Articles - The challenges of future modelling of longevity risk

 By Joseph Lu, Head of Longevity Modelling at Legal & General
 Latest figures indicate that the annuity market in the UK is worth close to £20bn of new business per annum, (See Table 1 below). The market can be broadly divided into annuities sold to individuals, individual annuities, and pension funds, bulk purchase annuities (BPA). These annuity products require insurance companies to assess the risk of people living longer than expected, the longevity risk.
 The annuity market has been growing and is expected to continue to expand rapidly over the next few years with demand for individual annuities with the post-war ‘baby boomers’ generation reaching retirement and demand for BPA increasing as pension funds become more proactive in managing longevity risk and transfer their liabilities to insurers. Key to continuing success and competitive advantage in thismarket is the accurate modelling of longevity risk. So, it is not so surprising that the understanding of longevity risk and factors affecting future longevity; such as lifestyle, medical advances, and health care policy are attracting more attention. 
 In addition, some emerging changes in regulation, product developments and technical know-how are making the assessment of longevity risk more complex. The key challenge for participants in the annuity market is how to deal with these changes and increased complexity. The inability to understand and react appropriately to these changes could have serious financial consequences for companies that sell the products associated with longevity risk. It could result in either unprofitable business or loss of market share. 
  The Challenges
   One of the key regulatory impacts on future longevity modelling is the recent European Court of Justice (ECJ) rulingon gender. The directive,which must be implemented by 21st December 2012, means that the differences in longevity for men and women, which have been one of the fundamental rating factors used in the pricing of individual annuities for over 25 years, may no longer be applied. The current perception is that the ban would affect individual but not bulk annuities, according to expert interpretation of the ECJ ruling. However, ultimately this will depend on the precise wording of the resulting UK legislation.
  In 2010, over £10bn of pension savings was used by individuals to fund their pension annuity (Table 1). For these customers, insurers used gender as a factor to determine the income secured as it is one of the most robust longevity indicators. Women have consistently lived longer than men, as shown in figure 1. As a result the premium required to secure a specified pension annuity for a woman is currently 5-10% higher than that for a man of the same age and circumstances.
  The industry now faces a challenge to model longevity risk without taking into account this gender difference. To tackle this challenge, a good understanding of the facts behind the longevity differences between men and women is required.One of those interesting facts is that the gap in life expectancy at age 65 between women and men has been changing. In the 1840s, women aged 65 used to live about half a year longer than their male counterparts. This gap increased, to what is now seen as a peak, of a 4 year gap, in the 1970s. Since then the gap has been reducing and in 2009 it was just 2.5 years. 
  This changing gap in life expectancy between genders maybe explained by non-biological and biological reasons. Some of the non-biological reasons are historical and may not be relevant to future longevity risk assessment, but others could still be relevant.
  Non-biological factors include, lifesyle, work environment and attitude to health. For example, men are more likely to smoke or work in harsher conditions, than women.They are also less likely to seek medical help at an early stage, which can hinder their chances of recovery from certain illnesses.These factors all reduce life expectancy for men, compared to women. However, the differences in smoking prevalence and working conditions between the genders have been reducing. In addition, attitude to healthcare through public health policy is shifting behaviour, so men are seeking medical advice sooner. It is these changes that are contributing to the recent narrowing of the gap in life expectancy between men and women.
  There is strong evidence that there are also biological reasons, such as hormones and genetics which can contribute to difference in longevity between genders. For example, women have higher levels of oestrogens which protect them against cardiovascular diseases but men have higher levels of testosterone which increase the risk of cardiovascular problems.  In addition, genetically, women have two sets of X chromosomes whereas men have just the one. So for women, if one of the X chromosomes is damaged, the undamaged one is able to compensate for that function. As men do not have the additional chromosome any damage to their X chromosome could result in a fatal condition or disease. The extra chromosome that all women have, arguably gives them an advantage, and so they should be able to survive longer than men. 
   Impact of gender differences in the future
    Given the historical trend, we may expect that the gap in life expectancy between genders to narrow in the future.  However, this is still unclear. If the gap is to disappear, we need to establish how long it would take for it to narrow to such an extent that any gender differences would be negligible for pricing purposes. 
   For longevity modelling purposes, it then becomes critical to identify how much of the difference in life expectancy between genders may be explained by those factors related to health such as smoking, hypertension or cholesterol levels. These factors will help to account for some of the difference in longevity between genders, but life expectancy differences due to biological and other unknown factors, some that we still need to identify and assess, still need to be taken into account in any longevity model. 
   So following the ban on using gender to price annuities, the challenge for annuity providers is to better understand the health risks associated with longevity to more accurately assess longevity risk in the future.
   With a new longevity risk model, this could then result in the emergence of new products in the individual annuity market. Historically, the dominant annuity product in the market has been the standard annuity.  They are priced using rating factors that are easily available such as age, gender, premium size and postcode. However, recently the market has seen the expansion of annuity products with more sophisticated underwriting criteria taken into account, such as lifestyle factors and health conditions such as hypertension, diabetes or cardiovascular diseases. These annuity products present opportunities and challenges for the modelling of longevity risk as different medical characteristics need to be assessed.
   This wider, ‘non-standard’, annuity market provides cheaper premiums for annuities to customers with a poorer health profile, expecting them to have shorter life expectancies and hence shorter expected period of payment of annuities.  As a result, the healthier customers who do not qualify for the non-standard annuity products would end up buying the standard annuity products.  This means that adjustments have to be made to the price of standard annuities to reflect the fact that people buying the product may be healthier, hence living longer.  These adjustments require an understanding of various factors affecting longevity.
