would fall along the diagonal red line and would produce a correlation coefficient of 100 percent. In reality, the data show a correlation of around 54 percent, which indicates a fairly strong positive linear relationship.
Results of my funnel effect experiment were encouraging. In general, companies with lower than average A/E ratios for business issued today tended to have lower than average A/E ratios for business issued 10 years ago, 15 years ago, 20 years ago and so forth.
The same held for companies with higher than average A/E ratios. While not conclusive, I believe the results provide some evidence that the level of a company’s early duration experience is predictive of the level of their later duration experience and will not necessarily grade back to an industry average as a block ages.
A company can make some improvement in its mortality experience by refining underwriting and marketing practices, but as long as it is “fishing in the same pond,” better bait will not necessarily attract better fish.