At four million, the small population of Denmark is not a reliable dataset for longevity projections. Rachel Fixsen finds out how ATP went global for a better model

Faced with a rising tide of ever older pensioners to provide for, Denmark's ATP pension fund had a choice: it could carry on as it had done, standing on the shore suffering sporadic and unpredictable hits to its reserves, or move forward, wading right in to the deep mathematics of the problem.

Increasing longevity in developed countries presents challenges to pensions sectors, but in Denmark ATP was looking for a once-and-for-all solution, a model that would allow it to smooth the inevitable rises in funding for which it would need to make provision.

Now actuaries at the DKK500bn (€67bn) Danish supplementary labour market fund have emerged with an answer that they hope will put an end to the stop-gap injections of reserves that have taken place over the past few years. And the process that led them to their new forward-looking mortality model could be of huge benefit to other, smaller funds grappling to find solutions to the longevity challenge they confront, ATP claims.

The new longevity model developed by ATP is called SAINT, which stands for Spread Adjusted International Trend. When, in December, the Danish Financial Services Authority (FSA or Finanstilsynet) introduced a new supervisory regime based on a benchmark for observed mortality rates as well as a benchmark for expected future development in life expectancy, ATP had already announced that as a result of its SAINT model, it was setting aside an additional DKK23bn (€3bn) to cover future pensions payments.

The regulator wrote to all Danish pension providers asking them to compare themselves against its new benchmarks and to relay the results of these comparisons to the FSA by July 2011.

Some pension funds, such as PensionDanmark and PenSam, were quick to announce that they were already taking account of increasing life expectancy in Denmark within their existing calculation assumptions. PenSam said it had already set aside an extra DKK1.5bn to ensure future pension payments.

The benchmark for expected future development in life expectancy introduced by the FSA adds a fixed annual percentage reduction in mortality intensity for all ages, and this percentage is given separately for men and women. The underlying data are those of the entire Danish population over a period of 30 years, while the method is one of linear regression and smoothing.

Chresten Dengsøe, chief actuarial officer at ATP, says that within the Danish pensions sector, the longevity problem has grown over the past 16 years because of the increase in life expectancy, although the challenges faced are not spread uniformly across the industry.

"I think it varies from fund to fund, depending on the products they're offering," he says. Danish pension funds differ in the pledges they make to scheme members and, therefore, the longevity risks they face. Most are collective DC schemes and hybrid schemes; while they are based on the DC principle, the investment risk is shared collectively.

But the FSA steps to make sure pension funds mend the potential hole is a positive sign. "The reason they did this is that they think there's something that can be fixed," according to Dengsøe. "The vast majority of pension funds will be able to handle this."

Most pension funds in Denmark are apparently fully funded, he says, but he questions whether all have the same notion of what this really means: "You have to take account of the future increases in life expectancy, and if you don't, you'll have to pay for it later. The analysis I've seen so far is that expectations of the evolution of life expectancy have been too low."

Denmark's pensions sector is far from alone in its struggle to match future pension provision to a group of pensioners now likely to live longer than anyone had expected them to. The challenge is there in other countries around the world. But the small size of its population poses particular difficulties when it comes to making projections about mortality.

ATP counts most of the Danish population as its members, who number around 4.5m. It is able to use the data from its own membership to make projections, but Dengsøe says that when devising the SAINT model, existing mortality tools - such as the popular mortality model proposed by Lee and Carter in 1992 - turned out not to work on a population as small as Denmark's.

"The Lee and Carter technique is a very robust tool, but for Danish data it was not robust at all, at 30 years back or even 40 years back. We tried all kinds of things, but we realised having four million people makes it unreliable."

In a working paper on the development of SAINT, authors Søren Jarner of ATP's actuarial department, and Esben Kryger of the University of Copenhagen explain why the Lee and Carter technique is unsuitable for use by Danish pension funds.

In its original form, the model - a purely statistical model extrapolating past trends - assumes that age groups with low rates of improvements in the past will have low rates of improvement in the future, and likewise for age groups with high historical improvement rates.

"This lack of structure may lead to biologically implausible forecasts with, for example, projected death rates for high-age groups crossing that of younger age groups," according to the paper's authors. They acknowledge, however, that the model was developed specifically for the US, and that like other large populations, the US has had a regular improvement pattern.

But for small populations like Denmark's, mortality development has been much more erratic, so straightforward extrapolations just do not work, they say.

So ATP's mathematicians turned to a much larger collection of data - the Human Mortality Database, a public database run by the University of California, Berkeley and the Max Planck Institute for Demographics Research in Germany.

"That gave us the opportunity to look at not five million people but 500 million, in North America, Australia and Europe. We put it all together and then we had a very robust trend, looking at the 20th century," says Dengsøe.

The evolution of mortality in Denmark basically tallied with this broader international set of data, even though there were differences in the shorter term. "There are differences between countries but if you go back in history, you realise there is little difference, long-term, between the countries. If you exclude Japan, you see that the other countries have very similar patterns," he says.

If the actuarial department at ATP was going to develop a longevity model that would work well, it had to ensure the data it used was coherent, Dengsøe stresses.

By using the international database, the SAINT model uses data volumes a hundred times greater than previously used for such models in the Scandinavian country - and much greater than the Denmark-only data underlying the FSA's new benchmark. Drawing on information from 18 OECD countries makes it much easier to assess life expectancy trends for various age groups, and this, in turn, allows ATP to determine a more stable forecast of long-term life expectancy patterns, the fund has said.

So the new mortality model combines small population data with information from a larger reference population. The idea behind it is that Denmark's mortality will follow that of the reference population in the long term, but that there may be major deviations in the short and medium term.

In mathematical terms, the model uses the reference population to estimate an underlying parametric trend, and a three-dimensional time series to model where Danish mortality deviates from that trend, over time and age groups. The mortality projections are made by combining trend extrapolation and standard time series methods.

The SAINT model also takes account of frailty theory - which relies on the assumption that some individuals in a population are genetically frailer than others. Under frailty theory, high age groups are more homogenous than younger ones, because less robust people tend to die at younger ages.

Even though ATP's model contains the word ‘international' in its full name, Jarner and Kryger say the reference data set does not need to represent an international trend. The proposed modelling approach is applicable whenever a suitable reference population can be found, they say - for example, for the population of a life insurance or pension company with a national or regional data set as reference.

Are there other lessons that pension fund managers, in Denmark and elsewhere, can learn from the work ATP has done?

"The first lesson is that this is extremely important," Dengsøe says. "ATP has deferred lifelong annuities, and if you have those kind of promises, then of course longevity is very important. You have to be aware of this."

Secondly, ATP's experience should teach other funds that it is not easy to get a robust prognosis based on their own data, he suggests.

"When you do a prognosis that goes into the future, then you need data that goes beyond your own pension fund, so other pension funds should consider this. Of course it would be very optimistic to think you can get this right 30 years into the future. But it is the process they need to have."

Learning to make more frequent, smaller adjustments is vital too: "An update every 10 years can be extremely costly. If you can do this every year, then the correction will be smaller," according to Dengsøe. "So it's also about the process and getting that right."