   This non-standard annuity market will see increased competition as annuity providers respond with more sophisticated underwriting processes. The current market share for these more tailored annuities has already grown to around 40% of the total annuities sold through independent advisers in 2010 (Please see Figure 2). 
   The underwriting of annuities using medical information is still at a relatively early stage and there is potential scope for the expansion of the non-standard annuity market, as providers use more sophisticated underwriting techniques. This will see providers strengthening their medical underwriting capability by linking risk factors and treatments that are available in the field of medicine; use of medical data in the statistical modelling plus the experience of a providers own underwriting databases.
   This more sophisticated underwriting of annuities will result in more accurate pricing of annuities for those customers with lower life expectancies, which could result in selection against those providers with less underwriting capability.
    Impact in the bulk purchase annuity market
    The bulk annuity market involves the transfer of liabilities from pension schemes to insurers, reinsurers or banks.  Historically, this market has been dominated by insurance companies buying out liabilities of pension schemes that became insolvent. Since 2006, financially healthy companies began to use the BPA market to manage the associated longevity risk in their pension funds using options such as a full buy out, a buy-in or more recently longevity swaps. This was largely due to potential changes in accounting rules and increased awareness by the managers of pension schemes on the options available to them to manage the pension scheme risks. Some examples of FTSE 100 companies, with relatively large pension schemes, above £300m, that have transferred their pension liabilities are shown in Table 2.  The larger pension schemes, which have their own mortality data, are able to submit this longevity risk information to an insurer or reinsurer, to secure better underwriting terms.
    The key challenge in the BPA market is assessing the uncertainty of using past experience of pension schemes to assess longevity risk. Most established models for the assessment of uncertainty of the schemes mortality experience, such as the Poisson model, assumes that the pension amount is evenly distributed among the schemes pensioners. However, it is quite common to have a high proportion of pension amounts concentrated in a relatively small number of people in that scheme. The concentration of pension amount to a small number of people increases the uncertainty around mortality experience and so stochastic models would have to be developed to measure this uncertainty. 
    Most pension schemes with liabilities below £1bn are expected to have fewer than 25,000 people. It is not uncommon to have half of the total pension amount belonging to about 10% of pensioners. At this level of concentration, a stochastic model estimates that the 95% confidence intervals for a 3-year mortality experience of a population with 5000 pensioners could be about ± 20%. The corresponding figure for a population of about 25,000 people is about ± 10%. A 10% error in assessing mortality rates may result in around a 3% change in the value of annuities for some schemes, and insurers may want to price taking account of this level of uncertainty.
    The use of this longevity modelling helps actuaries assess uncertainty relating to longevity risk and help insurers decide on the price for accepting the liabilities related to the pension scheme. Models that use information such as the postcodes of the individual scheme members, helps in modelling longevity risk. The results from this modelling may then be compared with the mortality experience provided by the pension scheme and, if required, further mathematical models may be developed to reconcile results between postcode modelling and scheme’s mortality experience.
    Impact of improvements in information
    The latest model developed by the Continuous Mortality Investigation (CMI) Bureau aims to extrapolate annual rates of improvement in mortality based on historical data of the total population in England and Wales. The CMI analysed the mortality trends of people in different socio-economic groups using mortality data from the English Longitudinal Study.  However the dataset covers only 1% of the population and mortality data is only analysed once every 4 to 5 years. The volume of data is too low and release of data too infrequent to provide a clear conclusion on differences in mortality trends of different socio-economic groups over the last 2 decades. So, it is currently unclear if annuitants of different socio-economic or health circumstances have experienced the same historical trends as the total population in the last 2 decades. More importantly, it is still uncertain how their mortality rates would change in the future. The availability of mortality data of people in different socio-economic circumstances from larger datasets with higher frequency of release, perhaps annually, would help elucidate these uncertainties.
    In addition, insurance and reinsurance companies operating in the European Union will be subject to a new regulatory requirement called Solvency II, which is expected to come into effect in 2013. Solvency II, as drafted but with the consultation still on-going, requires insurance and reinsurance companies to hold sufficient capital to meet its obligations over the future 12 months with a probability of at least 99.5%. This is called Solvency Capital Requirement (SCR). The regulation will provide some standard formulas for assessing the 1 in 200 year event, or the insurer can build their own ‘internal model’ to assess the risks in their business. But whether an internal model or the standard formula provided by the regulator is used to calculate the capital requirements, these models need to include future longevity assumptions to satisfy these capital requirements.  
    The market for financial products associated with longevity risk is going through a period of substantial change, where the modelling of longevity risk will be even more important in the future. Although the new regulatory requirements and product developments will provide challenges there are also opportunities for improvements in the modelling of longevity risk. To meet the future demands actuaries will need to make full use of a wide range of data and modelling techniques to ensure more accurate assessment and modelling of longevity risk.                
     Gjonca et al. (2005) Health Statistics Quarterly 26
     Abdulraheem et al. (2011) Journal of Peace, Gender and Development Studies Vol. 1 (1)
     CMI Working Papers 38 and 39.
     Human Mortality Database (HMD)
     Mullins, J (2010 Update) Hymans Robertson: Buy-outs, Buy-ins and Longevity Hedging; Q4 2010 and 2010

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