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The Actuary The magazine of the Institute & Faculty of Actuaries

German annuities

In many countries the volume of annuity business is growing as governments shift pension provision from the state to the private sector. At the same time, while the continuous increase of life expectancy is a widely accepted fact, there is much uncertainty about the actual development of mortality rates in the forthcoming decades.

German life tables
In the German annuity market, companies traditionally compete by expense loadings, product features, and the with-profits element, but not by mortality rates. Until recently, the industry both reserved and priced its annuity business using the standard DAV1994R table which, as implied by the name, dates from the mid-1990s. At the end of 2002, the German Actuarial Association (DAV) set up a committee to examine the appropriateness of this table, which recently recommended a new set of mortality rates, DAV2004R.
DAV2004R comprises two separate tables, one for deferred annuities and for annuities in payment. These are expected to become the industry standard for both valuation and pricing purposes for new annuity business from 1 January 2005. It is estimated that this will cause an increase of 5% to 20% in new business premium rates. A special version of DAV2004R has also been proposed for the valuation of business in force. It has been estimated that application of this table will require the strengthening of mathematical reserves by about e4bn across the industry in 2004.
These are undoubtedly large increases only ten years after the introduction of the previous table, and there are two important reasons for this:
– Development of German mortality experience during the 1990s clearly indicated that the trend assumption in DAV1994R does not appropriately reflect current mortality improvements.
– Gen Re and Munich Re in the meantime have each started systematically collecting insured data for annuity business, thus creating much more data than was available for the development of 1994 table. More detailed contractual items, such as annuity amounts and benefit options, are also available.
It has now become more important for the German market to get future annuity rates right. There has been an unprecedented annuity boom in Germany since the introduction of DAV1994R. At the end of 1996, annuities used to be a niche product, representing a mere 5% of all business in force. This had soared to 16% by the end of 2003. At present about half of all individual regular premium new business comes from annuity business. The importance of annuity business is likely to grow further in the near future because of new tax rules which took effect from 1 January 2005.
The new table DAV2004R consists of a base table and trend assumptions. The base table was derived from the experience collected by Gen Re and Munich Re. The experience analysis for annuities in payment revealed a strong relationship between mortality rates and annuity benefit levels. Mortality rates were therefore weighted by annuity amounts. The table 1 shows mortality rate by annuity amount class, measured against the aggregate mortality.

The selection effect
The German market has a tradition of strong guarantees, which is reflected in annuity business. As well as single premium immediate annuities, regular premium deferred annuities taken out typically at ages 30 to 40 are very popular. Deferred annuity contracts often include annuity rates that are guaranteed throughout life and at the end of the premium payment period offer an option of receiving regular annuity payments or commuting the policy into a lump sum. The interest rates are guaranteed as well as the mortality rates, but obviously the guarantees are not as onerous as in the UK in 1970s and 1980s.
This option creates a heavy self-selection effect which is visible in the experience of annuities in payment. This exacerbates the difference between the mortality rates in respect of annuitants and the population in general.
Figure 1 opposite compares annuitants’ mortality experience with that of the wider German population, both for deferred annuities and annuities in payment. Insured mortality is clearly lower than that of the population: both lines on the graph are below 100%. The self-selection effect is clearly visible on the graphs at ages 55 to 70. At these ages people have the option to surrender their polices and take a lump sum. Clearly, people who are less healthy are more likely to do this.
Therefore, a selection period was introduced for the annuities in payment table. The ultimate mortality level is attained five years after benefit payment starts. The table for a deferment period is simply an ultimate table with no distinction by policy year.
In the absence of sufficient data, both tables had to be extrapolated from age 100 to age 120, the termination age.
Finally, a safety margin of about 16% was applied to the whole table.

Assumed future improvements
A lot of attention was paid to the choice of the model for future trends. Three different models were examined:
– Traditional model
= exp(F(x))
with a trend function F(x) depending on current age x;
– Cohort model
= exp(G(t+1x))
with a trend function G(t+1x) depending on year of birth;
– Synthesis model
= exp(F(x)G(t+1x))
stemming from a combination of the two.
The likelihoodratio test results suggested that the synthesis model is the best for the purpose of modelling 33 German population mortality tables for the period 19671999. But although this model provided the best fit to the past data, the committee decided it was unsuitable for projecting German mortality rates because some projected rates made no sense. For instance, the mortality rate for an 89-year-old man would only be half the mortality rate of an 89-year-old woman in 2050.
The volume of deferred annuities sold in Germany has increased dramatically over the past ten years, and is still increasing. Also, annuities are usually sold with whole-of-life guarantees. For these two reasons the model is going to have implications mainly for the cohorts from the 1970s. However, the experience available for these cohorts is very limited. All things considered, it was decided that the traditional model is the most appropriate for projecting German mortality rates.
The trend assumption was then derived based on the short-term mortality improvements in the German population from 1990 to 1999. Various studies have shown that, as in the UK, mortality improvements of the insured group exceed those of general population. More generally, upper socioeconomic groups experience greater mortality improvements than lower socioeconomic groups. Based on the results from German statutory pension insurance, a loading of 0.2% to annual population mortality improvement factors was used for insured lives. The trend assumption then needed some smoothing, limits for younger ages, extrapolation for ages 90+ and the application of a safety margin.
Figure 2 shows the final trend assumption.

Brief comparison with the UK
Some features of the German market are very similar to the UK. In Germany, as in the UK, actual mortality improvements have exceeded expectations. Actuaries now have to review the standard mortality tables, and that will cause an increase in the regulatory reserves.
The difference between population and insured male annuitants’ mortality in Germany is similar to the UK.
The available insured data in Germany does not go back as far as the CMI Bureau data in the UK. On the other hand, German annuitants’ mortality is analysed by more risk factors, such as benefit size and a longer select period. Such analysis is not carried out by the CMI, and clearly it would be very useful if the CMI could do it in future.
Unlike the UK, the German market continues to offer guaranteed rates for guaranteed annuities both in terms of mortality and interest rates. This is perhaps justifiable because the annuities are with-profit and priced on a conservative basis. If the mortality guarantees bite, an insurer can still cut future bonus rates.
The German standard tables include a safety margin, whereas in the UK the standard tables are the best estimate and then each individual company adds a risk margin according to its own requirements. This needs to be remembered when comparing the tables.
Current UK projections assume that mortality improvements tail off from the current high level. On the other hand, the German table, which will be used for pricing, assumes that mortality improvements continue at high level.
In both countries there has been some evidence of the cohort effect: the past rates of German mortality improvements do not only depend on the age, but also on the year of birth. The CMI Bureau is currently reviewing its methodology of mortality projections and is planning to complete this work in 2005. One of the questions raised in the CMIB’s Working Paper 3 is whether the improvements should incorporate cohort effect or not. It is interesting that in Germany it was decided not to use the cohort model for projecting mortality improvements.
It will be interesting to see how other results of CMI work next year will compare to German assumptions.