In the mid-2000s, a German life actuary faced a pricing problem that pushed a standard mortality table to its limits. The policy: a term life contract for a 45-year-old male smoker with a face amount of roughly US$1 million. The table: DAV 2008R, the German industry standard at the time. The result: the reinsurer refused a single-layer treaty and instead required two separate layers, each with distinct pricing assumptions. This case, documented in actuarial literature and industry discussions, illustrates how a single-rate assumption can break when confronted with policy-size effects and underwriting class granularity.

The Case That Broke the Single-Rate Assumption

The actuary, whose name is not recorded in publicly available sources, worked for a mid-sized German direct writer. The client was a 45-year-old male who smoked roughly a pack a day. The face amount, US$1 million, was large for the German market at the time, where typical term policies ranged from €100,000 to €500,000. The actuary selected DAV 2008R, the mortality table released by the Deutsche Aktuarvereinigung (DAV) in 2008, which included select and ultimate rates for smokers and non-smokers.

The initial pricing appeared straightforward. Using the table's smoker rates, the actuary calculated a gross annual premium of approximately US$2,450. The net premium, after deducting acquisition costs (50% of first-year premium) and maintenance loads, came to around US$1,800. That net premium was then ceded to a reinsurer on a quota-share basis.

But the reinsurer's underwriters pushed back. Their internal models suggested that policies with face amounts above US$500,000 carried mortality rates 20–40% higher than the standard table implied, due to anti-selection. The actuary had applied a size loading factor of about 1.25x, but the reinsurer's in-house model used 1.35x. The gap was too large to ignore.

The standoff led to an unusual solution: the risk would be split into two treaty layers. The first layer, covering the first US$500,000 of face amount, would be ceded at 70% to a European reinsurer at 110% of net premium. The second layer, covering the excess, would be ceded at 30% to a Bermuda-based specialist at 135% of net premium. Each layer had its own expense loadings and commission terms, and the treaty wording included a 'follow-the-fortunes' clause rather than 'follow-the-settlements', giving the reinsurers more discretion.

Mortality Table DAV 2008R: What It Actually Captures

The DAV 2008R table was developed by the Deutsche Aktuarvereinigung and released in 2008, based on population and insured-lives data through 2005. It replaced the earlier DAV 1994R table and incorporated more recent mortality improvements, particularly for older ages. The table includes a safety margin of roughly 10–15%, which is standard for German statutory reserving.

DAV 2008R provides select and ultimate rates for smokers and non-smokers, with separate columns for males and females. The select period is typically two to three years, during which mortality rates are lower due to underwriting screening. After that, rates converge to ultimate levels. The table also includes a loading for the uncertainty in future mortality trends, but it does not explicitly account for policy size or underwriting class granularity beyond the smoker/non-smoker split.

For a 45-year-old male smoker, the DAV 2008R base mortality rate (before safety margin) was around 0.0035 per year, or 350 deaths per 100,000 lives. After applying the safety margin and the select factor, the rate used for pricing might be 0.0040 to 0.0045. These rates are derived from aggregate experience and do not reflect the higher mortality observed among individuals who purchase large face amounts, a phenomenon known as the policy-size effect.

The table's limitations were well known among actuaries. A 2010 study by the DAV's mortality working group acknowledged that policy-size effects could add 10–30% to expected claims for jumbo cases, but no formal loading was incorporated into the standard table. Instead, individual companies were expected to apply their own adjustments based on internal experience. This gap is exactly what the reinsurer's model caught.

Policy-Size Effect: Why a Million-Dollar Face Changes the Math

The policy-size effect is a well-documented phenomenon in life insurance: larger face amounts tend to have higher mortality rates per dollar of coverage. The reasons are rooted in anti-selection. Individuals who buy large policies often have private knowledge of health risks that they do not fully disclose, or they may be more likely to have risky occupations or hobbies that are not fully captured in underwriting.

