Showing posts with label life expectancy. Show all posts
Showing posts with label life expectancy. Show all posts

Jun 5, 2011

Short Term Longevity Risk

As well-born actuaries we all know the long term risks of longevity:

Lots of actuaries keep expending their energy on calculations of 50 years ahead mortality probabilities....  And indeed..., this is challenging....

Some research reports predict a decline in life expectation, others and more serious recent reports show a steady increase of life expectation.

Mission Impossible
Fact of actuarial life is that - although long term research is useful and educational - we are no Actuarial Magicians.

We should never suggest that we're able to value a bunch of complex and systemic risks  (liabilities, assets,mortality, costs, demographics, etc) into a reliable consistent model that predicts reality.

It's a farce!

What CAN we do?
Instead trying to compress a complex of long term risky cash flows into one representing unique value, we need to:
  1. Analyze and model the short term risks
  2. Develop a method (system) that enables boards of directors to manage and control their risky cash flows (profit share systems, experience rating, etc.).

Example: Short Term Longevity Risk
As a 2011 report of the National Research Council clearly shows:  The previous 50 years we've seen a 3 months yearly increase of lifespan every calendar year.

Instead of recalculating, checking and pondering this trend, let's take a look at the short term effects of this longevity increase trend.

Effect of 'one year life expectancy' increase 
First we take a look at the cost effect of the increase of 'one year of life expectancy' on a single-premium of a (deferred) life annuity (paid-up pensions)...
( Life table total population: United States, 2003 )

Depending on the discounting interest rate, a one year improvement of longevity for a 65 old person demands a 2,3% to 4,0% increase of the liabilities.

Of course the increase of the liabilities of a portfolio (of a pension fund) depends on the (liability weighted) age distrubution of the corresponding portfolio.

Here's a simple example:

This comes close to the rule of thumb as mentioned by AEGON:

10% mortality improvement adds one year to life expectancy, and one year of life expectancy adds 4% to the required value of a pension fund’s reserves

From the above presented visual sensitivity analysis we may conclude that for general (distributed) portfolio's a 'one year lifetime increase' will demand approximately 4-5% of the actual liabilities.

A three to four months yearly longevity-increase - as is still the actual trend - will therefore demand roughly a substantial 1,5% (yearly) of the liabilities.
This implies that in case your contribution is calculated at 4% and your average portfolio return is 7%, there's 3% left for financing longevity and indexation (=method). As 'longevity growth' in the near future will probably cost about 1,5%, there's  only 1,5% left for indexation on the long run.

Case closed

Related links:
Spreadsheet (xls) with data used in this blog
- Forecasting longevity of Dutch pension scheme members using postcodes
- Increasing life expectancy at pension funds (uvt;2011)
- Life Tables for the United States Social Security Area 1900-2100
- Valuing Pension Fund Liabilities on the Balance Sheet
- No limits to life expectancy?
- Broken Limits to Life Expectancy
- NRC: Explaining divergent levels of longevity (pdf;2011)
- Wolfram Alpha: Longevity U.S.
- AEGON: Longevity Rule of thumb

Jan 8, 2011

The Life Expectancy Variance Monster

After 'age', what would be the most important explanatory factor with regard to mortality rates or constructing life tables?

As actuaries we've demonstrated our innovation capabilities by developing life tables not only based on 'age' and 'gender', but also (two dimensional) on 'time', 'generation' and 'year of birth'. This helped us to extrapolate future mortality rates in order to predict future longevity with more accuracy.

However, despite our noble initiatives, these developments turn out to be insufficient to put the Longevity Variance Monster back in his cage.

Modern 'life expectancy at birth' predictions for periods of 40 to 50 year ahead, lead to 95% confidence intervals of 12 years or more. Unusable outcomes .....

Let's not even discuss more necessary accurate confidence intervals of 99% or more ....

In our attempt (duty?) to moderate and diminish future life expectancy variance, we'll have to develop new instruments.

