Part of my job as a research actuary is to review insurance industry papers that may have an impact on current pricing assumptions or underwriting decisions. One such paper examined all-cause mortality experience relating to motor vehicle records (MVR).1 This article explains my review of the paper and conversion of its information into practical knowledge for the line underwriter.
Reviewing the Paper
My first order of business was to review the background information and data sources to assure that the results would be appropriate for my purposes. The experience study had used exposures from 2007 through 2010 and contained approximately 73,000 deaths. The lives studied were from the general population (i.e., not necessarily "insured" lives), but this is not unusual for much of the mortality research I encounter.
The paper presented results in terms of actual-to-expected A/E ratios with a recent U.S. Population Life Table as the expected basis. More importantly, however, the paper translated these A/E ratios into relative mortalities for the various population segments that were analyzed. Thus, I could see how relative mortality experience differed by MVR severity and also in relation to attained age and gender.
For example, relative mortality for those lives with MVRs showing major violations was about 170% of all lives combined, compared to about 95% for those with clean records or only minor violations. The 170% was then further detailed to show males with about 160% relative mortality and females with about 200%. The paper also showed a high correlation between the number of violations (regardless of severity) and increasing mortality. However, for purposes of the article, I restricted analysis to major violations only.
Extracting Relevant Mortality Data
Having reviewed the paper’s results in detail, my next task was to extract the relevant mortality experience and convert this into a practical guide for the line underwriter. Figure 1 shows the information from the paper for those lives with MVRs showing major violations. In underwriting terminology, relative mortalities can be thought of as permanent table ratings, where each table represents 25% additional mortality over and above the base mortality for a standard life. For example,150% relative mortality represents two tables of additional mortality (100% base + 2 times 25% additional = 150%).
The paper provided only combined male/female mortality information by attained age. I used the overall male/female mortality relationship to calculate gender specific figures by attained age.
Converting the Information
There was a minor problem with the way the mortality results were presented in the paper. Currently, some underwriters in the industry prefer not to view mortality arising from insureds with major motor vehicle violations as a percentage increase, which is what a table rating implies. Instead, they impose an additional permanent flat extra premium. As a consequence, the extra mortality is "front-loaded" in that it becomes a smaller and smaller percentage of total mortality as the insured ages.
To convert the attained age table ratings into permanent flat extras, I used a spreadsheet that I created many years ago. The spreadsheet takes the present value of future mortality based upon the table rating and calculates an equivalent flat extra mortality. Figure 2 shows sample output from the spreadsheet. In this case, I had input Table 2 for a male age 25 and the spreadsheet calculated an equivalent permanent flat extra premium of $0.38 per $1000 of insurance.
The paper had provided a similar conversion example using the 2008 VBT as base mortality with a 6% lapse rate and a 6% discount rate. I followed suit with these assumptions to convert Table 1 figures into flat extras.
Even though the study’s mortality results differed by gender, underwriters do not typically take gender into consideration when determining flat extras for individuals showing MVRs with major violations. Thus, although I calculated separate flat extras for males and females, I combined the results when I presented my findings to the underwriters, using a gender distribution provided in the paper. Figure 3 expands the table-rated results to show unisex flat extras by attained age, rounded to the nearest ten cents.
The last column clearly shows how very differently table ratings and flat extras express the occurrence of mortality. While the table ratings are fairly flat by attained age for both genders, the underlying mortality rates increase very rapidly by attained age and a much higher flat extra is needed to create an equivalent flat mortality load.
Being able to search for and review the innumerable industry papers that are published each year is a vital part of a research actuary’s expertise. Analyzing sometimes ambiguous or anomalous results to extract appropriate nuggets of information and convert them into practical working knowledge can be as much of an art as a skill. ∞
1 Rushing, Scott and Rozar, Tim. “An Analysis of Motor Vehicle Records and All-Cause Mortality.” RGA Reinsurance Company and LexisNexis (2012).