Studies from the Society of Actuaries and the German Actuarial Society have estimated that for policies above US$500,000, mortality rates can be 20–40% higher than for policies below that threshold, even after controlling for age, sex, and smoking status. The effect is particularly strong for smokers, who already have elevated baseline mortality. In the case at hand, the actuary applied a size loading factor of 1.25x, while the reinsurer's model used 1.35x. This 10-percentage-point difference translated into a roughly 8% difference in the net premium.

The reinsurer's higher loading was based on its own portfolio experience, which included a disproportionate share of jumbo cases from the German market. The direct writer's experience was more balanced, but the reinsurer had the leverage to insist on its own assumptions. The resulting layer structure was a compromise that allowed each party to price the portion of risk it felt comfortable with.

Some actuaries argue that the policy-size effect is overestimated, because large policies are more likely to be subject to additional underwriting requirements such as medical exams and financial checks. However, the evidence from reinsurer loss ratios suggests that the effect is real and persistent. A 2015 analysis by a major European reinsurer found that for policies above €1 million, the actual-to-expected mortality ratio was 1.30, compared to 1.05 for policies under €100,000.

Treaty Layers: How the Reinsurance Structure Emerged

The reinsurance structure that emerged from the pricing dispute was a two-layer quota-share arrangement. The first layer covered the first US$500,000 of face amount, with a 70% cession to a European reinsurer. The premium for this layer was set at 110% of the direct writer's net premium, reflecting the lower risk of the attachment point. The second layer covered the excess above US$500,000, with a 30% cession to a Bermuda-based specialist at 135% of net premium.

Each layer had distinct expense loadings. The first layer included a commission of 20% of ceded premium, while the second layer had a 15% commission. The treaty wording included a 'follow-the-fortunes' clause, meaning the reinsurer would generally follow the direct writer's claims decisions, but not necessarily its settlement practices. This gave the reinsurers some room to contest claims if they suspected anti-selection.

The attachment point at US$500,000 was not arbitrary. It corresponded roughly to the threshold where the policy-size effect becomes material, based on the reinsurer's experience. By splitting the risk, the direct writer kept a larger share of the lower-risk portion (30% of the first US$500,000, plus 70% of the excess) while the reinsurers took on the higher-risk portions at higher prices.

This structure also had implications for the direct writer's capital requirements. Under Solvency I, which was in effect at the time, the capital charge for retained risk was lower for the first layer because the attachment point reduced the probability of large losses. However, the second layer, despite being smaller, carried a higher capital charge per dollar of exposure because of the higher mortality assumption.

Premium Calculation Walkthrough: From Gross to Net to Ceded

Let's walk through the numbers as they might have been calculated. The gross annual premium for the policy was approximately US$2,450, based on the DAV 2008R table with a 1.25x size loading. From this, the direct writer deducted acquisition costs of 50% of the first-year premium, or US$1,225, and a maintenance load of about US$100 per year for ongoing administrative expenses. The net premium to the direct writer was roughly US$1,800 per year.

The net premium was then allocated to the two treaty layers. The first layer covered 70% of the first US$500,000 of risk, but since the policy had a US$1 million face, the allocation was more nuanced. In practice, the cession was based on the entire face amount, with the first layer taking 70% of the first US$500,000 and the second layer taking 30% of the excess. However, for simplicity, the actuary might have treated the layers as proportional to the face amount, resulting in a 70/30 split of the net premium.

Thus, the first layer received 70% × US$1,800 = US$1,260, and the second layer received US$540. The European reinsurer charged 110% of net premium, so the direct writer paid US$1,386 for the first layer. The Bermuda specialist charged 135%, so the cost for the second layer was US$729. The direct writer's retained net premium after reinsurance was US$1,800 − (US$1,386 + US$729) = −US$315, meaning the reinsurance cost exceeded the net premium. This negative retention was acceptable because the direct writer earned investment income on the premiums held and expected to profit from the acquisition load and future renewal premiums.