The more we know which risk factors 'are responsible for the increase in 'life expectancy', the better we can estimate and diminish future variance.

One of those new approaches is to calculate life expectancies on basis of postcodes.

This new insight can be helpful, but there's a much more important risk factor that has to be included in our life expectancy predictions to definitely kill the Longevity Variance Monster:

Self-perception of aging

In a 2002 research "Longevity From Positive Self-Perceptions" by Levy ( et al.) it became undeniable clear that:
  • negative self-perceptions diminish life expectancy;
  • positive self-perceptions prolong life expectancy.
Older people with more positive self-perceptions of aging, measured up to 23 years earlier, lived on average (median survival) 7.6 years longer than those with less positive self-perceptions of aging. This advantage remained after age, gender, socioeconomic status, loneliness, and functional health were included as covariates.

Top 6 Life Expectancy Risk Factors
Here's Levy's top 6 list of risk factors on life expectancy (ordered from greatest to least impact on life expectancy):

  1. Age
  2. Self-Perceptions of aging
  3. Gender
  4. Loneliness
  5. Functional health
  6. Socio-economic status

As we can not change 'age' nor 'gender', let's put some more research on the other risk factors.

Once we achieve to 'explain' the cause of increase of life expectancy on basis of 'new' (soft) risk factors, we - as a society - will also be able to manage life expectancy better (information, education, training, coaching, etc.).

In this way actuaries can help society so that people live longer and stay happy in good health. All on basis of of a sound financial pension and health system, as predicted life expectancy will show a smaller variance.

Help to kill the Life Expectancy Variance Monster.....

Happy 2011, with better expectations and smaller variance!

Sources/related Links:

- Why population forecasts should be probabilistic
- On line Postcode Life Expectancy Tool
- Longevity From Positive Self-Perceptions
- Predicting successful aging (2010)

Aug 13, 2008

Netherlands: Rapid increase life expectancy

Last year, female life expectancy at birth was 82.3 years, as against 78.0 years for men. Life expectancy has risen dramatically since 2002.

Life expectancy at birth

Life expectancy at birth

Mortality down since 2002

Female life expectancy at birth was 82.3 years in 2007, i.e. 4.3 years more than for men who have a life expectancy of 78.0 years at birth. Since 1980, the gender gap has narrowed. Male and female life expectancy increased by 5.5 and 3.1 years respectively. The situation has improved considerably after 2002. Despite the ageing population mortality has annually declined since 2002. Such a long period of declining mortality is unprecedented in the Netherlands. In 2007, mortality was over 9 thousand (nearly 7 percent) down on 2002.

Declining mortality by age, 2007 relative to 2002

Declining mortality by age, 2007 relative to 2002

Situation favourable for people in their seventies

The decline in mortality was quite evenly spread across all age groups, but was particularly noticeable among people in their seventies. In 2007, mortality in the age group 70-80 declined by over 5 thousand (nearly 13 percent) relative to 2002. This decline is largely the result of the reduced risk of dying from cardiovascular diseases.

Lower risk of dying by age, 2002-2007

Lower risk of dying by age, 2002-2007

Lower mortality risk for 50 to 80-year-old men

In recent years, the mortality risk declined significantly for both genders. For men aged between 50 and 80, the risk of dying dropped more than for women in the same age bracket. Among the very old, the situation is more favourable for women.

Female life expectancy at birth, 2006

Female life expectancy at birth, 2006

Netherlands not in leading position

Dutch women marginally improved their position on the European record list, but in countries like France and Spain female life expectancy is considerably higher. Belgian and German women also had a somewhat higher life expectancy in 2006. In relative terms, the position of Dutch men on the European life expectancy list is better and comparable to the position French and Spanish men. Swiss, Swedish and Norwegian men, however, enjoy a considerably higher life expectancy.

Source : CBS , by Joop Garssen and Koos van der Togt