The SOA Mortality Model – Putting It to the Test
March  2009

As part of the recently released 2008 VBT mortality tables, the Society of Actuaries introduced a theoretical model of the mortality continuum for the insurable population. The model’s spectrum extends from the very best super-preferred risks to those who barely qualify for a residual-standard class. Also included in the theory are underlying distributions for each distinct level of mortality. So how does the SOA model hold up to real world empirical data? Our mortality experience database provides an ideal vehicle for putting the theory to the test.


Graphing the SOA Model

Distribution of Relative MortalityChart 1 illustrates the workings of the SOA model. Mortality is presented in relative terms, with the average mortality for the total population set to 100 percent. According to the graph in Chart 1, the very best risks have mortality that is 50-70 percent of the average, while the poorest individuals exhibit mortality of well over 150 percent.

Note that a large portion (60 percent) of the population’s mortality is clustered between 80 percent and 120 percent of the average.


Testing the SOA Model

Mortality experience for a preferred risk class structure can be used to test the predictive value of the SOA model. From our database, recent mortality experience was collected on companies having exactly three non-tobacco classes – Super-Preferred, Preferred and Residual-Standard. Table 2 shows the resulting statistics by underwriting class, where expected mortality is the SOA 2001 VBT. The study included policies issued from 2000 through 2007 with face amounts of $100,000 and more. The mortality exposure period covered January 2004 through June 2007.

Table 2:Transamerica Reinsurance Mortality Experience Results

Nontobacco Class Exposure (millions) Claim Count Actual Amt. (thousands) Expected Amt. (thousands) Distribution of Expected Amt. A/E Ratio by Amount
Super-Preferred 200,728 533 63,692 167,673 32.4 % 38.0 %
Preferred 174,597 850 101,402 189,350 36.6 % 53.6 %
Standard 129,119 1,138 113,489 159,943 30.9 % 71.0 %
TOTAL 504,445 2,521 278,582 516,965 100.0 % 53.9 %

 Jan. 2004 - June 2007. Expected Mortality is represented by the SOA 2001 VBT.   

With our experience results in hand, we now want to compare them to the theory. Accompanying the SOA mortality model is an Underwriting Criteria Scoring tool which, through an intricate point system, can be used to translate a set of preferred underwriting criteria (build, blood pressure, cholesterol HDL, family history, etc.) into relative mortality predictions by class. Using this tool, criteria sets roughly representing the underwriting classes used in the Transamerica Reinsurance experience were scored. Table 3 summarizes the SOA model’s resulting prediction of the relative mortality by underwriting class.

Table 3: SOA Model Results

Nontobacco Class Distribution of Mortality Relative Mortality
Super-Preferred 20.4 % 0.671
Preferred 30.2 % 0.873
Standard 49.3 % 1.214
TOTAL 100.0 % 1.000

Relative mortality for the preferred classes is lower than average. The higher relative mortality  
for Standard is due to the presence of the preferred classes. These classes are siphoning off some of the better risks that would have otherwise been in the standard pool.

Understanding the Differences
Before proceeding with the comparison of SOA theory and real-world experience, we need to understand the difference between the SOA model’s underlying distribution of mortality among classes versus Transamerica Reinsurance’s distribution of expected claim amounts. The SOA model theoretically distributes mortality among the various classes based solely on the underwriting qualification criteria. The experience study, on the other hand, reflects risks that have actually purchased life insurance.

The difference is due to market forces that cater to Super Preferred and Preferred applicants. While 49.3 percent of the insurable population’s mortality is from those who qualify for the Standard class, only 30.9 percent ends up being from those who actually sought out and purchased a policy. This phenomenon is particularly evident in the brokerage term market, which encompasses a large portion of the Transamerica Reinsurance experience database.

In order to have an “apples-to-apples” comparison, our proprietary experience was re-weighted using the SOA model’s distribution of mortality by underwriting class. The results are shown in Table 4, where our total mortality ratio of 53.9 percent was recalculated to 59.0 percent. This revised divisor was then used to calculate the values shown in the “Experience Relative Mortality” column.

Table 4: Comparing Transamerica Reinsurance Experience to the SOA Model

Nontobacco Class Experience Mortality Ratio Theoretical Distribution Re-weighted Experience Experience Relative Mort. SOA Model Relative Mort.
Super-Preferred 38.0 % 20.4 % 38.0 % 0.644 0.671
Preferred 53.6 % 30.2 % 53.6 % 0.908 0.873
Standard 71.0 % 49.3 % 71.0 ​​% 1.203 1.214
TOTAL 53.9 % 100.0 % 59.0 % 1.000 1.000

As may be expected with any use of real data, the re-weighted results do not match up perfectly, but the variances are within acceptable margins.

Conclusions
As we can see from the last two columns of Table 4, the SOA model compares well to Transamerica Reinsurance’s Preferred class experience – at least for companies with a three Nontobacco class structure. The SOA model predicts slightly worse relative mortality in the Super-Preferred class but slightly better relative mortality in the Preferred class. However, these variances could certainly be from the choice of underwriting criteria used to represent the classes in the experience study compared to the actual range of values.

Based upon overall results, the SOA mortality model appears to provide a valuable means of analyzing and predicting mortality from Preferred class structures and should be a welcome addition to the actuary’s tool kit.