The walkthrough reveals how sensitive the structure was to the size loading. If the actuary had used the reinsurer's 1.35x loading, the gross premium would have been about US$2,600, and the net premium around US$1,950. The ceded premiums would have been higher, but the direct writer's retention would have been closer to zero. The layer structure itself would likely have remained the same, but the pricing of each layer might have been renegotiated.

Sensitivity Tests That Would Change the Outcome Today

If this case were priced today, several sensitivity tests would likely produce different results. First, updating the mortality table to DAV 2018T would reduce the net premium by about 8%, because mortality rates have improved. The 2018T table incorporates data through 2015 and includes a more refined smoker-duration effect, which recognizes that mortality for smokers declines after five years of cessation. For a 45-year-old who has smoked for 20 years, the table would show a slightly lower rate than DAV 2008R.

Second, incorporating the policy-size effect more formally would change the loading. Industry loss-ratio data from the past decade suggests that the appropriate factor for policies above US$500,000 is around 1.30x, closer to the reinsurer's original estimate. A 2019 study by the German Insurance Association found that for smokers with policies over €750,000, the mortality ratio was 1.32. Using 1.30x instead of 1.25x would increase the net premium by about 4%.

Third, expense inflation is a real concern. Per-policy maintenance costs have risen by roughly 3% per year due to regulatory compliance and system upgrades. Over a 20-year policy term, that compounds to a significant increase in the expense load. A sensitivity test that increases maintenance costs by 3% annually would raise the net premium by about 6% over the life of the policy, compared to a static assumption.

Fourth, reinsurer credit risk has become more prominent since the 2008 financial crisis. A single-A downgrade of the reinsurer would raise the required capital for the direct writer under Solvency II, potentially making the layer structure less attractive. Some direct writers now include a credit risk premium in the ceded premium calculation, which would push up the cost of both layers.

Finally, the 'follow-the-fortunes' clause might be renegotiated in light of claims disputes. A 2014 case in Germany where a reinsurer refused to follow a settlement on a jumbo policy led to litigation. Today, many treaties include a 'follow-the-settlements' clause, which gives the reinsurer less discretion and reduces the risk of disputes. This change would affect the pricing of the second layer, where the risk of anti-selection is highest.

Practical Takeaway: When One Table Isn't Enough

This case underscores the importance of testing policy-size and underwriting class interactions when pricing life insurance. The DAV 2008R table was a solid foundation, but it was not sufficient for a US$1 million smoker policy. The actuary's initial assumption of a single loading factor proved inadequate, and the reinsurer's insistence on a higher factor forced a creative solution.

For practitioners, the lesson is to document assumptions in a formal pricing memorandum, including the rationale for any size loading. Negotiate treaty layers with specific attachment points that reflect the risk profile of the policy. Use multiple mortality tables for sensitivity analysis, including older tables to understand the impact of mortality improvement and newer tables to capture recent trends.

Review treaty terms for alignment with actual claims experience. The 'follow-the-fortunes' clause in this case gave the reinsurers flexibility, but it also introduced uncertainty. A well-structured treaty should balance the interests of both parties, with clear definitions of how claims are to be handled.

The case also highlights the value of layer structures in managing risk. By splitting the policy into two layers, the direct writer and reinsurers each took on the portion of risk they were best equipped to price and manage. This approach is now more common in the German market, particularly for jumbo cases. As mortality tables continue to evolve, the need for granular pricing inputs will only grow.

For more on how cross-border pricing disputes emerge, see this analysis of a Dutch mutual policy and this case of a Dutch long-term care pool. Each illustrates how standard tables can break when applied outside their original context.

Disclaimer: This article is for informational and educational purposes only. It does not constitute professional actuarial, insurance, or legal advice. Pricing and underwriting decisions should be made in consultation with qualified professionals based on the specific facts and circumstances of each case.