# Setting the trend

## Improvements

A hot topic at the moment is the subject of mortality improvements, i.e. the falling rates of mortality for pensioners and annuitants. As mortality rates fall, life expectancy goes up...and so does the cost of paying pensions. But how quickly are mortality rates falling? And is it part of a sustainable trend, or is is a short-lived phenomenon? Could it even be that the "improvement" is just a change in the profile of your portfolio over time?

## Analyse your *own* data

One avenue is to examine the mortality improvements in the population over the last forty years. However, this carries the risk that your portfolio is not representative of the wider population (which, in fact, is usually the case). This is particularly important, as strong socio-economic differentials exist, and insured benefits tend to be concentrated in the longest-lived socio-economic groups. And how can you tell what underlying mortality improvements have been if the socio-economic mix has been shifting over time?

The first answer is to analyse your own portfolio's experience, not that of the general population. This removes the so-called *basis risk*, i.e. the risk of assuming that a small subset of the population has the same characteristics of the whole.

The second answer is to build a model of mortality differentials which incorporates each of the major factors. If each source of mortality change is simultaneously present in the model, then each source can be measured with more confidence. For example, if the socio-economic mix of your portfolio has changed over time, a model with both lifestyle and time-trend will enable you to assess the true time-based change separately from the change in mix.

## Time trends in Longevitas

Longevitas can cope with all the risk factors you would associate with an individual: age, gender, lifestyle, smoker status etc. However, Longevitas can also simultaneously model time-varying effects. These include cohort effects, broad time trends and period effects such as seasonal variation. This can all be done simultaneously, thus enabling you to determine what is part of a durable, long-term trend, and what is merely due to a temporary fluctuation or a change in socio-economic mix.